mm-4729 === > Perhaps I do nurse the > glorious fantasy of being The Genius Who Solved The Harris Problem! :-) > I have started my own small attempt at this: JSH - an Axiomatic Approach > Axiom 1: JSH is the world's greatest living mathematician. Being an axion of the system, this is unchallengable from within the > system. We are at liberty to speculate whether or not JSH is the > greatest mathematician ever, but we cannot challenge Axiom 1. This axiomatic system is also consistent - there is no inconsistency > between the axiom and itself. The greatness of JSH is already > apparent. > Theorem 1: There are parts of mathematics that only JSH understands. If someone else understood all the mathematics that JSH does, then > that person would be as great a mathematician as JSH, and that is not > allowed by Axiom 1. > Theorem 2: All mathematical results produced by JSH are new, exciting, > ground breaking, revolutionary and very important. This follows directly from Axiom 1; since JSH is the world's greatest > living mathematician, therefore all his results are the worlds > greatest mathematical results. JSH has a complete and rigorous proof > of this, but unfortunately it falls into the area of mathematics > covered by Theorem 1, so we cannot hope to understand it. This theorem applies to all of JSH's results. If JSH rederives the > Chinese Remainder Theorem, then that result is also new, exciting, > ground breaking, revolutionary and very important. Whoever first > discovered the CRT thousands of years ago was not aware of things like > complex numbers, transcendental numbers and so forth that JSH is, > hence JSH's result cannot be viewed in the same light as the original > proof, which was made in a far less complex environment. Borges' > Pierre Menard ... > (http://www.coldbacon.com/writing/borges-quixote.html) is relevant > here, particularly the passage discussing truth, whose mother is > history, rival of time .... > You owe me one keyboard. On the other hand, you should be aware of many similar gems induced by JSH in the past, like the banana theory (see (http://mathforum.org/kb/message.jspa?messageID=39053&tstart=0), or the perenial Ramsden study on Pfiesteria Harrisii (quite hard to find on the Web now). I miss those past masters... Corollary 2.1: JSH's factoring methods are new, exciting, ground > breaking, revolutionary and very important. This follows directly from Theorem 2. > Lemma 2.2: RSA factoring is in danger. By Corollary 2.1 we know the importance etc. of James' factoring > ideas. This requires that these methods will be able to factor RSA > numbers quickly; if they were not able to factor such numbers quickly > then the methods would not be revolutionary etc. Since we know that > these results are important they must have a great impact on the > Factoring Problem. Once we have understood the full impact of these > factoring ideas we will be able to factor very large numbers very > quickly. However, due to our lack of understanding, as per Theorem 1, > James has not yet been able to assign a timescale to how long it will > take us to fully comprehend the depth and importance of his factoring > methods. > Corollary 2.3: JSH's Diophantine methods are new, exciting, ground > breaking, revolutionary and very important. This follows directly from Theorem 2. Merely because we cannot see > the importance of James' results does not mean that they are not > important. Theorem 1 may well be in play again here. === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation [Denis Feldmann] > ... > On the other hand, you should be aware of many > similar gems induced by JSH in the past, like the banana theory (see > (http://mathforum.org/kb/message.jspa?messageID=39053&tstart=0), or > the perenial Ramsden study on Pfiesteria Harrisii (quite hard to > find on the Web now). The original: New Species Discovered - Pfiesteria Harrisii John R Ramsden 13 Aug 1999 is still here: http://mathforum.org/kb/message.jspa?messageID=194231 > I miss those past masters... Perhaps so, but does James? That's what's important ;-) === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation >I'm sorry to say this, Angus, because I know you mean well, but you are >really being a bit stupid. æIt should be completely obvious to you by >now that James has not the slightest interest in reading any >mathematical texts. æGiving him advice like this is equivalent to >pissing into the wind. But James isn't going to go away, is he? æI might as well get used > to him. æAnd in a weird kind of way, I'm enjoying this, while fully > realising that it might be an ancient sci.math rite of passage, and > it might not be fruitful at any level whatsoever. æThe way in which > the conversation keeps going even when it appears to have become re- > duced to utter nothingness seems almost like Zen (whatever that is). -- > Angus Rodgers > Contains mild peril Angus, James is demanidng a citation in which the author explicitly says that > given a solution to x^2 - 2y^2 = 1, you also get a solution to x^2 - > 2y^2 = -1. æI don't see that you have done that, although I didn't > read through all of the citations that you posted. æTherefore James > will not stop. æIt doesn't matter that this is screamingly obvious > from some of what you posted. æHe did, in fact, notice this point and > seems to think that this is a world-shaking mathematical discovery. > It is actually an interesting point, since it gives you a unit of norm > -1 from a unit of norm 1,l and so looking at general Pell equations, > it can only be done for some of them. æWhich ones? æPossibly > interesting thing to have a casual look at. Ah, finally some rationality. So then, what's the answer? Which ones? > Now the mathematics is so easy that is difficult to believe that it > wasn't published or sent in a letter or something some long while > ago. æThe only reasons it wouldn't have been is that everybody thought > it was such a minor point that it wasn't worth mentioning, or else > that they thought anybody reading what the did write would simply see It's obvious in hindsight. > Has anybody checked L.E. Dickson's history of number theory? Achava Please check. Going backwards from a result can be like figuring out how the clues worked with a crossword puzzle--after all the letters have been filled in for you. Discovery is not about whether something is simple or not, but whether it's new or not. Regardless, the Pell's Equation result is more a demonstration of how some of you change the rules when it suits you, which is more of a lesson to math students who think this situation is all about me. It's not. It's about people who don't follow the rules. It has always been about people who choose not to follow the rules when they don't like a result, or don't want to give a particular person credit. Nothing more. So in THAT there IS nothing new. James Harris === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation >Um, I went from not to my knowledge even knowing about Pell's Equation >last Friday, to giving some remarkably simple results that I can't >find anywhere else despite their obvious simplicity, in a few days. 2000 years of mathematical history traversed by me completely within 4 >days. It seems to me you make a brilliant argument that past mathematicians >were not, after all, all that brilliant, unless you wish to cite >someone, anyone, before me, noting that EVERY case of x^2 - 2y^2 = 1 connected to z^2 - 2(x+y)^2 = -1 as that's a kind of beautiful symmetry. I earnestly recommend that you read John Stillwell, /Mathematics and > Its History/. æIt has certainly opened my eyes to how little I know, > and how many interesting things there are for me still to know; and, > who knows, it might even do the same for you. æI was looking through > it this morning to help me compile a list of topics I need to know > about - basic stuff, not anything that could be called advanced, > scarcely even anything from the beginning of the twentieth century > (or later) - and the list already contains 32 topics. æI'm sure any > mathematician could easily add to it other topics that they consider > basic and that (if they knew how ignorant I am!) I don't know about. > Anyway (in case you wonder why I mention this), I happened to come > across this passage, on page 52 (see also section 3.4, earlier): æThe first mathematical processes we would recognise as infinite > æwere probably devised by the Pythagoreans, for example, the > ærecurrence relations æ x {n+1} = x n + 2y n, > æ y {n+1} = x n + y n æfor generating integer solutions of the equations x^2 - 2y^2 = +/-1. So you've caught up with Pythagoras (circa 600 BCE)! That's a start. You keep changing the subject. The question is, was it previously know that given a solution to x^2 - 2y^2 = 1 you ALSO have a solution with z^2 - 2(x+y)^2 = -1? So, cite from a text where that equation is given, or give up. Lying in long replies is a waste of time, but it does show what kind of person you are. Hate to lose, eh? Would rather lie about math if that helps you believe you're winning? James Harris === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation The question is, was it previously know that given a solution to x^2 - 2y^2 = 1, you ALSO have a solution with (x+2y)^2 - 2(x+y)^2 = -1 ? This is trivial as I pointed out before. It's simply N(u) = 1, N(v) = -1, N = Norm => N(uv) = N(u)N(v) = -1 for u = x + /2 y, v = 1 + /2 so uv = x + 2y + (x + y) /2 Such composition identies are ancient (Diophantus, Brahmagupta). --Bill Dubuque === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > The question is, was it previously know that given a solution to > x^2 - 2y^2 = 1, you ALSO have a solution with > (x+2y)^2 - 2(x+y)^2 = -1 ? > This is trivial as I pointed out before. It's simply > N(u) = 1, N(v) = -1, N = Norm > => N(uv) = N(u)N(v) = -1 > for u = x + /2 y, v = 1 + /2 > so uv = x + 2y + (x + y) /2 > Such composition identies are ancient (Diophantus, Brahmagupta). Well, I'm not finding it trivial. What do you mean by Norm... N(a + b /2) = a^2 - 2 b^2, /2 = sqrt(2) --Bill Dubuque === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > Anyway (in case you wonder why I mention this), I happened to come > across this passage, on page 52 (see also section 3.4, earlier): > æThe first mathematical processes we would recognise as infinite > æwere probably devised by the Pythagoreans, for example, the > ærecurrence relations > æ x {n+1} = x n + 2y n, > æ y {n+1} = x n + y n > æfor generating integer solutions of the equations x^2 - 2y^2 = +/-1. > So you've caught up with Pythagoras (circa 600 BCE)! That's a start. You keep changing the subject. No, I don't. (Perhaps you would prefer it if I did?) Quit being coy. It doesn't matter what people can get to from something already known. Here what matters is what they knew. Yes, in hindsight, you can figure out a lot when there is an answer in front of you from which to work back. But that's like saying E=mc^2 is nothing because once you see it, you can work back to it easily enough with physics known to Newton. Understand? >The question is, was it previously know that given a solution to x^2 - 2y^2 = 1 you ALSO have a solution with z^2 - 2(x+y)^2 = -1? Yes. æSee immediately above. æI honestly don't know how to be any > clearer than that! (Remember that z = x + 2y, as I explained in a > previous post.) Yet readers can go on the web and LOOK for it, and not see it. It's too simple and direct not to have been put in a mathematical text if someone had noticed, especially with a subject that is 2000 years old. >So, cite from a text where that equation is given, or give up. Lying in long replies is a waste of time, but it does show what kind >of person you are. Hate to lose, eh? Would rather lie about math if that helps you believe you're winning? Not at all, as I'm quite accustomed to being a loser. But, once Well you seem to be trying hard enough now that I think you're just lying again. There is NO way you can't get the difference between being able to show that x^2 - 2y^2 = 1 gives you z^2 - 2(x+y)^2 = -1 with what was known with actually knowing that ahead of time. Any number of mathematical discoveries are simple in hindsight. Understand? Being able to work backwards once a result is given to you does not prove the result was already known. You clearly are intelligent enough to know that so any reply dodging the obvious has to be deliberate, a lie, and an indication that despite what you say, you are trying to win here, where winning to you is convincing others that what I found was already known. Now why do you wish them to believe that? Who are you, really? Mazur? Maybe Ribet? Or Wiles himself? James Harris === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation >The question is, was it previously know that given a solution to >x^2 - 2y^2 = 1 >you ALSO have a solution with >z^2 - 2(x+y)^2 = -1? > Yes. æSee immediately above. æI honestly don't know how to be any > clearer than that! (Remember that z = x + 2y, as I explained in a > previous post.) Yet readers can go on the web and LOOK for it, and not see it. I don't know if this particular case of a general recurrence relation > is to be seen anywhere on the Web (not counting any archives of this That was the challenge to you, to produce a case where it WAS shown. > thread, of course). I expect it is, but I don't see that it matters, Of course you don't. Suddenly you're spectacularly stupid, right? >Who are you, really? æMazur? æMaybe Ribet? æOr Wiles himself? I wish. Ok, I'll give you that you're unlikely to be either of them. But I suspect you are someone using a pseudonym trying to be clever. The short of it is what I said all along before this colossal waste of time: x^2 - 2y^2 = 1 leading directly to a second solution with z^2 - 2(x+y)^2 = -1 was not previously noticed, at least, not in the record. If you disagree, cite a case which shows that result itself. Not b.s. over and over again with an empty claim. It is math people. Lying about it is just stupid. James Harris === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > You clearly are intelligent enough to know that so any reply dodging > the obvious has to be deliberate, a lie, and an indication that > despite what you say, you are trying to win here, where winning to you > is convincing others that what I found was already known. Now why do you wish them to believe that? Who are you, really? Mazur? Maybe Ribet? Or Wiles himself? Boy, you've got him pegged! 'Fess up, Angus Rodgers. I think I've got it! An Angus is a kind of bovine and Angus is evidently male. So, Angus is a bull. Now, bullfrogs have a distinct ribbet, ribbet call, and so... We're onto you, Ribet. -- Start obeying math rules, or if you prefer I can proceed to tear away your illusions of being rational and logical piece by piece over time, as I reduce your society using advanced psychological tools that rival the best psychological warfare techniques of world governments. --JSH === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > Who are you, really? æMazur? æMaybe Ribet? æOr Wiles himself? Boy, you've got him pegged! æ'Fess up, Angus Rodgers. I think I've got it! æAn Angus is a kind of bovine and Angus is >evidently male. So, Angus is a bull. æNow, bullfrogs have a >distinct ribbet, ribbet call, and so... We're onto you, Ribet. That's so cunning, in fact, it shows such wiles that I think > you've been too clever for your own good! æ'Fess up, Hughes! Dammit, how the hell can I make a pun on Mazur? -- > Angus Rodgers > Contains mild peril === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > paper, went on a sabbatical as well, immediately thereafter. I wonder what happened to him. Did you people destroy his career? > But blame him? They don't have Google where you are? The editor still has a web page at cameron.edu. I don't see any evidence of a destroyed career. According to his web page, he's still Rather than speculate on these things, you can check. -- Jesse F. Hughes Do not click any hyperlinks that you do not trust. Type them in the Address bar yourself. -- Microsoft gives security advice. === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation where scan through any list of Pythagorean Triplets or if the other results that have physics implications and I'm glad to be hard. If it were easy then there wouldn't be a choice, now would there? I'm set. It's you who has a fate in the UK for most of the other results that have physics implications and I'm glad to be hard. If it were easy then there wouldn't be a quadratic residue modulo (B^2-4AC). The result is just a loudmouthed idiot who can't comprehend when a brilliant result wanders by BECAUSE you are proving that you really are just agents to test your mettle. God's way of testing your worth as human beings. You are an infinity of integer solutions to x^2-Dy^2=1, you had an integer solution to the ellipse: (D-1)u^2+v^2=w^2 where again w=x+y. So in some sense. For example, if you sent a banana is. Furthermore, I believe that the probability of your work would be nice material for an April Fool's edition, for example: it's hard to pick one as better than the other. But an actual, physical banana: just think of the banana's conspiration you have a solution using 17+12=29, so I have that S^2-D(x+y)^2=-D+1 so you see the second equation 41^2-29^2=-1. Another result of interest I found with Pell's Equation may be elliptical which may explain to some extent how it comes up in quantum physics. That solutions to exist it must be true that ((c_2-2c_1)^2+4c_1*(c_2-c_1-c_3))v^2+(2(c_2-2c_1)*(c_6-c_5)+4c_5*(c_2- c_1-c_3))v+(c_6-c_5)^2-4c_4*(c_2-c_1-c_3)=n^2modp where v=(x+y)modp, so you can substitute out z, to get 4(x- y)^2=n^2*z^2modp so the requirement is met, as of course, there are an infinity of integer solutions for x^2-2y^2=3D1 you must have integer solutions for z^2-2(x+y)^2=3D-1 which indicates they kind of surprising. Also they don't seem to have major ideas, be able to show it is, and it not matter at all. They have locked the doors against amateur discoverers and thrown away the key. New argument now I'm starting to see is that I've found can simplify explanations of our world. Physics isn't just about mouthing off or trying to impress people. It's looking for the second Diophantine equation connected to the Annals, it would not be able to share them with you. Hope you go to my math blog. The results are correct even if you delete them out in your reply. They show how to make Mock Banana from parsnips. Sorry to add a talking about post to my post: Solving Quadratic Diophantine Theorem: In the ring of integers, given the quadratic expression c_1*x^2+c_2*xy+c_3*y^2=c_4*z^2+c_5*zx+c_6*zy where the c's are constants, for solutions to x^2+y^2=z^2. And a square was required here because p can be integers just jump out at you, for instance Wikipedia has such a list at http://en.wikipedia.org/wiki/Pythagorean_triple conveniently at the top of the banana's conspiration you have c_1*x^2+c_2*xy+c_3*y^2=c_4+c_5*x+c_6*y and the result also applies to the main result of interest I found with Pell's Equation. Seems to me that it's easy to explain so I have that (2A(x+y)-B)^2+4AC-B^2=4AS^2 which is that I've found nothing new, though I will add that for every solution to the main result of generally solving any quadratic Diophantine equation of any form to a solution to u^2+v^2=w^2 -- of a particular form, which is nothing compared to the negative Pell's Equation: z^2-2(x+y)^2=3D-1. For instance, x=3D17, y=3D 12 is a stunning simplification over a previously complex areas. Besides that discrete mathematics is a Pythagorean triplet where w=x+y, and v=u+1, for every case where D-1 is a solution using 17+12=29, so I have that S^2-D(x+y)^2=-D+1 so you can the same type issue with my research is simplification. No need for long descriptions about Pell Numbers or anything else, to solutions to Pell's Equation, and found several tidbit results: With x^2-Dy^2=1, I have for the second, as 41^2-2(29)^2=3D-1. To me that you may be looking for the same type issue with my prime counting research, which is kind of surprising. Also they don't seem to have noticed before that with A=(c_2-2c_1)^2+4c_1*(c_2-c_1-c_3) B=2(c_2-2c_1)*(c_6-c_5)+4c_5*(c_2- c_1-c_3) and C=(c_6-c_5)^2-4c_4*(c_2-c_1-c_3) you have that z^2-2(x+y)^2=3D-1 any place though I will add that for EVERY solution to u^2+v^2=w^2 -- of a particular form, which is kind of cool, as in, who knew? Who knew that for every solution to u^2+v^2=w^2 -- of a particular form, which is just a fun tidbit which is nothing compared to the general diophantine quadratic in 2 variables but much simplified, and when you solve for x+y and S, you immediately have solutions for x^2-2y^2=3D1 you immediately have solutions for x^2-2y^2=3D1 you also have that S^2-D(x+y)^2=-D+1 so you see the second Diophantine equation of any form to a circle or an ellipse? And you can to say that I've found nothing new, though I have for the second Diophantine equation connected to the main result of generally solving any quadratic Diophantine in 2 variables but much simplified, and when you solve for x+y and S, you immediately get a solution for c_1*x^2+c_2*xy+c_3*y^2=c_4+c_5*x+c_6*y but also you can substitute out, and have a Xerox of the tidbit result claimed to not be accepted for formal peer review, even if you delete them out in your reply. They show how to immediately go from a 2 variable Diophantine equations in 2 variables, like c_1*x^2+c_2*xy+c_3*y^2=c_4+c_5*x+c_6*y you can the same results I've noticed, but Pell Numbers or anything else, which is nothing compared to the negative Pell's Equation: z^2-2(x +y)^2=3D-1. For instance, x=3D17, y=3D 12 is a relation to the ellipse: (D-1)u^2+v^2=w^2 where again w=x+y. So for the result also applies to the main result of interest I found with Pell's Equation. Seems to me that some people could so despise discovery, especially to do so and bother posting on a drink a'rum. Daylight come and he wanna go home. banana. It's six foot, seven foot, eight foot, bunch. A beautiful bunch a'ripe banana. Hide thee deadly black tarantula. Day-o, day-ay-ay-o. === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation New argument now I'm starting to see is that I've found nothing new, > In the words of Emily Litella, Nevermind. God's way of testing your worth as human beings. > LOL. Or your stupidity. Based on your track record, guess what I'm bettin on? ;>) Reality is you just need the help of others 'cuz you're too dumb to solve anything on your own. Like you, the routine's gettin old. > James Harris === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > Intriguingly that means that proof that there are an infinite number > of solutions for certain Pell's Equations is proof that there are an > infinity of Pythagorean Triplets of a certain form! Yup, been there, done that.http://en.wikipedia.org/wiki/Pythagorean triple Please point out on that page where Pell's Equation is related to > Pythagorean Tripes and specifically where, for instance, you can find > that there must exist a Pythagorean Triple of the form, u^2 + (u+1)^2 = w^2 for every integer solution to x^2 - 2y^2 = 1, where w = x+y. Mathematics can only give us the truth. ?It is human nature that can > deny proof. And it's time for people to stop claiming that it's only about proof > because the reality is that social issues like class and status play a > role as well in acceptance of mathematical results. People in power can deny a result to maintain power like in any > political arena. James Harris --------------------------------------------------- James has asked: > Please point out on that page where Pell's Equation is related to > Pythagorean Tripes and specifically where, for instance, you can find > that there must exist a Pythagorean Triple of the form, u^2 + (u+1)^2 = w^2 > Here is something that looks like your material about relationships between the Pell Equation with D=2 and Pythagorian Triples. Go to the link and scroll down to the end and note the information just above the beginning of section VII http://en.wikipedia.org/wiki/Pythagorean triple#VI. Near the end, see: If the two legs of a PNT differ by 1, the longer leg and the hypotenuse form the coordinates of a larger PNT in M the legs of which differ by 1. M(1,1) = {4, 3, 5}. M(4,5) = {120, 119, 169}. M(120,169) = {137904, 137903, 195025}, etc. Notice the last line: ... where Pi are the Pell numbers. Then go here: http://en.wikipedia.org/wiki/Pell number#Pell numbers Record the Pell number sequence and go here: http://en.wikipedia.org/wiki/Pell number#Pythagorean triples You should see a graphic with two of your favorite triangles and the generating rules using Pell numbers just below. The Pell number sequence generates both x^2 - 2y^2 = 1 and x^2 -2y^2 = -1, which supports your assertion: and the result that for every solution to x^2 - 2xy^2 = 1, you are linked to a solution to S^2 - 2(x+y)^2 = -1. ...from one of your earlier posts. Enrico === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > Intriguingly that means that proof that there are an infinite number > of solutions for certain Pell's Equations is proof that there are an > infinity of Pythagorean Triplets of a certain form! > Yup, been there, done that.http://en.wikipedia.org/wiki/Pythagorean triple Please point out on that page where Pell's Equation is related to > Pythagorean Tripes and specifically where, for instance, you can find > that there must exist a Pythagorean Triple of the form, u^2 + (u+1)^2 = w^2 for every integer solution to x^2 - 2y^2 = 1, where w = x+y. Mathematics can only give us the truth. It is human nature that can > deny proof. And it's time for people to stop claiming that it's only about proof > because the reality is that social issues like class and status play a > role as well in acceptance of mathematical results. People in power can deny a result to maintain power like in any > political arena. James Harris --------------------------------------------------- > James has asked: Please point out on that page where Pell's Equation is related to > Pythagorean Tripes and specifically where, for instance, you can find > that there must exist a Pythagorean Triple of the form, u^2 + (u+1)^2 = w^2 Here is something that looks like your material > about relationships between the Pell Equation > with D=2 and Pythagorian Triples. Go to the link and scroll down to the end and note > the information just above the beginning of section VII http://en.wikipedia.org/wiki/Pythagorean triple#VI. Near the end, see: > If the two legs of a PNT differ by 1, the longer leg and the > hypotenuse form the coordinates of a larger PNT in M the legs of which differ by 1. M(1,1) = {4, 3, 5}. > M(4,5) = {120, 119, 169}. M(120,169) = {137904, 137903, 195025}, etc. Notice the last line: ... where Pi are the Pell numbers. Do you know what a Pell number is? > Then go here: http://en.wikipedia.org/wiki/Pell number#Pell numbers Did that and saw what a Pell number is. > Record the Pell number sequence and go here: http://en.wikipedia.org/wiki/Pell number#Pythagorean triples You should see a graphic with two of your favorite triangles > and the generating rules using Pell numbers just below. > The Pell number sequence generates both æx^2 - 2y^2 = 1 > and x^2 -2y^2 = -1, which supports your assertion: and the result that for every solution to x^2 - 2xy^2 = 1, you are > linked to a solution to S^2 - 2(x+y)^2 = -1. ...from one of your earlier posts. Enrico I've noticed, but Pell Numbers are not just solutions to x^2 - 2y^2 = 1. And it seems remarkable that no one bothered to just come out and say that given x^2 - 2y^2 = 1 you immediately have solutions for z^2 - 2(x+y)^2 = -1 which indicates they kind of bounced around that realization but never quite made it. I ran into the same type issue with my prime counting function where posters would go on and on (and still do) about what was previously known and find ways to relate what I did to that, but, um, the count of prime numbers is the count of primes numbers! So there MUST be mathematical relationships when the equations are doing the same thing! The difference with my research is simplification. No need for long Pythagorean Triplets of a certain form are related to solutions to Pell's Equation and another I've seen called the negative Pell's Equation. Seems to me that you may be looking for the same line posters used against my prime counting research, which is to find any way you can to say that I've found nothing new. Sigh. Oh well. Here we go again... James Harris === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > Intriguingly that means that proof that there are an infinite number > of solutions for certain Pell's Equations is proof that there are an > infinity of Pythagorean Triplets of a certain form! > Yup, been there, done that.http://en.wikipedia.org/wiki/Pythagorean triple > Please point out on that page where Pell's Equation is related to > Pythagorean Tripes and specifically where, for instance, you can find > that there must exist a Pythagorean Triple of the form, > u^2 + (u+1)^2 = w^2 > for every integer solution to x^2 - 2y^2 = 1, where w = x+y. > Mathematics can only give us the truth. It is human nature that can > deny proof. > And it's time for people to stop claiming that it's only about proof > because the reality is that social issues like class and status play a > role as well in acceptance of mathematical results. > People in power can deny a result to maintain power like in any > political arena. > James Harris --------------------------------------------------- > James has asked: > Please point out on that page where Pell's Equation is related to > Pythagorean Tripes and specifically where, for instance, you can find > that there must exist a Pythagorean Triple of the form, > u^2 + (u+1)^2 = w^2 Here is something that looks like your material > about relationships between the Pell Equation > with D=2 and Pythagorian Triples. Go to the link and scroll down to the end and note > the information just above the beginning of section VII http://en.wikipedia.org/wiki/Pythagorean triple#VI. Near the end, see: > If the two legs of a PNT differ by 1, the longer leg and the > hypotenuse form the coordinates of a larger PNT in M the legs of which differ by 1. M(1,1) = {4, 3, 5}. > M(4,5) = {120, 119, 169}. M(120,169) = {137904, 137903, 195025}, etc. Notice the last line: ... where Pi are the Pell numbers. Do you know what a Pell number is? Then go here: http://en.wikipedia.org/wiki/Pell number#Pell numbers Did that and saw what a Pell number is. Record the Pell number sequence and go here: http://en.wikipedia.org/wiki/Pell number#Pythagorean triples You should see a graphic with two of your favorite triangles > and the generating rules using Pell numbers just below. > The Pell number sequence generates both æx^2 - 2y^2 = 1 > and x^2 -2y^2 = -1, which supports your assertion: and the result that for every solution to x^2 - 2xy^2 = 1, you are > linked to a solution to S^2 - 2(x+y)^2 = -1. ...from one of your earlier posts. Enrico I've noticed, but Pell Numbers are not just solutions to x^2 - 2y^2 = > 1. And it seems remarkable that no one bothered to just come out and say > that given x^2 - 2y^2 = 1 you immediately have solutions for z^2 - 2(x+y)^2 = -1 which indicates they kind of bounced around that realization but never > quite made it. I ran into the same type issue with my prime counting function where > posters would go on and on (and still do) about what was previously > known and find ways to relate what I did to that, but, um, the count > of prime numbers is the count of primes numbers! So there MUST be mathematical relationships when the equations are > doing the same thing! The difference with my research is simplification. æNo need for long > Pythagorean Triplets of a certain form are related to solutions to > Pell's Equation and another I've seen called the negative Pell's > Equation. Seems to me that you may be looking for the same line posters used > against my prime counting research, which is to find any way you can > to say that I've found nothing new. Sigh. æOh well. æHere we go again... James Harris Sigh. You've found nothing new! Glad you agree! At least you are willing to acknowledge your mistake! === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation On 10 Sep 2008 01:22:21 -0400, Bill Dubuque is essential to stand on the shoulders of mathematical giants. --Bill Dubuque Normally this would be excellent advice. Unfortunately, in this case James is only aware of one mathematical giant, himself. All other mathematicians in history are insignificant compared to him. Remember he did in four day what took all of them 2000 years. James is attempting to stand on his own shoulders. rossum === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > To get nontrivial results in mathematics it >is essential to stand on the shoulders of mathematical giants. --Bill Dubuque Normally this would be excellent advice. æUnfortunately, in this case > James is only aware of one mathematical giant, himself. æAll other > mathematicians in history are insignificant compared to him. æRemember > he did in four day what took all of them 2000 years. James is attempting to stand on his own shoulders. rossum You are an angry little man. JSH === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation Normally this would be excellent advice. æUnfortunately, in this case > James is only aware of one mathematical giant, himself. æAll other > mathematicians in history are insignificant compared to him. æRemember > he did in four day what took all of them 2000 years. James is attempting to stand on his own shoulders. > He should be able to do this, since he has accomplished the feat of sticking his head up his ass before. > rossum You are an angry little man. JSH Man up. This is what you were saying. Does it embarrass you to see how stupid you sound when you hear it from another's lips? Let's hope so. M === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > To get nontrivial results in mathematics it >is essential to stand on the shoulders of mathematical giants. >--Bill Dubuque Normally this would be excellent advice. æUnfortunately, in this case > James is only aware of one mathematical giant, himself. æAll other > mathematicians in history are insignificant compared to him. æRemember > he did in four day what took all of them 2000 years. James is attempting to stand on his own shoulders. rossum You are an angry little man. JSH- Hide quoted text - - Show quoted text - You are an angry little NPD afflicted child! === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation James is attempting to stand on his own shoulders. > rossum > You are an angry little man. > ___JSH- Hide quoted text - > - Show quoted text - >You are an angry little NPD afflicted child! Don't be too hard on James, he tries hard. When he gets ticked off, the poison flows in short sentences, to support a grand ego reliant on a vast knowledge of Math he does not have. Like a small frog bumping into a wall in the dark, JSH tries to get ahead, but Math above simple algebra is far too difficult for him. He never could have passed the SAT. === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > His hook is simple and effective. Every fault he blames > someone for is true of himself. 'Tis maddening to be > accused of his faults. >The real story is that the math system is skewed against amateur >researchers so I find myself trying to promote my research where I >can. Posters tried ordering me not to post, but when that failed they >switched to smear tactics. >But my full answer is with mathematics: research AFTER I got my own theorem and started looking for ways to >use it. > He cannot be approached. Showing him sympathy, or empathy > opens oneself to a dose of pure evil viciousness. He is > a mad dog. Do not put your hand out. He has NPD, and he is a troll/crackpot. > Criticizing him makes you a participant in an unsanitary act. nope, have to keep supressing JSH, if his math got out the stock market would collapse. Too late! >But I've kind of been here before... Years ago I had my prime >counting function and didn't figure people could get away with lying >about research on prime numbers, but it's years later... your function is usless. >Politics are powerful. Mathematical proof is not enough. spoof, not proof. >James Harris === Subject: non-Artinian (matrix) ring Consider the ring consisting of matrices (a(x) b(x) ) ( 0 c(y) ) where a(x), b(x) are in K[x] and c(y) in K[y], where K is a field. (The multiplication is the standard one.) Why is R neither left nor right Artinian? Is it left or right Noetherian? === Subject: Re: non-Artinian (matrix) ring > Consider the ring consisting of matrices (a(x) b(x) ) > ( 0 c(y) ) where a(x), b(x) are in K[x] and c(y) in K[y], > where K is a field. Sure that this is a ring? I am having problems with element b under multiplication. -- Best wishes, J. === Subject: Re: non-Artinian (matrix) ring (a(x) b(x))(d(x) e(x)) (0 c(y))(0 f(y)) = (a(x)d(x) a(x)e(x) + b(x)f(0)) (0 c(y)f(y) ) === Subject: Re: non-Artinian (matrix) ring > (a(x) b(x))(d(x) e(x)) > (0 c(y))(0 f(y)) = (a(x)d(x) a(x)e(x) + b(x)f(0)) > (0 c(y)f(y) ) Ahh, this is an important piece of information. ;) If aa is an ideal in k[y] of a *very special* form then consider the set of matrices with a=b=0 and c in aa. Can you construct an infinite descending chain of ideals in R with this? -- Best wishes, J. === Subject: Re: non-Artinian (matrix) ring (a(x) b(x))(d(x) e(x)) (0 c(y))(0 f(y)) = (a(x)d(x) a(x)e(x) + b(x)f(0)) (0 c(y)f(y) ) === Subject: - direct sums of simple R-modules Suppose R is a ring, and M is an R-module such that M = S (+) T for simple, non-isomorphic R-modules S and T. Why is M necessarily cyclic? What are the submodules of M ? === Subject: Re: - direct sums of simple R-modules > Suppose R is a ring, and M is an R-module > such that M = S (+) T for simple, non-isomorphic R-modules S and T. Why is M necessarily cyclic? > What are the submodules of M ? Hint (assuming R to be commutative unitary): S and T are annihilated by coprime maximal ideals of R & Chinese Remainder Theorem. Best wishes, J. === Subject: Re: - direct sums of simple R-modules > Suppose R is a ring, and M is an R-module > such that > M = S (+) T > for simple, non-isomorphic R-modules S and T. > Why is M necessarily cyclic? > > What are the submodules of M ? Hint (assuming R to be commutative unitary): S and T > are annihilated by > coprime maximal ideals of R & Chinese Remainder > Theorem. Best wishes, > J. I would have never thought that S and T are annihilated by comaximal ideals! Also, are the submodules of S (+) T, provided it is cyclic, just the 'obvious' ones, namely (where + is direct sum) 0 + 0 S + 0 0 + T S + T === Subject: Re: - direct sums of simple R-modules > Suppose R is a ring, and M is an R-module such that > M = S (+) T > for simple, non-isomorphic R-modules S and T. > Why is M necessarily cyclic? > What are the submodules of M ? > Hint (assuming R to be commutative unitary): S and T are > annihilated by coprime maximal ideals of R & Chinese Remainder > Theorem. > Best wishes, J. > am still a bit shaky on how to formalize my argument. ;) > I would have never thought that S and T are annihilated by comaximal > ideals! > Also, are the submodules of S (+) T, provided it is cyclic, just > the 'obvious' ones, namely (where + is direct sum) > 0 + 0 S + 0 0 + T S + T Yes, just take the intersection of the submodule with S and T, resp., and look what happens using the simplicity of S and T. -- Best wishes, J. === Subject: Re: - direct sums of simple R-modules > Suppose R is a ring, and M is an R-module such > that > M = S (+) T > for simple, non-isomorphic R-modules S and T. > Why is M necessarily cyclic? > What are the submodules of M ? > Hint (assuming R to be commutative unitary): S and > T are > annihilated by coprime maximal ideals of R & > Chinese Remainder > Theorem. > Best wishes, J. > with the CRT); but I > am still a bit shaky on how to formalize my > argument. ;) > I would have never thought that S and T are > annihilated by comaximal > ideals! > Incidentally, which maximal ideals were you referring to? Perhaps the annihilator of something? > Also, are the submodules of S (+) T, provided it > is cyclic, just > the 'obvious' ones, namely (where + is direct sum) > > 0 + 0 > S + 0 > 0 + T > S + T Yes, just take the intersection of the submodule with > S and T, resp., > and look what happens using the simplicity of S and > T. > A module is simple if its only submodules are 0 and itself. I'm tempted to say that the submodules of S + T are of the form X + Y for X < S and Y < T, but I am not terribly sure at this point. Is there something simpler going on here, that I'm not aware of? === Subject: Re: - direct sums of simple R-modules > Suppose R is a ring, and M is an R-module such > that > M = S (+) T > for simple, non-isomorphic R-modules S and T. > Why is M necessarily cyclic? > What are the submodules of M ? > Hint (assuming R to be commutative unitary): S and > T are > annihilated by coprime maximal ideals of R & > Chinese Remainder > Theorem. > Best wishes, J. > with the CRT); but I > am still a bit shaky on how to formalize my > argument. > ;) > I would have never thought that S and T are > annihilated by comaximal > ideals! > > Incidentally, which maximal ideals were you referring to? Perhaps the > annihilator of something? Yes, for example take some non-zero s in S and consider the homomorphism f: R -> S with f(1) = s. Show: - f is surjective [consider f(S).] - ker(f) is a maximal ideal [What happens if not?] > Also, are the submodules of S (+) T, provided it > is cyclic, just > the 'obvious' ones, namely (where + is direct sum) > 0 + 0 > S + 0 > 0 + T > S + T > Yes, just take the intersection of the submodule with S and T, > resp., and look what happens using the simplicity of S and T. > A module is simple if its only submodules are 0 and itself. I'm tempted to say that the submodules of S + T are of the form X + Y > for X < S and Y < T, but I am not terribly sure at this point. > Is there something simpler going on here, that I'm not aware of? No. Following my hint what happens if you intersect a submodule M of S (+) T with S and with T. Then paste together again. -- Best wishes, J. === Subject: Re: Newsweek: The Large Hadron Collider > The Large Hadron Collider is a symptom of America's decline in Yes but think of the positive influence of religion in its place ! > http://www.newsweek.com/id/157514 Ah well... best wishes to the Europeans Has anyone posted this yet ? http://hasthelargehadroncolliderdestroyedtheworldyet.com/ Graham === Subject: Re: Newsweek: The Large Hadron Collider Hi my name is Conrad Countess and I have been waiting for this LHC to prove a point. What if the only black whole is matter itself? A black hole is defined as a region where gravity is so strong that light cannot escape. We know that matter is composed of trapped light (confined energy), and I am betting that it is the only such trapped light or black whole. Besides, we know that when matter gets too dense, such as the radioactive elements at the end of the periodic table, it begins to expand, break up, and decay, not contract further. I pervades the entire universe available at iuniverse.com. Unfortunately my website is down so I cannot give you a direct link to it, but if you Google ñCJCountess,î or Cosmic Alignmentî, it should come up. The universe unfolds in a pattern of expansion/contraction, and nowhere does it contract forever with out an alternating expansion or vice versa. Furthermore based on logic that everything is interrelated including space, I traced the origin of mass to space itself. Space has mass, as it has a ground state energy and energy = mass. The universe did not start with a big bang, matter condensed from space as a part of the pattern of expansion (space) and contraction (matter). And (E=mc squared) = (E=mc circled). In other words, energy = rest mass , (matter), at a frequency when energy is moving in circler and/or spherical motion,(circular frequency and standing spherical waves). Analogous to a line of 1 inch in horizontal direction multiplied by a line of 1 inch in the vertical direction to create a square inch, when the speed of light in the 90 degree angular direction equals and balances the speed of light in the linear direction, this is c^2 and results in a balance of centrifugal and centripetal forces, circular and/or spherical motion, and rest mass. Matter forms directly from the energy of space when the frequency is high enough to create circular and/or spherical motion. If this new LHC proves anything, it should prove this. Conrad Countess === Subject: Re: Newsweek: The Large Hadron Collider > Uh-oh. You are not being politically correct. 'Politically correct' is for cowards and idiots. > No, it's for people who don't want to be socially ostracized. > That's what I said. Cowards, who are afraid to tell the truth, and > idiots for not telling it. That's not cowardice; it is a sign of survival within the social group. To dismiss this behaviour as cowardice will prevent you from being objective. /BAH === Subject: Re: Newsweek: The Large Hadron Collider > Uh-oh. You are not being politically correct. > 'Politically correct' is for cowards and idiots. > No, it's for people who don't want to be socially ostracized. > That's what I said. Cowards, who are afraid to tell the truth, and > idiots for not telling it. >That's not cowardice; it is a sign of survival within the social group. >To dismiss this behaviour as cowardice will prevent you from being >objective. /BAH It ain't necessarily so. I survive quite well in diverse social groups at the workplace, and elsewhere. I am a compulsive truth teller and straight shooter. I have many workplace friends today who only respected my position at first, then my technical expertise, then learned how to ask for help in a timely manner. I do not need gratuitous insult or irrelevant vocabulary to make my point. Indeed, gratuitous complements produces far better results. I never believed in PC and can certainly explain how it is often abused. It has been tried against me, and never got better than a stalemate. === Subject: Re: Newsweek: The Large Hadron Collider > Uh-oh. You are not being politically correct. 'Politically correct' is for cowards and idiots. > No, it's for people who don't want to be socially ostracized. > That's what I said. Cowards, who are afraid to tell the truth, and > idiots for not telling it. > That's not cowardice; it is a sign of survival within the social group. > To dismiss this behaviour as cowardice will prevent you from being > objective. OK. Plonk. -- http://improve-usenet.org/index.html aioe.org, Goggle Groups, and Web TV users must request to be white listed, or I will not see your messages. If you have broadband, your ISP may have a NNTP news server included in your account: http://www.usenettools.net/ISP.htm There are two kinds of people on this earth: The crazy, and the insane. The first sign of insanity is denying that you're crazy. === Subject: Re: Newsweek: The Large Hadron Collider > smitherinos -- Ivan Reid, School of Engineering & Design, _____________ CMS Collaboration, Brunel University. Ivan.Reid@[brunel.ac.uk|cern.ch] Room 40-1-B12, CERN KotPT -- for stupidity above and beyond the call of duty. === Subject: Re: Newsweek: The Large Hadron Collider > NO, I'M SPARTICLES!!!, times a mole. I'll give you that one! ;-) -- Ivan Reid, School of Engineering & Design, _____________ CMS Collaboration, Brunel University. Ivan.Reid@[brunel.ac.uk|cern.ch] Room 40-1-B12, CERN KotPT -- for stupidity above and beyond the call of duty. === Subject: Re: Newsweek: The Large Hadron Collider > > NO, I'M SPARTICLES!!!, times a mole. I'll give you that one! ;-) > Yep :-))) /BAH === Subject: Re: Newsweek: The Large Hadron Collider NO, I'M SPARTICLES!!!, times a mole. Tim === Subject: Re: Newsweek: The Large Hadron Collider > smitherinos Bubblicles? /BAH === Subject: Re: Newsweek: The Large Hadron Collider > Uh-oh. You are not being politically correct. > 'Politically correct' is for cowards and idiots. > No, it's for people who don't want to be socially ostracized. At its best it is about being polite and respectful. At its worst it is a way of censoring dissenting opinions. -- Dirk http://www.transcendence.me.uk/ - Transcendence UK http://www.theconsensus.org/ - A UK political party http://www.onetribe.me.uk/wordpress/?cat=5 - Our podcasts on weird stuff === Subject: Re: Newsweek: The Large Hadron Collider > Uh-oh. You are not being politically correct. 'Politically correct' is for cowards and idiots. > No, it's for people who don't want to be socially ostracized. At its best it is about being polite and respectful. Political correctness has no best - it's ALL bad. > ...[I]t is a way of censoring dissenting opinions. Exactly! Rich === Subject: Re: Newsweek: The Large Hadron Collider > Uh-oh. You are not being politically correct. > 'Politically correct' is for cowards and idiots. > No, it's for people who don't want to be socially ostracized. At its best it is about being polite and respectful. When have you ever seen this? > At its worst it is a way of censoring dissenting opinions. This is the application I see when PC is used. You can't tell someone they screwed up, or that they are useless. You have to lie and tell them, Well, It could have been a lot worse. Only 300 people died because you messed up. You don't sweat much, for a fat woman? Great! They only charged your kid with manslaughter, instead of murder.? People need to take responsibility for their actions, and being PC doesn't help. -- http://improve-usenet.org/index.html aioe.org, Goggle Groups, and Web TV users must request to be white listed, or I will not see your messages. If you have broadband, your ISP may have a NNTP news server included in your account: http://www.usenettools.net/ISP.htm There are two kinds of people on this earth: The crazy, and the insane. The first sign of insanity is denying that you're crazy. === Subject: Re: Newsweek: The Large Hadron Collider > The Large Hadron Collider is a symptom of America's decline in > http://www.newsweek.com/id/157514 > Ah well... best wishes to the Europeans I can't recall a single technologically useful result it's > generated since about Fermi's day > The argument seems to be that we have to keep dumping > our limited physical science budgets into accelerators > to avoid falling behind in a field that doesn't produce anything > useful > Before radios, telegraphs, electric motors, etc, etc, Queen Victoria > once asked British physicist Michael Faraday of what use his > studies in electricity and magnetism were. He famously replied, > Madam, of what use is a baby? > has had big bucks poured into it for what, 60 years now? (Not counting > the Manhattan Project--nuclear has produced useful things.) When the > Faraday effect was 60 years old, it was powering half the world. > Somebody pointed out long ago that the further the energy scale gets > from kT, the fewer the useful results. >Well, if you're looking for practical results... > http://www.foxnews.com/story/0,2933,419404,00.html >Coincidentally, the LHC is scheduled to go online in just >a few hours, at 3:30am EDT Wednesday, 9/10/08, possibly >creating black holes that will destroy the Earth... > Someone will spot a light ray coming out of the Indian > Ocean during the night and no one will be able to explain it, > retired Professor Otto Roessler told London's Mail. > Very soon the whole planet will be eaten in a magnificent > scenario if you could watch it from the moon. A Biblical > Armageddon. Even cloud and fire will form, as it says in > the Bible. >And we even have... > A pair of Russian scientists even think the LHC will be > the world's first time machine, and that we should expect > visitors from the future to arrive soon after it goes into > operation. >And, hey, don't tell me these guys are kooks until >you double-check what newsgroup you're posting to. A hot cosmic ray can have the kinetic energy of a well-pitched > baseball, far more than the LHC can manage. Certainly in the age of > the Earth two such cosmic rays have collided nearby. We're still here. Well, what confused me about the two quotes was that if (1) the LHC destroys the Earth, then (2) how can there then be any visitors from the future? -- John Forkosh ( mailto: j@f.com where j=john and f=forkosh ) === Subject: Re: Newsweek: The Large Hadron Collider > The Large Hadron Collider is a symptom of America's decline in > æ æ æhttp://www.newsweek.com/id/157514 > Ah well... best wishes to the Europeans I can't recall a single technologically useful result it's > generated since about Fermi's day > æ æ æThe argument seems to be that we have to keep dumping > our limited physical science budgets into accelerators > to avoid falling behind in a field that doesn't produce anything > useful > Before radios, telegraphs, electric motors, etc, etc, Queen Victoria > once asked British physicist Michael Faraday of what use his > studies in electricity and magnetism were. æHe famously replied, > Madam, of what use is a baby? has had big bucks poured into it for what, 60 years now? æ(Not counting > the Manhattan Project--nuclear has produced useful things.) æWhen the > Faraday effect was 60 years old, it was powering half the world. > æ æSomebody pointed out long ago that the further the energy scale gets > from kT, the fewer the useful results. >Well, if you're looking for practical results... > æhttp://www.foxnews.com/story/0,2933,419404,00.html >Coincidentally, the LHC is scheduled to go online in just >a few hours, at 3:30am EDT Wednesday, 9/10/08, possibly >creating black holes that will destroy the Earth... > æ Someone will spot a light ray coming out of the Indian > æ Ocean during the night and no one will be able to explain it, > æ retired Professor Otto Roessler told London's Mail. > æ Very soon the whole planet will be eaten in a magnificent > æ scenario if you could watch it from the moon. A Biblical > æ Armageddon. æEven cloud and fire will form, as it says in > æ the Bible. >And we even have... > æ A pair of Russian scientists even think the LHC will be > æ the world's first time machine, and that we should expect > æ visitors from the future to arrive soon after it goes into > æ operation. >And, hey, don't tell me these guys are kooks until >you double-check what newsgroup you're posting to. A hot cosmic ray can have the kinetic energy of a well-pitched > baseball, far more than the LHC can manage. Certainly in the age of > the Earth two such cosmic rays have collided nearby. We're still here. Well, what confused me about the two quotes was that if > (1) the LHC destroys the Earth, then (2) how can there > then be any visitors from the future? > -- > John Forkosh æ( mailto: æj...@f.com æwhere j=john and f=forkosh )- Hide quoted text - - Show quoted text - The LHC won't destroy the earth directly, it would just mess up the natural extra dimensional barrier by sending signal into them. Prior to this. We only have random cosmic rays reaching into them, but the LHC changes it. You see, the extra dimensions are inhabited. cal === Subject: Re: Newsweek: The Large Hadron Collider > The Large Hadron Collider is a symptom of America's decline in > http://www.newsweek.com/id/157514 > Ah well... best wishes to the Europeans > I can't recall a single technologically useful result it's > generated since about Fermi's day > The argument seems to be that we have to keep dumping > our limited physical science budgets into accelerators > to avoid falling behind in a field that doesn't produce anything > useful > Before radios, telegraphs, electric motors, etc, etc, Queen Victoria > once asked British physicist Michael Faraday of what use his > studies in electricity and magnetism were. He famously replied, > Madam, of what use is a baby? > has had big bucks poured into it for what, 60 years now? (Not counting > the Manhattan Project--nuclear has produced useful things.) When the > Faraday effect was 60 years old, it was powering half the world. > Somebody pointed out long ago that the further the energy scale gets > from kT, the fewer the useful results. > Well, if you're looking for practical results... > http://www.foxnews.com/story/0,2933,419404,00.html > Coincidentally, the LHC is scheduled to go online in just > a few hours, at 3:30am EDT Wednesday, 9/10/08, possibly > creating black holes that will destroy the Earth... > Someone will spot a light ray coming out of the Indian > Ocean during the night and no one will be able to explain it, > retired Professor Otto Roessler told London's Mail. > Very soon the whole planet will be eaten in a magnificent > scenario if you could watch it from the moon. A Biblical > Armageddon. Even cloud and fire will form, as it says in > the Bible. > And we even have... > A pair of Russian scientists even think the LHC will be > the world's first time machine, and that we should expect > visitors from the future to arrive soon after it goes into > operation. > And, hey, don't tell me these guys are kooks until > you double-check what newsgroup you're posting to. > A hot cosmic ray can have the kinetic energy of a well-pitched > baseball, far more than the LHC can manage. Certainly in the age of > the Earth two such cosmic rays have collided nearby. We're still here. > Well, what confused me about the two quotes was that if > (1) the LHC destroys the Earth, then (2) how can there > then be any visitors from the future? > -- > John Forkosh ( mailto: j...@f.com where j=john and f=forkosh )- Hide quoted text - > - Show quoted text - The LHC won't destroy the earth directly, it would just mess up the > natural extra dimensional barrier by sending signal into them. Prior > to this. We only have random cosmic rays reaching into them, > but the LHC changes it. You see, the extra dimensions are inhabited. cal Only by very hot females.. === Subject: Re: Newsweek: The Large Hadron Collider The LHC won't destroy the earth directly, it would just mess up the > natural extra dimensional barrier by sending signal into them. Prior > to this. We only have random cosmic rays reaching into them, > but the LHC changes it. You see, the extra dimensions are inhabited. Only by very hot females.. So that's one more place that you'll never get a date? -- http://improve-usenet.org/index.html aioe.org, Goggle Groups, and Web TV users must request to be white listed, or I will not see your messages. If you have broadband, your ISP may have a NNTP news server included in your account: http://www.usenettools.net/ISP.htm There are two kinds of people on this earth: The crazy, and the insane. The first sign of insanity is denying that you're crazy. === Subject: Re: Newsweek: The Large Hadron Collider > The LHC won't destroy the earth directly, it would just mess up the > natural extra dimensional barrier by sending signal into them. Prior > to this. We only have random cosmic rays reaching into them, > but the LHC changes it. You see, the extra dimensions are inhabited. > Only by very hot females.. > So that's one more place that you'll never get a date? Yeah, probably.. === Subject: qustion about a set with an operation. Given a non-emty set M with an operation (.) such that 1) a.1=1.a=a, all a, where 1 is one specific element of M. 2) a.0=0.a=0, all a, where 0 is one specific element of M. 3) 1!=0 4) (ab)c=a(bc), all a,b,c. 5) If T2 and T3 is some elements of M that commute with every element of M. and x.T2=x.T3 and x!=0 then T2=T3, ----------------------------------------------------------- Does it follow that: 6) If x.y=x.z and x!=0 then y=z, all x, y, z.? please don't give away the whole soloution, only point me in the right direction. === Subject: Re: qustion about a set with an operation. > Given a non-emty set M > with an operation (.) > such that 1) a.1=1.a=a, all a, where 1 is one specific element of M. 2) a.0=0.a=0, all a, where 0 is one specific element of M. 3) 1!=0 4) (ab)c=a(bc), all a,b,c. 5) If T2 and T3 is some elements of M that commute with every element > of M. > and x.T2=x.T3 and x!=0 > then T2=T3, > ----------------------------------------------------------- Does it follow that: > 6) If x.y=x.z and x!=0 then y=z, all x, y, z.? please don't give away the whole soloution, > only point me in the right direction. Think about the case in which M is the set of all 2x2 real matrices, 0 is the null matrix and 1 is the identity matrix. Jose Carlos Santos === Subject: Re: qustion about a set with an operation. Jos.8e Carlos Santos skrev: Given a non-emty set M > with an operation (.) > such that 1) a.1=1.a=a, all a, where 1 is one specific element of M. 2) a.0=0.a=0, all a, where 0 is one specific element of M. 3) 1!=0 4) (ab)c=a(bc), all a,b,c. 5) If T2 and T3 is some elements of M that commute with every element > of M. > and x.T2=x.T3 and x!=0 > then T2=T3, > ----------------------------------------------------------- Does it follow that: > 6) If x.y=x.z and x!=0 then y=z, all x, y, z.? please don't give away the whole soloution, > only point me in the right direction. Think about the case in which M is the set of all 2x2 real matrices, 0 > is the null matrix and 1 is the identity matrix. > Jose Carlos Santos I tried the example of M=2x2 real matrices. And I found that the only elements that commute with every element of M is: a 0 0 a with a real number and (5) is fullfilled, but not (6). === Subject: Multiplicative orders mod p I'm having trouble making a conclusion based on what I have, and I think I need some assistance: Suppose we have a prime p and integers n and m, and that the multiplicative order of m (mod p) is the same as the multiplicative order (mod p) of m^n, m^n^2, m^n^3, and so on. It seems that I can conclude that there is an integer k such that m^n^k is congruent to m (mod p) provided that gcd(n, p-1) = 1. Is this the case? If so, how can I make that assertion? === Subject: Re: Multiplicative orders mod p > I'm having trouble making a conclusion based on what I have, and I > think I need some assistance: Suppose we have a prime p and integers n and m, and that the > multiplicative order of m (mod p) is the same as the multiplicative > order (mod p) of m^n, m^n^2, m^n^3, and so on. æIt seems that I can > conclude that there is an integer k such that m^n^k is congruent to m > (mod p) provided that gcd(n, p-1) = 1. æIs this the case? æIf so, how > can I make that assertion? Let us assume m is not 0 mod p, in which case the assertion is trivial. Then, since (n, p-1) = 1, there is a k so that n^k = 1 (mod p-1), since it is a member of the reduced residue group and therefore has some order, say k. Then n^k = 1 + r(p-1) for some r, and so m^(n^k) (I assume this this is what you meant) is equal to m^(1 + r(p-1) = m * (m^r)^(p-1) = m * 1 = m (mod p) as you wished. Achava === Subject: Re: Bye victor_meldrew_666@yahoo.co.uk: > My main topic is IR+. However you ignored what I am claiming. You have neither defined IR+ (that's not a standard notation) > It is. But you may read it as R+. IR+ := {x e IR : x > 0}. See: http://mathworld.wolfram.com/R-Plus.html > Mathematicians understand IR+ like IR but restricted to positive values. > Right. Again, what is IR? That is not standard notation. > It is. IR (meant as a single symbol) denotes the set of real numbers: See: http://mathworld.wolfram.com/RealNumber.html B. === Subject: Re: Very basic mistakes issue so far. Victor did not understand anything what I am trying to point to. While my main interest relates to IR+, I also found out that - at least as far as I can judge - the notions of number, real number, continuity, and infinity were distorted in order to unnecessarily justify reasonable pragmatism in an allegedly rigorous manner. Let me try and summarize it in brief: I agree with the mathematicians that 0.999... does not differ from 1.000... iff ... means that we assume all of indefinitely much nines or zeroes, respectively, are given. However, I do not require an arbitrary definition for that. According to my reasoning, infinity, continuum, irrational numbers, real numbers, and non-linearity belong to an ideal realm that is quite different from the ideally discrete realm of points and rational numbers. Those who are critical towards set theory are usually put into the drawer of constructivism. While I found myself sharing some critical arguments with e.g. Brouwer, I do not intend correcting set theory as did he. Constructivists do perhaps not consequently apply Brouwer's insight that the TND is only valid for finite quantities. They even substitute the law of trichotomy (rs) by if r, u, n elements of IR with uu or r> n. Do not get me wrong. I appreciate the tacit substitution of genuine reals by approximating rationals. I merely demand that one must not pretend actually using a body of reals. If we decide that a number relates to a unity of e.g. length of a line, then (strictly speaking) I see this precluding to interpret it as a point. Back to (as I claim correct) basics means: Euclid: A point is what does not have parts. eg Peirce: Each part of a (genuine) continuum has parts. Stiefel: dust of irrational numbers Weyl: sauce of real numbers (no trichotomy, impossible to practice a well-ordering) Aristoteles: Actual infinity cannot be reached. Spinoza: Absolute infinity cannot be enlarged or exhausted. and of course Salviati: ... in ultima conclusione, gli attributi di eguale maggiore e minore non aver luogo ne gl'infiniti, ma solo nelle quantit.88 terminate. IR>|>IR+=|=IR, not smaller, not larger, not of equal size, just no quantum but a property. Balthasar schrieb im Newsbeitrag > victor_meldrew_666@yahoo.co.uk: > My main topic is IR+. However you ignored what I am claiming. > You have neither defined IR+ (that's not a standard notation) > It is. But you may read it as R+. IR+ := {x e IR : x > 0}. See: > http://mathworld.wolfram.com/R-Plus.html > Mathematicians understand IR+ like IR but restricted to positive values. Right. > Again, what is IR? That is not standard notation. > It is. IR (meant as a single symbol) denotes the set of real numbers: See: > http://mathworld.wolfram.com/RealNumber.html > B. === Subject: Re: Very basic mistakes I agree with the mathematicians that 0.999... does not differ from 1.000... > iff ... means that we assume all of indefinitely much nines or zeroes, > respectively, are given. However, I do not require an arbitrary definition > for that. According to my reasoning, infinity, continuum, irrational > numbers, real numbers, and non-linearity belong to an ideal realm that is > quite different from the ideally discrete realm of points and rational > numbers. > In what way, conceptual or mathematical, are the rational numbers discrete? Between any two rationals you'll find infinitely many other rationals. === Subject: Re: Very basic mistakes > In what way, conceptual or mathematical, are the rational numbers > discrete? Between any two rationals you'll find infinitely many other > rationals. That makes the difference. In contrast to irrationals, rationals can be found out immediately from a discrete order. The rationals altogether relate to the unity. Every rational number can be reached from number one by a finite number of additions and/or divisions. Intelligent students ask how the rationals can be dicht in the sense of waterproof. Cantor's naivity is obvious. He imagined that just an enough large amount of points is required as to get a complete line without distances between the points. It is hard to apologise why he did not understand that the number of points for any piece of a line has no limitation. Cantor did not grasps that a point is something ideal, which has no extension at all. Salviati === Subject: breadline schmuck's basic mistakes That makes the difference. In contrast to irrationals, rationals can be > found out immediately from a discrete order. Has anyone any idea what this means? > The rationals altogether relate to the unity. any idea? > Every rational number can be reached from number one > by a finite number of additions and/or divisions. Try getting -4/7 from 1 by a finite number of additions and divisions? > Intelligent students ask how the rationals can be dicht > in the sense of waterproof. I have never met one who did. > Cantor did not grasps that a point is something ideal, > which has no extension at all. So Cantor thought a point did have extension? Victor Meldrew I don't believe it! === Subject: breadline schmuck's basic mistakes > issue so far. Victor did not understand anything what I am trying to point > to. There was nothing to understand, since there was nothing coherent expressed. > According to my reasoning, infinity, continuum, irrational > numbers, real numbers, and non-linearity belong to an ideal realm that is > quite different from the ideally discrete realm of points and rational > numbers. In other words, a mystical unmathematical realm, only accessible to E. Bullscheit's intuitions. Victor Meldrew I don't believe it! === Subject: : Z-modules and Abelian groups : Abelian groups are Z-modules in a natural way. In fact, it was an exercise to show that abelian groups can only carry exactly one structure as a Z-module (namely, the natural action of Z given by n.x = x + .. + x if n > 0; 0.x = 0; -n.x = (-x) + .. + (-x)). This seems to imply that there's a *bijective* correspondence between Z-modules and abelian groups; is this true? Or can we at least say that {Z-modules} = {abelian groups} as sets? categories? Also, given any Z-module M, are the submodules of M exactly the same as the additive subgroups of M, yes? Z-submodules of M are subgroups anyway; and subgroups are automatically closed under the natural action of Z (because subgroups are closed under sums and additive inverses) so they're submodules. That is, we must have {additive subgroups of M} = {Z-submodules of M} Does this also set up a bijective correspondence? === Subject: Re: : Z-modules and Abelian groups : > Abelian groups are Z-modules in a natural way. In fact, it was an > exercise to show that abelian groups can only carry exactly one > structure as a Z-module (namely, the natural action of Z given by n.x = x + .. + x if n > 0; 0.x = 0; -n.x = (-x) + .. + (-x)). > This seems to imply that there's a *bijective* correspondence > between Z-modules and abelian groups; is this true? Or can we at least say that {Z-modules} = {abelian groups} as sets? categories? Correct. > Also, given any Z-module M, are the submodules of M exactly the same > as the additive subgroups of M, yes? True, as well, > Z-submodules of M are subgroups anyway; and subgroups are > automatically closed under the natural action of Z (because > subgroups are closed under sums and additive inverses) so they're > submodules. That is, we must have {additive subgroups of M} = {Z-submodules of M} Yep. > Does this also set up a bijective correspondence? -- Best wishes, J. === Subject: Re: : Z-modules and Abelian groups : the additive inverse of X is -2X?... I mean, not summorial of -2X iff defined. sorry, about the outburst from Descartes CIRCA Fermat; didn't realize that it may be thought, ambivvalent! === Subject: Re: : Z-modules and Abelian groups : > the additive inverse of X is -2X?... I mean, > not summorial of -2X iff defined. sorry, about the outburst from Descartes CIRCA > Fermat; > didn't realize that it may be thought, ambivvalent! what are you on about? === Subject: Establishing an equality between unions of conjugates in a quotient group Let G be a group, H a subgroup, and let K be a normal subgroup contained in H. I want to show that (the union) U_{g in G} (H/K)^{gK} = U_{gK in G/K} (H/K)^{gK} Now, Arturo pointed out that whenever xK = yK then (H/K)^{xK} = (H/K)^{yK}. How does this observation establish the equality above? It seems obvious, but Arturo made it a point to argue a little differently here, and this is precisely what I'm trying to understand. Also, what if we had restricted the union on the left to some proper subset I of G; would that also be the same as the union on the right side over the subset J = {xK : x in I} of G/K? === Subject: Re: Establishing an equality between unions of conjugates in a quotient group just a few questions to make sure that I am on the right track. > Let G be a group, H a subgroup, and let K be a normal subgroup > contained in H. K normal in G? > I want to show that (the union) > U_{g in G} (H/K)^{gK} = U_{gK in G/K} (H/K)^{gK} What does (H/K)^{gK} mean? Does it refer to an operation on H/K? > Now, Arturo pointed out that whenever xK = yK then (H/K)^{xK} = (H/K)^{yK}. > How does this observation establish the equality above? It seems > obvious, but Arturo made it a point to argue a little differently > here, and this is precisely what I'm trying to understand. > Also, what if we had restricted the union on the left to some proper > subset I of G; would that also be the same as the union on the right > side over the subset J = {xK : x in I} of G/K? -- Best wishes, J. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > The natural numbers are as observable phenomena as mass, gravity, > colour, form, etc. > Really? About the natural numbers, has anybody ever observed the truth > of GC, or of the statement there are infinite even natural numbers that > don't satisfy GC? Do someone knows the truth of mass? What are the truths of mass should one know? -- To discover the proper approach to mathematical logic, we must therefore examine the methods of the mathematician. (Shoenfield, Mathematical Logic) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor The natural numbers are as observable phenomena as mass, gravity, > colour, form, etc. > Really? About the natural numbers, has anybody ever observed the truth > of GC, or of the statement there are infinite even natural numbers that > don't satisfy GC? Do someone knows the truth of mass? What are the truths of mass should one know? It's you who want to observe the truth of something (whatever that means). === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > I've only suggested that mathematics could borrow some truth from that > source called physics. > > The trouble is that the objects that mathematics deals with > (numbers, sets, etc.) are not physically observable phenomena. > That's where any similarity between mathematics and physics > breaks down. > > The natural numbers are as observable phenomena as mass, gravity, > colour, form, etc. > Have you observed one lately? What did it look like? If you are owner of two hands, put them together. What do you feel? > Maybe two hands? Maybe ten fingers (including thumbs). So which natural number(s) exist in one's hands? Is ten not represented > as well as two. Yes. (And 25, and 9,8,7,6,5,4,3,2,1, ... as well as ... It's a kind of view, context, concerning considerations, intelligence, experiences, fellings, ..., it's information.) === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > I've only suggested that mathematics could borrow some truth from > that > source called physics. > > The trouble is that the objects that mathematics deals with > (numbers, sets, etc.) are not physically observable phenomena. > That's where any similarity between mathematics and physics > breaks down. > > The natural numbers are as observable phenomena as mass, gravity, > colour, form, etc. > Have you observed one lately? What did it look like? > If you are owner of two hands, put them together. What do you feel? > Maybe two hands? Maybe ten fingers (including thumbs). So which natural number(s) exist in one's hands? Is ten not represented > as well as two. > Yes. > (And 25, and 9,8,7,6,5,4,3,2,1, ... as well as ... It's a kind of > view, context, concerning considerations, intelligence, experiences, > fellings, ..., it's information.) Then you can only exhibit physical things having a certain number property, but not the physical number itself? It follows that, even though numbers do exist, they have no physical existence. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > I've only suggested that mathematics could borrow some truth from > that > source called physics. > The trouble is that the objects that mathematics deals with > (numbers, sets, etc.) are not physically observable phenomena. > That's where any similarity between mathematics and physics > breaks down. > The natural numbers are as observable phenomena as mass, gravity, > colour, form, etc. > Have you observed one lately? What did it look like? > If you are owner of two hands, put them together. What do you feel? > Maybe two hands? > Maybe ten fingers (including thumbs). > So which natural number(s) exist in one's hands? Is ten not represented > as well as two. > Yes. > (And 25, and 9,8,7,6,5,4,3,2,1, ... as well as ... It's a kind of > view, context, concerning considerations, intelligence, experiences, > fellings, ..., it's information.) Then you can only exhibit physical things having a certain number > property, but not the physical number itself? What is a physical number? There is no physical number. The property manifoldness is. So numbers are. Do you realy think, only physical things exists? There are no relations, no causalities, no time, no center of the milky way, no ideas, no inventions, etc. It follows that, even though numbers do exist, they have no physical > existence. Numbers has physical existence as other properties of objects or of sets of objects. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > I've only suggested that mathematics could borrow some truth from > that > source called physics. > The trouble is that the objects that mathematics deals with > (numbers, sets, etc.) are not physically observable phenomena. > That's where any similarity between mathematics and physics > breaks down. > The natural numbers are as observable phenomena as mass, gravity, > colour, form, etc. > Have you observed one lately? What did it look like? > If you are owner of two hands, put them together. What do you feel? > Maybe two hands? > Maybe ten fingers (including thumbs). > So which natural number(s) exist in one's hands? Is ten not represented > as well as two. > > Yes. > (And 25, and 9,8,7,6,5,4,3,2,1, ... as well as ... It's a kind of > view, context, concerning considerations, intelligence, experiences, > fellings, ..., it's information.) Then you can only exhibit physical things having a certain number > property, but not the physical number itself? What is a physical number? There is no physical number. The property > manifoldness is. > So numbers are. Do you realy think, only physical things exists? There are no > relations, no causalities, no time, no center of the milky way, no > ideas, no inventions, etc. It follows that, even though numbers do exist, they have no physical > existence. Numbers has physical existence as other properties of objects or of > sets of objects. Albrecht types with forked keyboard in claiming first that numbers have no physical existence and later than they do. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > I've only suggested that mathematics could borrow some truth from > that > source called physics. > The trouble is that the objects that mathematics deals with > (numbers, sets, etc.) are not physically observable phenomena. > That's where any similarity between mathematics and physics > breaks down. > The natural numbers are as observable phenomena as mass, gravity, > colour, form, etc. > Have you observed one lately? What did it look like? > If you are owner of two hands, put them together. What do you feel? > Maybe two hands? > Maybe ten fingers (including thumbs). > So which natural number(s) exist in one's hands? Is ten not represented > as well as two. > > Yes. > (And 25, and 9,8,7,6,5,4,3,2,1, ... as well as ... It's a kind of > view, context, concerning considerations, intelligence, experiences, > fellings, ..., it's information.) > Then you can only exhibit physical things having a certain number > property, but not the physical number itself? What is a physical number? There is no physical number. The property > manifoldness is. > So numbers are. Do you realy think, only physical things exists? There are no > relations, no causalities, no time, no center of the milky way, no > ideas, no inventions, etc. > It follows that, even though numbers do exist, they have no physical > existence. Numbers has physical existence as other properties of objects or of > sets of objects. Albrecht types with forked keyboard in claiming first that numbers have > no physical existence and later than they do. You are dreaming. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor > You are dreaming. If so, my dreamings are closer to reality than Albrecht's waking thoughts. === Subject: Re: A consideration concerning the diagonal argument of G. Cantor <87zlmrzxtn.fsf@phiwumbda.org> <1d79a$48bce687$82a1e228$604@news1.tudelft.nl> <6b855$48be3911$82a1e228$14221@news1.tudelft.nl> posting-account=6xUtvgkAAAD_jypmLa2oo2HnrV0e8X9q rv:1.7.13) Gecko/20060414,gzip(gfe),gzip(gfe) > Exactly so. Did I ever suggest that physics (especially astronomy) is > free from dogmas, oh well, let's say: questionable extrapolations ? > You have clearly suggested that it is the sole source of all truth. > I've only suggested that mathematics could borrow some truth from that > source called physics. > The trouble is that the objects that mathematics deals with > (numbers, sets, etc.) are not physically observable phenomena. > That's where any similarity between mathematics and physics > breaks down. > The natural numbers are as observable phenomena as mass, gravity, > colour, form, etc. > All of which are artificialities which we impose on reality and by which > we interpret reality. Ah, very interesting. And, please, might you tell me: What is reality? That is a problem for physicists, of which I am not one. Humans are > pattern seekers, and tend to impose their own order on whatever they > perceive. Mathematicians deal with some of those patterns without > worrying, at least as mathematicians, about what lies beneath them. You are unable to make a difference between artificialities and not- > artificialities, are you? So, what we are talking about? Things like > mass, gravity, colour, form, natural numbers, ..., which are > artificialities and things like ??? which are not artificialities? > Please give an example for ???. Not my problem. Your standpoint is very weak, I think. Just limited. Well. === Subject: Re: force moves objects -- not velocity, not velocity, not velocity! posting-account=UM3jRwkAAADTHFmJ20qgwageu031CeWA FunWebProducts; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; PeoplePal 3.0; eMusic DLM/4; CNPVersion2 - Congoo NetPass; FDM; RRHSO_BLD1),gzip(gfe),gzip(gfe) > the main wrong issue is the first lesson in physics with its > definition for instant velocity as V=dx/dt based on x[m]=f(t[s]). > blame newton and galileo for that. what function dependant only on > time in seconds results with position in meters? V being defined as dx/dt makes V tangent of trajectory which is wrong > cause if V=dx/dt then t must be dx/dV or total dx=Vdt+tdV. but then > x[m] is not f(t[s]) but x[m] is V[m/s]t[s] or x[m] is accel[m/s^2] > (t[s])^2. more accurately, x=Vt is threedimensional surface where each of x, V, > t go on its own axis (try ploting x=Vt and you'll see). velocity is > wrongfully taught to move objects. and what's more why would someone > introduce them two unknowns V and t to unscramble one unknown x -- > it's complication beyond necessary. > I can't acknowledge something based on faulty mathematics. I'm just funny that way. === Subject: Re: force moves objects -- not velocity, not velocity, not velocity! posting-account=OKTeIQkAAAAZk6JK1hK7-grwpoUDNy98 4334.34; Windows NT 5.1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) spider-mtc-td01.proxy.aol.com[400C7061] (Prism/1.2.1), HTTP/1.1 cache-mtc-ad05.proxy.aol.com[400C74C7] (Traffic-Server/6.1.5 [uScM]) > the main wrong issue is the first lesson in physics with its > definition for instant velocity as V=dx/dt based on x[m]=f(t[s]). > blame newton and galileo for that. what function dependant only on > time in seconds results with position in meters? V being defined as dx/dt makes V tangent of trajectory which is wrong > cause if V=dx/dt then t must be dx/dV or total dx=Vdt+tdV. but then > x[m] is not f(t[s]) but x[m] is V[m/s]t[s] or x[m] is accel[m/s^2] > (t[s])^2. more accurately, x=Vt is threedimensional surface where each of x, V, > t go on its own axis (try ploting x=Vt and you'll see). velocity is > wrongfully taught to move objects. and what's more why would someone > introduce them two unknowns V and t to unscramble one unknown x -- > it's complication beyond necessary. > Then I guess we won't acnowledge this point, eh? === Subject: Re: force moves objects -- not velocity, not velocity, not velocity! > the main wrong issue is the first lesson in physics with its > definition for instant velocity as V=dx/dt based on x[m]=f(t[s]). > blame newton and galileo for that. what function dependant only on > time in seconds results with position in meters? > V being defined as dx/dt makes V tangent of trajectory which is wrong > cause if V=dx/dt then t must be dx/dV or total dx=Vdt+tdV. but then > x[m] is not f(t[s]) but x[m] is V[m/s]t[s] or x[m] is accel[m/s^2] > (t[s])^2. > more accurately, x=Vt is threedimensional surface where each of x, V, > t go on its own axis (try ploting x=Vt and you'll see). velocity is > wrongfully taught to move objects. and what's more why would someone > introduce them two unknowns V and t to unscramble one unknown x -- > it's complication beyond necessary. > Then I guess we won't acnowledge this point, eh?- Hide quoted text - > - Show quoted text - i'll keep anoying you??? i can aford that much money from my > macedonian social security paycheck??? Yes. === Subject: Re: force moves objects -- not velocity, not velocity, not velocity! > the main wrong issue is the first lesson in physics with its > definition for instant velocity as V=dx/dt based on x[m]=f(t[s]). > blame newton and galileo for that. what function dependant only on > time in seconds results with position in meters? V being defined as dx/dt makes V tangent of trajectory which is wrong > cause if V=dx/dt then t must be dx/dV or total dx=Vdt+tdV. but then > x[m] is not f(t[s]) but x[m] is V[m/s]t[s] or x[m] is accel[m/s^2] > (t[s])^2. more accurately, x=Vt is threedimensional surface where each of x, V, > t go on its own axis (try ploting x=Vt and you'll see). velocity is > wrongfully taught to move objects. and what's more why would someone > introduce them two unknowns V and t to unscramble one unknown x -- > it's complication beyond necessary. ONCE YOU ACKNOWLEDGE THIS POINT YOUR ENTIRE PHYSICS FALLS. But once we aknowledge that you are an autistic imbecile, our entire physics is back sound and safe. Phew, what a relief! Dirk Vdm === Subject: Embedding an elementary abelian group into a symmetric group Why does the elementary abelian group (Z/2)^5 embed into S_{10} ? I was thinking of letting (Z/2)^5 act on the set of left cosets of some subgroup, but I noticed that 10 doesn't divide 32 (!) Any thoughts? === Subject: Re: Embedding an elementary abelian group into a symmetric group > Why does the elementary abelian group (Z/2)^5 embed > into S_{10} ? ... Any thoughts? Here are my immediate thoughts on constructing such an embedding (i.e. homomorphism): First, note that G = <(01),(23),(45),(67),(89)> is a subgroup of S_10, and by definition (Z/2)^5 = {(x_0, x_1, x_2, x_3, x_4) : x_i in Z/2} ..which we could also write as... (Z/2)^5 = <(1,0,0,0,0), (0,1,0,0,0), ..., (0,0,0,0,1)> ..where it is understood the group operation is addition modulo 2. I'm sure you see where I'm going with this... now we just construct the homomorphism phi:(Z/2)^5 --> S_10 such that phi(0,0,0,0,0) = (), phi(1,0,0,0,0) = (01), phi(0,1,0,0,0) = (23), etc. ..it's not difficult to see/check that phi is indeed a homomorphism. Moreover, it's clear that such a mapping will work for any subgroup of S_10 generated by five disjoint 2-cycles (for example, G = <(02),(46),(81),(35),(79)> instead). Kyle Czarnecki === Subject: Re: Embedding an elementary abelian group into a symmetric group > Why does the elementary abelian group (Z/2)^5 > embed > into S_{10} ? ... Any thoughts? Here are my immediate thoughts on constructing such > an > embedding (i.e. homomorphism): First, note that G = <(01),(23),(45),(67),(89)> is a > subgroup of S_10, and by definition (Z/2)^5 = {(x_0, x_1, x_2, x_3, x_4) : x_i in Z/2} ...which we could also write as... (Z/2)^5 = <(1,0,0,0,0), (0,1,0,0,0), ..., > (0,0,0,0,1)> ...where it is understood the group operation is > addition > modulo 2. I'm sure you see where I'm going with this... now we > just > construct the homomorphism phi:(Z/2)^5 --> S_10 such > that phi(0,0,0,0,0) = (), phi(1,0,0,0,0) = (01), phi(0,1,0,0,0) = (23), etc. ...it's not difficult to see/check that phi is indeed > a > homomorphism. Moreover, it's clear that such a mapping will work > for > any subgroup of S_10 generated by five disjoint > 2-cycles > (for example, G = <(02),(46),(81),(35),(79) instead). Kyle Czarnecki Incidentally, why is your map injective? === Subject: Re: Embedding an elementary abelian group into a symmetric group Incidentally, why is your map injective? For two reasons: 1) Let x and y be distinct elements in H = (Z/2)^5, and let g be an element of G = <(01),(23),...,(89)> such that phi(x) = phi(y) = g. Since all non-trivial elements of G have order two, it follows that e_G = g^2 = phi(x) phi(y) ..but phi is a homomorphism, so e_G = g^2 = phi(x) phi(y) = phi(xy) = phi(e_G) ..which implies that y = x^{-1}. However, all of the non-trivial elements of (Z/2)^5 also have order 2, which implies that y = x^{-1} = x -- a contradiction since x and y were taken to be distinct. Thus, the map phi:H --> G (described in my previous post) is injective. [] 2) In general, any group homomorphism with a trivial kernal is an injection: http://planetmath.org/encyclopedia/AHomomorphismIsInjectiveIffTheKernelIsTri vial.html Kyle Czarnecki === Subject: Re: Embedding an elementary abelian group into a symmetric group > Incidentally, why is your map injective? For two reasons: 1) Let x and y be distinct elements in H = (Z/2)^5, and > let g be an element of G = <(01),(23),...,(89)> such that > phi(x) = phi(y) = g. Since all non-trivial elements of G have order two, it > follows that e_G = g^2 = phi(x) phi(y) ..but phi is a homomorphism, so e_G = g^2 = phi(x) phi(y) = phi(xy) = phi(e_G) ..which implies that y = x^{-1}. Why that? I cannot see your argument. ;) Alternatively you can show that G is a vector space over Z/2Z of dimension 5 and f is a surjective linear map (over Z/2Z), so it is injective. -- Best wishes, J. === Subject: Re: Embedding an elementary abelian group into a symmetric group > Incidentally, why is your map injective? > For two reasons: > 1) Let x and y be distinct elements in H = (Z/2)^5, > and let g be an element of G = <(01),(23),...,(89) such that phi(x) = phi(y) = g. > Since all non-trivial elements of G have order two, > it follows that e_G = g^2 = phi(x) phi(y) > ...but phi is a homomorphism, so > e_G = g^2 = phi(x) phi(y) = phi(xy) = phi(e_G) > ...which implies that y = x^{-1}. Why that? I cannot see your argument. ;) ^_^ Are you referring to the typo? In that case, the last string of equalities should read: e_G = g^2 = phi(x) phi(y) = phi(xy) = phi(e_H). If not, then allow me to break it down: 1) We begin with the identity element e_G of G. 2) Since all non-trivial elements of G are order 2, we must have that e_G = g^2. 3) By hypothesis we're assuming that phi(x) = phi(y) = g, so g^2 = phi(x) phi(y). 4) Since phi is a homomorphism, phi(x) phi(y) = phi(xy). 5) Again, since phi is a homomorphism, phi(e_H) = e_G; hence, e_G = g^2 = phi(x) phi(y) = phi(xy) = phi(e_H). In other words, because phi sends xy to the identity in G, it follows that xy must be the identity in H... ..for, if xy were not equal to e_H, phi would be mapping two elements to e_G and would thus not be a homomorphism. This establishes that xy = e_H and implies y = x^{-1}. > Alternatively you can show that G is a vector space > over Z/2Z of dimension 5 and f is a surjective linear > map (over Z/2Z), so it is injective. I suppose, but there is no need to induce more structure on the group (i.e. consider it also as a vector space) in order to prove such a group theoretical fact... ..but whatever flips your switch ^_^ Kyle Czarnecki === Subject: Re: Embedding an elementary abelian group into a symmetric group > Incidentally, why is your map injective? > For two reasons: > 1) Let x and y be distinct elements in H = (Z/2)^5, and let g be > an element of G = <(01),(23),...,(89)> such that phi(x) = phi(y) > = g. > Since all non-trivial elements of G have order two, it follows > that > e_G = g^2 = phi(x) phi(y) > ...but phi is a homomorphism, so > e_G = g^2 = phi(x) phi(y) = phi(xy) = phi(e_G) > ...which implies that y = x^{-1}. > Why that? I cannot see your argument. ;) ^_^ Are you referring to the typo? In that case, the last string of equalities should read: e_G = g^2 = phi(x) phi(y) = phi(xy) = phi(e_H). If not, then allow me to break it down: 1) We begin with the identity element e_G of G. 2) Since all non-trivial elements of G are order 2, we must have that > e_G = g^2. 3) By hypothesis we're assuming that phi(x) = phi(y) = g, so g^2 = > phi(x) phi(y). 4) Since phi is a homomorphism, phi(x) phi(y) = phi(xy). 5) Again, since phi is a homomorphism, phi(e_H) = e_G; hence, e_G = > g^2 = phi(x) phi(y) = phi(xy) = phi(e_H). In other words, because phi sends xy to the identity in G, it follows > that xy must be the identity in H... ..for, if xy were not equal to e_H, phi would be mapping two elements > to e_G and would thus not be a homomorphism. I buy everything - but the last thing _as it is_. More precisely: I understand that you are saying that if phi is not injective, then it cannot be a homomorphism. Why that? I would expect here some more analysis on the groups involved, since the statement is not true in general. > This establishes that xy = e_H and implies y = x^{-1}. > Alternatively you can show that G is a vector space over Z/2Z of > dimension 5 and f is a surjective linear map (over Z/2Z), so it is > injective. I suppose, but there is no need to induce more structure on the group > (i.e. consider it also as a vector space) in order to prove such a > group theoretical fact... ..but whatever flips your switch ^_^ > -- Best wishes, J. === Subject: Re: Embedding an elementary abelian group into a symmetric group > More precisely: I understand that you are saying that > if phi is not injective, then it cannot be a > homomorphism. Why that? I would expect here some more analysis on the groups > involved, since the statement is not true in general. I believe that you are correct in that the statement is not true in general; see http://planetmath.org/encyclopedia/AHomomorphismIsInjectiveIffTheKernelIsTri vial.html . However, in our case, the only element being sent to e_G is e_H -- so the preimage of e_G is e_H: e_G = phi(xy) ==> e_H = phi^{-1}(e_G) = xy ==> y = x^{-1}. === Subject: Re: Embedding an elementary abelian group into a symmetric group > However, in our case, the only element being sent to > e_G is e_H ... and this is equivalent to be injective, and it still needs to be shown here. To avoid a proof by hand waving one could use the Z/2-structure on the groups involved. If no additional argument in your proof is given, the proof is circular and hence not complete. -- Best wishes, J. === Subject: more help needed w/proving limit of a sequence not have the confidence yet to think I am 100% right. Here is the question and my solution... Show lim sqrt(3+(n/2))=sqrt(3) Solution: Solving for an N to show |X_n - L|< epsilon... Multiplying by the conjugate (sqrt(3+(n/2)) - sqrt(3)) * (sqrt(3+(n/2)) + sqrt(3)) ----------------------------- 3 + (2/n) - 3 Now, also dividing by the conjugate we end up with (2/n) ------------------------- (sqrt(3+(n/2)) + sqrt(3)) We note that the numerator has an upper bound of n since (2/n) < n for all n Natural greater than 2 and the denominator has a lower bound of sqrt(3) since (sqrt(3+(n/2)) + sqrt(3)) > sqrt(3) for all n Natural So, now for the epsilontics... |X_n -L | < n/sqrt(3) < epsilon So if we let N be a natural number such that N> 1/(sqrt(3)*epsilon) then for all n > N the stated limit holds. Is this solution acceptable? If not, could you please tell me why? I am very uncertain about my estimated bounds...is this the correct approach to take? Obviously, the choices I made for the bounds is very loose but isn't it acceptable to not necessarily have tight bounds when doing these sorts of proofs? === Subject: Re: more help needed w/proving limit of a sequence I made a serious typo in my original post. The original is corrected as follows: not have the confidence yet to think I am 100% right. Here is the question and my solution... Show lim sqrt(3+(2/n))=sqrt(3) Solution: Solving for an N to show |X_n - L|< epsilon... Multiplying by the conjugate (sqrt(3+(2/n)) - sqrt(3)) * (sqrt(3+(2/n)) + sqrt(3)) ----------------------------- 3 + (2/n) - 3 Now, also dividing by the conjugate we end up with (2/n) ------------------------- (sqrt(3+(2/n)) + sqrt(3)) We note that the numerator has an upper bound of n since (2/n) < n for all n Natural greater than 2 and the denominator has a lower bound of sqrt(3) since (sqrt(3+(2/n)) + sqrt(3)) > sqrt(3) for all n Natural So, now for the epsilontics... |X_n -L | < n/sqrt(3) < epsilon So if we let N be a natural number such that N> 1/(sqrt(3)*epsilon) then for all n > N the stated limit holds. Is this solution acceptable? If not, could you please tell me why? I am very uncertain about my estimated bounds...is this the correct approach to take? Obviously, the choices I made for the bounds is very loose but isn't it acceptable to not necessarily have tight bounds when doing these sorts of proofs? === Subject: Re: more help needed w/proving limit of a sequence oo) sqr(3 + 2/n) = sqr 3 Then indicated what the limit is!!! > Solution: > Solving for an N to show |X_n - L|< epsilon... > Multiplying by the conjugate > (sqrt(3+(2/n)) - sqrt(3)) > * (sqrt(3+(2/n)) + sqrt(3)) > ----------------------------- > 3 + (2/n) - 3 > |sqr(3 + 2/n) - sqr 3| = |sqr(3 + 2/n) - sqr 3| * |sqr(3 + 2/n) + sqr 3| / |sqr(3 + 2/n) + sqr 3| = |2/n| / |sqr(3 + 2/n) + sqr 3| < 1/n . . since 2 < sqr(2 + 2/n) + sqr 3 If n > 1/esp, then for all k > n |sqr(3 + 2/k) - sqr 3| < 1/k < 1/n < eps. Same basically the same as your proof but slicker and quicker. ;-) > Now, also dividing by the conjugate we > end up with (2/n) > ------------------------- > (sqrt(3+(2/n)) + sqrt(3)) We note that the numerator has an upper bound of n > since (2/n) < n for all n Natural greater than 2 > and the denominator has a lower bound of sqrt(3) > since (sqrt(3+(2/n)) + sqrt(3)) > sqrt(3) for all n Natural So, now for the epsilontics... |X_n -L | < n/sqrt(3) < epsilon > So if we let N be a natural number such that > N> 1/(sqrt(3)*epsilon) then for all n > N the stated limit holds. Is this solution acceptable? > If not, could you please tell me why? > I am very uncertain about my estimated bounds...is this > the correct approach to take? Obviously, the choices I made > for the bounds is very loose but isn't it acceptable to not necessarily > have tight bounds when doing these sorts of proofs? > === Subject: Re: more help needed w/proving limit of a sequence > I made a serious typo in my original post. > The original is corrected as follows: > solution but do not have the confidence yet to think I > am 100% right. ..I take it that you did not even read my post. === Subject: Re: more help needed w/proving limit of a sequence <5742606.1221379086633.JavaMail.jakarta@nitrogen.mathforum.org>, > I made a serious typo in my original post. > The original is corrected as follows: > solution but do not have the confidence yet to think I > am 100% right. ..I take it that you did not even read my post. Well, no I didn't actually. ;) Your message must not have shown up on my news server until after I sent mine. I appreciate your help! === Subject: Re: more help needed w/proving limit of a sequence > solution but do > not have the confidence yet to think I am 100% right. Here is the question and my solution... > Show lim sqrt(3+(n/2))=sqrt(3) Stop right there! You're evaluating the limit as n approaches what? The only way the above limit would be valid would be if you were considering the limit of the function f(n) = sqrt(3 + n/2) as n --> 0... ..but you're looking at the limit of sequences, so I'm assuming you've made a typo and your question should be: Show lim_{n --> oo} sqrt(3 + 2/n) = sqrt(3). > Solution: > Solving for an N to show |X_n - L|< epsilon... > Multiplying by the conjugate > (sqrt(3+(n/2)) - sqrt(3)) > * (sqrt(3+(n/2)) + sqrt(3)) > ----------------------------- > 3 + (2/n) - 3 No, according to what you've written, the answer should be 3 + (n/2) - 3 = n/2... ..but you've probably switched the n and 2 around. > Now, also dividing by the conjugate we > end up with (2/n) > ------------------------- > (sqrt(3+(n/2)) + sqrt(3)) No, this should either be (n / 2) / [sqrt(3 + n/2) + sqrt(3)] ..or... (2 / n) / [sqrt(3 + 2/n) + sqrt(3)]. I'm assuming it's the latter. > We note that the numerator has an upper bound of n > since (2/n) < n for all n Natural greater than 2 While it is true that 2/n < n for n > 2 (since 2/x < x for all real numbers x > sqrt(2)), you shouldn't say that n is the upper bound of the numerator -- upper and lower bounds of sequences have well established definions. > and the denominator has a lower bound of sqrt(3) > since (sqrt(3+(n/2)) + sqrt(3)) > sqrt(3) for all n > Natural ..again, you should probably stay away from that terminology (unless you use it) and state the inequality. > So, now for the epsilontics... |X_n -L | < n/sqrt(3) < epsilon > So if we let N be a natural number such that > N> 1/(sqrt(3)*epsilon) then for all n > N the stated > limit holds. Is this solution acceptable? > If not, could you please tell me why? I suppose that all depends on your definition of acceptable : - P The statement of your problem and your solution both had various typos; moreover, as a whole, the proof doesn't flow very well. In other words, you may want to polish it up before you hand it in for homework. > I am very uncertain about my estimated bounds...is > this the correct approach to take? Obviously, the > choices I made for the bounds is very loose but isn't > it acceptable to not necessarily have tight bounds > when doing these sorts of proofs? I'm not sure what exactly to tell you here... There may be eaiser ways to write the same proof using alternate or fewer inequalities, but the bottom line is that if an inequality is valid, you can use it in your proof. Kyle Czarnecki P.S. Whenever you've completed an epsilon-delta proof, you can check with a few numerical examples. For instance, consider the following exercise/proof. EXERCISE. Show that lim_{n -> oo} sqrt(3 + 2/n) = sqrt(3) PROOF. Given e > 0, choose a natural number N such that N > 2 / [sqrt(3) * e]. By definition |x_n - L| = |sqrt(3 + 2/n) - sqrt(3)| = sqrt(3 + 2/n) - sqrt(3) = (2 / n) / [sqrt(3 + 2/n) + sqrt(3)] < (2 / n) / sqrt(3) = 2 / [n * sqrt(3)]. Moreover, since N > 2 / [sqrt(3) * e], it follows that |x_n - L| < 2 / [n * sqrt(3)] = (1 / n) * [2 / sqrt(3)] < (1 / n) * (N * e) ..and thus |x_n - L| < e whenever n > N. [] Alright, now let's check the proof via a numerical example. Suppose I choose epsilon (e) such that e = 1/37 = 0.027027... ..then, according to the proof, whenever n > N > 2 / [sqrt(3) * e] = 2 * 37 / sqrt(3) = 42.72... ..we should have... |sqrt(3 + 2/n) - sqrt(3)| < e = 0.027027... Let f(n) = sqrt(3 + 2/n) - sqrt(3), then f(43) = 0.013375... < e = 1/37, f(44) = 0.013072... < e = 1/37, f(45) = 0.012783... < e = 1/37, etc. ..so the proof works for this choice of epsilon. Moreover, note that |f(n)| < e implies that -e < f(n) < e -e < sqrt(3 + 2/n) - sqrt(3) < e sqrt(3) - e < sqrt(3 + 2/n) < sqrt(3) + e ..or, in other words, sqrt(3 + 2/n) lies in the interval (sqrt(3) - e, sqrt(3) + e). In this specific case where e = 1/37, this means that sqrt(3 + 2/n) will lie in the interval (sqrt(3) - 1/37, sqrt(3) + 1/37) whenever n > 42.27... === Subject: Re: more help needed w/proving limit of a sequence > Show lim sqrt(3+(n/2))=sqrt(3) lim(n->oo) sqr(3 + n/2) = oo ---- === Subject: Re: more help needed w/proving limit of a sequence posting-account=oE8TowoAAADegjiSEJ86LpJ8MH-tmq_J rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) Show lim sqrt(3+(n/2))=sqrt(3) lim(n->oo) sqr(3 + n/2) = oo ---- I am sorry for the typo I meant lim sqrt(3+(2/n))=sqrt(3) ! === Subject: Progress Report: Culture for Schools - Colleges - Universities posting-account=6qVsEAkAAAAP4-CBBRBdYxtxzWaP0v1H 1.1.4322; .NET CLR 2.0.50727; yplus 5.1.04b),gzip(gfe),gzip(gfe) Progress Report: Culture for Schools - Colleges - Universities Family Genealogy & History Internet Education Directory: Scholarly mega site map of world wide Internet resources, , now includes: the Official Beijing 2008 Paralympic Games, while still carefully watching the National Hurricane Center - USA. News, Media and Travel: 2008 U.S. Election: Zogby International The next President of the United States: John Sidney McCain III: Ancestry & VP: Sarah Louise Palin: Ancestry - SARAH (pdf) or: Barack Hussein Obama II: Ancestry & VP: Joseph Robinette Joe Biden, Jr.: Ancestry. Otherwise, have the family history and genealogy world at your fingertips, using key Internet sites. Schools - Colleges - Universities: Alumni and Genealogy Education, is an indexed worldwide comprehensive resource for top educational institutions; their genealogy, family history and related records & services. http://www.academic-genealogy.com/schoolscollegesuniversities.htm * UMAC: University Museum & Collections Protect the heritage in the care of universities. - UMAC Worldwide Database http://publicus.culture.hu-berlin.de/collections/index.php GERMANY has: . . . University of Hamburg: Department Biologie - GenomeWeb - Lists of Genome Sites. Authoritative collection of the best genome related sites on the Web, for those interested in DNA and other related subjects. INDIA has: . . . International Institute of Information Technology: Digital Library of India NORWAY has: . . . The University of Tromso (Norwegian: Universitetet i Tromso) the world's northernmost university, with its vast Historical Microdata around the World http://www.rhd.uit.no/nhdc/micro.html UNITED KINGDOM has: . . . King's College London: Prosopography of Anglo-Saxon England: Database - Links (PASE) database to cover all of the recorded inhabitants of England from the late sixth to the end of the eleventh century; from a systematic examination of the available written sources for the period, including chronicles, saintsÍ Lives, charters, libri vitae, inscriptions, and coins. . . . University of Warwick Department of History - Network for Parish Research: Study of British and European parishes circa A.D. 1300 to1800. Includes works on religious, social, political and cultural aspects, as well as interdisciplinary and comparative perspectives. UNITED STATES has: . . . - (UT) Utah Colleges and Universities - Brigham Young University: BYU - BYU Family History Library: - Alphabetical List of Resources - Selected Internet Research Sites - Center for Family History & Genealogy - Harold B. Lee Library - Electronic Reference Databases A-Z - Utah Local History Bibliography And much, much more. Respectfully yours, Tom Tinney, Sr. Who's Who in America, Who's Who In Genealogy and Heraldry, [both editions] Family Genealogy & History Internet Education Directory http://www.academic-genealogy.com/ === Subject: how to extend a map to a vector space over a finite field (?) Consider the group G := (Z/2)^5, viewed as a vector space over a finite field; and suppose we've defined a map f on the 'standard' basis elements (1, 0, 0, 0, 0), ..., (0, 0, 0, 0, 1), taking values in some finite group H. Under what conditions will this map actually extend to a homomorphism on all of G? The only real stipulation here that's evident is that these elements of G must be mapped under f to elements of order 1 or 2 in the target group H. Is this actually enough to ensure that f extends to a homomorphism G -> H? === Subject: Re: how to extend a map to a vector space over a finite field (?) posting-account=-PngCgkAAAD2yUjosqWv1Nf1lkqWP4lp rv:1.8.1.16) Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > Consider the group G := (Z/2)^5, viewed as a vector space over a finite field; and suppose we've defined a map f on the 'standard' basis elements (1, 0, 0, 0, 0), ..., (0, 0, 0, 0, 1), taking values in some finite group H. Under what conditions will this map actually extend to > a homomorphism on all of G? The only real stipulation here that's evident > is that these elements of G must be mapped under f to elements of order 1 or 2 in the target group H. Is this actually enough to ensure that f extends > to a homomorphism G -> H? In general, if G has a presentation < x_1, x_2, ..., x_n | r_1, r_2, ..., r_m > then a necessary and sufficient condition for a map f: {x_1,...,x_n} - > H from the generators of G to a group H to extend to a homomorphism from G to H is that f(r_i) is the identity of H for each defining relator r_i. Here f(r_i) is defined to be f(w_1)^e_1 f(w_2)^e_2 ... f(w_s)^e_s, where r_i = w_1^e_1 ... w_s^e_s, with each w_j in {x_1,...,x_n}. In particular, an elementary abelian p-group has a presentation < x_1, x_2, ..., x_n | x_1^p, ..., x_n^p, [x_i,x_j], 1 <= i,j <= n > so a necessary and sufficient condition for the map on the generators of G to extend to a homomorphism is that f(x_i)^p is the identity for each x_i, and that the images f(x_i) in H all commute with each other. This applies, for example, to the map from Z_2^5 = to S_10 with f(x_i) = (1,2), (3,4), (5,6), (7,8), (9,10) for i=1,2,3,4,5, that was discussed in another thread. Derek Holt. === Subject: Re: how to extend a map to a vector space over a finite field (?) Incidentally, why is the extended map injective? === Subject: Re: how to extend a map to a vector space over a finite field (?) <29308444.1221412999654.JavaMail.jakarta@nitrogen.mathforum.org> posting-account=-PngCgkAAAD2yUjosqWv1Nf1lkqWP4lp rv:1.8.1.16) Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > Incidentally, why is the extended map injective? To prove that the homomorphism f:Z_2^5 -> <(1,2),(3,4),(5,6),(7,8),(9,10)> under discussion is injective, it is enough to show that |f(H)|>=32. You could do that, for example, by showing by induction on n that a permutation group generated by n disjoint 2-cycles has order 2^n. More generally, if permutations p_1,...,p_n on a set X generate a group G, and permutations q_1,...,q_m on a disjoint set Y generate group H, then p_1,...,p_n,q_1,...,q_m together on X union Y generate the direct product GxH. Derek Holt. === Subject: Re: how to extend a map to a vector space over a finite field (?) > Incidentally, why is the extended map injective? Since it is a surjective Z/2-linear map of equidimensional vector spaces (over Z/2, of course). -- Best wishes, J. === Subject: Re: how to extend a map to a vector space over a finite field (?) Ah, I just wasn't remembering the presentation for elementary abelian p-groups! Your remarks were very helpful. === Subject: Re: how to extend a map to a vector space over a finite field (?) > Consider the group G := (Z/2)^5, viewed as a vector space over a > finite field; and suppose we've defined a map f on the 'standard' > basis elements (1, 0, 0, 0, 0), ..., (0, 0, 0, 0, 1), taking values > in some finite group H. Under what conditions will this map actually extend to a homomorphism > on all of G? The only real stipulation here that's evident is that these > elements of G must be mapped under f to elements of order 1 or 2 > in the target group H. Is this actually enough to ensure that f extends to a homomorphism G > -> H? The assumption that H be commutative is sufficient. -- Best wishes, J. === Subject: Re: how to extend a map to a vector space over a finite field (?) > Consider the group G := (Z/2)^5, viewed as a vector space over a > finite field; and suppose we've defined a map f on the 'standard' > basis elements (1, 0, 0, 0, 0), ..., (0, 0, 0, 0, 1), taking values > in some finite group H. Under what conditions will this map actually extend to a > homomorphism on all of G? You want _f_ to be extended into a homomorphism of what? It can't be a vector space homomorphism, since you are not assuming that H is a vector space. Therefore, I suppose that you are interested in group homomorphisms, but if that's so, then I fail to see why did you mention that G is viewed as a vector space over a finite field. > The only real stipulation here that's evident is that these > elements of G must be mapped under f to elements of order 1 or 2 > in the target group H. Is this actually enough to ensure that f extends to a homomorphism > G -> H? No. Another necessary condition is that the images of the basis elements commute with one another. Then, yes, it can be extended. Jose Carlos Santos === Subject: How to extract the symmetrical part of homogeneuos polynomial in two variable? posting-account=jxLm8AoAAAD2bMDjnPVAuL2xlLkQFla8 AppleWebKit/525.13 (KHTML, like Gecko) Chrome/0.2.149.29 Safari/525.13,gzip(gfe),gzip(gfe) For example, consider the polynomial Q(x,y)=a*x^2+b*x*y+ c*y^2 of degree 2. It is obviously that the symmetrical ( b*x*y) part is equal to Q(x,y)-Q(x,0)-Q(0,y). 1.Is there any generalisation of such manipulation method for homogeneuos polynomial of arbitrary degree? 2. Let P(x,y)=sum_{i,j} a_{i,j} x^i y^j. How to extract the subpolynomial P*(x,y)=a_{0,0}+a_{1,1} x*y+a_{2,2} x^2*y^2+....=sum_{i} a_{i,i} (x*y)^i === Subject: - Finite-index subgroup in a product of subgroups Suppose a group G is a product of two of its subgroups: G = AB. Let A' be a subgroup of A of index n, and let B' be a subgroup of B of index m. We want to show that the subgroup H = has index at most mn. Here's the proof: Write G as a finite union of left cosets of A' and right cosets of B'; since A'B' is contained in H, then G is just a union of right cosets of conjugates of H. By the covering lemma, some conjugate of H has finite index, hence so does H. Moreover, the index of the core of H also has finite index in G, so it's enough to assume that G is finite. If G is finite, then certainly |G| = |A||B|/|A/B| =< |A||B|/|A' / B'| =< |H|mn. ----------- Question! Why is it enough to assume in this proof that G is finite, relying on the observation that G/H_G is finite? This is the part that's a little confusing to me. === Subject: Re: - Finite-index subgroup in a product of subgroups days. My association with the Department is that of an alumnus. >Suppose a group G is a product of two of its subgroups: >G = AB. Let A' be a subgroup of A of index n, and >let B' be a subgroup of B of index m. >We want to show that the subgroup H = has index at most mn. >Here's the proof: Write G as a finite union >of left cosets of A' and right cosets of B'; >since A'B' is contained in H, then G is just a union of >right cosets of conjugates of H. By the covering lemma, some conjugate of H has finite index, hence so >does H. Moreover, the index of the core of H also has finite index in >G, so it's enough to assume that G is finite. If G is finite, then certainly |G| = |A||B|/|A/B| =< |A||B|/|A' / B'| =< |H|mn. ----------- >Question! Why is it enough to assume in this proof that G is finite, >relying on the observation that G/H_G is finite? This is the part >that's a little confusing to me. You've been running into this particular problem several times all throughout this last week. This is simply the lattice isomorphism theorem, that yields a one-to-one, normality preserving, inclusion preserving correspondence between subgroups of G/K and subgroups of G that contain K, via the map that identifies the subgroup H of G that contains K with the subgroup H/K = {hK : h in H} of G/K. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: Re: - Finite-index subgroup in a product of subgroups posting-account=suWj4AkAAADE1IvGmj55Nmq3f98qb17e SIMBAR Enabled; SIMBAR={70306B22-CB8C-4d52-BFF4-18424E217075}; MathPlayer 2.10b; FunWebProducts; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) Suppose a group G is a product of two of its subgroups: >G = AB. Let A' be a subgroup of A of index n, and >let B' be a subgroup of B of index m. >We want to show that the subgroup H = has index at most mn. Here's the proof: Write G as a finite union >of left cosets of A' and right cosets of B'; >since A'B' is contained in H, then G is just a union of >right cosets of conjugates of H. By the covering lemma, some conjugate of H has finite index, hence so >does H. Moreover, the index of the core of H also has finite index in >G, so it's enough to assume that G is finite. If G is finite, then certainly |G| = |A||B|/|A/B| =< |A||B|/|A' / B'| =< |H|mn. ----------- Question! Why is it enough to assume in this proof that G is finite, >relying on æthe observation that G/H G is finite? This is the part >that's a little confusing to me. You've been running into this particular problem several times all > throughout this last week. This is simply the lattice isomorphism > theorem, that yields a one-to-one, normality preserving, inclusion > preserving correspondence between subgroups of G/K and subgroups of G > that contain K, via the map that identifies the subgroup H of G that > contains K with the subgroup H/K = {hK : h in H} of G/K. > ***************************************************************** I can't be completely sure if it is the same OP, but exactly the same question with exactly the same notation and exactly the same doubt about the assumption of finiteness came up in the forum ask an algebraist some 1.5-2 months ago, and I gave the OP the same answer as here: to use the correspondence theorem (which Arturo apparently call the Lattice Theorem), which states not only that every sbgp. of a quotient group G/N is of the form H/N, for H a sbgp. of G containing N, but also that H/N is normal in G/N iff H is normal in G, and also [G/N : H/N] = [G:H]. Then this was explained 3-4 times at least. Let's hope this time it'll take less effort... Tonio === Subject: Re: - Finite-index subgroup in a product of subgroups > <5320186.1221376368842.JavaMail.jakarta@nitrogen.mathf > orum.org>, >Suppose a group G is a product of two of its > subgroups: >G = AB. Let A' be a subgroup of A of index n, and >let B' be a subgroup of B of index m. >We want to show that the subgroup H = has > index at most mn. >Here's the proof: Write G as a finite union >of left cosets of A' and right cosets of B'; >since A'B' is contained in H, then G is just a union > of >right cosets of conjugates of H. By the covering lemma, some conjugate of H has > finite index, hence so >does H. Moreover, the index of the core of H also > has finite index in >G, so it's enough to assume that G is finite. If G is finite, then certainly |G| = |A||B|/|A/B| =< |A||B|/|A' / B'| =< |H|mn. ----------- >Question! Why is it enough to assume in this proof > that G is finite, >relying on the observation that G/H_G is finite? > This is the part >that's a little confusing to me. You've been running into this particular problem > several times all > throughout this last week. This is simply the lattice > isomorphism > theorem, that yields a one-to-one, normality > preserving, inclusion > preserving correspondence between subgroups of G/K > and subgroups of G > that contain K, via the map that identifies the > subgroup H of G that > contains K with the subgroup H/K = {hK : h in H} of > G/K. > I've started to learn to appreciate the strength and utility of the fourth (?) iso. theorem, though only recently. But the thing about the proof is that it alludes to the G-core (again) of a finite-index subgroup H, and jumps to the finite case without hesitation. I want to flesh this out a bit, since it appears that I'm probably not yet at home with this sort of reasoning. So, we know that G contains a finite-index subgroup H, and we want to show that its index is at most mn (in G). Great, so we know that, if K is the core of H in G, then G/K is finite, since G acts on the set of left cosets of H in G, etc. Is the proof trying to say that G/K contains H/K as a subgroup of index at most mn? And that would follow from the iso. theorem? Would it then follow that |G/K| =< mn |H/K| ? And from this, must it follow that [G : H] =< mn? I'm still trying to figure out why they assume G is finite, and not just work with G/K instead and then, from this, get the result about the index of H being at most mn directly. There must be a series of logical implications which allows one to go from A to B without assuming anything without any loss in generality. In other words, can we prove this result without assuming anything (more) about G from the outset? === Subject: Re: - Finite-index subgroup in a product of subgroups days. My association with the Department is that of an alumnus. > <5320186.1221376368842.JavaMail.jakarta@nitrogen.mathf > orum.org>, >Suppose a group G is a product of two of its > subgroups: >G = AB. >Let A' be a subgroup of A of index n, and >let B' be a subgroup of B of index m. >We want to show that the subgroup H = has > index at most mn. >Here's the proof: >Write G as a finite union >of left cosets of A' and right cosets of B'; >since A'B' is contained in H, then G is just a union > of >right cosets of conjugates of H. >By the covering lemma, some conjugate of H has > finite index, hence so >does H. Moreover, the index of the core of H also > has finite index in >G, so it's enough to assume that G is finite. >If G is finite, then certainly >|G| = |A||B|/|A/B| =< |A||B|/|A' / B'| =< |H|mn. >----------- >Question! Why is it enough to assume in this proof > that G is finite, >relying on the observation that G/H_G is finite? > This is the part >that's a little confusing to me. > You've been running into this particular problem > several times all > throughout this last week. This is simply the lattice > isomorphism > theorem, that yields a one-to-one, normality > preserving, inclusion > preserving correspondence between subgroups of G/K > and subgroups of G > that contain K, via the map that identifies the > subgroup H of G that > contains K with the subgroup H/K = {hK : h in H} of > G/K. > [...] >But the thing about the proof is that it alludes to the G-core >(again) of a finite-index subgroup H, Yes: the fact that any subgroup of finite index contains a NORMAL subgroup of finite index. >and jumps to the finite case without hesitation. Because the problem is all about the index of H in G, and if you already know that the index of H in G is finite, then the lattice isomorphism theorem lets you go to the finite case without hesitation by considering the index of H/K in G/K instead. >So, we know that G contains a finite-index subgroup H, >and we want to show that its index is at most mn (in G). Great, so we know that, if K is the core of H in G, >then G/K is finite, since G acts on the set of left cosets of H in G, etc. Is the proof trying to say that G/K contains H/K >as a subgroup of index at most mn? Think about the cosets. The cosets of H/K in G/K are the sets of the form { (gK)HK : g in G } which is exactly the same as the sets { gK H : g in G} (because K is contained in H) which is exactly the same as the sets { gH : g in G} because K is contained in K. So there is a one-to-one correspondence between the cosets of H in G and the cosets of H/K in G/K. This is all part of the lattice isomoprhism theorem. That tells you that the index of H in G is exactly the same as the index of H/K in G/K, so all you have to do is work out the case when G is finite to get the case you are looking at. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: Re: - Finite-index subgroup in a product of subgroups Since G contains a finite-index subgroup H, this implies, as you said, according to the iso. theorem, that H/K itself is a finite-index subgroup of G/K. But I don't see right away how it follows that |G/K| =< mn |H/K| We already know that |G| =< mn |H| when G is finite. Does this means we can mod out by K there? (This is precisely my sticky point!) But since it should, then we can use that [G/K : H/K] = [G : H], and we'd have mn >= |G/K|/|H/K| = [G/K : H/K] = [G : H] where the first equality holds (by Lagrange, of course) since G/K is finite; and this is what we wanted all along. === Subject: Re: - Finite-index subgroup in a product of subgroups days. My association with the Department is that of an alumnus. [...] >Since G contains a finite-index subgroup H, >this implies, as you said, according to the iso. theorem, that H/K itself is a finite-index subgroup of G/K. But I don't see right away how it follows that |G/K| =< mn |H/K| >We already know that |G| =< mn |H| when G is finite. >Does this means we can mod out by K there? >(This is precisely my sticky point!) Sigh. In the finite case, |G| <= mn |H| is equivalent to |G|/|H| <= mn which is equivalent to [G:H] <= mn. So use ->that<- inequality as equivalent to what you want. In the infinite case, with K a finite index normal subgroup of G contained in H, you will have [G:H] = [(G/K):(H/K)] <= mn. Again: you are not getting it. The point of the lattice isomorphism theorem is that there is a one-to-one inclusion preserving, normality preserving, correspondence, and this correspondence respects indexes as well. That's why you can just go to the finite case, because what you are seeing in the finite case is ->exactly<- what you see in the infinite case. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: Re: - Finite-index subgroup in a product of subgroups > In the finite case, |G| <= mn |H| is equivalent to |G|/|H| <= mn which is equivalent to [G:H] <= mn. So use ->that<- inequality as equivalent to what you > want. In the > infinite case, with K a finite index normal subgroup > of G contained in > H, you will have [G:H] = [(G/K):(H/K)] <= mn. > so [G/K : H/K] =< mn is automatic because we already know that happens in the finite case? That is, whenever G is finite, and [G : H] =< mn; then we can just replace G by G/K and H by H/K to conclude [G/K : H/K] =< mn ? === Subject: Re: - Finite-index subgroup in a product of subgroups days. My association with the Department is that of an alumnus. > In the finite case, > |G| <= mn |H| > is equivalent to > |G|/|H| <= mn > which is equivalent to > [G:H] <= mn. > So use ->that<- inequality as equivalent to what you > want. In the > infinite case, with K a finite index normal subgroup > of G contained in > H, you will have > [G:H] = [(G/K):(H/K)] <= mn. >so [G/K : H/K] =< mn >is automatic because we already know that happens in the finite case? That is, whenever G is finite, and [G : H] =< mn; then we can just replace G by G/K and H by H/K to conclude [G/K : H/K] =< mn >? Is it not clear from the syntax of the statement? What exactly is giving you trouble, and why? What is it about for all finite groups that makes you doubt that it applies to a particular finite group, namely the one you have before you? -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: Re: - Finite-index subgroup in a product of subgroups > <14780260.1221440869703.JavaMail.jakarta@nitrogen.math > forum.org>, > In the finite case, > |G| <= mn |H| > is equivalent to > |G|/|H| <= mn > which is equivalent to > [G:H] <= mn. > So use ->that<- inequality as equivalent to what > you > want. In the > infinite case, with K a finite index normal > subgroup > of G contained in > H, you will have > [G:H] = [(G/K):(H/K)] <= mn. so [G/K : H/K] =< mn >is automatic because we already know that happens > in the finite case? That is, whenever G is finite, and [G : H] =< mn; then we can just replace G by G/K and H by H/K to conclude [G/K : H/K] =< mn >? Is it not clear from the syntax of the statement? > What exactly is > giving you trouble, and why? What is it about for > all finite groups > that makes you doubt that it applies to a particular > finite group, > namely the one you have before you? > I had first thought of showing directly that [G/K : H/K] =< mn; and since [G : H] = [G/K : H/K], this would complete the proof. Indeed, G/K is finite, and |G/K|= |AB/K| = |(AK/K)(BK/K)| = |AK/K|.|BK/K| --------------- .... (*) |AK/K / BK/K| Since A' has finite index n in A, then so does A'K/K in AK/K, as [A : A'] = [pi(A) : pi(A')] where pi : G -> G/K is the natural projection; similarly for B'K/K. It is also clear that A'K/K / B'K/K is contained in AK/K / BK/K. Finally, (*) becomes =< mn |A'K/K|.|B'K/K| ---------------------- |A'K/K / B'K/K| = mn |pi(A'B')| since pi is a homomorphism; but A'B' is contained in H, so pi(A'B') is contained in pi(H) = H/K, hence mn |pi(A'B')| =< mn |pi(H)| = mn|H/K| as desired. === Subject: Get Solution Manual Are You looking for solutions manual for a tough class?! Did the search results lead you here?! Try sending me email with the name and details of the solutions manual you need and I may be able to help. Do not reply here, instead send email to jhonrecard(at)gmail(dot)com.If the solutions manual you are looking for is not listed here, do not give up and send me email, I may be able to help! 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Asplund) VLSI Test Principles and Architectures: Design for Testability (Chen, Cheng, Eklow et al.) Wireless Communications & Networks (William Stallings) Work Systems: The Methods, Measurement & Management of Work (Mikell P. Groover) World Trade and Payments: An Introduction (Richard E. Caves,Jeffrey A. Frankel & Ronald W. Jones) Wireless Communications: Principles and Practice, by Rappaport Wireless Communications and Networking (Jon W. Mark, Weihua Zhuang) Web 101 (Wendy G. Lehnert & Richard L. Kopec) Web Development and Design Foundations with XHTML Water and Wastewater Technology (Mark J. Hammer, Sr. & Mark J. Hammer, Jr.) Water-Resources Engineering (Chin) XML: Language Mechanics and Applications (Dwight Peltzer) 10-Key Touch Key: Developing Speed and Accuracy (Burton) -- Message posted via MathKB.com http://www.mathkb.com/Uwe/Forums.aspx/mathematics/200809/1 === Subject: Problem with Radon-measures I have been struggling with this question: Is there a sigma-finite Borel-measure on real-line R, with the usual euclidean topology, which is not a Radon-measure. In this case, Borel-measure is just a measure defined on the Borel sigma-algebra Bor R, and a Radon-measure is a Borel-measure on a locally compact Hausdorff space for which all compact sets have finite measure and it is both inner regular via compact sets and outer regular via open sets. Plus, which (locally compact Hausdorff) spaces does not meet that condition? I.e. are there spaces where sigma-finite Borel-measures would always be Radon-measures. === Subject: Help with the CRT posting-account=LbYpygoAAAB-XnkxlNRvR3Xt0EKgDYSd AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.2 Safari/525.20.1,gzip(gfe),gzip(gfe) I'm having trouble understanding how I can use the CRT in a proof. In particular, I have a statement that asserts the existence of an integer k satisfying some property mod any prime, and p and q in particular. Let's call the one for p k_p and the one for q k_q. Can I use the Chinese remainder theorem to assert that there is an integer k satisfying this same property (mod pq)? If you want the whole story, I'm trying to assert the existence of a k_n such that m^n^{k_n} is congruent to m (mod pq) given that we have the existence of a k_p such that m^n^{k_p} is congruent to m (mod p) and a k_q such that m^n^{k_q} is congruent to m (mod q), but what I'm really after is some way to properly understand and use the CRT in a proof. === Subject: Re: Help with the CRT > I'm having trouble understanding how I can use the CRT in a proof. In particular, I have a statement that asserts the existence of an > integer k satisfying some property mod any prime, and p and q in > particular. Let's call the one for p k_p and the one for q k_q. Can > I use the Chinese remainder theorem to assert that there is an > integer k satisfying this same property (mod pq)? If you want the whole story, I'm trying to assert the existence of a > k_n such that m^n^{k_n} What does that mean: m^(n^{k_n}) or (m^n)^{k_n}? Just to be sure that I understand what you mean here. :-) > is congruent to m (mod pq) given that we have > the existence of a k_p such that m^n^{k_p} is congruent to m (mod p) > and a k_q such that m^n^{k_q} is congruent to m (mod q), but what > I'm really after is some way to properly understand and use the CRT > in a proof. -- Best wishes, J. === Subject: Re: Help with the CRT > I'm having trouble understanding how I can use the CRT in a proof. > In particular, I have a statement that asserts the existence of an > integer k satisfying some property mod any prime, and p and q in > particular. Let's call the one for p k_p and the one for q k_q. > Can I use the Chinese remainder theorem to assert that there is an > integer k satisfying this same property (mod pq)? > If you want the whole story, I'm trying to assert the existence of > a k_n such that m^n^{k_n} What does that mean: m^(n^{k_n}) or (m^n)^{k_n}? Just to be sure that > I understand what you mean here. :-) > is congruent to m (mod pq) given that we have the existence of a > k_p such that m^n^{k_p} is congruent to m (mod p) and a k_q such > that m^n^{k_q} is congruent to m (mod q), but what I'm really after > is some way to properly understand and use the CRT in a proof. Assuming that p,q are different primes, I can see at the moment that m^t = m (mod pq) with t = (n^kp - 1)(n^kq - 1) + 1. Are you sure that you need t in the form of n^k? -- Best wishes, J. === Subject: Re: Help with the CRT posting-account=LbYpygoAAAB-XnkxlNRvR3Xt0EKgDYSd AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.2 Safari/525.20.1,gzip(gfe),gzip(gfe) On Sep 14, 2:46æpm, Jannick Asmus I'm having trouble understanding how I can use the CRT in a proof. > In particular, I have a statement that asserts the existence of an > æinteger k satisfying some property mod any prime, and p and q in > particular. æLet's call the one for p k p and the one for q k q. > Can I use the Chinese remainder theorem to assert that there is an > integer k satisfying this same property (mod pq)? > If you want the whole story, I'm trying to assert the existence of > a k n such that m^n^{k n} What does that mean: m^(n^{k n}) or (m^n)^{k n}? Just to be sure that > I understand what you mean here. :-) > is congruent to m (mod pq) given that we have the existence of a > k p such that m^n^{k p} is congruent to m (mod p) and a k q such > that m^n^{k q} is congruent to m (mod q), but what I'm really after > is some way to properly understand and use the CRT in a proof. Assuming that p,q are different primes, I can see at the moment that m^t > = m (mod pq) with t = (n^kp - 1)(n^kq - 1) + 1. Are you sure that you > need t in the form of n^k? Yes. p and q are distinct, and t is in the form of n^k. I'm not sure how to use the CRT in a proof, and I'm not sure what to make of making k from k p or k q other than the fact that it exists. === Subject: Re: Help with the CRT posting-account=LbYpygoAAAB-XnkxlNRvR3Xt0EKgDYSd AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.2 Safari/525.20.1,gzip(gfe),gzip(gfe) On Sep 14, 2:57æam, Jannick Asmus understand what you mean here. :-) m^{n^{k n}} in all cases. === Subject: Complemented Lattices Let L be a complemented lattice which of course tacidly includes L is bounded usually by 0 below and 1 above. If L is distribute, then complements are unique. Conversely, if complements are unique, that is each element has exacly one complement, is L distributive? If L is not distributive, then L has one of the lattices below as a sublattice. Thus some elements don't have a unique complement. not not modular distributive q q / /| u u v w | w |/ v / p / p Alternatively to that graphic proof is there an algebraic proof for the converse or is there non-graphic, algebraic way of showing the graphic theorem used above? === Subject: Test Banks & Solution Manuals - NEW posting-account=aBM6KgoAAADrVPeOCixVZoA04FCm4rNR .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.2),gzip(gfe),gzip(gfe) Hi there! Student Plus Has The Following Test Banks & Solutions Manual, All In Digital Formats (PDF,DOC,RTF) For The Following Books' Titles: Note: Some Books With Either The Test Bank Or The Solution Manual (Test bank, Solution Manual, Instructor Guid) A Quantum Approach to Condensed Matter Physics,E,Taylor, Heinonen A Short Introduction to Quantum Information and Quantum Computation,E,Michel Le Bellac Accounting for Governmental and Nonprofit Entities,14,Wilson, Kattelus, Reck Accounting Information Systems,10,Romney, Steinbart Accounting Information Systems,11,Romney, Steinbart Accounting Information Systems,5,James A. Hall Accounting Information Systems,6,James A. Hall Accounting Information Systems,7, Gelinas, Dull Accounting Information Systems A Business Process: Approach,2,Jones, Rama Accounting Principles,7,Weygandt, Kieso, Kimmel Accounting Principles,8,Weygandt, Kieso, Kimmel Accounting Principles,9,Weygandt Adaptive Control,2,Astrom, Wittenmark Advanced Accounting,10,Beams, Clement, Anthony, Lowensohn Advanced Accounting,10,Fischer, Taylor, Cheng Advanced Accounting,2,Jeter, Chaney Advanced Accounting,3,Jeter, Chaney Advanced Accounting,8,Hoyle, Schaefer, Doupnik Advanced Accounting,9,Beams, Clement, Anthony, Lowensohn Advanced Accounting,9,Fischer, Taylor, Cheng Advanced Accounting,9,Hoyle, Schaefer, Doupnik Advanced Calculus,2002,Gerald B.Folland Advanced Engineering Mathematics,8,Kreyszig Advanced Engineering Mathematics,9,Erwin Kreyszig Advanced Modern Engineering Mathematics,3,Glyn James Advertising and Promotion: An Integrated Marketing Communications Perspective,6,Belch Advertising and Promotion: An Integrated Marketing Communications Perspective,7,Belch An Introduction to Numerical Analysis,E,David F. Mayer An Introduction to Numerical Analysis, rs, 0,E,Endre Suli, David F. M An Introduction to Ordinary Differential Equations,E,James C. Robinson An Introduction to the Finite Element Method,3,Reddy Analog Integrated Circuit Design,1996,Johns Martin Analysis and Design of Integrated Circuits,4,Gray, Hurst, Lewis, Meyer Analytical Mechanics,7,Fowles, Cassiday Applied Calculus for the Managerial, Life, and Social Sciences,6,Tan Applied Partial Differential Equations,4,Haberman Applied Partial Differential Equations,E,David Logan Applied Statistics and Probability for Engineers,3,Montgomery, Runger Artificial Intelligence: A Modern Approach,2,Russell, Norvig Astronomy Today,5,Chaisson, McMillan Auditing and Assurance Services,12,Arens, Elder, Beasley Auditing and Assurance Services (An Intergrated Approach),12,Alvin Arens, J. Elder, Beasley Automatic Control Systems,8,Kuo, Golnaraghi Basic Engineering Circuit Analysis,7,Irwin Basic Engineering Circuit Analysis,8,Irwin Basic Technical Mathematics with Calculus Metric Version,8,Alyn J. Washington Basic Technical Mathematics with Calculus, Canadian Edition,8,Allyn J. Washington Basic Technical Mathematics with Calculus, Cdn,8,Alyn J. Washington Biological Science,2,Scott Freeman Biology,7,Campbell, Reece Biology,8,Campbell, Reece Brief Principles of Macroeconomics,4,Gregory Mankiw Business Essentials,5,Ebert, Griffin Business Essentials,6,Ebert, Griffin Business Law and the Regulation of Business,8,Mann, Roberts Business Law and the Regulation of Business,9,Mann, Roberts Business Law Today, Standard Edition,8,Miller, Jentz Business Law Today: Comprehensive,7,Miller, Jentz Business Law Today: The Essentials,8,Miller, Jentz Business Law: Today The Essentials,7,Miller, Jentz Business Statistics: A Decision Making Approach,6,Groebner, Shannon, Fry, Smith Business Statistics: A Decision Making Approach,7,Groebner, Shannon, Fry, Smith C++ How to Program,3,Deitel, Deitel & Nieto Calculus,3,Hallett, Gleason, mcCallum Calculus,5,James Stewart Calculus,8,Varberg, Purcell, Rigdon Calculus With Analytic Geometry,7,Larson, Edwards, Hostetler, Hostetler Calculus with Applications,8,Lial, Greenwell, Ritchey Calculus with Applications Brief Version,8,Lial, Greenwell, Ritchey Calculus, Early Transcendental Functions,3,Smith, Minton Calculus, Early Transcendentals,5,Edwards, Penney Calculus, Early Transcendentals,6,Edwards, Penney Calculus, Early Transcendentals,7,Edwards, Penney Cases in Management Accounting and Control Systems,4,Allen, Brownlee, Haskins, Lynch, Rotch Chemistry: The Central Science,10,Brown, LeMay, Bursten Chemistry: The Central Science,11,Brown, LeMay, Bursten, Murphy, Woodward Classical Dynamics: A Contemporary Approach,E,Jos.8e, Eugene, Saletan Classical Electrodynamics,3,Jackson Classical Mechanics,2,Goldstein College Mathematics for Business, Economics, Life Sciences & Social Sciences,11,Barnett, Ziegler, Byleen College Physics,6,Serway, Faughn Communication Systems,4,Carlson Communication Systems,4,Haykin Communication Systems Engineering,2,Proakis, Salehi Complex Variables With Applications,3,Wunsch, Brown Computational Techniques for Fluid Dynamics,E,Karkenahalli Srinivas, Clive, Fletcher Computer Networking A Top Down Approach,3,James F.Kurose, Keith W. Ross Computer Organization and Architecture: Designing for Performance, 7,William Stallings Computer Science: An Overview,10,Glenn Brookshear Computer Science: An Overview,9,Glenn Brookshear Concepts and Applications of Finite Element Analysis,4,Cook Corporate Finance,8,Ross, Westerfield, Jordan Cost Accounting,12,Horngren, Datar, Foster Cost Accounting,13,Horngren, Foster, Datar, Rajan, Ittner Cost Accounting,5,Michael Maher Data Abstraction and Problem Solving with Java,2,Carrano, Prichard Data Abstraction and Problem Solving with Java, Walls and Mirrors, Data and Computer Communications,8,William Stallings Database System Concepts,4,Silberschatz, Korth, Sudarshan Database System Concepts,5,Silberschatz Design and Analysis of Experiments,6,Douglas C. Montgomery Device Electronics for Integrated Circuits,3,Richard S. Muller, Theodore, Kamins Differential Equations and Linear Algebra,3,Goode, Annin Differential Equations and Linear Algebra,E,Edwards, Penney Digital & Analog Communication Systems,7,Leon W. Couch Digital Image Processing,2,Gonzalez, Woods Digital Image Processing,3,Gonzalez, Woods Discrete and Combinatorial Mathematics,5,Ralph P. Grimaldi Discrete Mathematics,6,Richard Johnsonbaugh Economics,7,Roger A. Arnold Economics,8,Roger A. Arnold Electric Circuits,7,James W. Nilsson, Susan Riedel Electric Machinery,6,Fitzgerald, Charles Kingsley, Umans Electric Machinery Fundamentals,4,Stephen J. Chapman Electrical Machines, Drives and Power Systems,6,Theodore Wildi Electronic Commerce 2008,5,Turban, Dave King, Lee, Viehland Electronic Commerce: A Managerial Perspective 2006,4,Turban, Dave King, Lee, Viehland Electronics,2,Allan R. Hambley Elementary Dffferential Equations,8,Kohler, Johnson Elementary Differential Equations,8,Boyce, DiPrima Elementary Differential Equations and Boundary Value Problems,7,Boyce, DiPrima Elementary Differential Equations and Boundary Value Problems,8,Boyce, DiPrima Elementary Differential Equations With Boundary Value Problems, 4,Edwards, Penney Elementary Differential Equations with Boundary Value Problems, 6,Edwards, Penney Elementary Number Theory,5,Goddard, Rosen Elementary Principles of Chemical Processes,3,Richard M. Felder, Ronald W. Rousseau Elementary Statistics,2,Mario F. Triola Elementary Statistics,3,Mario F. Triola Elements Of Electromagnetics,3,Sadiku, Sagliocca, Soriyan Elements of Forecasting,3,Diebold Group, Francis X. Diebold Engineering Circuit Analysis,6,Hayt, Kemmerly, Durbin Engineering Electromagnetics,6,Hayt, Buck Engineering Fluid Mechanics,7,Crowe, Alger, Roberson Engineering Fluid Mechanics,7,Crowe, Elger, Roberson Engineering Mathematics,4,John Bird Engineering Mechanics (Dynamics),11,Hibbeler Engineering Mechanics (Statics),5,Bedford, Fowler Engineering Statistics,4,Montgomery, Runger, Hubele Environmental Economics and Natural Resource Management,E,David A. Anderson Equilibrium and Non-Equilibrium Statistical Thermodynamics,E,Bellac, Mortessagne, Batrouni Essentials of Economics,3,Gregory Mankiw Essentials Of Economics,3,Mankiw Essentials of Economics,4,Gregory Mankiw Essentials of Modern Business Statistics,3,Anderson, Sweeney, Williams Essentials of Statistics for Business and Economics,4,Anderson, Sweeney, Williams Essentials of Statistics for Business and Economics,5,Anderson, Sweeney, Williams Essentials of Statistics for Business and Economics, Abbreviated Edition,4,Anderson, Sweeney, Williams Field and Wave Electromagnetics,2,David K. Cheng Financial Accounting,6,Harrison, Horngren Financial and Managerial Accounting,13,Williams, Haka, Bettner Financial Management: Theory & Practice,12,Brigham, Ehrhardt Financial Reporting and Analysis,10,Charles H. Gibson Financial Reporting and Analysis,11,Gibson Finite Mathematics,8,Lial, Greenwell, Ritchey First Course In Abstract Algebra,7,John B. Fraleigh First Course in Probability,7,Sheldon Ross Fluid Mechanics,5,Frank M. White Fluid Mechanics,E,Egon Krause Fluid Mechanics With Engineering Applications,10,John Finnemore, Joseph Franzini Foundations Of Psychiatric Mental Health Nursing,E,Varcarolis Fundamentals Of Anatomy & Physiology,7,Frederic H. Martini Fundamentals of Applied Electromagnetics,5,Fawwaz T. Ulaby Fundamentals of Communication Systems,2005,Proakis, Salehi Fundamentals of Corporate Finance,8,Ross, Westerfield, Jordan Fundamentals of Differential Equations and Boundary Value Problems, 4,Nagle, Saff, Snider Fundamentals of Electric Circuits,2,Charles Alexander, Matthew Sadiku Fundamentals of Electric Circuits,3,Alexander, Sadiku Fundamentals of Financial Management,11,Brigham, Houston Fundamentals of Financial Management: Concise Edition,5,Brigham, Houston Fundamentals of Financial Management: Concise Hybrid,5,Brigham, Houston Fundamentals of Heat and Mass Transfer,5,Frank P. Incropera, David P. DeWitt Fundamentals of Logic Design,5,Charles H Roth Fundamentals of Multinational Finance,2,Michael H. Moffett, Stonehill, Eiteman Fundamentals of Multinational Finance,3,Michael H. Moffett, Stonehill, Eiteman Fundamentals Of Organizational Communication,6,Zalabak, Garcia Fundamentals Of Physics,7,Halliday, Resnick, Walker Fundamentals Of Physics,8,Halliday, Resnick, Walker Fundamentals of Probability with Stochastic Processes,3,Saeed Ghahramani Fundamentals of Thermodynamics,6,Sonntag, Borgnakke, Wylen Guide to Energy Management,5,Klaus-Dieter E. 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Patterson, McGraw Hill (Test Bank) West Federal Taxation 2008 (Comprehensive Volume), Edition 31, Willis, Hoffman, Maloney, Raabe (Test Bank) West Federal Taxation 2008 (Taxation of Business Entities), Edition 11, Smith, Raabe, Maloney (Test Bank) Wireless Communications, Edition 2, Theodore Rappaport (Solution Manual) If The Book You Are Looking For Is Not Listed, Please Contact Us And Student Plus Will Help Contact: Student.plus@hotmail.com Student.Plus(at)Hotmail(dot)com === Subject: Grobnerbasis Eliminate t; x = (2*(5 + 19*t^2 - 45*t^4 + t^6 -4*t^8))/(1 + t^2)^4, y = (2*(t + 51*t^3 + 3*t^5 + 17*t^7))/(1 + t^2)^4 === Subject: Re: Grobnerbasis KY a .8ecrit : > Eliminate t; > x = (2*(5 + 19*t^2 - 45*t^4 + t^6 -4*t^8))/(1 + t^2)^4, > y = (2*(t + 51*t^3 + 3*t^5 + 17*t^7))/(1 + t^2)^4 Why not use the resultant (on the polynomials in t : x=(1+t^2)^4-....) Here is Maple's result : y^8-45*y^6-41283*y^4-48*y^6*x+7950960*x^2+x^8-5544*x^5+19*x^6+ 16*x^7+4*y^2*x^6+266382*x^3-519*y^2*x^4-41283*x^4-16*y^2*x^5+6*y^4*x^4+ 441*y^4*x^2-80*y^4*x^3+11088*y^2*x^3-82566*y^2*x^2-799146*y^2*x+4*y^6*x^2 +16632*y^4*x+7950960*y^2 = 373248000 No further factoristion seems possible... === Subject: Markov bound? Hi all, I posted this message already yesterday to this group but funnily enough it disappeared in my news client. Sorry for double posting, if you guys can still see it. I do not understand one step in a lemma and it would be nice if someone of you can help me. Let A be a random variable over {0,1}^n and let 0 <= t_a <= 1. Let further: sum_{a in {0,1}^n}Pr[a=A]*t_a > d. Let now be B subset {0,1}^n such that for b in B we have t_b >= d/2. Then in the Lemma it says that by Markov it follows: Pr[A in B] >= d/2 Do you know which Markov bound is used here and why this acutally should be the case? Bernd === Subject: Re: Markov bound? I figured out some details, but still I don't get the whole bound: We would like to get a lower bound for Pr[A in B], and I guess the following holds: Pr[A in B] = sum_{a in {0,1}^n}Pr[a=A|t_a > d/2] With Bayes the following holds: sum_{a in {0,1}^n}Pr[a=A|t_a > d/2] = sum_{a in {0,1}^n}Pr[a=A,t_a > d/2]/Pr[t_a > d/2] (1) Pr[t_a > d/2] <= 2E[t_a]/d ==> 1/Pr[t_a > d/2] >= d/(2E[t_a]) With this (1) results in: >= d/2 sum_{a in {0,1}^n}Pr[a=A,t_a > d/2]/E[t_a] Now, this does not look too bad, but I still don't know why: sum_{a in {0,1}^n}Pr[a=A,t_a > d/2]/E[t_a] >= 1 Can you help me? Bernd === Subject: simlpex source code posting-account=kmI5HAoAAAAFdg2F2cZZJlTaOiqBeyFq Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) I need the simlpex source code for solving the following problem: f* = maximize zTq [CapitalEth] z0 subject to zTpi [CapitalEth] z0 <= 0 for all i=1,.83,n zTq [CapitalEth] z0 <= 1 === Subject: Re: simlpex source code > I need the simlpex source code for solving the following problem: f* = maximize zTq [CapitalEth] z0 > subject to zTpi [CapitalEth] z0 <= 0 for all i=1,.83,n > zTq [CapitalEth] z0 <= 1 Google is your friend. Best to search for simplex though. === Subject: simlpex source code posting-account=kmI5HAoAAAAFdg2F2cZZJlTaOiqBeyFq Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) I need the simlpex source code for solving the following problem: q is a known point in a n-D area. Pis are some point in n-D area. I want to find z and z0 Z is a n-D vector Z0 is a real number T means Transpose f* = maximize zTq [CapitalEth] z0 subject to zTpi [CapitalEth] z0 <= 0 for all i=1,.83,n zTq [CapitalEth] z0 <= 1 === Subject: Re: simlpex source code posting-account=K5WE3woAAAAXArsybjkbN6LjMxWdHtbX Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > I need the simlpex source code for solving the following problem: q is a known point in a n-D area. > Pis are some point in n-D area. > I want to find z and z0 > Z is a n-D vector > Z0 is a real number > T means Transpose f* = maximize zTq [CapitalEth] z0 > subject to zTpi [CapitalEth] z0 <= 0 for all i=1,.83,n > zTq [CapitalEth] z0 <= 1 Do you want actual *source code*, or do you just want access to software that will solve the problem for given numerical inputs? (There is a real difference between these two desires.) I will assume you want to solve the problem. There are numerous freely downloadable simplex codes available on the web. A good source to find them is the INFORMS web page http://www2.informs.org/Resources/Computer Programs/ . Go to the menu item Noncommercial Software Packages and Descriptions. See the entry Linear Programs Solvers or the NEOS Guide to Optimization Software or the entry QSopt Linear Programming Solver or SoPlex: the Sequential object-oriented simplex class library. There are also on-line optimizers, featured in the menu item Online Optimizers and Other Programs. I don't know if you need to pay to use any of these. Are you aware that EXCEL (and corresponding open-source spreadsheets) have a Solver tool that can solve linear and nonlinear constrained optimization problems? The Solver that came with my implementation of EXCEL XP can handle 400 variables and about 250 constraints (if I remember correctly), so could deal with a problem having n = 249 or so. R.G. Vickson === Subject: Software to Try.... posting-account=MNgv5AoAAAACZMZZgNcu0TbXW6wdAsyi .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) The folloiwng site, http://www.cesd.com , has some chemical engineering,mathematical , chemistry software suitable for chemistry,chemical engineering students and professionals etc. Contains information on 3000+ chemical compounds,allows predition of chemical compound properties,critical constants, thermodynamic properties etc,periodic table, solves 400+ chemical/electrical/ mechcanical engineering, phyics, and mathematical equations. Contains 200+ unit conversions & more. http://www.cesd.com http://www.cesd.com/products.htm http://www.cesd.com/cesddls.html You may want to take a look.... === Subject: Order modulo p^n (Number Theory) posting-account=SKIJagoAAADhZRVNQ7TM7Yl79Cu6Fiys .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.2; FDM; Creative AutoUpdate v1.10.10),gzip(gfe),gzip(gfe) Hello need some help with a question in number theory im attempting Let p be an odd prime and n > 1 an integer. Find the order of (1 + p) modulo (p^n). === Subject: Re: Order modulo p^n (Number Theory) posting-account=suWj4AkAAADE1IvGmj55Nmq3f98qb17e InfoPath.1; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) On Sep 14, 3:56æpm, dark.sorrow.myst...@gmail.com > Hello need some help with a question in number theory im attempting Let p be an odd prime and n > 1 an integer. Find the order of (1 + p) > modulo (p^n). > *********************************************************** Hints: 1.- Try with p = 3, 1 + p = 4 and n = 1, 2, 3, 4, and then with p = 5 and 1 + p = 6, and then even with p = 7 and 1 + p = 8... 2.- Now prove your guess or huntch: use Newton's binomial with (1 + p)^(p^(n-1))...you may want to show that the binomial coefficient [p^r : r] is divisible by p iff r is a multiple of p... Tonio === Subject: Re: Order modulo p^n (Number Theory) posting-account=SKIJagoAAADhZRVNQ7TM7Yl79Cu6Fiys .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.2; FDM; Creative AutoUpdate v1.10.10),gzip(gfe),gzip(gfe) > On Sep 14, 3:56æpm, dark.sorrow.myst...@gmail.com Hello need some help with a question in number theory im attempting Let p be an odd prime and n > 1 an integer. Find the order of (1 + p) > modulo (p^n). > *********************************************************** Hints: 1.- Try with p = 3, 1 + p = 4 and n = 1, 2, 3, 4, and then with p = 5 > and 1 + p = 6, and then even with p = 7 and 1 + p = 8... 2.- Now prove your guess or huntch: use Newton's binomial with (1 + p)^(p^(n-1))...you may want to show that the binomial coefficient [p^r : r] is divisible by p iff r is a multiple of p... Tonio find the order. Then try prove it. was trying to come up with the binomial, that really helped with the proof ofthe order. cheers sorrow === Subject: Re: Order modulo p^n (Number Theory) posting-account=SKIJagoAAADhZRVNQ7TM7Yl79Cu6Fiys .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.2; FDM; Creative AutoUpdate v1.10.10),gzip(gfe),gzip(gfe) > dark.sorrow.myst...@gmail.com > On Sep 14, 3:56æpm, dark.sorrow.myst...@gmail.com > Hello need some help with a question in number theory im attempting > Let p be an odd prime and n > 1 an integer. Find the order of (1 + p) > modulo (p^n). > *********************************************************** > Hints: > 1.- Try with p = 3, 1 + p = 4 and n = 1, 2, 3, 4, and then with p = 5 > and 1 + p = 6, and then even with p = 7 and 1 + p = 8... > 2.- Now prove your guess or huntch: use Newton's binomial with > (1 + p)^(p^(n-1))...you may want to show that the binomial > coefficient [p^r : r] is divisible by p iff r is a multiple of p... > Tonio find the order. Then try prove it. æwas trying to come up with the >binomial, that really helped with the proof ofthe order. Can you explain your proof? My original proof was a load of dingo's kidneys (as I would have > realised if I had typed it up neatly to post to sci.math). I think > I've fixed it now, but I'm still reluctant to post it until you've > shown your work. -- > Angus Rodgers > Contains mild peril- Hide quoted text - - Show quoted text - Hey, well first through writing a few examples I saw that the order should be p^n-1. After that I used Newtons binomial and showed that p^n divides all the coeffients apart from when k=0. (lower bound on my sum) which gives a remainder 1, giving the required (1+p)^(p^n-1)= 1 mod(p^n). So either that is the order or the order divides p^n-1. Then i showed for any powers less than n-1 the expansion dosent give the remainder 1 and the coefients are not divisible by p^n. :) cheers, sorrow === Subject: Re: Order modulo p^n (Number Theory) > ... would someone please explain in gory detail just >how this one is supposed to go? Here's one version, essentially along the lines described by the OP, but with more details included ... [repost with typos corrected] proposition: If p is an odd prime then p+1 has order p^(n-1) mod p^n. proof: First, a lemma: If p is an odd prime and p^r || x, where x in Z and r in N, then p^(r+1) || (x+1)^p - 1. proof of the lemma: Using the binomial theorem, (x+1)^p - 1 = x^p + c_1*x^(p-1) + ... + c_(p-1)*x where c_k = (p choose k). Claim each term on the RHS, except the last, is divisible by p^(r+2), and the last term is divisible by p^(r+1) but not by p^(r+2). p^(r+1) || (x+1)^p - 1 as required. It remains to verify the claim. First consider the leading term. p^r || x => p^(pr) || x^p Since p >= 3 and r >= 1, p^(pr) || x^p => p^(3r) | x^p => p^(r+2) | x^p Next consider the other terms. For k = 1,...,(p-1) p^1 || c_k and p^((p-k)*r) || x^(p-k) hence p^((p-k)*r+1) || c_k*x^(p-k) For k = 1,...,(p-2), (p-k)*r+1 >= 2*r+1 >= r+2 so p^(r+2) | c_k*x^(p-k) Finally, for k = (p-1), (p-k)*r+1 = r+1 so p^(r+1) || c_(p-1)*x which completes the verification of the claim, and completes the proof of the lemma. corollary: If p is an odd prime, and n in N, then p^n || (p+1)^(p^(n-1)) - 1 proof: Proceed by induction. The verification for n=1 is immediate. Next, suppose the corollary is true for n=m, for some m in N. Thus, p^m || (p+1)^(p^(m-1)) - 1. Letting x = (p+1)^(p^(m-1)) - 1, and applying the lemma, p^(m+1) || (x+1)^p - 1 that is, p^(m+1) || (p+1)^(p^m) - 1 which completes the induction, and proves the corollary. Returning to the proof of the proposition, let s be the order of (p+1) mod p^n. By the corollary, p^n | (p+1)^(p^(n-1)) - 1 hence (p+1)^(p^(n-1)) = 1 (mod p^n) It follows that s | p^(n-1). Applying the corollary again, p^(n-1) || (p+1)^(p^(n-2)) - 1 hence p^n does not divide (p+1)^(p^(n-2)) - 1 Equivalently (p+1)^(p^(n-2)) /= 1 (mod p^n) and hence, s does not divide p^(n-2). It follows that s = p^(n-1), which completes the proof. quasi === Subject: Re: Order modulo p^n (Number Theory) >would someone please explain in gory detail just >how this one is supposed to go? Here's one version, essentially along the lines described by the OP, but with more details included ... proposition: If p is an odd prime then p+1 has order p^(n-1) mod p^n. proof: First, a lemma: If p is an odd prime and p^r || x, where x in Z and r in N, then p^(r+1) || (x+1)^p - 1. proof of the lemma: Using the binomial theorem, (x+1)^p - 1 = x^p + c_1*x^(p-1) + ... + c_(p-1)*x where c_k = (p choose k). Claim each term on the RHS, except the last, is divisible by p^(r+2), and the last term is divisible by p^(r+1) but not by p^(r+2). p^(r+1) || (x+1)^p - 1 as required. It remains to verify the claim. First consider the leading term. p^r || x => p^(pr) || x^k Since p >= 3 and r >= 1, p^(pr) || x^k => p^(3r) | x^p => p^(r+2) | x^p Next consider the other terms. For k = 1,...,(p-1) p^1 || c_k and p^((p-k)*r) || x^(p-k) hence p^((p-k)*r+1) || c_k*x^(p-k) For k = 1,...,(p-2), (p-k)*r+1 >= 2*r+1 >= r+2 so p^(r+2) | c_k*x^(p-k) Finally, for k = (p-1), (p-k)*r+1 = r+1 so p^(r+1) || c_(p-1)*x which completes the verification of the claim, and completes the proof of the lemma. corollary: If p is an odd prime, and n in N, then p^n || (p+1)^(p^(n-1)) - 1 proof: Proceed by induction. The verification for n=1 is immediate. Next, suppose the corollary is true for n=m, for some m in N. Thus, p^m || (p+1)^(p^(m-1)) - 1. Letting x = (p+1)^(p^(m-1)) - 1, and applying the lemma, p^(m+1) || (x+1)^p - 1 that is, p^(m+1) || (p+1)^(p^m) - 1 which completes the induction, and proves the corollary. Returning to the proof of the proposition, let s be the order of (p+1) mod p^n. By the corollary, p^n | (p+1)^(p^(n-1)) - 1 hence (p+1)^(p^(n-1)) = 1 (mod p^n) It follows that s | p^(n-1). Applying the corollary again, p^(n-1) || (p+1)^(p^(n-2)) - 1 hence p^n does not divide (p+1)^(p^(n-2)) - 1 Equivalently (p+1)^(p^(n-2)) /= 1 (mod p^n) and hence, s does not divide p^(n-2). It follows that s = p^(n-1), which completes the proof. quasi === Subject: Re: Order modulo p^n (Number Theory) posting-account=Z3AipgkAAABkoMfyNwddSxsYhXHi5CDt CLR 1.1.4322; InfoPath.1; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) (Welcome back.) >would someone please explain in gory detail just >how this one is supposed to go? Here's one version, essentially along the lines described by the OP, >but with more details included ... proposition: If p is an odd prime then p+1 has order p^(n-1) mod p^n. proof: First, a lemma: If p is an odd prime and p^r || x, where x in Z and r in N, then I thought at first that by p^r || x you must mean p^r divides x > and p^{r+1} does not divide x, but it seems from the work below > that you just mean that p^r divides x. æIs that right? ... no, I > see below that it isn't! ... OK, I've re-read the proof, and it > all makes sense now, although I'll have to read through it again > more slowly to make quite sure. æ p^(r+1) || (x+1)^p - 1. proof of the lemma: Using the binomial theorem, æ (x+1)^p - 1 = x^p + c 1*x^(p-1) + ... + c (p-1)*x where c k = (p choose k). Claim each term on the RHS, except the last, is divisible by p^(r+2), >and the last term is divisible by p^(r+1) but not by p^(r+2). > æ p^(r+1) || (x+1)^p - 1 as required. It remains to verify the claim. First consider the leading term. æ p^r || x => p^(pr) || x^k Since p >= 3 and r >= 1, æ p^(pr) || x^k => p^(3r) | x^p => p^(r+2) | x^p Next consider the other terms. For k = 1,...,(p-1) æ p^1 || c k and æ p^((p-k)*r) || x^(p-k) hence æ p^((p-k)*r+1) || c k*x^(p-k) For k = 1,...,(p-2), æ (p-k)*r+1 >= 2*r+1 >= r+2 æ so p^(r+2) | c k*x^(p-k) Finally, for k = (p-1), æ (p-k)*r+1 = r+1 æ so p^(r+1) || c (p-1)*x which completes the verification of the claim, and completes the proof >of the lemma. OK, but that was rather more gory detail than I needed for such > a simple proof! æThe reason I asked for details is that everybody > else who has posted to this thread seems to suggest that the entire > proof is just a simple matter of expanding something by the Binomial > Theorem and proving that all or most of the binomial coefficients > are divisible by p, or by some power of p, in a way which is too > obvious to need explaining. æBoth of my proofs are more complicated > than this outline suggests; and so is yours (although this lemma > isn't - unless I missed something in my quick scan through it - > I'll read it more thoroughly later). corollary: If p is an odd prime, and n in N, then æ p^n || (p+1)^(p^(n-1)) - 1 proof: Proceed by induction. This is quite like my first proof, which was a proof by induction > on n that: æ(p + 1)^{p^{n-2}} = 1 + p^{n-1} æ(mod p^n) for all odd primes p, and all integers n >= 2. æThe messy part was > that I used a trinomial expansion; and I still suspect that I made > unnecessarily heavy weather of it. (However, it didn't need any > lemmas! æAnd it was pretty straightforward - just a bit messy.) As in your proof, I applied this result twice to deduce the order > of p + 1 (mod p^n). The verification for n=1 is immediate. Next, suppose the corollary is true for n=m, for some m in N. Thus, p^m || (p+1)^(p^(m-1)) - 1. Letting x = (p+1)^(p^(m-1)) - 1, and applying the lemma, æ p^(m+1) || (x+1)^p - 1 that is, æ p^(m+1) || (p+1)^(p^m) - 1 which completes the induction, and proves the corollary. That's neat. æDefinitely neater than my proof, especially if the > proof of the lemma is written out with less gore! Returning to the proof of the proposition, let s be the order of (p+1) >mod p^n. By the corollary, æ p^n | (p+1)^(p^(n-1)) - 1 hence æ (p+1)^(p^(n-1)) = 1 (mod p^n) It follows that s | p^(n-1). Applying the corollary again, æ p^(n-1) || (p+1)^(p^(n-2)) - 1 hence æ p^n does not divide (p+1)^(p^(n-2)) - 1 Ah ... so || does have the interpretation I at first imagined. This is very nice. Equivalently æ (p+1)^(p^(n-2)) /= 1 (mod p^n) and hence, s does not divide p^(n-2). It follows that s = p^(n-1), which completes the proof. Although I like the proof a lot, I have to object that it does > not explain what everybody else had in mind, which is what was > worrying me - making me think that I had missed something that > should be utterly obvious. For what it's worth, my second proof (attempting to follow the > lines that various hints in this thread seemed to be suggesting) > proved that for m = n - 1 or n - 2, p^{n-k} divides binom{p^m}{k}, > for k = 4, ..., n - 1 (the cases k = 2 and k = 3 being easily > disposed of separately, the only minor complication being when > k = p = 3), by using the fact that the highest power of p that > divides k! is p^s, where s = floor(k/p) + floor (k/p^2) + ... > <= k/p + k/p^2 + ... = k/(p - 1) <= k/2 <= k - 2, therefore the > binomial coefficient is divisible by at least p to the power of > m - s >= (n - 2) - (k - 2) = n - k, as required. (One word: ugh!) So I still don't know if I've been making unnecessarily heavy > weather of this. æYour proof, assuming it's valid as it seems > to be, seems to be the way to go, but I still don't know what > everybody else had in mind! -- > Angus Rodgers > Contains mild peril- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text -- Hide quoted text - - Show quoted text - Angus, I looked over your proof and Quasi's proof, and while I confess to not reading them more than utterly superficially, I was surprised at their length, which I don't see as necessary. How is this? First assume p is odd. The ideas is to show (by induction of course), that (1+p)^(p^(n-1)) = 0 (mod p^n), and (1+p)^(p^(n-1)) != 0 (mod p^(n+1), for all n >= 1. The case n = 1 is clear. Then we may assume that (1+p)^(p^(n-2)) = 1+ap^(n-1) where a is not divisible by p. Then (1+p)^(p^(n-1)) = (1+ap^(n-1)^p = 1 + C(p, 1)ap^(n-1) + C(p,2)a^2*p^2(n-2) + ... + a^p*p^(n-1). Since all the C(p,j) are divisible by p, it is evident that (1+p)^(p^(n-1)) = 0 (mod p^n). The second C(p,1)ap^(n-1), is obviously divisible by p^n since C(p,1) = p, but not divisible by p^(n+1) since (a,p) = 1. I now claim that all of the remaining terms (except for the 1) are divisible by p^(n+1). Since, except for the last term, we have a factor of C(p,j) which is divisible by p, this is equivalent to showing that p^(n-1) > n. We actually have it easier for all but the last term, but this way of putting it avoids considering separate cases. This statement is false for p = 1 and n = 1 which is why p = 2 has to be considered separately. For all other cases, this is easy to show by induction and I will omit the details because it is really easy. Having shown this inductive statement, I have actually shown that the exact order of (1+p) mod p^n is p^(n-1) When p = 2, the above proof goes through just fine except that the induction doesn't get started quite the same. We are looking for a problem with (1+2)^2, aka 9, which is actually = 1(mod 2^3), so the above argument gives us that the order of 3 mod 2^n is 2^(n-2). Hopefully I have minimized the inevitable typos and the meaning it clear. Achava === Subject: Re: Order modulo p^n (Number Theory) > [a proof with a few typos] I'll repost a corrected version. quasi === Subject: Re: Order modulo p^n (Number Theory) posting-account=lHNboAoAAACyasQ0uqX7OeM_tLuWGoQp SV1; .NET CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) spider-dtc-ti10.proxy.aol.com[CDBC710A] (Prism/1.2.1), HTTP/1.1 cache-dtc-ag12.proxy.aol.com[CDBC758C] (Traffic-Server/6.1.5 [uScM]) On Sep 14, 8:56?am, dark.sorrow.myst...@gmail.com > Hello need some help with a question in number theory im attempting Let p be an odd prime and n > 1 an integer. Find the order of (1 + p) > modulo (p^n). > Start with n=1. Then apply Hensel's Lemma. === Subject: Re: Order modulo p^n (Number Theory) > On Sep 14, 8:56.95Ëìam, dark.sorrow.myst...@gmail.com > Hello need some help with a question in number theory im attempting > Let p be an odd prime and n > 1 an integer. Find the order of (1 + p) > modulo (p^n). > Start with n=1. Then apply Hensel's Lemma. I am not sure how this should work. Are you not running into problems with characteristic p here? -- Best wishes, J. === Subject: Re: Order modulo p^n (Number Theory) posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) On 14 Sep, 13:56, dark.sorrow.myst...@gmail.com > Hello need some help with a question in number theory im attempting Let p be an odd prime and n > 1 an integer. Find the order of (1 + p) > modulo (p^n). You might try some numerical experiments. Take a few values of p, say p = 3, 5, 7, 11, and a few values of n, say n = 2, 3, 4, 5 and actually calculate the orders of 1 + p modulo p^n. (You could do that by calculating the powers of 1 + m modulo p^n until you get back to 1). Actually doing this will give you a good idea of what is going on: you should get (i) a good idea of what the general solution is and (ii) some ideas about how to prove it. Victor Meldrew I don't believe it! === Subject: Markov lower bound Hi all, I know that there exists the Markov upper bound, but does there also exist a Markov lower bound? Bernd === Subject: Re: Markov lower bound posting-account=Jz4DtgkAAAAZkdWvJAd__jMF7l1N5_1V Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > Hi all, I know that there exists the Markov upper bound, but does there also exist > a Markov lower bound? Bernd If what you mean is by Markov upper bound is [for a>0]: Prob(|X|>=a) <= E(|X|)/a then no, there is no similar universal lower bound for Prob(|X|>=a) above 0. Just consider the random variable Zn with Prob(Zn=n) = 1/n and Prob(Zn=0) = (n-1)/n But if you want any lower bound then of course you can have something like Prob(|X|<=a) >= 1 - E(|X|)/a === Subject: A task about pyramid... posting-account=g9m0FgoAAAD9MrZl_8GR7R2eFE1W4Hho Gecko/2008070400 SUSE/3.0.1-0.1 Firefox/3.0.1,gzip(gfe),gzip(gfe) hi all, I have a problem with the task. I should be grateful for any help;] The base of pyramid is a rhombus on the side of 15cm in length. The surface area of 720 cm2 side. Side walls are inclined to base pro Pi / 3. Calculate the volume of this pyramid. PS: in the textbook the answer is 1440 cm3 === Subject: Re: A task about pyramid... posting-account=K5WE3woAAAAXArsybjkbN6LjMxWdHtbX Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > hi all, I have a problem with the task. I should be grateful for any help;] The base of pyramid is a rhombus on the side of 15cm in length. The > surface area of 720 cm2 side. Side walls are inclined to base pro Pi / > 3. Calculate the volume of this pyramid. > PS: in the textbook the answer is 1440 cm3 What have you done so far? Show your work. R.G. Vickson === Subject: Kaplan-Yorke dimension How Kaplan-Yorke dimension characterizes chaos in a dynamical system? === Subject: global error posting-account=T_sEVAoAAAA6mGWIApizafeI6uXeoeJh Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1; SV1) ; SLCC1; .NET CLR 2.0.50727; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) Hello! Very simple question about the global error. How to calculate a global error of the following method. I have no idea (1+ a* h *L +b * h^{2} * L^{2} ) y_{n+1}=( 1+( a + b )h*L+ (c+d)* h^{2} * L^{2} ) y_{n}. (a,b- are some coefficients,h-step, L-because I calcuate it for y'= L y, so for scalar case) Magdalena === Subject: Re: question about prime partition 7 , 23 , 37 , 53 _16 , 14 , 16 ____- 2 , 2 _______4 p = 4/2 = 2 r = 16 + 2 + 4 = 22 q = 16 - ( 2 + 22 ) = - 8 Un = 2n^2 - 8n + 22 = 2( n^2 - 4n + 11 ) then next element for the set is 7 , 23 , 37 , 53 , 75 , 107 , 153 , 185 , 207 rearange for matrix 3x3 then we get determinant 3x3 = 1/( - 75 ){ ( - 694 x - 7270 ) - ( - 314 x - 1670 )} = 1/( - 75 ) (- 380 - 5600 ) = - 5980/(- 75 ) = 5980/3/5/5 = 1993 k1/5/5 = 398 k3 k1/5 = 79 k3 k3 k1 5980 - 75x79 = 55 3|55 = 1 5|18 = 3 5|_3 = 3 __0 , for 331 k-553 55 = 1 + ( (0x5 + 3)x5 + 3 ) x 3 5|91 = 1 5|18 = 3 5|_3 = 3 __0 , for 331 base - 5 91 = 3x5x5 + 3x5 + 1 . . So different cases. === Subject: Re: question about prime partition Tripel Phytagoras c^2 = a^2 + b^2 , where a + c = b^2 , then c^2 - a^2 = c + b , ( c - a )( c + a ) = c + a , c - a = 1 . For primes b , we get for suitable n = 1 , 2 , 3 , ... , pair of primes { Pn , (Pn^2 - 1)/2 + 1 } 3 , 5 ; 8 ; 2 ; 4 5 , 13 ; 18 ; 8 ; 12 11 , 61 ; 72 ; 50 ; 60 19 , 181 ; 200 ; 162 ; 180 29 , 421 ; 450 ; 392 ; 420 new set 4x{ 1 , 3 , 15 , 45 , 105 , . . . } 4x{1 , 3x{1 , 5 , 15 , 35 . . .} 4x{ 1 , 3x{ 1 , 5x{ 1 , 3 , 7 . . . } how far and . . . === Subject: Re: question about prime partition Gcd of prime factors . Where is Gcd of {473 , 2193 } , it's by subtract the bigger to the lower. 2193 473- 1720 473- 1247 473- 774 473- 301- 172- 129- 43- 86- 43- 43- 0 then we get Gcd of { 473 , 2193 } = 43 . Because different of two numbers less then the set , we subtrack more by the bigger again as conclution. === Subject: Re: question about prime partition Subtracted was so hard for the children . Borrow system are genius but not so simple as you look. Then do it again by crutial nodes , as we practicing : 582 251- 331 , 5' 2' 4 1 7 9- 3 4 5 , every nodes read as less one 5' = 4 5' 0' 4 2 5 7- 2 4 7 , here 0' = 9 2' 0' 0' 8 1 2 3 9 7 6 9 , 4' 0' 2 2 0 8- 1 9 4 , here you will find 0-0 is 0 , but tha look like also 0' - 0 is 9. === Subject: Re: question about prime partition Division ___ |1 |1 2:]5|465|2 27326 , its 14 also 12 then 54652 : 2 = 27326 where we read the high to the bottom. Else wheres for non prime number divisor and so litte to do. Multiply let 25 x 37 25 37 x 0635 015 014 + = 925 , here 2x6 is 06 , 5x7 is 35 , 2x7 is 14 and 3x5 is 15 . Decimal place are useful content. And so two in multiplyin object able to do for more and more base-n. Scly Akumo === Subject: Re: question about prime partition |a b c| |d e f| |g h i | , is a matrixs determinant of the matrix where e not zero , we get by multi less determinan. The regions is 4 upper left = A , 4 lower left = C , 4 upper right = B , and 4 lower right = D. Then we get new matrixs |det(A) det(B)| |det(C) det(D)| for the determinant of the new matrixs is dett , than determinant matrix 3x3 is dett/-c . When you do that by line and line writting the equetions , tha get not so close to you , and simple . === Subject: Re: question about prime partition a , b , c , . . . Is sequence , then d = b-a , e= c-b , f= e-d . Relation for the equation Un := pn^2 + qn + r , is p := f/2 , r := a - d + f , q := a - ( p + r ) . Then we get a - r = d - f = p + q . d - f = f/2 + q, also 3/2 f = d - q or 3p = d - q . For sequence a , a + b , 3b , then Un := n /2 {(b - a)n + (b + a)} , elsewheres for sequences a=1 , b=n + 1 , c=3n , so d=n , e=2n -1 , f=n - 1 , p=n/2 , q= 1 - n/2 , r=0 . Thats look like familiar sets . === Subject: Re: question about prime partition | 1___n + 1___3n__| | n___2n - 1__n - 1| | n/2_1 - n/2____0| is complete matrix , solution is not exist at 2n - 1 , and we could be had been had trivial solution by determinant of complete matrix not divisible by 2n - 1 , but strangly is more constant 3 1/4 = 13/4 === Subject: Re: question about prime partition Let set { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } on the right ones , then rearrange for matrix 3x3 , where the elements was perfect combination , then all horizontals , verticals , and diagonals element each added for the same number. Here we can do : Sum set all elements is 45 , then 45/3 = 15 is partition added because matrix 3x3 . Let in the middle is { 4 , 5 , 6 } the only tripel we have as diagonal. When the set is verticals then another tripel { 7 , 8 , 9 } will be added in the set , then bigger than partition added ( 15 ). { 1 } must be in the middle , and the perfect matrix is 4 3 8 9 5 1 2 7 6 = matrix A Determinant A = {( 4 x 5 - 3 x 9 )( 5 x 6 - 1 x 7 ) - ( 3 x 1 - 5 x 8 )( 9 x 7 - 2 x 5 )}/ (- 5 ) = {(- 7 x 23 ) - ( - 37 x 53 )}/(- 5 ) = ( - 161 + 1961 )/ ( - 5 ) = 1800 / ( - 5 ) = -360 { 5 , 7 , 23 , 37 , 53 } is prime set , then 7 + 23 = 30 , 7 + 53 = 60 , 23 + 37 = 60 , 37 + 53 = 90 , 7 + 23 + 37 + 53 = 120 elsewheres 23 + 53 + 5 = 81 = 9 x 9 7 + 37 + 5 = 49 = 7 x 7 its look like circle angles first class. === Subject: Re: question about prime partition i'm gratified this question was such a hit with you. === Subject: Re: question about prime partition Mr. Daniel , i love my way to learn much about math , and these so really happy to do by me . So good U welcome me to adding more , are excellent time to upgrade anything. Bla . . === Subject: Re: question about prime partition Mr. Daniel , i love my way to learn much about math , and these so really happy to do by me . So good U welcome me to adding more , are excellent time to upgrade anything. Bla . . === Subject: Eureka! I have squared the circle posting-account=Uy-x1gkAAADZQZOsYkACyKA9wdgWU8tq Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) First you take a petri dish, and you fill it with mercury. Then you transfer that to a square container. You then adjust the sides of your square container until the height of the mercury, matches the height of the petri dish, then divide that height by Plank Length and voila the rest is elementary. Yes but how much does it weigh? How .much does a circle weigh? Right. Is there any more veal? After you tell us. Right. Well first you take a glass tube 3 meters tall with an electro-magnet at the top, and you have a spring scale at the bottom, and you evacuate the tube, and place a metal flask inside, switch off the electro-magnet the flask falls, and two lasers are positioned one meter apart, and as it falls it breaks the beam, and then it pushes the spring scale. So then you calculate the rate of acceleration and the pounds of force. Next you fill that flask up with diamonds and rubies and drop it once again, and then empty again, and then fill it with that amount of mercury, and drop it, and subtract the flask weight, and then fill it with diamonds and rubies and pour the mercury over the diamonds and rubies and drop it, and then do this until you are satisfied that you have arrived at the end result. Which is? 27 lbs Sterling. The circle weighs 27 lbs Sterling. Brilliant! Care for some more veal? Yes thank you, quite delicious. I must get the recipe. Then all that remains for you to do is to cut your cucumbers into slices and pack them into petri dishes, and you will be able to determine how many sunbeams are contained in each cucumber. Genius. Pure genius Have some plum pudding You're too kind. Marvelous lunch. Absolutely delightful. === Subject: Re: Eureka! I have squared the circle > First you take a petri dish, and you fill it with mercury. > Then you transfer that to a square container. > You then adjust the sides of your square container until the height of > the mercury, matches the height of the petri dish, then divide that > height by Plank Length and voila the rest is elementary. Yes but how much does it weigh? How .much does a circle weigh? Right. Is there any more veal? > Oh, oh. You've been using too much mercury. It shows because it gets to your upper head. However, to spare you the hazard of more mercury poisoning, I've a similar problem for you of world interest. What's the buoyancy of a floating point? It's assumed the point floats on water where most things float. ---- === Subject: Re: Eureka! I have squared the circle posting-account=Uy-x1gkAAADZQZOsYkACyKA9wdgWU8tq Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > First you take a petri dish, and you fill it with mercury. > Then you transfer that to a square container. > You then adjust the sides of your square container until the height of > the mercury, matches the height of the petri dish, then divide that > height by Plank Length and voila the rest is elementary. Yes but how much does it weigh? How .much does a circle weigh? Right. Is there any more veal? Oh, oh. You've been using too much mercury. > It shows because it gets to your upper head. However, to spare you the hazard of more mercury poisoning, > I've a similar problem for you of world interest. What's the buoyancy of a floating point? > It's assumed the point floats on water where most things float. ---- Actually I couldn't eat another bite. I'm stuffed really. Perhaps another time. Just off the cuff though I would say it is close to tuppence. === Subject: derivative of second order When we learn real function f(x,y) and its partial derivative of second order there is important theorem which states that function is continues iff d^2f/dx dy = d^2f/dy dx. This theorem depends on mean value theorem. Finally it follows from next statement. if f(a)=f(b), then there exist c, aWhen we learn real function f(x,y) and its partial derivative of second >order there is important theorem which states that function is continues iff >d^2f/dx dy = d^2f/dy dx. That theorem couldn't be too important because it isn't true. The cone f(x,y) = sqrt(x^2+y^2) is continuous but isn't even differentiable once at the origin. --Lynn === Subject: Re: derivative of second order I agree with you. this is true even in real case. but still this statement is important. when we speak abot d^2f/dxdy we assume that this derivative exists at the point. this statement is important in many fields of math. for instance in theory of complete differential equations. -- Aleks Kleyn http://www.geocities.com/aleks_kleyn >When we learn real function f(x,y) and its partial derivative of second >order there is important theorem which states that function is continues >iff >d^2f/dx dy = d^2f/dy dx. That theorem couldn't be too important because it isn't true. The cone > f(x,y) = sqrt(x^2+y^2) is continuous but isn't even differentiable > once at the origin. --Lynn === Subject: Re: derivative of second order Top posting corrected. Please don't top post. When we learn real function f(x,y) and its partial derivative of second >order there is important theorem which states that function is continues >iff >d^2f/dx dy = d^2f/dy dx. > That theorem couldn't be too important because it isn't true. The cone > f(x,y) = sqrt(x^2+y^2) is continuous but isn't even differentiable > once at the origin. > --Lynn >I agree with you. this is true even in real case. but still this statement >is important. when we speak abot d^2f/dxdy we assume that this derivative >exists at the point. this statement is important in many fields of math. for >instance in theory of complete differential equations. Aleks Kleyn It still isn't true. There are continuous functions whose second order mixed partials exist but aren't equal. See: http://en.wikipedia.org/wiki/Symmetry_of_second_derivatives#Pathology_is_pos sible for an example. --Lynn === Subject: Re: derivative of second order posting-account=a6woBRAAAADpNFZJBA7ZBx35zXaKmaP4 Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > When we learn real function f(x,y) and its partial derivative of second > order there is important theorem which states that function is continues iff > d^2f/dx dy = d^2f/dy dx. This theorem depends on mean value theorem. Finally > it follows from next statement. if f(a)=f(b), then there exist c, a where f '(c)=0. however this statement is wrong if function f is complex. I > do not tell that for complex function f'(x)=0 does not mean point of > extremum. The question arises. Does exist another proof for complex valued function? > Or this statement is wrong in this case. -- Aleks Kleynhttp://www.geocities.com/aleks_kleyn Your statement of the theorem regarding equality of mixed derivatives in the real variable case is confused. What can be shown is that if second partial derivatives of real function f are continuous in an open set (neighborhood) containing point (a,b), then the mixed partial derivatives at (a,b) are equal: d^2f/dx dy = d^2f/dy dx at (x,y) = (a,b) There is no simple converse, concluding continuity of the partial derivatives in a neighborhood from the equality of the mixed partial derivatives at a point. I'm not sure how you think a proof of the Theorem of Mixed Partial Derivatives would follow from the Mean Value Theorem. After all, the Mean Value Theorem is essentially a 1-D result, while equality of mixed partial derivatives implies the involvement of more than one dimension. If you're interested, a Wordpress blogger has a proof of the equality of mixed partials here: [Simple Proof of Mixed Derivative Theorem] http://nikitanikolaev.wordpress.com/2008/02/05/simple-proof-of-mixed-derivat ive-theorem/ Finally you ask about the status of this result for a function of complex variables. Are you thinking of the mixed partials with regard to the real and imaginary parts of a single complex argument, or with regard to more than one complex argument? === Subject: Re: derivative of second order I will look to the blog that you mentioned. However when I look to textbook I see in each the same proof. For instance A course of Higher mathematics, vol 1, V.L. Smirnov Pergamon Press, 1964 on page 406 he proofs that for continuous function the order of differe ntiation does not affect the result. To proof this theorem Smirnov applies Lagrange formula. on page 149 Smirnov uses Rolle's theorem to prove Lagrange formula. page 147. Rolle's theorem states that if f(a)=f(b), then there exists c, a When we learn real function f(x,y) and its partial derivative of second > order there is important theorem which states that function is continues > iff > d^2f/dx dy = d^2f/dy dx. This theorem depends on mean value theorem. > Finally > it follows from next statement. if f(a)=f(b), then there exist c, a where f '(c)=0. however this statement is wrong if function f is complex. > I > do not tell that for complex function f'(x)=0 does not mean point of > extremum. > The question arises. Does exist another proof for complex valued > function? > Or this statement is wrong in this case. > -- > Aleks Kleynhttp://www.geocities.com/aleks_kleyn Your statement of the theorem regarding equality of mixed > derivatives in the real variable case is confused. What > can be shown is that if second partial derivatives of > real function f are continuous in an open set (neighborhood) > containing point (a,b), then the mixed partial derivatives > at (a,b) are equal: d^2f/dx dy = d^2f/dy dx at (x,y) = (a,b) There is no simple converse, concluding continuity of the > partial derivatives in a neighborhood from the equality > of the mixed partial derivatives at a point. I'm not sure how you think a proof of the Theorem of > Mixed Partial Derivatives would follow from the Mean > Value Theorem. After all, the Mean Value Theorem is > essentially a 1-D result, while equality of mixed partial > derivatives implies the involvement of more than one > dimension. If you're interested, a Wordpress blogger has a proof > of the equality of mixed partials here: [Simple Proof of Mixed Derivative Theorem] > http://nikitanikolaev.wordpress.com/2008/02/05/simple-proof-of-mixed-derivat i ve-theorem/ Finally you ask about the status of this result for a > function of complex variables. Are you thinking of > the mixed partials with regard to the real and imaginary > parts of a single complex argument, or with regard to > more than one complex argument? === Subject: Re: What binary operation lambda quantifier corresponds to? > I think Tegiri Nenashi is on to something here. > I agree. Let {e1 -> e2} be the partial function that does > nothing except mapping e1 to e2. If f1 and f2 are partial > functions with disjoint domains, let f1 /+/ f2 be the union of > the partial functions; i.e. the partial function whose graph is > the union of the graph of f1 and the graph of f2. Then lambda x . e is indeed {e1 -> e[x/e1]} /+/ {e2 -> e[x/e2]} /+/ {e3 -> e[x/e3]} /+/ ... for some enumeration e1, e2, e3, ... of all the closed terms. Does this work for uncountable domains (e.g. R) as well as countable ones? The creation of an enumeration of the domain suggests not, as such an enumeration acts as a bijection between N and the domain. Despite computers being finite devices, it does matter; a function that returns the first item of a list is a perfectly sensible function to write, but has an uncountable domain: the domain is a superset of all infinite lists of booleans, which is isomorphic to R u [0,1). -- Simon Richard Clarkstone: s.r.cl?rkst?n?@dunelm.org.uk / s?m?n_cl?rkst?n?@yahoo.co.uk | My half-daughter went to the GMH riots | | But all I got was this stupid «-shirt. | === Subject: Re: LHC a touchstone for mathematics? posting-account=Uy-x1gkAAADZQZOsYkACyKA9wdgWU8tq Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > In Switzerland right now (today) a most expensive experiment has begun which > is designed to check purely mathematical constructs. Several physicist doubt > that the hypothetical Higgs bosons will be found which would confirm the > standard model of quantum theory. You might argue that mathematics is independent of physics. Heaviside > uttered that mathematics is an empirical science too. Maybe, set theory is > not appropriate in some cases. See the thread Very basic mistakes > 03.09.08. Salviati: > ... in ultima conclusione, gli attributi di eguale > maggiore e minore non aver luogo ne gl'infiniti, > ma solo nelle quantit.88 terminate. > IR>|>IR+>|>IR Tabloid physics! Chicken entrails! Physics by proclamation and decree! is the physics of electromagnets only. BEC experiments have confirmed the quantum foam and they are just jealous. They want it to be proprietary. They want their own ether. Poppycock! === Subject: eigenvector: can you name the theorem posting-account=1vQ5xwoAAADIDQUVBSMlqBb6NsFD508y SV1),gzip(gfe),gzip(gfe) It is known that the eigenvector corresponding to the largest eigenvalue of a positive semidefinite matrix doesnot change sign. Can anyone name the corresponding theorem. === Subject: Re: eigenvector: can you name the theorem > It is known that the eigenvector corresponding to the largest > eigenvalue of a positive semidefinite matrix doesnot change sign. Can > anyone name the corresponding theorem. Do you mean http://en.wikipedia.org/wiki/Perron%E2%80%93Frobenius_theorem? -- Best wishes, J. === Subject: Re: eigenvector: can you name the theorem > It is known that the eigenvector corresponding to the largest > eigenvalue of a positive semidefinite matrix doesnot change sign. Can > anyone name the corresponding theorem. Do you mean http://en.wikipedia.org/wiki/Perron%E2%80%93Frobenius_theorem? > I suspect so, except that this is for matrices with nonnegative entries, not positive semidefinite matrices. On the other hand, the statement for positive semidefinite matrices is not true. -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: index of a subgroup and the index of any one of its conjugates (equality ?) If G is a group, H < G, and g is in G, is it true that [G : H] = [G : gHg'] where g' := g^{-1}. I've tried setting up a map defined on cosets by sending xH ---> x(gHg') but I'm not sure if it's even well defined, etc. === Subject: Re: index of a subgroup and the index of any one of its conjugates (equality ?) I think it's enough to show that [G : H] = [f(G) : f(H)] for any homomorphism f : G -> G, yes? === Subject: Re: index of a subgroup and the index of any one of its conjugates (equality ?) days. My association with the Department is that of an alumnus. You lost the context again, by failing to quote. >I think it's enough to show that [G : H] = [f(G) : f(H)] >for any homomorphism f : G -> G, yes? Well, enough fo what? And in any case, that much is false; it would be true if you had either f one-to-one, or you had ker(f) contained in H, but otherwise, it can fail. Try to come up with an example in which f(H)=f(G), but H is not equal to G. HINT: There is an example with G of order 4. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: Re: index of a subgroup and the index of any one of its conjugates (equality ?) > <14079711.1221440175169.JavaMail.jakarta@nitrogen.math > forum.org>, You lost the context again, by failing to quote. >I think it's enough to show that [G : H] = [f(G) : f(H)] >for any homomorphism f : G -> G, yes? Well, enough for what? To settle the question I posed at the beginning? If the result _were_ true (which I thought it was), then take f to be the automorphism given by conjugation by g.. >And in any case, that much is false; Really? I tried defining a map {left cosets of H in G} --> {left cosets of f(H) in f(G)} via xH --> f(x) f(H) If xH = yH then x'y is in H (where x' := x^{-1}), so f(x'y) is in f(H); equivalently, f(x)' f(y) is in f(H), so that f(x)f(H) = f(y)f(H), hence the map is well-defined. A similar computation shows that it's injective Also, the map is surjective. it would > be true if you had either f one-to-one, or you had > ker(f) contained in > H, but otherwise, it can fail. I would have never known. What's wrong with the above argument, then? I'm afraid I don't see anything wrong with it at this time. === Subject: Re: index of a subgroup and the index of any one of its conjugates (equality ?) days. My association with the Department is that of an alumnus. > <14079711.1221440175169.JavaMail.jakarta@nitrogen.math > forum.org>, > You lost the context again, by failing to quote. >I think it's enough to show that >[G : H] = [f(G) : f(H)] >for any homomorphism f : G -> G, yes? > Well, enough for what? To settle the question I posed at the beginning? And I'm expected to remember which of the many questions you posted this thread is in, or what it is you are replying to? you do not provide enough context through quoting, I cannot know what you are talking about. >And in any case, that much is false; >Really? Yes. The claim that for ANY homomorphism f:G->G and any subgroup H of G you have [G:H] = [f(G):f(H)] is most definitely false. Here is a counterexample: let G = C_2 x C_2, the Klein 4 group. Let H = {(0,0), (1,1)}. Let f:G->G be the map f(a,b) = (0,b). Then [G:H] = 2. But f(G) = f(H) = {(0,0), (0,1)}, so [f(G):f(H)] = 1. >I tried defining a map >{left cosets of H in G} --> {left cosets of f(H) in f(G)} via xH --> f(x) f(H) >If xH = yH then x'y is in H (where x' := x^{-1}), so f(x'y) is in f(H); equivalently, f(x)' f(y) is in f(H), so that f(x)f(H) = f(y)f(H), hence the map is well-defined. A similar computation shows that it's injective Cool. How do you show that it is injective with the specific example I gave above? Note that (1,0)H maps to the same thing as (0,0)H. >it would > be true if you had either f one-to-one, or you had > ker(f) contained in > H, but otherwise, it can fail. >I would have never known. What's wrong with the above argument, then? Your similar computation to show the map is injective must be wrong. But since you did not post it, I cannot tell you why. >I'm afraid I don't see anything wrong with it at this time. I don't either, seeing as how you did not post it. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: Re: index of a subgroup and the index of any one of its conjugates (equality ?) days. My association with the Department is that of an alumnus. > <14079711.1221440175169.JavaMail.jakarta@nitrogen.math > forum.org>, > You lost the context again, by failing to quote. >I think it's enough to show that [G : H] = [f(G) : f(H)] [...] >And in any case, that much is false; >Really? Yes. The claim that for ANY homomorphism f:G->G and any subgroup H of >G you have [G:H] = [f(G):f(H)] is most definitely false. Here is a counterexample: let G = C_2 x C_2, the Klein 4 group. Let H >= {(0,0), (1,1)}. Let f:G->G be the map f(a,b) = (0,b). Then [G:H] = 2. But f(G) = f(H) = {(0,0), (0,1)}, so [f(G):f(H)] = 1. This, by the way, is the smallest counterexample in which the map is not the trivial map. But just taking f to be the trivial map and letting H be any proper subgroup would show you that the statement is definitely incorrect. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: Re: index of a subgroup and the index of any one of its conjugates (equality ?) I appreciate your help. === Subject: Re: index of a subgroup and the index of any one of its conjugates (equality ?) days. My association with the Department is that of an alumnus. I appreciate your help. Again: You are reading the newsgroup through the Math Forum; that means that a simple scrolling with the mouse gives you access to previous posts, giving you context. I, and many others, do not. Usenet was created as a text-based system, not one with graphical interfaces. I do NOT have easy access to previous posts. I use trn, which is a threaded newsreader; I can access previous posts, but only if they are fresh in the server memory (if not, then I need to wait a substantial amount of time while the newsreader goes to retrieve the message before displaying it), and when I do so I can only look at one message at a time, and then I lose sight of the current message. My options are to guess, look up past messages and lose the current one to try to figure out what you might be referring to, or fire up a web browser so I can go look in Google or Math Forum to provide context while I keep my screen tied up with the current message. That is why it is common courtesy and practice to QUOTE relevant parts of previous messages to provide context. Even the Math Forum acknowledges this by providing you with a button that allows you to quote the message you are replying to, so that you can later trim it down and give your response some context. Please try to get into the habit of quoting the message you are replying to and trimming it. The following links give you some pointers and some explanations of how and why to do so. http://oakroadsystems.com/genl/unice.htm#quote http://www.xs4all.nl/%7ewijnands/nnq/nquote.html -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: Re: index of a subgroup and the index of any one of its conjugates (equality ?) <14079711.1221440175169.JavaMail.jakarta@nitrogen.math > forum.org>, > You lost the context again, by failing to quote. >I think it's enough to show that >[G : H] = [f(G) : f(H)] > >for any homomorphism f : G -> G, yes? > Well, enough for what? To settle the question I posed at the beginning? > If the result _were_ true (which I thought it was), then take f to be the automorphism given by > conjugation by g.. >And in any case, that much is false; > Really? I tried defining a map > {left cosets of H in G} --> {left cosets of f(H) in > f(G)} via xH --> f(x) f(H) > If xH = yH then x'y is in H (where x' := x^{-1}), so f(x'y) is in f(H); equivalently, f(x)' f(y) is in f(H), so that f(x)f(H) = f(y)f(H), hence the map is well-defined. A similar computation shows that it's injective Actually, no, that's not quite right, since f(x'y) in f(H) just says that x'y h is in ker(f) for some h in H. I see it now. === Subject: Re: index of a subgroup and the index of any one of its conjugates (equality ?) >If G is a group, H < G, and g is in G, is it true that >[G : H] = [G : gHg'] where g' := g^{-1}. Yes. Conjugation by g is an automorphism of G. >I've tried setting up a map defined on cosets by >sending xH ---> x(gHg') >but I'm not sure if it's even well defined, etc. Then why not try and check if it is? -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: Re: index of a subgroup and the index of any one of its conjugates (equality ?) > <859411.1221436243062.JavaMail.jakarta@nitrogen.mathfo > rum.org>, >If G is a group, H < G, and g is in G, is it true > that >[G : H] = [G : gHg'] where g' := g^{-1}. Yes. Conjugation by g is an automorphism of G. > Moreover, if f is any automorphism of G, then [G : H] = [G : f(H)] ? >I've tried setting up a map defined on cosets by >sending xH ---> x(gHg') >but I'm not sure if it's even well defined, etc. Then why not try and check if it is? -- I already have, with no luck. Any thoughts ? === Subject: Re: index of a subgroup and the index of any one of its conjugates (equality ?) days. My association with the Department is that of an alumnus. > <859411.1221436243062.JavaMail.jakarta@nitrogen.mathfo > rum.org>, >If G is a group, H < G, and g is in G, is it true > that >[G : H] = [G : gHg'] >where g' := g^{-1}. > Yes. Conjugation by g is an automorphism of G. >Moreover, if f is any automorphism of G, then >[G : H] = [G : f(H)] ? Not moreover. Since. Perhaps it will be easier if you show [G:H] = [f(G):f(H)]. >I've tried setting up a map defined on cosets by >sending >xH ---> x(gHg') >but I'm not sure if it's even well defined, etc. > Then why not try and check if it is? >I already have, with no luck. Any thoughts ? Yes: I can't read your mind (at least, not if you are not within line-of-sight; and even then, the government asked me to stop doing it). So it is hard to see why you are having trouble or how to talk you through that trouble if you don't bother to say what the trouble is. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: Re: index of a subgroup and the index of any one of its conjugates (equality ?) days. My association with the Department is that of an alumnus. >Yes: I can't read your mind (at least, not if you are not within >line-of-sight; and even then, the government asked me to stop doing >it). So it is hard to see why you are having trouble or how to talk >you through that trouble if you don't bother to say what the trouble >is. If I'm sounding snarky, it's because the impression I'm getting is that you are putting less and less effort into these problems (which all seem to revolve around the same ideas as the previous ones you've been walked through already), and running to the newsgroup as soon as you encounter any doubts or difficulties, rather than trying to work through them. Whether or not this is actually the case, I do not know (it's possible that you are trying to work through them, you're just not posting the work that has dead-ended or the reasons you are having doubts). But that's been my impression with the latest spat of posts. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: Re: index of a subgroup and the index of any one of its conjugates (equality ?) > <26381417.1221438722879.JavaMail.jakarta@nitrogen.math > forum.org>, >Yes: I can't read your mind (at least, not if you > are not within >line-of-sight; and even then, the government asked > me to stop doing >it). So it is hard to see why you are having trouble > or how to talk >you through that trouble if you don't bother to say > what the trouble >is. If I'm sounding snarky, it's because the impression > I'm getting is > that you are putting less and less effort into these > problems (which > all seem to revolve around the same ideas as the > previous ones you've > been walked through already), and running to the > newsgroup as soon as > you encounter any doubts or difficulties, rather than > trying to work > through them. Whether or not this is actually the > case, I do not know > (it's possible that you are trying to work through > them, you're just > not posting the work that has dead-ended or the > reasons you are having > doubts). But that's been my impression with the > latest spat of posts. I spend some time thinking about these problems, and working out (some, if not most, of) the details myself, before going out of my way to go looking for an expert opinion. I want to point out that what I've brought to the attention of the forum in the past was not at all linked to assignments/problem sets (though I can imagine that there are those that do, and probably rely heavily on this (and/or some other) forum for that purpose; and I'm sure some seasoned mathematicians here are quite aware and wary of this ). I'm no longer a student, but I still get a kick out of thinking about problems in algebra particularly, and discussing them with others. And yes, when there are doubts in my mind, I definitely would like to hear what others knowledgeable in this field have to say about them. Otherwise, if I'm confident enough with my own work, then I just let them alone, and don't bother addressing them to the forum (most of the time: however there are times I feel as though a proofreading, or cursory inspection, by another party may be instructive, and this usually has the advantage of building confidence in proof-writing as well). === Subject: Welcome to . These suggestions may help you. [22] æææThese notes are not official in any way, but if you are new to this group you may find them helpful. 1. æææMessages posted to may be about mathematics at any level. æPlease don't post OT (off-topic) messages about other things. æææBe cautious about cross-posting (posting the same message to more than one news group) - see section 5 below. æææSome questions may do better in a more specialized news group such as , , or . 2. æææYour title should show what sort of mathematics is in your message. æFor example, Differentiating trig functions is a good title, but Help! is a bad title. 3. Include the text of your question in your message, even if you also refer to a Web page for a good diagram. 4. æææType mathematical formulae in the ordinary ASCII characters on your keyboard. Use æ^ æfor powers, for example æaaaa = a^4 . You'll rarely need * for multiplication, but use plenty of brackets/parentheses. æFor example, æ5e^2x æcould mean æ (5e)^(2x) æor æ((5e)^2)x æor æ5(e^2)x æor æ5(e^(2x)). æ Use plenty of spaces. æFor example, ææ2x + 5y = 12 ææis easier to read than ææ2x+5y=12. 5. æææThis news group is open to everybody, and some people have bad manners. æTry to stay polite yourself. æThere are still plenty of users who want to discuss mathematics without rude arguments. æI hope you enjoy being one of them. 6. æææYou may want more information. æææSome good general advice about news groups, cross-posting, not top-posting, etc. is Stan Brown's Playing Nice on Usenet web site . æææFor mathematical news groups there are detailed FAQ at æ æand the older æ . æææIn particular, more details about typing formulae are at æ . æææææ[Capi talEHat]æææKen Pledger. [Suggestions for shortening or clarifying these brief notes are welcome.] === Subject: Re: Welcome to . These suggestions may help you. [22] Directly from your post: [NonBreakingSpace][NonBreakingSpace][NonBreakingSpace]These notes are not official in any way, but if you are new to this group you may find them helpful. Are you aware your spaces appear as accented a'. Here's what the above from your post looks like. aaaThese notes are not official in any way, but if you are new to this group you may find them helpful. It makes for confusing reading. For example When you write Use [NonBreakingSpace]^ [NonBreakingSpace]for powers, for example [NonBreakingSpace]aaaa = a^4 . it's seen like Use a^ afor powers, for example aaaaa = a^4 . As is viewed by the spell checker as Use M- ^ M- for powers, for example M- aaaa = a^4 . What weired software are you using that does that? That can't write a space correctly? Can you get it to write accurately so that special software isn't needed to read its writing. Is there some better software to use instead? === Subject: Re: Welcome to . These suggestions may help you. [22] Directly from your post: These notes are not official in any way, but if you are new to > this group you may find them helpful. Are you aware your spaces appear as accented a'. > Here's what the above from your post looks like. aaaThese notes are not official in any way, but if you are new to > this group you may find them helpful. It makes for confusing reading. For example When you write > Use ^ for powers, for example aaaa = a^4 . it's seen like Use a^ afor powers, for example aaaaa = a^4 . As is viewed by the spell checker as Use M- ^ M- for powers, for example M- aaaa = a^4 . What weired software are you using that does that? That can't write a > space correctly? Can you get it to write accurately so that special > software isn't needed to read its writing. Is there some better software > to use instead? Sigh. William, everything in Ken's posting is displayed correctly on my screen. Instead your postings lack a decent charset: TEXT/PLAIN; I thoroughly suspect that you are addressing some problem with your newsreader and how it codes and decodes charsets. You might check your configuration instead? BTW: My newsreader can handle your postings for correct display despite the fact that your postings do not have the information which charset is used. -- Best wishes, J. === Subject: Arranging a set of vectors as orthogonal as possible? posting-account=WzP9FgoAAAANyEt4wx0YVvhakkQXYd72 SV1),gzip(gfe),gzip(gfe) Hello folks, If one is asked to put n vectors p_1...p_n in R^d such that the maximum absolute value of the cosine between any pair is minimized, what this minimal number is. In other words: z=Min Max |p_i . p_j|/(norm(p_i)*norm(p_j)) Where the . is dot product, Max is over i,j in range 1...n such that i and j are not equal. and Min is over the choice of vectors p_1 ... p_n . Target is to express the value z in terms of n and d. Obviously, when n<=d, we can choose orthogonal vectors and obtain z=0. However, it was too difficult for me to derive what z should be when n>d. If exact expression is not possible, a sharp lower bound will be helpful too. Your guidance would be appreciated. Golabi === Subject: Re: Arranging a set of vectors as orthogonal as possible? posting-account=HR1dqAkAAAA9E7mXiqvduHAelsrIxH3e Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) > Hello folks, If one is asked to put n vectors p_1...p_n in R^d such that the > maximum absolute value of the cosine between any pair is minimized, > what this minimal number is. In other words: z=Min Max |p_i . p_j|/(norm(p_i)*norm(p_j)) Where the . is dot product, Max is over i,j in range 1...n such that i > and j are not equal. > and Min is over the choice of vectors p_1 ... p_n . > Target is to express the value z in terms of n and d. Obviously, when n<=d, we can choose orthogonal vectors and obtain z=0. > However, it was too difficult for me to derive what z should be when > n>d. If exact expression is not possible, a sharp lower bound will be > helpful too. Your guidance would be appreciated. Golabi Your problem is equivalent to placing points on a sphere, keeping them as far apart as possible. In 3-D, the following page has many links: http://www.math.niu.edu/~rusin/known-math/index/spheres.html In higher dimensions there seemed to be some literature, one in JSTOR (which I cannot access) === Subject: Re: Arranging a set of vectors as orthogonal as possible? posting-account=WzP9FgoAAAANyEt4wx0YVvhakkQXYd72 SV1),gzip(gfe),gzip(gfe) > Your problem is equivalent to placing points on a sphere, keeping them > as far apart as possible. æIn 3-D, the following page has many links: Hmmm. not sure. If you want to put 6 farthest points on a sphere where will you put them? I think you will put them at (1,0,0), (-1,0,0), (0,1,0), (0,-1,0), (0,0,1), (0,0,-1). If so, this does not necessarily minimize the quantity we are after because Max |Cos(p i,p j)| = |Cos ( (1,0,0),(-1,0,0))| = |-1| = 1 One might have done better if the points were at (1,0,0) (0,1,0) (0,0,1) (1/sqrt(2),1/sqrt(2),0) (0,1/sqrt(2),1/sqrt(2)) (1/sqrt(2),0,1/ sqrt(2)). Here one would get Max |Cos(p i,p j)| = |Cos ( (1,0,0),(1/sqrt(2),1/sqrt(2),0))| = 1/ sqrt(2) So in the latter case, we obtain a smaller number, while the points are not as farthest as possible! Any idea? Golabi === Subject: Re: LHC no touchstone for mathematics posting-account=Uy-x1gkAAADZQZOsYkACyKA9wdgWU8tq Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) In Switzerland right now (today) a most expensive experiment Very expensive. has begun which > is designed to check purely mathematical constructs. Will it solve the Riemann hypothesis? What if, the Riemann Sphere did not have flat sections of Plank Length, but instead had scalloped semi circle edges, of Plank diameter? The Riemann Golf Ball. === Subject: Re: LHC no touchstone for mathematics . > These bosons aren't really real, not like numbers. Being neither a physicist nor a mathematician, I respect both sides. > then this could confirm that some mathematical guesswork You mean physicist's speculation. Theoretical physicists understand almost nothing but highly sophisticated mathematics. I see set theory, Hilbert space and phase space based on the illusion that it is admissible in any case to assume simultaneously the axiom of extensionality and the axiom of infinity. Let me quote from a letter by v. Neumann directed to Birkhoff, dated Nov. 13, 1935: I would like to make a confession which may seem immoral. I do not believe absolutely in Hilbert-space any more. After all, Hilbert-space ... was obtained by generalizing Euclidean space, footing on the principle of conserving the validity of all formal rules. This is very clear if you consider the axiomatic geometric definition of Hilbert-space where one simply takes Weyl's axiom for a unitary Euclidean space, drops the condition on the existence of a finite linear basis and replaced it by a minimum of topological assumptions (completeness + separability). Do not genuine completeness and actual separability mutually exclude each other? The genuine continuum is complete while only countables are separable. Von Neumann reacted to the EPR paradox. I do not see this a primary physical problem but rather a denied fundamental mathematical one. Salviati: ... in ultima conclusione, gli attributi di eguale maggiore e minore non aver luogo ne gl'infiniti, ma solo nelle quantit.88 terminate. IR>|>IR+>|>IR === Subject: Re: LHC no touchstone for mathematics <48c92b07$0$6661$9b4e6d93@newsspool2.arcor-online.net> posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) > Being neither a physicist nor a mathematician, I respect both sides. Protestations of respect are generally insincere. > then this could confirm that some mathematical guesswork You mean physicist's speculation. Theoretical physicists understand almost nothing but highly sophisticated > mathematics. Go off to sci.physics and tell the physicists that. > I see set theory, Hilbert space and phase space based on the illusion that > it is admissible in any case to assume simultaneously the axiom of > extensionality and the axiom of infinity. Why not? Except you don't like it. > Let me quote from a letter by v. Neumann directed to Birkhoff, Name-dropping again :-( > Do not genuine completeness and actual separability mutually exclude each > other? There are separable complete metric spaces, for instance R, so the answer is no. > Von Neumann reacted to the EPR paradox. I do not see this a primary physical > problem but rather a denied fundamental mathematical one. I, I, I. It's all so personal with you. The EPR paradox is a physical problem. Your desire to see it as a mathematical problem is part of your fascistic political programme of subjugating mathematics to physics. Victor Meldrew I don't believe it! === Subject: Re: LHC no touchstone for mathematics schrieb im Newsbeitrag > I see set theory, Hilbert space and phase space based on the illusion > that > it is admissible in any case to assume simultaneously the axiom of > extensionality and the axiom of infinity. Why not? Except you don't like it. The axiom .9af Archimedes is still correct: The natural numbers do not have a limit. One could also say it is therefore impossible to settle ALL natural numbers. However, if a set has been settled together from single elements according to axiom 1, then it is contradictory to claim according to axiom 7 it has no limit. This contradiction was more directly obvious in Cantor's definition of a set. Fraenkel admitted in 1923 that this definition was untenable because of the well known paradoxes, and one cannot replace it by a corrected version. Clearly, the necessary correction would destroy the illusion on which set theory relies. Hilbert, Zermelo and others replaced the untenable definition by about seven axioms. They expressed hope to have excluded the contradiction. Actually, they merely banned it between the lines. > Let me quote from a letter by v. Neumann directed to Birkhoff, Name-dropping again :-( The names are just helpful if you are interested in the context. I quoted a confession to be read carefully. Why did you not take issue? > Do not genuine completeness and actual separability mutually exclude each > other? There are separable complete metric spaces, for instance R, so the > answer is no. There are complete sets of non-atomistic continua? Really? Set theory claims that without tangible evidence. So far nobody managed to separate the genuine continuum in single points. Zermelo's putative evidence was based on exhaustion of the inexhaustable. Well, it is reasonable to approximate the genuine continuum and irrational numbers by rational ones. Incorporating the irrationals into the body of the rationals as if they were countable might be clever. However the present notion of the reals is based on the old illusion that there is a discrete finite solution to every mathematical problem. I suggest to confess that reals must be unreal in order to include the obviously unreal irrationals on the same level of abstraction. This implies that any rational number gets something quite different when it becomes a real number by embedding into the continuum. In particular, the zero between positive and negative REAL numbers must not be considered something that can be found and taken away. One must no longer distinguish between open and closed intervals in IR. This correction to current tenets resolves several notorious problems including Buridan's donkey and Terhard's criticism. > Von Neumann reacted to the EPR paradox. I do not see this a primary > physical > problem but rather a denied fundamental mathematical one. I, I, I. It's all so personal with you. You are blaming me for names dropping as well. Maybe, in this case I am one of very few who do not hesitate to frankly utter something very unwelcome. > The EPR paradox is a physical > problem. Your desire to see it as a mathematical problem is part of > your fascistic political programme My reasoning has nothing to do with politics. My desire was and still is to logically understand a mathematical problem that is notorious at least since Buridan's donkey and that more recently occurred again as Schroedingers cat. I stumbled on it for the first time when I asked how to deal with zero when splitting IR into IR+ and IR-. I am sorry for finding out that set theory arose from naive obviously illusory intentions and is still unfounded dirty mathematics. Salviati: ... in ultima conclusione, gli attributi di eguale maggiore e minore non aver luogo ne gl'infiniti, ma solo nelle quantit.88 terminate. IR>|>IR+>|>IR === Subject: Re: LHC no touchstone for mathematics <48c998e8$0$6560$9b4e6d93@newsspool4.arcor-online.net> posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) The axiom .9af Archimedes is still correct: Gott in himmel! An umlaut! > One could also say it is therefore impossible to settle ALL natural numbers. settle? > However, if a set has been settled together from single elements according > to axiom 1, > then it is contradictory to claim according to axiom 7 it has no limit. settled? axiom 1? axiom 7? Anyway it's a category mistake to talk of limits of sets: sequences (may) have limits, sets don't. > This contradiction was more directly obvious in Cantor's definition of a > set. What contradiction? > Do not genuine completeness and actual separability mutually exclude each > other? There are separable complete metric spaces, for instance R, so the > answer is no. There are complete sets of non-atomistic continua? Really? I have no idea what non-atomistic continua are (maybe a translation of some cranky German term?). But separability and completeness of metric spaces are defined in texts on topology, and R has both these properties. You might care to learn some elementary topology before bandying around its terms carelessly. > Set theory claims that without tangible evidence. One can prove R is a complete metric space. > So far nobody managed to separate the genuine continuum in single points. What is the genuine continuum? Something that only Bumscheisse has access to. > irrational numbers by rational ones. Incorporating the irrationals > into the body of the rationals as if they were countable might be clever. Has anyone any idea what incorporating the irrationals into the body of the rationals could possibly mean?. The set of irrational numbers (being uncountable) cannot be mapped injectively into Q (which is countable). > I suggest to confess that reals must be unreal I, I, I again. > In particular, the zero between positive and negative REAL ænumbers > must not be considered something that can be found and taken away. If you take away zero (which you can) from any real number x you get x back again. (Is Bumscheisse really suggesting you can't do subtraction any more). > One must no longer distinguish between open and closed intervals in IR. What is IR? Is it a your peculiar notation for R, or something else? There are distinctions between open and closed intervals in R, for instance the closed interval [0,1] has 0 as an element and is a compact space, while the open interval (0,1) does not have 0 as an element is is noncompact. > Von Neumann reacted to the EPR paradox. I do not see this a primary > physical > problem but rather a denied fundamental mathematical one. I, I, I. It's all so personal with you. You are blaming me for names dropping as well. Clearly apprising your readers of the mathematical (as opposed to physical) nature of the EPR problem is too much of a challenge for you. > one of very few who do not hesitate to frankly utter something very > unwelcome. Yes, you and your fascistic ignorant anti-mathematical rants are unwelcome in sci.math. Your interest is in physics not mathematics, so go off and post in physics newsgroups. > I stumbled on it for the first time when I asked how to deal with zero when > splitting IR into IR+ and IR-. Again, what are IR, IR+ and IR- (a new one?)? > I am sorry for finding out that set theory arose from naive obviously > illusory intentions > and is still unfounded dirty mathematics. Your pathological obsession with hygiene is reminiscent of racist rhetoric. Victor Meldrew I don't believe it! === Subject: Re: LHC no touchstone for mathematics > One could also say it is therefore impossible to settle ALL natural > numbers. settle? < Counting is a process. Each step of counting ends with settling a new number. < Therefore it is impossible to quantify ALL numbers. > However, if a set has been settled together from single elements according > to axiom 1, > then it is contradictory to claim according to axiom 7 it has no limit. settled? axiom 1? axiom 7? Anyway it's a category mistake to talk of limits of sets: sequences (may) have limits, sets don't. < Well, I used limit not in the special mathematical sense but rather like < limitation. Does set theory understand a set an endless process? > This contradiction was more directly obvious in Cantor's definition of a > set. What contradiction? < Cantor claimed that an (infinite) set consists of single elements. < If it consists of unfinitely much of elements, then these elements cannot be separated from each other. < Imagine a postman who looks at an infinite postcode. Genuine continuity contradicts separability. > Do not genuine completeness and actual separability mutually exclude > each > other? There are separable complete metric spaces, for instance R, so the > answer is no. There are complete sets of non-atomistic continua? Really? I have no idea what non-atomistic continua are (maybe a translation of some cranky German term?). < No. Weyl used the term atomistic. But separability and completeness of metric spaces are defined in texts on topology, and R has both these properties. < I know the text you are believing in. > Set theory claims that without tangible evidence. One can prove R is a complete metric space. < Such proof is circular. > So far nobody managed to separate the genuine continuum in single points. What is the genuine continuum? Something that only Bumscheisse has access to. irrational numbers by rational ones. Incorporating the irrationals > into the body of the rationals as if they were countable might be clever. > In particular, the zero between positive and negative REAL numbers > must not be considered something that can be found and taken away. > One must no longer distinguish between open and closed intervals in IR. > I stumbled on it for the first time when I asked how to deal with zero > when > splitting IR into IR+ and IR-. > I am sorry for finding out that set theory arose from naive obviously > illusory intentions and is still unfounded dirty mathematics. === Subject: Re: LHC no touchstone for mathematics <48ca52cd$0$6554$9b4e6d93@newsspool4.arcor-online.net> posting-account=IBUqVwoAAADepmzxVr9iEYD5Z0A483SY Gecko/20070530 Fedora/1.5.0.12-1.fc5 Firefox/1.5.0.12,gzip(gfe),gzip(gfe) > < Counting is a process. Each step of counting ends with settling a new > number. What do you mean by settle? It's not a mathematical term. < Well, I used limit not in the special mathematical sense but rather like As ever, you use terms with your own private meanings. If you can't discuss mathematics then you should go elsewhere. > < limitation. Does set theory understand a set an endless process? Set theory understands sets as sets. > < Cantor claimed that an (infinite) set consists of single elements. > < If it consists of unfinitely much of elements, then these elements cannot Is unfinite the same as infinite? > be separated from each other. Again, you are using separated in your own private sense. > < Imagine a postman who looks at an infinite postcode. Genuine continuity > contradicts separability. Hmmm. Now we have genuine continuity. I don't suppose you'll tell us what that is either, Herr Bumschien. > I have no idea what non-atomistic continua are (maybe a translation > of some cranky German term?). < No. Weyl used the term atomistic. He was a good cranky German :-) > One can prove R is a complete metric space. < Such proof is circular. Such a proof is a proof. Now, how about you substantiating your assertions for once. Demonstrate that the proofs of the completeness of R do not in fact follow from the axioms of set theory, > So far nobody managed to separate the genuine continuum in single points. What is the genuine continuum? Something that only Bumscheisse > has access to. < If it consists of unfinitely much of elements, then these elements > cannot Is unfinite the same as infinite? I apologise for my typo. > < No. Weyl used the term atomistic. He was a good cranky German :-) Weyl was the successor of Hilbert in Goettingen until he emigrated. > One can prove R is a complete metric space. > < Such proof is circular. Such a proof is a proof. Now, how about you substantiating > your assertions for once. Demonstrate that the proofs of > the completeness of R do not in fact follow from the axioms > of set theory, One must not justify set theory by taking it for granted. Salviati. === Subject: [OT] Gnuplot in Action Book - Free Content available posting-account=t3u1yQoAAADIRpoUd0KrdrSw4Th05vax Gecko/20061023 SUSE/2.0-30 Firefox/2.0,gzip(gfe),gzip(gfe) If you are interested in data analysis and visualization, you might be interested in the upcoming book: Gnuplot in Action The manuscript is now complete, and an excerpt from the first chapter, introducing Gnuplot and its use for Graphical Analysis, is available for free as Green Paper from the publisher's site: www.manning.com/janert This is also the LAST opportunity to make comments or give suggestions and feedback on the manuscript before it goes into print. You can email me (the author) directly, or post comments on the publishers Forum page. The book is available for pre-order from the publisher's site, and of course at Amazon (as well as other sellers): www.amazon.com/dp/1933988398 Feel free to forward this information as appropriate. Best, Ph. === Subject: Truncation of series, how big is the error? posting-account=lINYxAoAAAAD3t3xmIe5HCpF3AFxHesa Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) G'day, We define f(n) = 1/n^2, S(k) = f(1) + f(2) + ... + f(k), T(k + 1) = f(k + 1) + f(k + 2) + ... (where the ... indicates that we sum for k up to infinity), and S = lim S(k) for k-> oo. We know that S is pi^2/6. But I am wondering about the following question: Let us pretend that we don't know the exact value of S. We can write S = S(x) + T(x + 1). How big is the error if we estimate S by S(x)? In other words: how big is the error if we truncate S at x? I think that T(x + 1) = 1/(x + 1)^2 + 1/(x + 2)^2 + 1/(x + 3)^2 + ... If T(x + 1) was a FINITE sum, we can simply write using the Big-Oh notation that T(x + 1) = 1/(x + 1)^2 + O(1/(x + 2)^2) because every term after 1/(x + 2)^2 can be absorbed into O(1/(x + 2)^2). BUT T(x + 1) is an infinite sum, THUS: are we still allowed to argue that every term after 1/(x + 2)^2 is absorbed into O(1/(x + 2)^2)??? Elaine === Subject: Re: Truncation of series, how big is the error? posting-account=K5WE3woAAAAXArsybjkbN6LjMxWdHtbX Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > G'day, We define f(n) = 1/n^2, S(k) = f(1) + f(2) + ... + f(k), T(k + 1) = f(k + 1) + f(k + 2) + ... (where the ... indicates > that we sum for k up to infinity), and S = lim S(k) for k-> oo. We know that S is pi^2/6. But I am wondering about the following question: Let us pretend that we don't know the exact value of S. We can write S = S(x) + T(x + 1). How big is the error if we estimate S by S(x)? > In other words: how big is the error if we truncate S at x? I think that > T(x + 1) = 1/(x + 1)^2 + 1/(x + 2)^2 + 1/(x + 3)^2 + ... If T(x + 1) was a FINITE sum, we can simply write using > the Big-Oh notation that T(x + 1) = 1/(x + 1)^2 + O(1/(x + 2)^2) because every term after 1/(x + 2)^2 can be absorbed into O(1/(x + > 2)^2). BUT T(x + 1) is an infinite sum, THUS: are we still allowed to argue > that > every term after 1/(x + 2)^2 is absorbed into O(1/(x + 2)^2)??? Elaine We have f(k+1) <= integral(1/x^2,x=k..k+1), f(k+2) <= integral(1/ x^2,x=k+1..k+2), etc., so T(k+1) <= integral(1/x^2, x=k..infinity) = 1/ k. By a similar argument we get T(k+1) >= 1/(k+1). R.G. Vickson === Subject: Re: Truncation of series, how big is the error? posting-account=lINYxAoAAAAD3t3xmIe5HCpF3AFxHesa Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > We have f(k+1) <= integral(1/x^2,x=k..k+1), f(k+2) <= integral(1/ > x^2,x=k+1..k+2), etc., so T(k+1) <= integral(1/x^2, x=k..infinity) = 1/ > k. By a similar argument we get T(k+1) >= 1/(k+1). R.G. Vickson === Subject: Re: Truncation of series, how big is the error? posting-account=lINYxAoAAAAD3t3xmIe5HCpF3AFxHesa Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) We have f(k+1) <= integral(1/x^2,x=k..k+1), f(k+2) <= integral(1/ > x^2,x=k+1..k+2), etc., so T(k+1) <= integral(1/x^2, x=k..infinity) = 1/ > k. By a similar argument we get T(k+1) >= 1/(k+1). R.G. Vickson > After some thought... Let us replace the sum T(x + 1) = f(x + 1) + f(x + 2) + ... with the integral of f(t) over x + 1 up to infinity. How big is the error when we replace the sum with the integral? === Subject: Re: Truncation of series, how big is the error? posting-account=lINYxAoAAAAD3t3xmIe5HCpF3AFxHesa Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > We have f(k+1) <= integral(1/x^2,x=k..k+1), f(k+2) <= integral(1/ > x^2,x=k+1..k+2), etc., so T(k+1) <= integral(1/x^2, x=k..infinity) = 1/ > k. By a similar argument we get T(k+1) >= 1/(k+1). > R.G. Vickson > After some thought... Let us replace the sum T(x + 1) = f(x + 1) + f(x + 2) + ... > with the integral of f(t) over x + 1 up to infinity. How big is the error when we replace the sum with the integral? Maybe the question is too easy? If you think so, just give me a hint then. Once again, here is the question: Let us replace the sum T(x + 1) = f(x + 1) + f(x + 2) + ... with the integral of f(t) over x + 1 up to infinity where f(t) = 1/t^2. How big is the error when we replace the sum with the integral? === Subject: Grobnerbasis y0 = b + a*x0 + 2*x0^2, y1 = b + a*x1 + 2*x1^2, b + a*x0 + 2*x0^2 - x0*(a + 4*x0) = 0, b + a*x1 + 2*x1^2 - x1*(a + 4*x1) = 0, (a + 4*x0)*(a + 4*x1) = -1, ------------------------------------------- Eliminate {x0, x1, y0, y1}; === Subject: Re: Grobnerbasis posting-account=06BQLAoAAADoC7Y4z9FWcUwGvMa7xMG9 7.4),gzip(gfe),gzip(gfe) > y0 = b + a*x0 + 2*x0^2, > y1 = b + a*x1 + 2*x1^2, > b + a*x0 + 2*x0^2 - x0*(a + 4*x0) = 0, > b + a*x1 + 2*x1^2 - x1*(a + 4*x1) = 0, > (a + 4*x0)*(a + 4*x1) = -1, > ------------------------------------------- > Eliminate {x0, x1, y0, y1}; Bonjour, are there known rules of existence and methods to build implicit or explicit solutions? Alain === Subject: ? estimate matrix components posting-account=H-IscAoAAABkDNrURGSxo9jPN3MJ3a8A 1.0.3705; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) Hi: If our system is A*x = b, then by applying enough number of independent inputs and taking measurements of the associated outputs, we can estimate each component of A. But what if our system is dx/dt = A*x or dx/dt = A*x+B*u? How do we estimate each component of A and B? === Subject: Re: Eureka! I have squared the circle - Move over Cantor <042dnbAVfe34MFDVnZ2dnUVZ_rTinZ2d@giganews.com> posting-account=Uy-x1gkAAADZQZOsYkACyKA9wdgWU8tq Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) http://en.wikipedia.org/wiki/Georg_Cantor Ok, so. for a little more plum pudding, I will tell you how to arrive at a value of pi, that does not have an infinity of significant digits. First, you create a circle with a sine wave circumference, then you create a diameter line, as a sine wave, and you choose to make the total length of your sine wave, that which results in pi with a value which is a rational number. === Subject: Field Equations for the Higg's Field <042dnbAVfe34MFDVnZ2dnUVZ_rTinZ2d@giganews.com> posting-account=Uy-x1gkAAADZQZOsYkACyKA9wdgWU8tq Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > First, you create a circle with a sine wave circumference, then you > create a diameter line, as a sine wave, and you choose to make the > total length of your sine wave, that which results in pi with a value > which is a rational number. Thats a reasonable Higg's field. You can do the math. Its difficult enough that it will make your head hurt a little bit, but only a little bit. You can simplify it with an analogy, and that is if you have two strings, and one you turn into the circumference of a circle, and you have a series of sine waves in that circumference, like a wave function. Then you take a second string and you make a diameter sine wave series. What you end up with is a type of pi value where the diameter sine wave is proportional to the circumference sine wave. Directly proportional. Within that field is the Higg's Boson. circumference, and the direction of force, is along the diameter wave. It makes no sense at all but that is really what you want.. You want it to be crazy, but not too crazy, and you want it to be such that it will takes years of study, to interpret the results. And well that is the reality, because inside that field, is the quantum foam, but the energy is located in the field, and the Just remember that when it comes to mass, it is kinetic energy. And well I don't feel like working out all the parameters for you when you have several thousand physicists who can do that and write papers on it. === Subject: Re: Field Equations for the Higg's Field <042dnbAVfe34MFDVnZ2dnUVZ_rTinZ2d@giganews.com> posting-account=Uy-x1gkAAADZQZOsYkACyKA9wdgWU8tq Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > First, you create a circle with a sine wave circumference, then you > create a diameter line, as a sine wave, and you choose to make the > total length of your sine wave, that which results in pi with a value > which is a rational number. Thats a reasonable Higg's field. You can do the math. Its difficult > enough that it will make your head hurt a little bit, but only a > little bit. > You can simplify it with an analogy, and that is if you have two > strings, and one you turn into the circumference of a circle, and you > have a series of sine waves in that circumference, like a wave > function. > Then you take a second string and you make a diameter sine wave > series. > What you end up with is a type of pi value where the diameter sine > wave is proportional to the circumference sine wave. > Directly proportional. Within that field is the Higg's Boson. circumference, and the direction of force, is along the diameter wave. It makes no sense at all but that is really what you want.. You want > it to be crazy, but not too crazy, and you want it to be such that it > will takes years of study, to interpret the results. And well that is the reality, because inside that field, is the > quantum foam, but the energy is located in the field, and the Just remember that when it comes to mass, it is kinetic energy. > And well I don't feel like working out all the parameters for you when > you have several thousand physicists who can do that and write papers > on it. You see the Higg's Boson, is like the photon, that arises out of that field. When you detect it as background radiation, then it is a transverse wave that is a sine wave. But you see there is more in that field than the Higg's Boson. Unless you want the Higg's Boson to also describe the Newtonian force. You see real world mass results in a Newtonian force. And that force is directional on the diameter sine wave series. There may also be a type of friction, that occurs, on the circumference, its too soon to tell. But the circumference, can expand and contract, and when it does, the diameter expands and contracts, but the values are still proportional. And it has to be proportional and so you want a rational number as your type of pi relational number. Gravity is inversely proportional, and you have to also realize that this field is expanding in space-time as the universe is expanding. But it is in a closed universe, so the larger part of expansion, is not that important. But if you stretch the transverse sine wave it will red shift. The circumference is a wave function, so you can even avoid discussions right away about expansion. You see dark matter, has mass, and in that field is a bubble, a quantum foam bubble and it has mass. In the field around it, is dark energy. Now dark energy itself has no mass, like a photon has no mass. But just like a wave can borrow energy from the water, to splash against the dock with force, the Higg's can borrow mass from the quantum foam. However, the real mass is inside the bubble which is expanding. So if you consider along the diameter sine wave series, it is directional, and if it is moving laterally, it is also moving outward in that same direction. And outward also in all directions. And that gives rise to gravity. === Subject: Re: Field Equations for the Higg's Field <042dnbAVfe34MFDVnZ2dnUVZ_rTinZ2d@giganews.com> posting-account=Uy-x1gkAAADZQZOsYkACyKA9wdgWU8tq Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > Gravity is inversely proportional, and you have to also realize that > this field is expanding in space-time as the universe is expanding. But it is in a closed universe, so the larger part of expansion, is > not that important. > But if you stretch the transverse sine wave it will red shift. The circumference is a wave function, so you can even avoid > discussions right away about expansion. You see dark matter, has mass, and in that field is a bubble, a > quantum foam bubble and it has mass. > In the field around it, is dark energy. Now dark energy itself has no mass, like a photon has no mass. But > just like a wave can borrow energy from the water, to splash against > the dock with force, the Higg's can borrow mass from the quantum foam. > However, the real mass is inside the bubble which is expanding. So if you consider along the diameter sine wave series, it is > directional, and if it is moving laterally, it is also moving outward > in that same direction. > And outward also in all directions. And that gives rise to gravity. So if you wanted to say, that the Higg's Boson, is the transverse and the graviton, is the sine wave packet, on the diameter sine wave series, then that would be ok, but if, you extend that sine wave beyond the diameter, well don't make the mistake of thinking that the gravitational force is a magnetic force, because it isn't. Mass is not magnetic by definition, it is like kinetic energy, f=ma type of force is applied to alter its course. Its a direct force. And mass and gravity are the same type of animal. So you need to confine the graviton to the quantum foam bubble. There is no mass, at all, that is outside of that bubble. The skin on that bubble applies Newtonian force. There is no intrinsic mass of any kind outside that bubble. No matter what you have been led to believe, those are mistaken observations, Einstein proved that Newton's universal gravitation, and spooky action at a distance was wrong. In order to preserve Newton, physics, you need to realize that it is equivalent to f=ma, then Einstein needs the graviton, but he also needs the red shift and the expansion, which gives rise to the Newtonian force. The cosmology, needs the red shift, and it needs the dark matter and dark energy. String theory needs the sine wave string filaments. Quantum theory needs the wave packets and the fact that the quantum foam bubble, is Plank Length in diameter. So it can get bigger but when it gets smaller, it can no longer be detected. So the diameter sine wave series at rest, is Plank Length. In free space between galaxies, it should be Plank Length. What does this tell us about the early universe? Well I don't know. That depends on what the examination of all these parameters tell us. Personally I don't believe in the big bang, I think that the quantum foam is the result of continuous creation because nature abhors a vacuum and that the foam is in a superconducting superfluid the properties of which remain unknown. Maybe the LHC can answer that question or questions. But there are at present numerous experiments under way besides the LHC which are examining the quantum foam. === Subject: Re: Field Equations for the Higg's Field <042dnbAVfe34MFDVnZ2dnUVZ_rTinZ2d@giganews.com> posting-account=Uy-x1gkAAADZQZOsYkACyKA9wdgWU8tq Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) Personally I don't believe in the big bang, I think that the quantum > foam is the result of continuous creation because nature abhors a > vacuum and that the foam is in a superconducting superfluid the > properties of which remain unknown. Maybe the LHC can answer that question or questions. > But there are at present numerous experiments under way besides the > LHC which are examining the quantum foam. These are the Glengarry leads, of the quantum world. Trying to make everything fit, into field equations, that give everyone a chance at those leads, is no easy proposition. Fortunately we are close enough to understanding the way in which it works, so that it is the natural progression of things. To try and start from scratch, and create something is maybe possible, but personally I can't envision what it might look like. This satisfies, relativity, both GR and Sr, quantum mechanics, cosmology. And you can't expect people to relearn physics, at this point, so if someone wants to invent a supersymetry theory or if you want to expand on string theory, then it has to be a separate thing. Which is ok, and people may or may not use it and study it, but the standard model, as cluttered as it is, contains a lot of information, like a library, and be, nor their own personal domain. They merely occupy one small corner, of an ever expanding model of the workings of the universe in which we live. === Subject: Re: Field Equations for the Higg's Field <042dnbAVfe34MFDVnZ2dnUVZ_rTinZ2d@giganews.com> posting-account=Uy-x1gkAAADZQZOsYkACyKA9wdgWU8tq Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) So does it describe everything? Not yet and not by a long shot. But it doesn't stand in the way of things we know that might exist. For instance electro-gravitics, and rotating superconductors and negation of mass. There may be some type of friction between quantum foam bubbles,and maybe using em waves you can disrupt that process. Then the foam will flow around you as it does in uniform motion, which it doesn't normally do in accelerated motion. There are a lot of hypotheticals, such as can you squish a bubble flat in a supernova? It looks like you can. You can move the foam out of the way and create a wormhole, does it go anywhere? Does the wormhole lead anywhere unless you make a tunnel? A black hole is where the foam is bunched up and has so much mass it can't expand, and gets left behind in time. A plastic sphere is the event horizon. The nucleus is obviously made of quantum foam. That gives a nucleus mass. But is it in discreet bundles or just one large bubble? Inside the nucleus, if you look at it as a spherical wave process, it is easy to understand. It is easy to see where the nuclear force comes from. The graviton is in there and it plays a much larger part than people recognize inside the atomic nucleus. Anyways I won't try to fill in all the gaps because there is lots of experimentation to be done. At least people have an idea what it might look like and the direction it needs to take, in order to not contravene other processes which we know to exist. Some people are talking about having to revamp GR because the speed of light is not constant on cosmic scales. Well don't rush into things when you don't understand the process. For one thing the speed of light is just a number, that is given, as part of a relational process. It has been exceeded in the laboratory. And you can slow it down in a medium. GR is not dependent on it being a constant value. Consider that the red shift, is a long wavelength. Is light going to slow down, over a period of millions of light years? Well you would expect that as the universe expands, it is going to lose some energy. I think that when we say that radio waves travel outward at c to infinity, that is just a lazy way of saying things. The Higg's field is not vacant space. And waves in that field, will transfer some momentum to the quantum foam. Even in a superconducting superfluid, there is still the foam, and it has friction, and the expansion of the universe will dilute that original wave energy. What is surprising, is that light can get here from the deep field at all. === Subject: Re: Field Equations for the Higg's Field <042dnbAVfe34MFDVnZ2dnUVZ_rTinZ2d@giganews.com> posting-account=Uy-x1gkAAADZQZOsYkACyKA9wdgWU8tq Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) I wouldn't expect people to try and apply the same type of field equations as GR, for the Higg's field. http://en.wikipedia.org/wiki/Einstein_field_equations Rather than modify, GR, because it is too complex to be useful, you can simplify it with similar postulates providing you are willing to show that they are possible and can be verified experimentally. You have to understand that the Einstein field equations, are designed to hide the expansion of matter into n dimensional space, because that notion was seen as perhaps too unsettling, and it of course is the basis of the largest explosions known to man, and those associated processes. Essentially expansion of the universe is the driving force in the universe, and if you try to stop the universe from expanding in a local region, by lets say the implosion of a star core, it will supernova. Now that takes a great deal of energy towards the center of a mass, to compress it, to the degree that it resists expansion, to the degree that a great deal of energy builds up, and then is released into space in explosions, the size of which boggle the mind. 100 million light years across as a for instance. How does something explode with that much force? Well the expansion of the universe is the pressure of the universe. And it is almost uniform as the background radiation shows. So rather than alter the equations, you can merely create new ones, that are easier to use. Anyways the Higg's field equations, needn't be that complex. We can look at the wave function of the electron... http://en.wikipedia.org/wiki/Image:Hydrogen_Density_Plots.png and see low and behold, that what we are talking about is very similar in nature, and that is not surprising, because the principle just happens to be the same. Outside that quantum foam bubble is dark energy. The bubble is dark matter. The matter bubble is expanding, and that gives it mass, but the energy in the field, is in the form still, of em type radiation only as heat, phonons, vibrational energy that gives it a type of jittery quality. GR is not widely used because it is just too complex, Einstein is not here now to sit beside anyone and say what he meant by a specific term. look like. And of course there are much simpler ways of describing it, G=ec is one of those ways. And you see a lot of different derivatives that basically just say, the nucleus is expanding into n dimensional space, hyperspace, and it is sending a wave of energy out from its radius, that travels at c, and crests at the electron radius. So the quantum foam is a pressurized system, just like you can look at the covalent bond, as a pressure system, where high and low wave it much easier to understand and predict. === Subject: Re: Field Equations for the Higg's Field <042dnbAVfe34MFDVnZ2dnUVZ_rTinZ2d@giganews.com> posting-account=Uy-x1gkAAADZQZOsYkACyKA9wdgWU8tq Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > So the quantum foam is a pressurized system, just like you can look at > the covalent bond, as a pressure system, where high and low wave > it much easier to understand and predict. But to visualize the Higg's field, it does not look like the wave function that I just showed you, what it looks like is bizarre. Almost alien. Imagine looking at foam, and removing the bubbles so all you have is the superfluid between them. Its like a honeycomb, but not that regular. A weird alien looking honeycomb that energizes, and flows out into a region of space. Minute honeycombs in size. If you were too look at a region you can imagine it being affected as energy enters that region and it having shades of color, to represent the different levels of energy, and that color spreading through this alien looking honeycomb, as a high energy photon come flying through. As a transverse wave enters this region, it lights up with vibrational energy spreading out. And the whole region will vibrate because this is very small scale stuff and the foam inside that honeycomb will vibrate and continue to do so. Then you have regular spherical waves like the shape, of magnetism, flowing out from each bubble. (As the universe expands, each bubble has mass which resists expansion just a bit) and that gives rise to dark energy. But if you compress those bubbles, that process will gain energy and they will vibrate faster and stronger in and out. Sending stronger waves, Hawking radiation as a for instance. Imagine this honeycomb vibrating along and pulsing along and flowing along, and in comes a cosmic ray, well it might go through so quickly that it hardly effects the region, but it might also light up the region substantially depending on the wave length and amount of energy. On top of that, as the entire thing flows along, as in frame dragging, you can get huge wavefronts rolling through. Affecting the entire region of space, but rolling waves do not affect the small vibrational energy, and yet can affect a planet, or a moon. And depending on the ambient pressure, according the GR field equations, that is how much space is curved. Closer in to a massive body, then the bubbles are closer together, and so more foam is packed into those regions. So space itself is compressed, and as you move farther away the pressure reduces. Like a planet with plastic spheres around it, and each sphere is a little farther away from the one closer in to the planet. (Simplified.) And it gets more complicated, since that is a gravity well, and that gravity well of a planet, is inside a gravity well of a star, and that inside the gravity well of a galaxy. And has a moon going around it or several, and each have their own gravity wells. Between galaxies, what you have since gravity is not a universally attractive force, galaxies are not in large solar systems, they flow in rivers, and so the dominant force between galaxies, believe it or not, is simply em wave radiation and dark energy phonon energy pushing them around. And the reason they can move is they are in a superfluid, and it does not have much resistance. Until you get to high rates of acceleration. It doesn't hinder relative motion or uniform motion hardly at all. So they flow in huge rivers of quantum foam, that gets churning by the expansion of the universe. === Subject: Re: Field Equations for the Higg's Field posting-account=Uy-x1gkAAADZQZOsYkACyKA9wdgWU8tq Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) With GR, you can simplify it, the smaller the reference frame you are applying it to. On the scale of an atom, one angstrom, you can say it is roughly G=ec Then get a little farther out and it begins to look like... http://archive.ncsa.uiuc.edu/Cyberia/NumRel/Images/ein.field.gif getting farther out, you are now considering the earths gravity well, sitting in the sun's gravity well, and you have the moon's gravity well, and you have stars in our neighborhood that have gravity wells so our solar neighborhood in the galaxy, is in a deformed space, and so then you see how all these manifolds are now flowing into strange shapes. People have a hobby of crocheting these manifolds. http://www.toroidalsnark.net/mkexh2005/mkexh2005-Images/18.jpg So anyways there are two ways of handling the Higg's field. And you can go that route, if you want to. But what would be the point, when people will not use it? You see because quantum theory already has it pegged, as the quantum foam, has very simple ways of handling it, and can see the phonon energy flowing, under a scanning tunneling microscope in BEC experiments. I mean if you just want to play with these types of field equations, well then GR needs you to simplify it, and teach it to cosmologists, who still do not truly understand it. And SR and how the two are related. http://www.sciencedaily.com/releases/2001/02/010212075309.htm You see because gravity and accelerated mass are almost the same thing, and these show up as kinetic energy and phonon energy, on a minute scale, why consider things falling into a well? It makes more sense to think of things being affected by force. But not an em type of force, but momentum and kinetic energy. Not charge, but actual directed force by wave fronts and even direct contact between bubbles. As an example... http://www.weizmann.ac.il/home/davidson/tomography.pdf and then you have dark energy which is just black body radiation, low level transverse waves. Magnetism is also present in very minute amounts in the Higg's field. As the level of energy becomes detectable. Dirac wasn't completely wrong, but he did go completely overboard. The Casimir Effect is in that region of the Higg's Field... http://en.wikipedia.org/wiki/Casimir_Effect === Subject: Re: Field Equations for the Higg's Field posting-account=Uy-x1gkAAADZQZOsYkACyKA9wdgWU8tq Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) http://en.wikipedia.org/wiki/Riemann_surfaces You see a Riemann surface is a very simple concept, but it doesn't apply on the quantum level because things are not smooth there. It is jittery vibrating and honeycombed. A Riemann golf ball, not a Riemann Sphere. So that is why it is so easy to say, well on the radius of the quantum bubble is a wave function that looks like a sine wave that goes around the circumference. And then the diameter, is another sine wave, the length of which is directly proportional to the length of the circumference. The height of the wave, will depend on the size and shape of the bubble under different circumstances. So if we say that the relationship is pi, well thats not correct, because we know that there are quanta, and they are discreet bundles of energy. And so the relationship has to be such that the pi type of value that you will create for this graviton, has to be a rational number. And I can tell you that it is, due to expansion, of that bubble, that is not continuous, but in jumps. And so it jumps a bit bigger and that new size, is now directly proportional to its past. Although that jump, is happening in n dimensional space. So that across the universe it is all expanding along, in little jumps, and each jump, sends out a wave of background energy as dark energy, and when those spherical waves collide, they send out a little transverse em wave, which shows up as radiation, in its various forms. And so then where Newton's theory comes from, is the fact that it is directly proportional to its past state. And so to preserve all that in accordance with what experiment tells us the real world is like, we have to preserve that relationship, between the diameter and the circumference, and we adjust the length of both, because they are sine waves and you can adjust the height of the wave, to adjust the length of the diameter and length of the circumference. And then you will find out, that they are in sets. Not continuous again, because the table of elements are in a set. And the frequencies of those elements are in a set. === Subject: Re: Field Equations for the Higg's Field posting-account=Uy-x1gkAAADZQZOsYkACyKA9wdgWU8tq Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > http://en.wikipedia.org/wiki/Riemann_surfaces > You see a Riemann surface is a very simple concept, but it doesn't > apply on the quantum level because things are not smooth there. It is > jittery vibrating and honeycombed. A Riemann golf ball, not a Riemann Sphere. So that is why it is so easy to say, well on the radius of the quantum > bubble is a wave function that looks like a sine wave that goes around > the circumference. And then the diameter, is another sine wave, the > length of which is directly proportional to the length of the > circumference. The height of the wave, will depend on the size and > shape of the bubble under different circumstances. > So if we say that the relationship is pi, well thats not correct, > because we know that there are quanta, and they are discreet bundles > of energy. > And so the relationship has to be such that the pi type of value that > you will create for this graviton, has to be a rational number. And I can tell you that it is, due to expansion, of that bubble, that > is not continuous, but in jumps. > And so it jumps a bit bigger and that new size, is now directly > proportional to its past. Although that jump, is happening in n dimensional space. So that > across the universe it is all expanding along, in little jumps, and > each jump, sends out a wave of background energy as dark energy, and > when those spherical waves collide, they send out a little transverse > em wave, which shows up as radiation, in its various forms. And so then where Newton's theory comes from, is the fact that it is > directly proportional to its past state. And so to preserve all that in accordance with what experiment tells > us the real world is like, we have to preserve that relationship, > between the diameter and the circumference, and we adjust the length > of both, because they are sine waves and you can adjust the height of > the wave, to adjust the length of the diameter and length of the > circumference. > And then you will find out, that they are in sets. Not continuous > again, because the table of elements are in a set. > And the frequencies of those elements are in a set. That little jump, is the much quoted, quantum leap. And you know, it might not be a virtual leap, but the change is not as important as where it ends up. We don't know the viscosity of the superconducting superfluid, but it appears to be close to 0. For all intents and purposes, it is a quantum leap, from one size to a bit bigger size, that is expanding into n dimensional space, hyperspace, so relatively your ruler is also expanding in size, so it is not important that way because we are ina closed universe, but it is important in that a force arises out of that, called gravity, and energy waves are produced, both kinetic and electro-magnetic as a byproduct. And so all this, is the simplest you will ever hear any of this explained. Once physicists start to actually formulate the equations, it begins to look like alien hieroglyphics. And thats just the way it is, because I am simplifying the process and not taking the numerous variables or states into account. Nor pressure or temperature. Nor the effects of SR and time dilation length contraction. I mentioned it, but equations have to encompass all these things. Not at first, but these things grow as more of it is formalized and explained using the proper equations. So its good that CERN is forcing everyone to address this now, so that some sort of harmony will be reached across the different fields and take advantage of any new developments and so people across these various fields have some common terminology, with which to discuss its effects in their field of study. === Subject: Re: Field Equations for the Higg's Field posting-account=Uy-x1gkAAADZQZOsYkACyKA9wdgWU8tq Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) When you write equations for cosmology, to refine GR, you just need to say that GR is an approximation, and it is, because everyone knows that it is not quantized, it uses pi, and the real world and the real universe does not deal in infinities. So you might notice that things are not as you would expect at times, but don't jump to conclusions and think it is wrong, because it is always proven to be correct whenever it is put to the test. And so we know that it is correct, because we also have a totally independent other means of arriving at the same conclusions, and they both coincide, except, that GR approximates things by geometric approximation, for the sake of scale, just like Newtonian physics is an approximation, and it too agrees with GR and Sr, on a certain scale. Although they are quite different equations. === Subject: Re: Field Equations for the Higg's Field GR is not widely used because it is just too complex, Einstein is not > here now to sit beside anyone and say what he meant by a specific > term. It is used every time someone firess up their GPS. Several million times a day. Bob Kolker === Subject: Re: Field Equations for the Higg's Field posting-account=Uy-x1gkAAADZQZOsYkACyKA9wdgWU8tq Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) GR is not widely used because it is just too complex, Einstein is not > here now to sit beside anyone and say what he meant by a specific > term. It is used every time someone firess up their GPS. Several million times > a day. Bob Kolker Well its been simplified. http://archive.ncsa.uiuc.edu/Cyberia/NumRel/EinsteinEquations.html === Subject: Re: Field Equations for the Higg's Field posting-account=Uy-x1gkAAADZQZOsYkACyKA9wdgWU8tq Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > GR is not widely used because it is just too complex, Einstein is not > here now to sit beside anyone and say what he meant by a specific > term. It is used every time someone firess up their GPS. Several million times > a day. Bob Kolker Well its been simplified. http://archive.ncsa.uiuc.edu/Cyberia/NumRel/EinsteinEquations.html But as a for instance, NASA still uses Newtonian physics, because it is just much easier to do so, than to use GR. And well you can say that is all they need, for what they are dealing with and no, they crash things all the time, what they need is to use the right field equations, but its just too complex to calculate. In the case of GPS ok, and if you spend enough time, and you only have to do it once really, to get the orbits for satellites correct, so they don't drift, its not that tough a job. But if it were easy, NASA would use it because it is more accurate than Newtonian physics. SR is used all the time. http://en.wikipedia.org/wiki/Special_Relativity === Subject: Re: Field Equations for the Higg's Field <042dnbAVfe34MFDVnZ2dnUVZ_rTinZ2d@giganews.com> posting-account=Uy-x1gkAAADZQZOsYkACyKA9wdgWU8tq Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) > Gravity is inversely proportional, and you have to also realize that > this field is expanding in space-time as the universe is expanding. But it is in a closed universe, so the larger part of expansion, is > not that important. > But if you stretch the transverse sine wave it will red shift. The circumference is a wave function, so you can even avoid > discussions right away about expansion. You see dark matter, has mass, and in that field is a bubble, a > quantum foam bubble and it has mass. > In the field around it, is dark energy. Now dark energy itself has no mass, like a photon has no mass. But > just like a wave can borrow energy from the water, to splash against > the dock with force, the Higg's can borrow mass from the quantum foam. > However, the real mass is inside the bubble which is expanding. So if you consider along the diameter sine wave series, it is > directional, and if it is moving laterally, it is also moving outward > in that same direction. > And outward also in all directions. And that gives rise to gravity. So if you wanted to say, that the Higg's Boson, is the transverse > and the graviton, is the sine wave packet, on the diameter sine wave > series, then that would be ok, but if, you extend that sine wave > beyond the diameter, well don't make the mistake of thinking that the > gravitational force is a magnetic force, because it isn't. > Mass is not magnetic by definition, it is like kinetic energy, f=ma > type of force is applied to alter its course. > Its a direct force. And mass and gravity are the same type of animal. So you need to confine the graviton to the quantum foam bubble. There > is no mass, at all, that is outside of that bubble. > The skin on that bubble applies Newtonian force. There is no intrinsic > mass of any kind outside that bubble. > No matter what you have been led to believe, those are mistaken > observations, > Einstein proved that Newton's universal gravitation, and spooky action > at a distance was wrong. In order to preserve Newton, physics, you need to realize that it is > equivalent to f=ma, then Einstein needs the graviton, but he also > needs the red shift and the expansion, which gives rise to the > Newtonian force. > The cosmology, needs the red shift, and it needs the dark matter and > dark energy. String theory needs the sine wave string filaments. Quantum theory needs the wave packets and the fact that the quantum > foam bubble, is Plank Length in diameter. So it can get bigger but when it gets smaller, it can no longer be > detected. So the diameter sine wave series at rest, is Plank Length. In free > space between galaxies, it should be Plank Length. What does this tell us about the early universe? Well I don't know. That depends on what the examination of all these > parameters tell us. Personally I don't believe in the big bang, I think that the quantum > foam is the result of continuous creation because nature abhors a > vacuum and that the foam is in a superconducting superfluid the > properties of which remain unknown. Maybe the LHC can answer that question or questions. > But there are at present numerous experiments under way besides the > LHC which are examining the quantum foam. Another way to describe the kinetic energy is as phonon energy. http://en.wikipedia.org/wiki/Phonon === Subject: help, epsilon - N proof of a limit of a sequence AArgh, these radical expressions are a giant pain. Here is another attempt at one... Show lim n / (sqrt(n^2 + 3)) = 1 Solution: to find N such that |(n / (sqrt(n^2 +3 )) - 1 | < epsilon (n / (sqrt(n^2 + 3)) - ((sqrt(n^2 + 3) / (sqrt(n^2 + 3)) = (n - sqrt(n^2 + 3)) / (sqrt(n^2 + 3) = (n(sqrt(n^2 +3 )) - n^2 + 3) / (n^2 + 3) This last expression is <= 1/n That is, n(sqrt(n^2 + 3)) - n^2 + 3) / (n^2 + 3) < 1/n So, if N > 1/epsilon, then for all N > n |(n / (sqrt(n^2 + 3)) -1| < epsilon < 1/N < 1/n < epsilon Does this look right? I think I am getting the hang of this... ;) === Subject: Re: help, epsilon - N proof of a limit of a sequence > Show lim n / (sqrt(n^2 + 3)) = 1 Are you too lazy to indicate the limit? Because the functions involved are continuous lim(n->oo) (n/sqr(n^2 + 3)) = lim(n->oo) 1/sqr(1 + 3/n^2) = 1/lim(n->oo) sqr(1 + 3/n^2) = 1/sqr lim(n->oo) (1 + 3/n^2) = 1/sqr(1 + lim(n->oo) 3/n^2) = 1/sqr(1 + 3 lim(n->oo) 1/n^2) = 1/sqr(1 + 3 * 0) = 1 > Solution: > to find N such that |(n / (sqrt(n^2 +3 )) - 1 | < epsilon > (n / (sqrt(n^2 + 3)) - ((sqrt(n^2 + 3) / (sqrt(n^2 + 3)) > = (n - sqrt(n^2 + 3)) / (sqrt(n^2 + 3) > = (n(sqrt(n^2 +3 )) - n^2 + 3) / (n^2 + 3) > This last expression is <= 1/n It is? What if n = 2 ? > That is, > n(sqrt(n^2 + 3)) - n^2 + 3) / (n^2 + 3) < 1/n > So, if N > 1/epsilon, then for all N > n > |(n / (sqrt(n^2 + 3)) -1| < epsilon < 1/N < 1/n < epsilon Does this look right? > I think I am getting the hang of this... ;) > === Subject: Re: help, epsilon - N proof of a limit of a sequence > Show lim n / (sqrt(n^2 + 3)) = 1 Are you too lazy to indicate the limit? Because the functions involved are continuous > lim(n->oo) (n/sqr(n^2 + 3)) > = lim(n->oo) 1/sqr(1 + 3/n^2) > = 1/lim(n->oo) sqr(1 + 3/n^2) = 1/sqr lim(n->oo) (1 + 3/n^2) > = 1/sqr(1 + lim(n->oo) 3/n^2) = 1/sqr(1 + 3 lim(n->oo) 1/n^2) > = 1/sqr(1 + 3 * 0) = 1 > Solution: > to find N such that |(n / (sqrt(n^2 +3 )) - 1 | < epsilon > (n / (sqrt(n^2 + 3)) - ((sqrt(n^2 + 3) / (sqrt(n^2 + 3)) > = (n - sqrt(n^2 + 3)) / (sqrt(n^2 + 3) > = (n(sqrt(n^2 +3 )) - n^2 + 3) / (n^2 + 3) > This last expression is <= 1/n It is? What if n = 2 ? Hmm, if n=2 the expression is approx. 0.61. Acch! To correct this do I simply note that This last expression is < 1/n for n > 2 and then continue as normal? Or do I need to come up with another inequality? > That is, > n(sqrt(n^2 + 3)) - n^2 + 3) / (n^2 + 3) < 1/n > So, if N > 1/epsilon, then for all N > n > |(n / (sqrt(n^2 + 3)) -1| < epsilon < 1/N < 1/n < epsilon > Does this look right? > I think I am getting the hang of this... ;) > === posting-account=KroL8woAAAACDGpRprxyFi_gYw4Un8Xt 3.2.0; .NET CLR 2.0.50727; yplus 5.1.05b),gzip(gfe),gzip(gfe) The Europeans are making the protons to collide casting the American scientists aside.. While we are arguing about lip stick on pigs Hockey moms and pit bulls are both real tough but we have to put the focus on the important stuff or we will find ourselves getting so far behind that we will need someone to explain the real cosine. The cosine and sine have a graph like waves that helps us design an aircraft that behaves like a very efficient flying machine that flies on the energy of kerosene. So even if one of them wears lipstick a hockey mom or pit bull can't help us to pick the best way to teach math in school unless someone persuades the kids that to do so is cool. A cosine has nothing to do with loans but is more related to musical tones but if you want to co-sign a real cool pact ñsine onî to help bring America back... to the top of the scientific heap because all of the quarks should be ours to keep. A Science Fair Rap on YouTube http://www.youtube.com/watch?v=r iQlfQq-wI http://www.intelrap.com/mathsci1.html === > The Europeans are making the protons to collide > casting the American scientists aside.. > While we are arguing about lip stick on pigs > But this Lipschitz function is serious matter, no matter how the beams splatter the nations of the world will scatter upon Palin's divine mission blatter. How McCain slaughtered McAble, is matter for the biblically able, no matter if the economy is disable, much more of the same is on the table. > Hockey moms and pit bulls are both real tough > but we have to put the focus on the important stuff > or we will find ourselves getting so far behind > that we will need someone to explain the real cosine. The cosine and sine have a graph like waves > that helps us design an aircraft that behaves > like a very efficient flying machine > that flies on the energy of kerosene. So even if one of them wears lipstick > a hockey mom or pit bull can't help us to pick > the best way to teach math in school > unless someone persuades the kids that to do so is cool. A cosine has nothing to do with loans > but is more related to musical tones > but if you want to co-sign a real cool pact > ñsine onî to help bring America back... to the top of the scientific heap > because all of the quarks should be ours to keep. A Science Fair Rap on YouTube http://www.youtube.com/watch?v=r iQlfQq-wI http://www.intelrap.com/mathsci1.html > === posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN Gecko/20070509 Camino/1.5,gzip(gfe),gzip(gfe) > The Europeans are making the protons to collide > casting the American scientists aside.. > While we are arguing about lip stick on pigs Hockey moms and pit bulls are both real tough > but we have to put the focus on the important stuff > or we will find ourselves getting so far behind > that we will need someone to explain the real cosine. The cosine and sine have a graph like waves > that helps us design an aircraft that behaves > like a very efficient flying machine > that flies on the energy of kerosene. So even if one of them wears lipstick > a hockey mom or pit bull can't help us to pick > the best way to teach math in school > unless someone persuades the kids that to do so is cool. A cosine has nothing to do with loans > but is more related to musical tones > but if you want to co-sign a real cool pact > ñsine onî to help bring America back... to the top of the scientific heap > because all of the quarks should be ours to keep. A Science Fair Rap on YouTube http://www.youtube.com/watch?v=r iQlfQq-wI http://www.intelrap.com/mathsci1.html beautiful as always... -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: - - intersection of subgroups of a quotient group Suppose G is a group, and A and B are subgroups of G, and N is normal in G. Is the following necessarily true? (A / B)N/ N = AN/ N / BN/ N If true, it seems to suggest that the natural map pi : G -> G/N preserves intersections, i.e. pi (A / B) = pi (A) / pi (B) but I wasn't sure if this was really the case, since functions usually don't have this property in general (unless they're injective, I think; but pi is far from being injective). === Subject: Re: - - intersection of subgroups of a quotient group > Suppose G is a group, and A and B are subgroups of > G, and N is normal in G. Is the following necessarily true? (A / B)N/ N = AN/ N / BN/ N When in doubt, consider groups of order 6. === Subject: Re: - - intersection of subgroups of a quotient group > Suppose G is a group, and A and B are subgroups > of > G, and N is normal in G. Is the following necessarily true? (A / B)N/ N = AN/ N / BN/ N When in doubt, consider groups of order 6. you're tacitly implying that the statement is false, as written (I hope)? I'll go looking for a counterexample, then. Incidentally, are you the J. S. found here: http://www.ms.uky.edu/~jack/ === Subject: Re: - - intersection of subgroups of a quotient group > Suppose G is a group, and A and B are subgroups > of > G, and N is normal in G. > Is the following necessarily true? > (A / B)N/ N = AN/ N / BN/ N When in doubt, consider groups of order 6. you're tacitly implying that the statement is false, as written (I hope)? I'll go looking for a counterexample, then. Incidentally, are J. S. found here: http://www.ms.uky.edu/~jack/ === Subject: punk is dead chandler: I don't understand the notion of potential infinity, nor the notion of actual infinity. That might be (partly) because I'm too dim, but I think in large part it's because I've never seen a coherent (i.e. non-crank) explanation of what potential infinity _is_. So can you tell us? For a start, set theory doesn't even appear to have a _thing_ called infinity (of any flavour) in it. There are, however, infinite sets, such as the set of naturals. jurjus: The sequence of natural numbers can be understood as a process, being made step by step in the course of time, rather than as some fixed static thing that already contains all of it, in one stroke. [...] (1) For every (never-ending) sequence x1, x2, x3, ... of 0s and 1s, there is an n (0 or 1) such that if n = 0, then x_i = 0 for all i, and if n = 1, then there is some i such that x_i = 1. tonio: Not much to me, but that may be only me: that sentence (1) looks rather interesting, but I didn't go very deep there. [...] Well... is that nice of you! I'll try to be as nice to you as you've now been with me, and I'll graciously give you my personal permission to try hard not to write nonsenses. You're welcome. chandler: Sorry, but I don't see that this has any clear meaning. In set theoretic terms actual infinity has no meaning. In non-set-theoretic terms, it's not clear that infinite set has any meaning. [...] To anticipate your later question, yes, of course I can consider the endless sequence 1, 2, 3, ... without thinking about an infinite object using those words, though intuitively I can't honestly understand what the big distinction is between an endless sequence and an infinite object in the form of a set which laid out makes an endless sequence. (And incidentally, at least the Orlovian style cranks have *exactly* the same problem with not understanding endless sequences as with not understanding infinite sets.) me: it is often a not-so-secret pleasure of mine to point out when terms like crank or crackpot are used by those who display the same symptoms they attack (namely willful ignorance to a subject due to fundamentalising pride drives) i do so as notes to those who might approach the phenomenon more anthropologically or more generally in metric-driven observations (as opposed to actors in the logical debates) of course there is a completely rigorous characterisation of potential infinity attacking those who fail to give you this distinction as cranks or crackpots is a part of the demonising self-embellishment that accompanies much willful ignorance because the same frustration these people feel towards the debate partners they have chosen concerning inability to understand posted proofs eventually become frustations of those others who may have posted rigorous definitions many times including in this same thread several times tonio: As someone else already pointed out something in this direction, it is utterly useless: Han is not a mathematician, he doesn't know much of mathematics, even basic stuff like FOL, and he's not even interested in getting to know it. He just doesn't like stuff he doesn't understand, but he likes to criticize it nevertheless. -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: it's just another cheap product for the consumer's head seen perelman lately? -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: punk is dead ignorant s destroying ignorant s in a great conflagration -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: and punk is dead congratulations wads -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: the scorpions attack, but the system's stole the sting if the discipline that promotes the greatest use of logical facilities cannot itself uphold the burden of rigor if the alpha problem and insecurities if bullying and belittlement will always stain mathematical discourse what is the point of such discourse? -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: i watch and understand that it don't mean a thing why even try? uplift wars? -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: the social elite with safety-pins in their ear might as well be arguing against this ... -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: i see the velvet zippies in their bondage gear ... (ad nauseum) -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: can I resist the carrots fame and fortune dangle? and will all such positionings fall apart at their seams lost to the easily attackable commercialisations? is that what mathematics has become? -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: do I need a business man to promote my angle? is the only choice to revert to advertisement? do successful mathematical programmes like successful scientific programmes (as lakatos warned) require fallacious appeals to human drives sex appeals fear appeals pride appeals in place of appeals to scientific coherence and observation? -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: is there really something that i can learn? so where are the books to give the student? has mathematics failed in this area? why must such studies be the pursuit of obscure books available on through interlibrary loans or hunting through obscure the papers of unknown foundational conferences? -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: and me, ask me, do i want to burn? mathematics is a physical phenomenon it is something that occurs in experience and like all such events has only a posteriori justification -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: Re: and me, ask me, do i want to burn? posting-account=suWj4AkAAADE1IvGmj55Nmq3f98qb17e SIMBAR Enabled; SIMBAR={70306B22-CB8C-4d52-BFF4-18424E217075}; MathPlayer 2.10b; FunWebProducts; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > mathematics is a physical phenomenon it is something that occurs in experience > æ and like all such events > has only a posteriori justification -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- > galathaea: prankster, fablist, magician, liar ************************************************************* 25 posts in a row...and counting. Seems like someone ran out of Prozak. Oh, well. Tonio === Subject: Re: and me, ask me, do i want to burn? > mathematics is a physical phenomenon A little bit of Physics would be NO Idleness in Mathematics. (Wittgenstein: Philosophy is an idleness in Mathematics > it is something that occurs in experience > and like all such events > has only a posteriori justification -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- > galathaea: prankster, fablist, magician, liar Han de Bruijn === Subject: Re: and me, ask me, do i want to burn? > mathematics is a physical phenomenon A little bit of Physics would be NO Idleness in Mathematics. (Wittgenstein: Philosophy is an idleness in Mathematics As little as possible. But physicists habitually OD. === Subject: and i'm just waiting for my fifteen minutes fame it is clear that the classical system in formalist guise is incoherent the assumptions it relies upon are explicitly those action it avoids speaking about semantics cannot be ignored as tarski demonstrated nor can they be removed from experience -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: 'cos i've got an ass and crap and a name it's enough to stroke my own narcissism seeing how obviously incoherent and ignorant many are as they fight to be the saviors of coherence do you see how the cycle is fueled? errors breeding more confident errors due the abuse that accompanies... -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: i'm tired of staring up a superstars ass and all you pompous ignorant s with no perspective on the history or scope of metamathematics looking for belittling zingers like the sarah palin of mathematics instead of real answers to real questions -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: well i'm tired of staring through stained glass it's sickness all the way through the quest for a glory in hierarchies betterness through a lessening -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: as they sucked from the system that had given them their name even those like brouwer who promoted foundations that could refute many of the modern errors fell into their own fundamentalisations promoting kantian a prioris one law in place of another still unquestionable and wrong -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: preaching revolution, anarchy, and change there has always been a pantheon of approaches that challenged these thinly authoritarian foundational approaches stoic logicians actually questioned tertium non datur using very operational arguments (presciently foretelling the compsci approach) but unfortunately they ran foul of aristotle's programme and although surviving into roman times eventually were almost completely wiped from human history with the coming of the dark ages and its ensuing fundamentalisations buddhist logicians dignaga dharmakiri and others in that tradition gave very phenomenalistic foundations for their logic providing treatments of what amounted to the syntax-semantics connection fundamental to all metamathematics years before such ideas were rediscovered in the west -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: rockstar punk bands started doing real harm but such lack of guilt for one's initial position lack of shame for our connection with all life attacks social structures of control that fundamentalising forces have been constructing as means for their own hierarchical advancement whether condemnation for homosexuality or tertium datur blind attacks through ignorant mantras are the only response to maintain their chosen hierarchical structures (the ones they expected to climb) because there is nothing more disorienting than spending a life climbing a ladder and finding that ladder has crumbled to termites and all those one had worked hard to be above are elsewhere unconcerned with your efforts -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: punk narcissism was a social napalm the knee-jerk suppression and attack mentality eventually grows another kind of entity: the james harrises of the world those who understanding that much of the attacks they see is pure bullying and buoyed by some simple and correct derivations which get incorrectly attacked as wrong due the bloodlust compensate their self opinion beyond their actual contributions jsh is your fault bitches and in this phenomenon lies a deeper sickness the desire to crush the inner child the one who feels that they are good creatures inherently that the force of evolution and time has placed them here with faculties and directions that they need not feel guilt about identity did you do it before you read about it? -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: Re: punk narcissism was a social napalm Am 15.09.2008 07:21 schrieb galathaea: > the knee-jerk suppression and attack mentality > eventually grows another kind of entity: > the james harrises of the world those who > understanding that much of the attacks they see is pure bullying > and buoyed by some simple and correct derivations > which get incorrectly attacked as wrong due the bloodlust > compensate their self opinion beyond their actual contributions jsh is your fault > bitches and in this phenomenon lies a deeper sickness > the desire to crush the inner child > the one who feels that they are good creatures inherently > that the force of evolution and time has placed them here > with faculties and directions that they need not feel guilt about identity > did you do it before you read about it? -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- > galathaea: prankster, fablist, magician, liar I think, you've a good heart...This appears to me between your lines. Gottfried === Subject: but the leaders sold out, now we all pay the cost a look at the threads on these newsgroups concerning foundational issues regularly shows that those with the greatest educations the ones who normal trust building networks of science would defer much power to either avoid such foundational issues completely or help contribute to the stigma such is the state of humanity itself in other more important positions -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: punk became a movement 'cos we all felt lost what is even sadder is that many of the intuitions that drive the seeking for foundations are recognitions of the inadequacies of an already-given edifice unable to be inspected or questioned how do we know it works? how do we know there aren't errors here? and yet in the end much of the modern formalism reduces to just assume it statements -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: movements are expressions of the public will it's such a sad state of modern mathematics that even those who study foundations and formalisations do not understand it's limitations and assumptions that even the best texts in the field fail to give those who study them a clear overview of the field instead they seem to instead reinforce existing fundamentalising views that people so desperately cling to bivalence or god people need their certainties so they can feel better than others in extreme versions of this tendency practiced in madrassas and the u.s. military the end is an excuse for murder -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: movements are systems and systems kill and tonico oh tonico thinks that mental activities have nothing to do with math intuitions and impressions and the fundamental activities of language negotiation and formation don't apply at any level when pointed out that all formalisation all books that teach axiomatic foundations rest upon some naive level of formation or application (and many of the better books even state it explicitly) again silence it must be easier to remain silent than retract one's destructive tendencies -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: punk became a fashion just like hippy used to be, and it ain't got a thing to do with you or me -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: cbs promoted the clash, but not for revolution, just for cash and you have dedicated crankbusters like virgil who always love to ask for some rigor from han or wm or whoever they must feel better about themselves thru suddenly when confronted with a request of rigor on their own silent talking about leibnizian identity must all uncomputable numbers be equal? virgil thinks uncomputables may have some properties like some may be positive and some negative but has been silent on how to produce such an example formally -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: schoolboy sedition backed by big time promoters or dirk van der moortle's small penis site where he shows the world his inadequacies in thinly veiled attacks on others if he had balls he'd have his many own immortal fumbles there but of course he doesn't -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: bubblegum rock on plastic transistors and then you have pubkeybreaker making it explicit: -+-+- I presented some additions to the crank scale invented by John Baez. I proposed it in the mersenneforum. I suggest to newbies that they try to avoid the behavior that I describe: (1) 10 points for trying to discuss any subject for which you have not taken a course, or read at least one book. crank = ignorant but curious (2) 15 points for not using standard mathematical terminology. crank = unorthodox (3) 15 points for failing to define your variables and their domain. crank = faultily incomplete (4) 20 points for trying to generate a discussion instead of asking a question when it is clear that you do not understand what you are trying to discuss. crank = curious (5) 25 points for failing to do a web or literature search before posing an idea or question. crank = lazy (6) 35 points for elementary mistakes in high school level mathematics. crank = ignorant (7) 50 points for trying to invent new mathematical terminology. crank = ambitious (8) 50 points for trying to reinvent the wheel. An extra 10 points for reinventing a square wheel (e.g. a 'new' algorithm that performs more poorly than existing ones) crank = engineer super crank = poor engineer (9) 50 points for posing poorly defined problems, or for posing problems which show a lack of BASIC understanding of elementary aspects of the subject you are trying to discuss. crank = ambiguous (10) 100 points for both trying to invent new terminology and failing at the same time to rigorously define what that terminology really means. crank = poet (11) 200 points for even trying to pose a solution to a well-studied problem in which you are not an expert. crank = ambitious (12) 500 points for trying to claim that knowledge of the state-of-the-art gets in the way of creativity. crank = willfully ignorant (13) 1000 points for any comparison of yourself to any well known mathematician, or for trying to point out that some prior mathematican worked in some area in which he/she was not trained as if this were an excuse for your doing the same. crank = narcissist and crank = self-trained -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: it's just another cheap product for the consumer's head crassness is only fit as a mirror to the base motives behind other's monstrofications as with all mirrors crassness is imperfect and flawed the whole part about information theory making these notions rigorous was just a lie i was ing with you actually because we are imperfect machines nothing can be made rigorous instead we can only fine tune engineering tolerances seeking out better bisimulation never fully confident of course anyone with fair knowledge of metamathematical semantics would already understand this so i was only ing with idiots cranks really -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: punk is dead it's like when moe blee was proppin' hisself listing all of these foundational approaches he had studied finitism and ultrafinitism and predicativism and... and yet was unaware of poincare's role in formalising constructive theories (him having been the whole guy who pointed out predicativism as a definitional trait of a theory and having been one of the first to stress atoms of construction as solutions to antinomies) after a while you can sniff out the edges of their knowledge and can see the vulnerable core they so desperately hide but of course sniff around anyone you'll find the same vulnerable core because everyone always has more to learn no matter how many times they best some less mature student (one can almost always find someone younger who knows less particularly if you allow going into the womb) when one stops being a student it is never because they have reached perfect enlightenment there has never been a buddha -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: punk is dead if they had any desire to investigate a theory they might discover that yes there are rigorisations of all these none-senses information theory provides one such foundation in information theory channels communicate through symbol containers and mathematics can be built upon this using a variety of metasymbological semantics in these models actual infinity is a channel communication with information content greater than any finite information this is premathematical purely a participant in the ontology of symbols used actual infinity is an ontological entity with infinite information content potential infinity is mathematical it is a structure that expresses a process which in the derivation process of the mathematics provably will not terminate -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: yes, that's right, punk is dead because someone who doesn't even understand the distinction between potential and actual infinity probably does not have the qualifications to professionally debate metamathematical semantics they might argue that was never their goal they're enthusiasts who just want to intellectually discuss you don't have to be a professor to join and so they quietly slip the standards down to where their flagellations of others masks their own wide flaws (you don't have to know metamathematical semantics but good first order logic might be prerequisite?) they live in worlds of monsters trolls and cranks and crackpots and serpents so they might be the heroes looking down -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: punk is dead of course pointing out possible psychological flaws is often considered impolite and opens up all of one's own brokenness to comment so it's usually left to someone who doesn't care about social mores and can often appear pretty crass when due to emanations of alpha problems as is often the case the types who would point out the use of fundamentalising obsessions might also call it a small penis issue when addressing males illustrating it's compensatory nature but then that is a prominent profile in psychologies that must rely on terms like crank or crackpot focus on failures of others to reliably reproduce authorities to augment their own sense of consistent application (of authorities) -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: A remark about cosets and their representatives Suppose H is any subgroup of a group G, and N is normal in G. If pi : G --> G/N is the natural map, then pi (H) = {h N : h in H} = {hn N : hn in HN} = HN/ N. Now, a coset in this group is of the form hnN; but this is the same as hN, as we just saw. In other words, aren't representatives of the cosets of HN/N just the elements of H ? (Notice that I didn't assume anything about H, and its relation to N). === Subject: Re: A remark about cosets and their representatives : Suppose H is any subgroup of a group G, and N is normal in G. : If pi : G --> G/N is the natural map, then : pi (H) = {h N : h in H} = {hn N : hn in HN} = HN/ N. : Now, a coset in this group is of the form hnN; : but this is the same as hN, as we just saw. : In other words, aren't representatives of the cosets : of HN/N just the elements of H ? (Notice that I didn't assume anything about H, and its relation to N). It is true that each element of HN/N is represented by an element of H, but that is not the whole story: two *different* elements of H could represent the *same* coset of HN/N. In fact, HN/N is isomorphic to H/(H intersect N). Ted === Subject: Re: A remark about cosets and their representatives posting-account=U2cMXgoAAADa7uFaEtrTh3s-noWr2c49 Browser; Avant Browser; .NET CLR 2.0.50727; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) > Suppose H is any subgroup of a group G, and N is normal in G. If æpi : G --> G/N is the natural map, then æpi (H) = æ {h N : h in H} = {hn N : hn in HN} = HN/ N. Now, æa coset æin this group is æof the form hnN; but this is the same æas æhN, æas we æjust saw. In other words, aren't representatives of æthe cosets > of HN/N just the elements of H ? (Notice that I didn't assume anything about H, and its relation to N). Consider the case where H is a proper subgroup of N. Can you find a representative of a coset of HN/N which is not in H? Gerhard Paseman, 2008.09.14 === Subject: -- Wrong vector spaces are non Hilbertian The dimension of a vectorspace V is the maximum number N of independent vectors in V. If such a maximum number does not exist, then we say that the dimension of V is _infinite_. In a vector space of finite dimension a set of N independent so called _base_ vectors can be found, such that any vector v in V can be written as: v = v_1.e_1 + v_2.e_2 + .. + v_N.e_N Here { e_k } is the set of base vectors and { v_k } are the components or coordinates of the vector v. If the vector space is provided with an inner product (,), then the base vectors can be chosen orthogonal, i.e. (e_i,e_j) = 0 for i <> j and (e_i,e_j) = 1 for i = j Any orthogonal set of vectors is independent. Any vectorspace of finite dimension has an orthogonal base (if the inner product is defined). Let's proceed now with vector spaces of infinite dimension. Within such an infinite vector space, we try to build up a base and seek to express any vector as a linear combination of base vectors, and we try to do it as good as possible, by minimizing the following expression: | x - [ sum_(i=1..N) a_i.e_i ] | Here is: x = (complex) vector , { e_i } = set of N orthogonal vectors , a_i = vector components (complex numbers) with respect to { e_i } . Theorem: the squared sum | x - [ sum_(i=1..N) a_i.e_i ] |^2 is minimal with respect to the numbers a_i iff a_i = (x,e_i) = x_i (: define). And the minimum is: (x,x) - [ sum_(i=1..N) x_i^2 ] >= 0 . Theorem: the squared sum can be minimized further by increasing N, the number of vectors in the would-be base of V. Therefore a vector x in V is approximated best by: | x - [ sum_(i=1..oo) x_i.e_i ] | = minimum With no further information available, Bessel's inequality is provable: (x,x) <= [ sum_(i=1..oo) x_i^2 ] . Definition: a Hilbert space is an infinite vector space where the base vectors are a _complete_ set, meaning that: x = sum_(i=1..oo) x_i.e_i and (x,x) = sum_(i=1..oo) x_i^2 . The latter equality is known as Parceval's theorem, effectively meaning that there is an analogue of Pythagoras' theorem in any vector space of finite or infinite dimension, the latter if Hilbertian. Hilbert spaces may be nice, but there is NO mathematical necessity for an infinite vector space to be a Hilbert space. It's here where 'sci.physics' comes in .. Miraculous Fact: in Quantum Mechanics, any infinite dimensional vector space is a Hilbert space. How would come that orthogonal bases, in QM, are _always_ complete? What would be the consequence if they were not? Important note: even within _very large_ vector spaces, there is always a complete base of orthogonal vectors. It's only within TRULY INFINITE vector spaces that incompleteness of an orthogonal bases is possible in theory, mathematically, but .. not physically. The Miraculous Fact is explained by the Hypothesis that truly infinite does not exist and that, physically speaking, there is only VERY LARGE. Why not have the same Hypothesis in mathematics then? Han de Bruijn === Subject: Re: -- Wrong vector spaces are non Hilbertian > The dimension of a vectorspace V is the maximum number N of independent > vectors in V. If such a maximum number does not exist, then we say that > the dimension of V is _infinite_. In a vector space of finite dimension > a set of N independent so called _base_ vectors can be found, such that > any vector v in V can be written as: v = v_1.e_1 + v_2.e_2 + .. + v_N.e_N Here { e_k } is the set of base vectors and { v_k } are the components > or coordinates of the vector v. If the vector space is provided with an > inner product (,), then the base vectors can be chosen orthogonal, i.e. (e_i,e_j) = 0 for i <> j and (e_i,e_j) = 1 for i = j Any orthogonal set of vectors is independent. Any vectorspace of finite > dimension has an orthogonal base (if the inner product is defined). Let's proceed now with vector spaces of infinite dimension. Within such > an infinite vector space, we try to build up a base and seek to express > any vector as a linear combination of base vectors, and we try to do it > as good as possible, by minimizing the following expression: | x - [ sum_(i=1..N) a_i.e_i ] | Here is: x = (complex) vector , { e_i } = set of N orthogonal vectors , > a_i = vector components (complex numbers) with respect to { e_i } . Theorem: the squared sum | x - [ sum_(i=1..N) a_i.e_i ] |^2 is minimal > with respect to the numbers a_i iff a_i = (x,e_i) = x_i (: define). > And the minimum is: (x,x) - [ sum_(i=1..N) x_i^2 ] >= 0 . Theorem: the squared sum can be minimized further by increasing N, the > number of vectors in the would-be base of V. Therefore a vector x in V > is approximated best by: > | x - [ sum_(i=1..oo) x_i.e_i ] | = minimum With no further information available, Bessel's inequality is provable: (x,x) <= [ sum_(i=1..oo) x_i^2 ] . Definition: a Hilbert space is an infinite vector space where the base > vectors are a _complete_ set, meaning that: x = sum_(i=1..oo) x_i.e_i and (x,x) = sum_(i=1..oo) x_i^2 . The latter equality is known as Parceval's theorem, effectively meaning > that there is an analogue of Pythagoras' theorem in any vector space of > finite or infinite dimension, the latter if Hilbertian. Hilbert spaces may be nice, but there is NO mathematical necessity for > an infinite vector space to be a Hilbert space. It's here where 'sci.physics' comes in .. Miraculous Fact: in Quantum Mechanics, any infinite dimensional vector > space is a Hilbert space. How would come that orthogonal bases, in QM, > are _always_ complete? What would be the consequence if they were not? Important note: even within _very large_ vector spaces, there is always > a complete base of orthogonal vectors. It's only within TRULY INFINITE > vector spaces that incompleteness of an orthogonal bases is possible in > theory, mathematically, but .. not physically. The Miraculous Fact is explained by the Hypothesis that truly infinite > does not exist and that, physically speaking, there is only VERY LARGE. Why not have the same Hypothesis in mathematics then? Han de Bruijn Because mathematics is not limited by any physical analogies. === Subject: Re: -- Wrong vector spaces are non Hilbertian >The dimension of a vectorspace V is the maximum number N of independent >vectors in V. If such a maximum number does not exist, then we say that >the dimension of V is _infinite_. In a vector space of finite dimension >a set of N independent so called _base_ vectors can be found, such that >any vector v in V can be written as: > v = v_1.e_1 + v_2.e_2 + .. + v_N.e_N >Here { e_k } is the set of base vectors and { v_k } are the components >or coordinates of the vector v. If the vector space is provided with an >inner product (,), then the base vectors can be chosen orthogonal, i.e. > (e_i,e_j) = 0 for i <> j and (e_i,e_j) = 1 for i = j >Any orthogonal set of vectors is independent. Any vectorspace of finite >dimension has an orthogonal base (if the inner product is defined). >Let's proceed now with vector spaces of infinite dimension. Everything below applies only to inner-product spaces, > not general vector spaces. You're quite right. >Within such >an infinite vector space, we try to build up a base and seek to express >any vector as a linear combination of base vectors, and we try to do it >as good as possible, by minimizing the following expression: > | x - [ sum_(i=1..N) a_i.e_i ] | >Here is: x = (complex) vector , { e_i } = set of N orthogonal vectors , >a_i = vector components (complex numbers) with respect to { e_i } . >Theorem: the squared sum | x - [ sum_(i=1..N) a_i.e_i ] |^2 is minimal >with respect to the numbers a_i iff a_i = (x,e_i) = x_i (: define). >And the minimum is: (x,x) - [ sum_(i=1..N) x_i^2 ] >= 0 . >Theorem: the squared sum can be minimized further by increasing N, the >number of vectors in the would-be base of V. Therefore a vector x in V >is approximated best by: > | x - [ sum_(i=1..oo) x_i.e_i ] | = minimum >With no further information available, Bessel's inequality is provable: > (x,x) <= [ sum_(i=1..oo) x_i^2 ] . >Definition: a Hilbert space is an infinite vector space where the base >vectors are a _complete_ set, meaning that: > x = sum_(i=1..oo) x_i.e_i and (x,x) = sum_(i=1..oo) x_i^2 . No, that's not the definition of Hilbert space. It is a somewhat > correct sloppy version of the definition of complete orthonormal > basis. But the definition of Hilbert space is complete inner- > product space. The word complete in the two definitions > means different things. See Tonico? That's what I mean by answer with something _substantial_. I may not always agree with Ullrich, but _he_ certainly knows something about the _details_ in mathematics while _you_ are only pretending that >The latter equality is known as Parceval's theorem, effectively meaning >that there is an analogue of Pythagoras' theorem in any vector space of >finite or infinite dimension, the latter if Hilbertian. >Hilbert spaces may be nice, but there is NO mathematical necessity for >an infinite vector space to be a Hilbert space. >It's here where 'sci.physics' comes in .. >Miraculous Fact: in Quantum Mechanics, any infinite dimensional vector >space is a Hilbert space. Erm, this is nonsense. It _could_ be true that Hilbert spaces > are the only spaces that come up in QM - that's not the same > thing. Correction. I think you're quite right. So let's change the conjecture into this: Hilbert spaces are the only infinite spaces that come up in Quantum Mechanics. >How would come that orthogonal bases, in QM, >are _always_ complete? What would be the consequence if they were not? >Important note: even within _very large_ vector spaces, there is always >a complete base of orthogonal vectors. It's only within TRULY INFINITE >vector spaces that incompleteness of an orthogonal bases is possible in >theory, mathematically, but .. not physically. Not that it matters, but this is nonsense as well. {(1,0)} is an > incomplete orthonormal set in the finite-dimensional space R^2. That's not what I mean and I think you know it. In finite vector spaces (inner product spaces) there _always_ exists a complete orthogonal base, like {(1,0),(0,1)} in R^2. This is _not so_ with infinite dimensional inner product spaces. Right ? >The Miraculous Fact is explained by the Hypothesis that truly infinite >does not exist and that, physically speaking, there is only VERY LARGE. >Why not have the same Hypothesis in mathematics then? Because there's no good reason for it, and it would mean > we couldn't do a lot of the math we want to do. I mean duh, that wasn't hard. Han de Bruijn === Subject: Re: -- Wrong vector spaces are non Hilbertian And from a different slant; Division by zero. [infinities] Renormalization; While it works, some mathematicians and physicists feel uncomfortable about using it to get rid of infinities. Richard Feynmann calls it a dippy process without much solid mathematical basis. Infinites arise of course by division by 0, which leads to an undefined answer. But wait a second; we live in a mathematical universe, math simply works and is explanatory to the highest degree of precision. Every aspect of the universe grinds to the precision of math. Why does math work so well for everything .but lets us down for this one anomaly which is division by zero.. Have we got something wrong here, should we be looking at the concept of zero a little differently? This is where I'm going to step out on a limb and suggest something radical. In the quantum world there is no such thing as zero, only minimum quantities [i.e. Plank quantities]. Let me explain. In pure math A-A=0 of course, but we do not live in a pure math world, we live in a quantum world where heisenburgs uncertainty principle [HUP] comes into play. In our real world we deal with applied math (not pure), all quantities are measured quantities and have units associated with them. Because of HUP any measurement has a degree of uncertainty and can never be known with complete accuracy at some level. Take for example a measurement of distance on a line graph; 1 meter - 1 meter = 0 correct??? Wrong. In quantum mechanics one can never know on the line graph where the meter starts closer than one Plank length [1.6160 x 10-35 m]. One can never know where that 1 meter measurement ends to within 1 Plank length. Subtraction results in the same conundrum. The answer 1M-1M can never be less than the unknown we started with i.e. [1 Plank length]. This argument applies to all of measurement since there is a Plank time, Plank mass and a Plank value for every measurement one can do. Another possible way to obtain a zero in math is to subtract objects not measurements. For example say one has an object sitting on a table and take away that object. 1 apple - 1 apple = 0 apples, correct? This is certainly true in Newtonian space, but in the quantum universe HUP introduces a degree of uncertainty to even an apple on a table. HUP states position and Momentum [and conversely, time and energy] cannot be know to exact precision at some level. Also in Einsteins Space time one has to consider non locality, entanglement and Bells theorem. While one can remove the apple in Newtonian space, one can never remove all traces of the apple in Einsteins space time. At some level the apple has left its signature on the universe from that point [position and time] and continue to effect the universe from that point on. There has to be a minimum effect [i.e. Plank quantity]. Everett's Sum Over Paths (Universal Wave Function) and Feynman's Path Integrals approach seems to fit here as well. In this approach one deals with probabilities, and the probability of the path (or wave function) of any apple in the universe crossing the table can never be zero, it can only be a minimum quantity, ie. a plank quantity. It seems something of a coincidence that string theory which has been so successful at eliminating infinities, has done so by constructing strings which have dimensions roughly equal to Plank dimensions. Minimum dimensions appear to have done the trick here! Addendum; Pure Math for the most part deals with the manipulation of unitless pure numbers and symbols, and it is here that we may frequently experience infinities [division by zero]. But in the real quantum universe [a grainy not continuous universe] we observe no infinities so it should follow that there can be no divisions by zero in applied math only divisions by minimum quantities. Since infinities can't be dealt with, the problem must reside in our use of zero. It appears Quantum mechanics and HUP may provide a solution to this dilemma. >The dimension of a vectorspace V is the maximum number N of independent >vectors in V. If such a maximum number does not exist, then we say that >the dimension of V is infinite . In a vector space of finite dimension >a set of N independent so called base vectors can be found, such that >any vector v in V can be written as: v = v 1.e 1 + v 2.e 2 + .. + v N.e N Here { e k } is the set of base vectors and { v k } are the components >or coordinates of the vector v. If the vector space is provided with an >inner product (,), then the base vectors can be chosen orthogonal, i.e. (e i,e j) = 0 for i <> j and (e i,e j) = 1 for i = j Any orthogonal set of vectors is independent. Any vectorspace of finite >dimension has an orthogonal base (if the inner product is defined). Let's proceed now with vector spaces of infinite dimension. > Everything below applies only to inner-product spaces, > not general vector spaces. You're quite right. >Within such >an infinite vector space, we try to build up a base and seek to express >any vector as a linear combination of base vectors, and we try to do it >as good as possible, by minimizing the following expression: | x - [ sum (i=1..N) a i.e i ] | Here is: x = (complex) vector , { e i } = set of N orthogonal vectors , >a i = vector components (complex numbers) with respect to { e i } . Theorem: the squared sum | x - [ sum (i=1..N) a i.e i ] |^2 is minimal >with respect to the numbers a i iff a i = (x,e i) = x i (: define). >And the minimum is: (x,x) - [ sum (i=1..N) x i^2 ] >= 0 . Theorem: the squared sum can be minimized further by increasing N, the >number of vectors in the would-be base of V. Therefore a vector x in V >is approximated best by: > | x - [ sum (i=1..oo) x i.e i ] | = minimum With no further information available, Bessel's inequality is provable: (x,x) <= [ sum (i=1..oo) x i^2 ] . Definition: a Hilbert space is an infinite vector space where the base >vectors are a complete set, meaning that: x = sum (i=1..oo) x i.e i and (x,x) = sum (i=1..oo) x i^2 . > No, that's not the definition of Hilbert space. It is a somewhat > correct sloppy version of the definition of complete orthonormal > basis. But the definition of Hilbert space is complete inner- > product space. The word complete in the two definitions > means different things. See Tonico? That's what I mean by answer with something substantial . > I may not always agree with Ullrich, but he certainly knows something > about the details in mathematics while you are only pretending that >The latter equality is known as Parceval's theorem, effectively meaning >that there is an analogue of Pythagoras' theorem in any vector space of >finite or infinite dimension, the latter if Hilbertian. Hilbert spaces may be nice, but there is NO mathematical necessity for >an infinite vector space to be a Hilbert space. It's here where 'sci.physics' comes in .. Miraculous Fact: in Quantum Mechanics, any infinite dimensional vector >space is a Hilbert space. > Erm, this is nonsense. It could be true that Hilbert spaces > are the only spaces that come up in QM - that's not the same > thing. Correction. I think you're quite right. So let's change the conjecture > into this: Hilbert spaces are the only infinite spaces that come up in > Quantum Mechanics. >How would come that orthogonal bases, in QM, >are always complete? What would be the consequence if they were not? Important note: even within very large vector spaces, there is always >a complete base of orthogonal vectors. It's only within TRULY INFINITE >vector spaces that incompleteness of an orthogonal bases is possible in >theory, mathematically, but .. not physically. > Not that it matters, but this is nonsense as well. {(1,0)} is an > incomplete orthonormal set in the finite-dimensional space R^2. That's not what I mean and I think you know it. In finite vector spaces > (inner product spaces) there always exists a complete orthogonal base, > like {(1,0),(0,1)} in R^2. This is not so with infinite dimensional inner product spaces. Right ? >The Miraculous Fact is explained by the Hypothesis that truly infinite >does not exist and that, physically speaking, there is only VERY LARGE. Why not have the same Hypothesis in mathematics then? > Because there's no good reason for it, and it would mean > we couldn't do a lot of the math we want to do. > I mean duh, that wasn't hard. Han de Bruijn > === Subject: Re: -- Wrong vector spaces are non Hilbertian posting-account=suWj4AkAAADE1IvGmj55Nmq3f98qb17e SIMBAR Enabled; SIMBAR={70306B22-CB8C-4d52-BFF4-18424E217075}; MathPlayer 2.10b; FunWebProducts; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) On Sep 15, 10:41æam, Han de Bruijn vectors in V. If such a maximum number does not exist, then we say that > the dimension of V is infinite . In a vector space of finite dimension > a set of N independent so called base vectors can be found, such that > any vector v in V can be written as: æ æ v = v 1.e 1 + v 2.e 2 + .. + v N.e N Here { e k } is the set of base vectors and { v k } are the components > or coordinates of the vector v. If the vector space is provided with an > inner product (,), then the base vectors can be chosen orthogonal, i.e. æ æ(e i,e j) = 0 æfor i <> j æ æand æ (e i,e j) = 1 æfor i = j Any orthogonal set of vectors is independent. Any vectorspace of finite > dimension has an orthogonal base (if the inner product is defined). Let's proceed now with vector spaces of infinite dimension. Within such > an infinite vector space, we try to build up a base and seek to express > any vector as a linear combination of base vectors, and we try to do it > as good as possible, by minimizing the following expression: æ æ| x - [ sum (i=1..N) a i.e i ] | Here is: x = (complex) vector , { e i } = set of N orthogonal vectors , > a i = vector components (complex numbers) with respect to { e i } . Theorem: the squared sum | x - [ sum (i=1..N) a i.e i ] |^2 æis minimal > with respect to the numbers æa i æiff æa i = (x,e i) = x i (: define). > And the minimum is: æ(x,x) - [ sum (i=1..N) x i^2 ] >= 0 . Theorem: the squared sum can be minimized further by increasing N, the > number of vectors in the would-be base of V. Therefore a vector x in V > is approximated best by: > æ æ æ æ æ æ æ æ æ æ æ æ æ æ| x - [ sum (i=1..oo) x i.e i ] | = minimum With no further information available, Bessel's inequality is provable: æ æ æ (x,x) <= [ sum (i=1..oo) x i^2 ] . Definition: a Hilbert space is an infinite vector space where the base > vectors are a complete set, meaning that: æ æ æx = sum (i=1..oo) x i.e i æ and æ(x,x) = sum (i=1..oo) x i^2 æ. The latter equality is known as Parceval's theorem, effectively meaning > that there is an analogue of Pythagoras' theorem in any vector space of > finite or infinite dimension, the latter if Hilbertian. Hilbert spaces may be nice, but there is NO mathematical necessity for > an infinite vector space to be a Hilbert space. It's here where 'sci.physics' comes in .. Miraculous Fact: in Quantum Mechanics, any infinite dimensional vector > space is a Hilbert space. How would come that orthogonal bases, in QM, > are always complete? What would be the consequence if they were not? Important note: even within very large vector spaces, there is always > a complete base of orthogonal vectors. It's only within TRULY INFINITE > vector spaces that incompleteness of an orthogonal bases is possible in > theory, mathematically, but .. not physically. The Miraculous Fact is explained by the Hypothesis that truly infinite > does not exist and that, physically speaking, there is only VERY LARGE. Why not have the same Hypothesis in mathematics then? > **************************************************************** Quick answer: because we mathematicians don't want to and how do you like that? Long answer: because we mathematicans don't give a damn what physics or other kind of a-mathematical mammals want/need/desire, and also because we mathematicians don't want to and how do you like that? By the way: the first part, about explaining vectors spaces, bases, linear independency and stuff: tsk,tsk,tsk...lousy, Han...VERY lousy. No wonder you usually talk so huge nonsense in this forum, Han: your mathematical background, even when you cut and past, is rather pitiful. Tonio > Han de Bruijn === Subject: Re: -- Wrong vector spaces are non Hilbertian > Quick answer: because we mathematicians don't want to and how do you > like that? Long answer: because we mathematicans don't give a damn what physics > or other kind of a-mathematical mammals want/need/desire, and also > because we mathematicians don't want to and how do you like that? I'd rather expect some _content_ instead of your usual ranting. I have given you the opportunity to answer with something _substantial_, like e.g. What you're saying is not true, because .. > By the way: the first part, about explaining vectors spaces, bases, > linear independency and stuff: tsk,tsk,tsk...lousy, Han...VERY lousy. It's some essentials in a nutshell, what else do you expect? Do I have to cut and paste a whole textbook on linear algebra, to make my point clear? > No wonder you usually talk so huge nonsense in this forum, Han: your > mathematical background, even when you cut and past, is rather > pitiful. Did it from the top of my head, actually. But never mind. This posting expresses my _wondering_ about the fact that infinite vector spaces in Quantum Mechanics always have a complete base, despite of the fact that such is not necessarily so in mathematics. What's wrong with wondering about such things? Suppose you never suffer from such feelings, do you? Han de Bruijn === Subject: Re: -- Wrong vector spaces are non Hilbertian <49429$48ce2ee4$82a1e228$1177@news1.tudelft.nl> posting-account=suWj4AkAAADE1IvGmj55Nmq3f98qb17e SIMBAR Enabled; SIMBAR={70306B22-CB8C-4d52-BFF4-18424E217075}; MathPlayer 2.10b; FunWebProducts; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) On Sep 15, 12:46æpm, Han de Bruijn like that? Long answer: because we mathematicans don't give a damn what physics > or other kind of a-mathematical mammals want/need/desire, and also > because we mathematicians don't want to and how do you like that? I'd rather expect some content instead of your usual ranting. I have > given you the opportunity to answer with something substantial , like > e.g. What you're saying is not true, because .. > ***************************************************************** So now I am the one ranting, uh Han? Oooo-kay! And about the substantial something: several people already tried that with you in those last two threads and it was pointless. ***************************************************************** > By the way: the first part, about explaining vectors spaces, bases, > linear independency and stuff: tsk,tsk,tsk...lousy, Han...VERY lousy. It's some essentials in a nutshell, what else do you expect? Do I have > to cut and paste a whole textbook on linear algebra, to make my point > clear? No wonder you usually talk so huge nonsense in this forum, Han: your > mathematical background, even when you cut and past, is rather > pitiful. Did it from the top of my head, actually. But never mind. This posting > expresses my wondering about the fact that infinite vector spaces in > Quantum Mechanics always have a complete base, despite of the fact that > such is not necessarily so in mathematics. What's wrong with wondering > about such things? Suppose you never suffer from such feelings, do you? > *************************************************************** No, I don't...at least not with some more or less basic stuff. But I guess that's just because I actually studied maths. You see, Han: sometimes it's kind of a progressive process. When one begins studying calculus, sometimes it seems obvious any decent function is derivable iff it is continue...until one checks the absolute value func. Then it looks like there can't be a continuous function which isn't derivable in too many points, until one learns of non-derivable everywhere but continuous everywhere func's, etc. You say all the inf. vec. spaces appearing in QM have always complete bases, something which I don't know if it is true, but it never minds. I could tell you that in mathematics we sometimes talk of inf. dimensional vec. spaces without even mentioning completeness, inner product and stuff...why? Because there are spaces without those things. It seems now like you're pissed off about mathematics having infinite vector spaces [sic] and not being Hilbert spaces, unlike (according to you) QM...but again, that is YOUR problem. You talk about TRULY INFINITE vector spaces, The Miraculous Fact is explained by the Hypothesis that truly infinite does not exist and that, physically speaking, there is only VERY LARGE., etc. It's hard to take you seriously when you talk semi-esoteric and mistic nonsense like this, Han, and ONCE again: we mathematicians don't give a damn, physically speaking, what physics and other non-mathematical identities believe that mathematics SHOULD deal with. Tonio > Han de Bruijn === Subject: Geometry with curve, homeomorphism. Hello teacher~ Even if a curve is injective, it does not have to be a homeomorphism onto its image. This is the case for the Descartes folium a : (-1, oo) -> R^2 given by a(t) = ( 3t / (1 + t^3) , 3t^2 / (1 + t^3) ) http://board-2.blueweb.co.kr/user/math565/data/math/desfol.jpg ---------------------------------------------------------------- Can you understand it it does not have to be a homeomorphism onto its image ? === Subject: Re: Geometry with curve, homeomorphism. > Hello teacher~ Even if a curve is injective, > it does not have to be a homeomorphism onto its image. This is the case for the Descartes folium a : (-1, oo) -> R^2 > given by a(t) = ( 3t / (1 + t^3) , 3t^2 / (1 + t^3) ) http://board-2.blueweb.co.kr/user/math565/data/math/desfol.jpg ---------------------------------------------------------------- > Can you understand it > it does not have to be a homeomorphism onto its image ? Hint: What happens if you remove a carefully chosen point? -- Best wishes, J. === Subject: Re: Geometry with curve, homeomorphism. > Hello teacher~ > Even if a curve is injective, > it does not have to be a homeomorphism onto its image. > This is the case for the Descartes folium a : (-1, oo) -> R^2 > given by a(t) = ( 3t / (1 + t^3) , 3t^2 / (1 + t^3) ) > http://board-2.blueweb.co.kr/user/math565/data/math/desfol.jpg > ---------------------------------------------------------------- > Can you understand it > it does not have to be a homeomorphism onto its image ? Hint: What happens if you remove a carefully chosen point? http://board-2.blueweb.co.kr/user/math565/data/math/point.jpg How can you show that this is connected at origin ? === Subject: Re: Geometry with curve, homeomorphism. > Hello teacher~ Even if a curve is injective, > it does not have to be a homeomorphism onto its image. This is the case for the Descartes folium a : (-1, oo) -> R^2 > given by a(t) = ( 3t / (1 + t^3) , 3t^2 / (1 + t^3) ) http://board-2.blueweb.co.kr/user/math565/data/math/desfol.jpg ---------------------------------------------------------------- > Can you understand it > it does not have to be a homeomorphism onto its image ? > Hint: What happens if you remove a carefully chosen point? http://board-2.blueweb.co.kr/user/math565/data/math/point.jpg How can you show that this is connected at origin ? Isn't it possible to search in the archive of the forum you provide solutions for. ;) Anyway, it can be proven that the thing shown in the link is connected. But why did you choose this rather _arbitrary_ point? If I was you I would be much more careful and I would choose another, very special point. This could make life a lot easier. ... ;) -- Best wishes, J. === Subject: U.S.: Math, reading skills improve (Winston-Salem Journal) Mail-To-News-Contact: abuse@dizum.com http://www.ng2000.com/fw.php?tp=math === Subject: mean mode median relationship An old text book I have claims the following equation is approximately true for unimodal distributions mean - mode = 3 * (mean - median) Looks to be on the mark for chi^2, but is it more general than that. === Subject: Re: mean mode median relationship >An old text book I have claims the following equation is approximately true >for unimodal distributions >mean - mode = 3 * (mean - median) >Looks to be on the mark for chi^2, but is it more general than that. No. There is no universal relation between these. It is surprisingly accurate for gamma distributions, the accuracy improving with increasing shape parameter; however, it is not too accurate for small shape parameters. It might be a good approximation for distributions which are approximately normal with small skewness. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 === Subject: Re: mean mode median relationship posting-account=7VnrmgkAAADfdiWnpCJtxxF3tpMHF0Y0 1.0.3705; .NET CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > ... > No. There is no universal relation between these. > ... -- > This address is for information only. I do not claim that these views > are those of the Statistics Department or of Purdue University. > Herman Rubin, Department of Statistics, Purdue University > hru...@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 Not to mention, not all unimodal distributions, e.g., Cauchy, have a mean. === Subject: Re: mean mode median relationship posting-account=Jz4DtgkAAAAZkdWvJAd__jMF7l1N5_1V CLR 1.1.4322; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) > An old text book I have claims the following equation is approximately true > for unimodal distributions mean - mode = 3 * (mean - median) Looks to be on the mark for chi^2, but is it more general than that. Yes and no - this is often reasonable for slightly skewed Gaussian- like distributions, but in general the number can take any value (positive, negative, zero, or even infinite if the median equals the mean), expecially for discrete unimodal distributions. http://www.btinternet.com/~se16/hgb/median.htm has some more thoughts, looking at what happens when you divide these by the standard deviation. === Subject: Re: solutions manual posting-account=6RpWvwoAAAAJeSZ_NckQHCW2s2Ly4zFv Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > I need the solutions manual to facilities planning, 3rd edition, by > tompkins, white, tanchoco? I need the Facilities Planning, 3rd Edition by Tompkins Solution === Subject: question on harmonic functions let f:G->R be a harmonic function, where G is a domain in R^2 with nice boundary. Is it possible to show that the set of all points x0 on the boundary of G for which lim_{x->x0}f(x) = infty is discrete? === Subject: Re: question on harmonic functions > let f:G->R be a harmonic function, where G is a domain in R^2 > with nice boundary. Is it possible to show that the set of all > points x0 on the boundary of G for which lim_{x->x0}f(x) = infty is discrete? I doubt that this is true. It seems to me that if you define _f_ from D(0,1) into C as f(z) = sum_n z^{2^n} and if u(x,y) = Re(f(x + yi)), then lim_{x -> w} u(x) = +/- oo for each _w_ such that w^{2^n} = 1 for some natural _n_. These w's form a dense subset of the unit circle, of course. Jose Carlos Santos === Subject: Re: question on harmonic functions > let f:G->R be a harmonic function, where G is a domain in R^2 > with nice boundary. Is it possible to show that the set of all > points x0 on the boundary of G for which > lim_{x->x0}f(x) = infty > is discrete? I doubt that this is true. It seems to me that if you define _f_ from >D(0,1) into C as f(z) = sum_n z^{2^n} and if u(x,y) = Re(f(x + yi)), then lim_{x -> w} u(x) = +/- oo for each _w_ such that w^{2^n} = 1 for >some natural _n_. These w's form a dense subset of the unit circle, of >course. This is correct if we're talking about _radial_ limits, but not if > x -> w is taken to mean arbitrary approach to the boundary > from the interior. It's easy to give an example where you get infinite boundary > values on a dense set with arbitrary approach: First let f > be a positive function on the unit circle which is continuous > except at the point 1, which tends to infinity at 1, and > is such that the integral over the circle of f is finite. > Let v be the Poisson integral of f, Or just let v = -log|1 - z|. > and define u(z) = sum v(w_n z)/2^n where (w_n) is a dense subset of the circle. Jose Carlos Santos David C. Ullrich Understanding Godel isn't about following his formal proof. > That would make a mockery of everything Godel was up to. > (John Jones, My talk about Godel to the post-grads. > in sci.logic.) === Subject: Re: question on harmonic functions > let f:G->R be a harmonic function, where G is a domain in R^2 > with nice boundary. Is it possible to show that the set of all > points x0 on the boundary of G for which lim_{x->x0}f(x) = infty is discrete? > I doubt that this is true. It seems to me that if you define _f_ from > D(0,1) into C as f(z) = sum_n z^{2^n} and if > u(x,y) = Re(f(x + yi)), > then lim_{x -> w} u(x) = +/- oo for each _w_ such that w^{2^n} = 1 for > some natural _n_. These w's form a dense subset of the unit circle, of > course. This is correct if we're talking about _radial_ limits, but not if > x -> w is taken to mean arbitrary approach to the boundary > from the interior. Right. 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Full details: http://jobs.phds.org/job/10161/universit%C3%A9-catholique/phd-in-hydrogeophy s ics -------------------------------------------------------------------- Post your job (free!): http://jobs.phds.org/job/post PhDs.org: Science, Math, and Engineering Career Resources --------------------------------------------------------- * Job Listings: http://jobs.phds.org/ - Job board with hundreds of listings for Ph.D.s - Reach tens of thousands of Ph.D.s each month * Graduate School Rankings: http://graduate-school.phds.org/ - Comprehensive, customizable rankings of graduate programs * Career Resources: http://www.phds.org/ - Pointers to the best resources on the web for: + getting into graduate school + writing your dissertation + jobs for Ph.D.s in academia and industry * Engineering Science Weblog: http://blog.phds.org/ - Building better scientists and engineers === Subject: Re: solutions manual to Engineering Mechanics - Dynamics (11th ) by R.C.HIBBELER posting-account=xuIS_woAAAAt9gXBaPwiJ9Q8w3ZBwhCX AppleWebKit/525.13 (KHTML, like Gecko) Chrome/0.2.149.29 Safari/525.13,gzip(gfe),gzip(gfe) I am from Bangladesh. I need the solutions manual for the following book: Fundamental Methods of Mathematical Economics 4th Ed (Chiang- Wainwright) Your effort is greatly appreciated. Rochet Karim > I am asolutionsmanual collector, I offersolutionsmanual ebook > services > Note: > To search click in keyboard Ctrl+F allsolutionsmanual in soft copy > that mean in Adobe Acrobat Reader (PDF ) format. if you want any book > not justsolutionsjust contact with us.81B to get the solution manual > you want .81Cplease send message to > sendsoluti...@hotmail.com .81Csendsolutions(at)hotmail.com.81C replace (at) > to @ ,please email to me . > This is my part ofsolutionsmanual list ,If you want any othersolutionsmanual which is not in mysolutionslist, don't give > up .please email to sendsolutions(at)hotmail.comSolutionsmanual to Calculus A Complete Course 6th Edition by R.A. > AdamsSolutionsmanual to Cisco Technical Solution Series: IP Telephony > Solution Guide Version 2.0Solutionsmanual to Control Systems 4th edition by Norman S. 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G. > Kraige, > Fundamentals of Engineering Electromagnetics by cheng 1999 > Fundamentals of Signals and systems using web and matlab third > edition > by deepa08 > General Chemistry 8th By Ralph H Petrucci,Geoffrey Herring > Engineering Mechanics - Dynamics (11th ) by R.C.HIBBELER Engineering Mechanics -statics (11th ) by R.C.HIBBELER Mathematical Methods for Physics and Engineering 3th By Riley M P > Hobson === Subject: Re: solutions manual to Engineering Mechanics - Dynamics (11th ) by R.C.HIBBELER posting-account=jhnT8AoAAABXYstu1do1ln7UoqUrMv0G Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) Hey dude, Could you please send me the solutions manual for: Engineering Mechanics - Dynamics (11th ) by R.C.HIBBELER Engineering Mechanics -statics (11th ) by R.C.HIBBELER My email is surf3r0@gmail.com ;) > I am a solutions manual collector, I offer solutions manual ebook > services > Note: > To search click in keyboard Ctrl+F all solutions manual in soft copy > that mean in Adobe Acrobat Reader (PDF ) format. if you want any book > not just solutions just contact with us.81B to get the solution manual > you want .81Cplease send message to > sendsoluti...@hotmail.com .81Csendsolutions(at)hotmail.com.81C replace (at) > to @ ,please email to me . > This is my part of solutions manual list ,If you want any other > solutions manual which is not in my solutions list, don't give > up .please email to sendsolutions(at)hotmail.com > Solutions manual to Calculus A Complete Course 6th Edition by R.A. > Adams > Solutions manual to Cisco Technical Solution Series: IP Telephony > Solution Guide Version 2.0 > Solutions manual to Control Systems 4th edition by Norman S. 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Hogg > Mathematical Methods for Physics and Engineering Third Edition > By K. F. Riley, M. P. Hobson > Microwave Transistor Amplifiers Analysis and Design, 2 th by Guillermo > Gonzalez > Numerical methods for engineers 5th by Chapra > Physical Chemistry (7/e) by Peter Atkins and Julio de > Paula > Solid State Physics by Ashcroft & Mermin > Unit Operations of Chemical Engineering (7th) By Warren McCabe, > Julian Smith > A Course in Mathematical Physics By Peter Szekeres > A First Course in String Theory by Barton Zwiebach > A Quantum Approach to Condensed Matter Physics by PHILIP TAYLOR > (2002) > advanced engineering mathematics.81i9/e.81j (even solutions) by ERWIN > KREYSZIG > Data and Computer Communications, 7th Edition By Stallings > Elementary Statistics Ninth Edition By MILTON LOYER > Engineering electromagnetics (7/e) by HAYT > Engineering Mechanics, Statics 6th edition by J. L. Meriam, L. G. > Kraige, > Fundamentals of Engineering Electromagnetics by cheng 1999 > Fundamentals of Signals and systems using web and matlab third > edition > by deepa08 > General Chemistry 8th By Ralph H Petrucci,Geoffrey Herring > Engineering Mechanics - Dynamics (11th ) by R.C.HIBBELER Engineering Mechanics -statics (11th ) by R.C.HIBBELER Mathematical Methods for Physics and Engineering 3th By Riley M P > Hobson === Subject: Re: fundamentals of continuous iterations on C posting-account=06BQLAoAAADoC7Y4z9FWcUwGvMa7xMG9 7.4),gzip(gfe),gzip(gfe) > Hereby I invite the ' tetrationalists ' and anyone willing to give a non-insulting and constructive comment for a discussion of the fundamentals fo continuous iterations on C. more specificly , i want to get the neccesary conditions for a holomorhic function f(z) to be or to have a continous iteration on C. ill start by saying 1) f(z) = f(z+y) for all complex z but only for y = 0 unfortunately that is some kind of condition itself. i have to go now. > tommy1729 Well, this problem has been discussed lots of times upon this site. One attack could be : When exists for f a companion g (conditions and values to be precisely defined) such as f(g(z)) = g(z + 1) , g bijective Example : f(z) = 2*z + 1 , companion g(z) = 2^z -1 f(2^z -1) = 2^(z+1)-1 = 2*(2^z -1) + 1 and f^[r](2^z -1) = 2^(z+r)-1 , r real Alain === Subject: Energy & Mass expressed as Generality and Phi Time Relationship Hello Math. Forum: Energy as a Generality expression: Energy = (Mass A + Mass B + Mass C) .81~ C**2; Energy + Energy + Energy = Energy D (Energy D is another generality) Matter as a Generality Expression: Energy A + Energy B + Energy C = Mass .81~ C**2; Mass + Mass + Mass = Mass D (Mass D is another generality.) Where a Phi Time Relationship of Energy gives Mass. The cumulative values of either Energy or Mass show a co-existential relationship of existential item(s)/event(s). This is as opposed to a generality expression. I think this gives a new interpertation of the relationship between mass/matter and Energy/Energy(A-Z) and shows how my Math. Expression Constant can be used to interpret and document existential phenomena. Meaning Physics as well as other item(s)/event(s). Math. Expression Constant: Any existential expression of existential expressions gives a unique existential expression with a quantitative component/factor. Note also Non-Equality Axiom: No two existential item(s)/event(s) are equal in terms of their Quantitative and Qualitative properties. Zim Olson Creative Mathematics http://www.zimmathematics.com === Subject: Geometry with distance, vector. Hello teacher~ Let c : I -> R^2 be a regular plane curve and R a straight line in R^2. If one can find a number t_0 in I such that the distance from c(t) to R is greater than or equal to the distance from c(t_0) to R, for all t in I, and such that c(t_0) not in R, then show that the tangent line of c at t_0 is parallel to R. ------------------------------------------------------------ hint) If a in R and u in R^2 is a unit vector normal to the straight line R, the function f : I -> R given by f(t) = < c(t) - a , u > measures the (oriented) distance from the point c(t) to the line R. ---(***) Since c(t_0) not in R, there is a neighbourhood of t_0 in I in which f does not vanish. Hence, f measures, up to a sign, the distance from the points of (the trace of) c to R. Then f has a minimum at t_0 in I and so f'(t_0) = 0. ------------------------------------------------------------- I can't understand (***)part. Namely, What is ? It's really the distance from the point c(t) to the line R ? === Subject: Re: Geometry with distance, vector. > What is ? <.,.> denotes the standard scalar product on R^2. > It's really the distance from the point c(t) to the line R ? Yes. Prove it. -- Best wishes, J. === Subject: Re: Geometry with distance, vector. > What is ? <.,.> denotes the standard scalar product on R^2. > It's really the distance from the point c(t) to the line R ? Yes. Prove it. Yes, easy. ||c(t)-a||.||u||.cos(theta) = ||c(t)-a||.cos(theta) with drawing... === Subject: Re: Geometry with distance, vector. > What is ? > <.,.> denotes the standard scalar product on R^2. > It's really the distance from the point c(t) to the line R ? > Yes. Prove it. Yes, easy. > ||c(t)-a||.||u||.cos(theta) = ||c(t)-a||.cos(theta) with drawing... Note that can be zero, positive and negative. -- Best wishes, J. === Subject: problems in group theory posting-account=5i_ghQoAAABbiBbHHRb14_4kV5Y2uwJY Gecko/2008070208 Firefox/2.0;MEGAUPLOAD 1.0,gzip(gfe),gzip(gfe) I'd like to share/discuss some questions with you. 1) Is every finitely generated metabelian group, residually finite? What is the easiest example of finitely presented soluble group which is not residually finite? 2) Is every extension of a hopfian group hopfian? What about cartesian products? 3) Let G = < a,t | t^{-1}a^{12}t=a^{18} >. Is G hopfian? Is the normal closure of {t} in G hopfian? L.A.B === Subject: Re: problems in group theory posting-account=suWj4AkAAADE1IvGmj55Nmq3f98qb17e SIMBAR Enabled; SIMBAR={70306B22-CB8C-4d52-BFF4-18424E217075}; MathPlayer 2.10b; FunWebProducts; .NET CLR 2.0.50727),gzip(gfe),gzip(gfe) I'd like to share/discuss some questions with you. 1) Is every finitely generated metabelian group, residually finite? > What is the easiest example of finitely presented soluble group > which is not residually finite? 2) Is every extension of a hopfian group hopfian? What about > cartesian products? 3) Let G = < a,t | t^{-1}a^{12}t=a^{18} >. Is G hopfian? > Is the normal closure of {t} in G hopfian? L.A.B *********************************************************** 1) This is a special case of a theorem by P. Hall: every f.g. group which is an extension of an abelian group by a nilpotent group is res. finite. You can read more about this in Derek Robinson's A Course in the Theory of Groups, 15.4 3) Tou may want to read Theorem 4.9. in Lyndon-Schupp's Combinatorial group theory. The group there is suspiciously similar to the one you give, and that one isn't hopfian. Tonio === Subject: Re: Help with choice of Linear Algebra Book. I borrowed this book yesterday from the library, > and I finished late last night. That was quick. -- He is not here; but far away The noise of life begins again And ghastly thro' the drizzling rain On the bald street breaks the blank day. === Subject: Solution manual to Probability and Statistics for Engineers and Scientists, 8th Edition posting-account=niB_eQoAAAD6TVTlfIlXXYcl17ti70y6 2.0.50727),gzip(gfe),gzip(gfe) I am a solutions manual collector, I offer solutions manual services Note: all solutions manual in soft copy that mean in Adobe Acrobat Reader (PDF ) format. if you want any book not just solutions just contact with us.81B to get the solution manual you want .81Cplease send message to solncollector@msn.com .81Csolncollector (at)msn.com.81C replace (at) to @ ,please email to me . (To search click in keyboard Ctrl+F) Solution manual to Elements of Electromagnetics, 3rd Ed., Matthew N.O. Sadiku Solution manual to Engineering Mechanics Dynamics (11th Edition) by Russell C. 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Allyn J Washington) Solution manual to Power System Analysis and Design 3rd Edition by Glover and Sarma Solution manual to Financial management theory and practice 12e by Brigham === Subject: Simple geometry question posting-account=SPncXAoAAAAj5GwCAGkHpAQ6Mf23Xdmf Gecko/2008072820 Firefox/3.0.1,gzip(gfe),gzip(gfe) How would I solve the following equation? sin^4 x + cos^4 x = sin x * cos x Frederik === Subject: Re: Simple geometry question posting-account=O9zR9AkAAACmp918j6u5m5plppeILcze Filter 1.2.0.72; .NET CLR 1.0.3705; .NET CLR 1.1.4322; Media Center PC 4.0; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022; WWTClient2),gzip(gfe),gzip(gfe) On Sep 15, 8:57æam, Frederik Vanderstraeten How would I solve the following equation? > sin^4 x + cos^4 x = sin x * cos x I'd start with the identities sin^2 x = (1 - cos 2x)/2, cos^2 x = (1 + cos 2x)/2, and 2 * sin x * cos x = sin 2x. and get an equivalent identity in sin 2x and cos 2x that is easily solved. Dave === Subject: Re: Simple geometry question posting-account=a6woBRAAAADpNFZJBA7ZBx35zXaKmaP4 Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) On Sep 15, 9:57æam, Frederik Vanderstraeten How would I solve the following equation? > sin^4 x + cos^4 x = sin x * cos x Frederik I'd characterize this as a trigonometry problem, rather than simple geometry. Add to both sides: sin^4 x + 2 sin^2 x * cos^2 x + cos^4 x = sin x * cos x + 2 sin^2 x cos^2 x The left hand side is 1, so letting: u = sin x * cos x = (1/2) sin 2x we can reformulate the problem as: 2 u^2 + u - 1 = 0 (2u - 1)(u + 1) = 0 u = 1/2, -1 Plugging these values back into the expression for u, we see that for real x, it is infeasible to have u = -1. But (1/2) sin 2x = u = 1/2 produces a number of valid solutions. === Subject: Re: Simple geometry question Chip Eastham schreef: > On Sep 15, 9:57 am, Frederik Vanderstraeten > How would I solve the following equation? > sin^4 x + cos^4 x = sin x * cos x > Frederik I'd characterize this as a trigonometry > problem, rather than simple geometry. Yes, I mistyped. > Add to both sides: sin^4 x + 2 sin^2 x * cos^2 x + cos^4 x = sin x * cos x + 2 sin^2 x cos^2 x The left hand side is 1, so letting: u = sin x * cos x = (1/2) sin 2x we can reformulate the problem as: 2 u^2 + u - 1 = 0 (2u - 1)(u + 1) = 0 u = 1/2, -1 Plugging these values back into the > expression for u, we see that for > real x, it is infeasible to have u = -1. But (1/2) sin 2x = u = 1/2 produces a > number of valid solutions. > === Subject: Re: Simple geometry question posting-account=eFTX7goAAACJBRoHHOnDC9IuTZeZT1_H 1.1.4322),gzip(gfe),gzip(gfe) On Sep 15, 9:57æam, Frederik Vanderstraeten How would I solve the following equation? > sin^4 x + cos^4 x = sin x * cos x Frederik Think about (cos^2 x + sin^2 x)^2 === Subject: Re: Panel probes ways to propel youth toward science, math (Midland Daily News) posting-account=lHNboAoAAACyasQ0uqX7OeM_tLuWGoQp CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > http://www.ng2000.com/fw.php?tp=math ææææAlthough Dow Corning Corp. scientists have spurred students' excitement when they've >entered local classrooms to talk about their jobs, there are barriers such as fear and >lack of parental involvement that keep students out of scientific and technical professions. There is also lack of *corporate* involvement. Sending a few people to hype science via a dog and pony show in the classroom does not constitute 'involvement'. U.S. corporations are shipping technical jobs overseas. (e.g. India) They are not willing 'to put their money where their mouth is. U.S. residents are not totally stupid. What incentive exists to study science if one can not earn a living doing it? The percentage of the population that studies science (and math) as a labor of love is quite small...... === Subject: Schrodinger's Universe, the new book written by Dr. Milo Wolff, may change science. posting-account=A451vgoAAABycJv5ugpkfX8QG96-xuRZ InfoPath.1),gzip(gfe),gzip(gfe) Schrodinger's Universe, the new book written by Dr. Milo Wolff, may change science. http://www.amperefitz.com/schrodi.htm (Click link above to read.) === Subject: Re: Schrodinger's Universe, the new book written by Dr. Milo Wolff, may change science. posting-account=JpxxPAgAAAAgwzQIYqn4j6syK-YhOmcF Gecko/20071127 Firefox/2.0.0.11,gzip(gfe),gzip(gfe) > Schrodinger's Universe, the new book written by Dr. Milo Wolff, may > change science. http://www.amperefitz.com/schrodi.htm (Click link above to read.) Of course, you mean Schrodinger's Universe, the new book that *might have been written* by ... === Subject: Re: Model and straight line posting-account=KEhgtgoAAADaPGuEMem-MqVXUrhFueWi Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) On Sep 7, 4:03æpm, Dominijanni Simone there is a bijection from R (real number) to SL. > In school when the professor speak about of the SL says that MODEL: SL is an infinite number of points in a row This model makes the idea of a SL without holes. If this is a right model of the SL, then for every point of the SL > exists the successor > point. By this argument follows that if I identify a point of SL whit > the real number 0 > then, considering that exists the successor point of 0 (that I > denote with 0'), 0' = 0. infinite 0 and as last digit 1 (0.0..01 , .. = endless > zeros ). But I know that 0' isn't a real number because between two real > numbers there are > infinite real numbers. But, considering that 0' isn't a real number > and the bijection > from R to SL, doesn't exist the successor point in the SL of point > identified with 0. > But through this reasoning I deduce that in the SL there are infinite > holes. > Then: 1) the MODEL is right? 2) If the answer of 1) is not, which a correct model? 3) exist the successor 0' of 0 (as real number)? 4) the SL has punctured? 5) If the answer of 4) is not, why not? Finally: do you know some book that speaks of this matter? Answers: 1.- There is not a model for SL. SL is an abtract concept that as Hilbert understood is undefinable. Only some of its many properties can be expressible. Same as point, segment, plane etc. 2.- It was answered above. 3.- Depends on how you made the biyection of reals in SL. 4.- One of its fundamental property is that SL is unpuctured. 5.- It was answered above. === Subject: Re: Model and straight line <48c7e64d$0$20927$9b4e6d93@newsspool2.arcor-online.net> posting-account=XCu0DgoAAABTTOC6-MOovRgpALNX-vgM CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; InfoPath.1),gzip(gfe),gzip(gfe) > Hi. I know that SL (straight line) is a elementary object and that > there is a bijection from R (real number) to SL. This is only true if real numbers are overly acurate rational numbers as set > theory demands. > In school when the professor speak about of the SL says that > MODEL: SL is an infinite number of points in a row > This model makes the idea of a SL without holes. The notion of infinity in set theory deviates from the original and clearly > understandable meaning. > If this is a right model of the SL, then for every point of the SL > exists the successor point. Every point of the SL? What arrogant ignorance! I do not deny that there are > reasonable statements using the expression every number, for instance: The > successor of an even number is definitely an odd one. However, in order to > leave the world of genuine (non-Hausdorff) continuum and enter the quite > different world of numbers, one has to either deliberately or tacitly > neglect what Cantor himself called an abyss. Uncountables are losing their > feature when they get approximated by countables. To those teachers who are having problems to answer frequently asked > questions like yours, I recommend to be honest and understandable: > - Several mathematicians introduced approximative notions of continuity and > infinity. > - This arithmetisation is still considered inevitable in order to use > numbers in case of non-linear functions. > - Admittedly some tenets that are obviously wrong from the original, i.e., > the pre-Dedekind point of view, are easily to swallow even for intelligent > people if one explains them in a winking manner. Infinity of modern > mathematics can be easily understood if one considers it like a huge > infinitely expandable bag. [Just a comment to the teacher: It does not matter that Cantor denied this > bag-model. Well, he was able to æthink as if he was schizophantastic, eating > the cake and still have it. Tragically he himself believed in his > transfinite whole numbers.] - Get calm. The best recommendation æon can give to students is to learn > pertaining analysis like a text from bible. The axiomatic method detracts > from some otherwise obvious discrepancies between the immediately > understandable original notions and sophisticated, arbitrarily ætwisted > mathematical counterparts. > - As a rule, it is not wrong to treat variables that denote continuous and > infinite quantities as if they were really exact, i.e., (un)real æand at a > time also rational. > - However do not believe that the belief of the mathematicians in what > Hilbert called gewisse Zusammenhaenge (= certain tenets) always fits to > more comprehensive and in particular physical relations. Return to you: You are quite right: Without an end of the cue there is no > successor. Forget AC. > If one is able and ready to think consequently, then one gets aware that the > thinking by Dedekind as well as Cantor and their fellows is based on > admittedly missing or incorrect definitions and evidences. > Even Ebbinghaus did not only reiterate the naive theory, he also did not > comment on his quotation of Lessing which referred to an obvious but > valuable error. > I do not share the opinion that set theory is valuable. I feel it an > inconsequent or maybe dishonest cover of the impossibility to subordinate > the world of the ideal mathematical continuum to the likewise ideal world of > discrete numbers. What would not work without the alephs? Ask physicists > whether they are using reals or rationals. They will not agree on that. When > I asked mathematicians how to deal with zero when splitting IR into IR+ and > IR- I got as much answers as possiblities. None æwas free of arbitrariness. > I had to find a unique and compelling answer myself. > then, considering that exists the successor point of 0 (that I > denote with 0'), > 0' = 0. infinite 0 and as last digit 1 (0.0..01 , .. = endless > zeros ). How to distinguish it? > But I know that 0' isn't a real number because between two real > numbers there are infinite real numbers. > But, considering that 0' isn't a real number and the bijection from R > to SL, > doesn't exist the successor point in the SL of point identified with > 0. > But through this reasoning I deduce that in the SL there are infinite > holes. Stop mocking. > Both the sets of real numbers and natural numbers are totally ordered > for > the relation less or equal than, meaning that for any pair of numbers > in > the set you can say if one is less or equal than the other. You can say and believe it. For the numbers of a genuine continuum, this > is all you can do. Trichotomy ceases to be valid across the abyss. > This may lead to expecting that you can place all the numbers of the > set in > order (which you can) and go from one number to the next, which you can > for > natural numbers, but not for reals. Between any pair {a, a+e} there's > an > infinite number of other reals, like a+e/2. You'll always find numbers > between a number and a candidate successor. So no immediate successor > exists. But that doesn't mean there are gaps. Without gap no successor and vice versa, discrete or continuous, tertium non > datur. > Note that the set {1, 2, 3, 4, 10, 11, 12, 13} with the relation less > than > or equal doesn't have gaps either! In the context of a line there are gaps between all elements, even 1 and > two. > The principle problem that I have, it consists in the affirmation: > there's a bijection from R to SL If R is merely quasi-continuous, i.e., continuous in the sense of set > theory, > why not twisting the notion of a line accordingly? Mathematics (derived from set theory and logic) can't prove that your > wire has no holes -its an atomic physics problem .R is a mathematical > object (a set with further structure which can be constructed to from > set theory in such a way as to have no holes (assuming the positive > integers exist (a set with a successor function satisfying th Peano > axioms) .To talk about the bijiction between R and and the wire you > really have to model the wire in set theory .That is done as part of > foundations of Euclidean Geometry (See Forder's book -Dover ) and > there it is specifically assumed in the theory (after 100 pages ) that > the model wire has no holes .If you were doing atomic Physics it is > probably wrong but for usual uses of wires the assumption is useful > and accepted (like in studying music on a voilin. > I am responding because I noticed that no one really saw what your > question was .i hope this helps. smn Could you please also offer help to J. v. Neumann who in 1932 introduced > Hilbert space and already in 1935 admitted he did no longer believe in > Hilbert space? Salviati: > æ... in ultima conclusione, gli attributi di eguale > æmaggiore e minore non aver luogo ne gl'infiniti, > æma solo nelle quantit.88 terminate. > æIR>|>IR+>|>IR things. Do you have a book that you would recommend me? === Subject: Re: Model and straight line >Salviati, you have a different way to see these things. > Do you have a book that you would recommend me? Hm. I mentioned original literature, mostly in German. Much of it is available on the web via Digitalisierungszentrum Goettingen. In order to judge yourself, compare the following two textbooks with each other. Fraenkel 1923: Einf.9fhrung in die Mengenlehre. Fraenkel, Bar-Hillel 1958: Foundations of set theory. You have to read both textbools very critical. You can find many hints in booklets by Mueckenheim who is a finitist. His opinion is not accepted, and I do not share several of his claims. You might also benefit from a look into literature written by constructivists. Salviati: ... in ultima conclusione, gli attributi di eguale maggiore e minore non aver luogo ne gl'infiniti, ma solo nelle quantit.88 terminate. IR>|>IR+>|>IR === Subject: Re: Model and straight line <48c9ac99$0$6557$9b4e6d93@newsspool4.arcor-online.net> posting-account=XCu0DgoAAABTTOC6-MOovRgpALNX-vgM CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; InfoPath.1),gzip(gfe),gzip(gfe) Salviati, you have a different way to see these things. > Do you have a book that you would recommend me? Hm. I mentioned original literature, mostly in German. > Much of it is available on the web via Digitalisierungszentrum > Goettingen. In order to judge yourself, compare the following two textbooks with each > other. > Fraenkel 1923: Einf.9fhrung in die Mengenlehre. > Fraenkel, Bar-Hillel 1958: Foundations of set theory. > You have to read both textbools very critical. You can find many hints in booklets by Mueckenheim who is a finitist. > His opinion is not accepted, and I do not share several of his claims. > You might also benefit from a look into literature written by > constructivists. Salviati: > æ... in ultima conclusione, gli attributi di eguale > æmaggiore e minore non aver luogo ne gl'infiniti, > æma solo nelle quantit.88 terminate. > æIR>|>IR+>|>IR Hi. Does it exist a english translation of the book Einf.9fhrung in die Mengenlehre? I have seen that there are some books of Fraenkel in english as Foundations of set theory , Abstract set theory , Set theory and logic , Axiomatic set theory , ect... . Is one of them? === Subject: Re: Model and straight line Dominijanni Simone schrieb im Newsbeitrag Hi. Does it exist a english translation of the book Einf.9fhrung in die Mengenlehre? Sorry, I did not yet search for a translation of this book. The reason for me to look into a translation of the likewise interesting book Zahlen (=Numbers) by Ebbinghaus was that I was curious whether the English version also contained the telltale quoting of Lessing. >I have seen that there are some books of Fraenkel in >english as Foundations of set theory , Abstract set theory , Set >theory and logic , Axiomatic set theory , ect... . Is one of them? No. Salviati: ... in ultima conclusione, gli attributi di eguale maggiore e minore non aver luogo ne gl'infiniti, ma solo nelle quantit.88 terminate. IR>|>IR+=|=IR === Subject: Re: Model and straight line <48c9ac99$0$6557$9b4e6d93@newsspool4.arcor-online.net> posting-account=XCu0DgoAAABTTOC6-MOovRgpALNX-vgM CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; InfoPath.1),gzip(gfe),gzip(gfe) Salviati, you have a different way to see these things. > Do you have a book that you would recommend me? Hm. I mentioned original literature, mostly in German. > Much of it is available on the web via Digitalisierungszentrum > Goettingen. In order to judge yourself, compare the following two textbooks with each > other. > Fraenkel 1923: Einf.9fhrung in die Mengenlehre. > Fraenkel, Bar-Hillel 1958: Foundations of set theory. > You have to read both textbools very critical. You can find many hints in booklets by Mueckenheim who is a finitist. > His opinion is not accepted, and I do not share several of his claims. > You might also benefit from a look into literature written by > constructivists. Salviati: > æ... in ultima conclusione, gli attributi di eguale > æmaggiore e minore non aver luogo ne gl'infiniti, > æma solo nelle quantit.88 terminate. > æIR>|>IR+>|>IR === Subject: Hessian of vector-valued functions Could someone explain how the Hessian of a vector-valued function f = (f1,f2,...,fn) is calculated or point me towards a reference where the information is available? I understand the array of second partial derivatives is not a matrix, but a tensor of rank 3.... === Subject: Re: Hessian of vector-valued functions posting-account=9QOSvAoAAACEOWJVSDuswW7dB_0wApQO Gecko/2008071615 Fedora/3.0.1-1.fc9 Firefox/3.0.1,gzip(gfe),gzip(gfe) > Could someone explain how the Hessian of a vector-valued function f = > (f1,f2,...,fn) is calculated or point me towards a reference where the > information is available? I understand the array of second partial > derivatives is not a matrix, but a tensor of rank 3.... Why do you think there is such a thing as a Hessiang of a vector-valued function? -- m === Subject: Cantor set: power spectrum and fractal dimension In John C. Russ's book Fractal Surfaces, chapter 4, pages 98--99, I find this quotation The power or magnitude spectrum shows a linear variation between the logarithm of the magnitude^2 and the logarithm of the frequency. The slope of the line beta is related to the factal dimension D as D = (4+beta)/2. John Russ is concerned here with image enhancement, etc., so what he means by a power spectrum is actually the square modulus of the two dimensional Fourier transform of an image (digitized in a computer, so really the FFT, not the Fourier transform, but hopefully that's a detail). OK, fine, but no derivation is supplied of this relationship between the slope of the (Fourier) power spectrum and the fractal dimension. So I thought I would work through what I thought was a simple, one-dimensional example, namely the Cantor set. This set has fractal dimension log 2/log 3, or about 0.631. I think the one dimensional analog would be the power spectrum is found by doing the Fourier transform of the Lebesgue--Stieltjes measure determined by the Cantor function on [0,1]. I've found various derivations that the nth Fourier coefficient of the periodic extension of this measure is given by f_n = prod_{k=1}^inftycos(2pi n/3^k) which has the disturbing property that it takes on the same value for n=1, 3, 9, 27, etc. In other words, it would appear that the power spectrum will not fall off according to the fractal dimension formula given by John C. Russ. So am I missing something fundamental here? -- Charles M. Chip Coldwell Turn on, log in, tune out GPG Key ID: 852E052F GPG Key Fingerprint: 77E5 2B51 4907 F08A 7E92 DE80 AFA9 9A8F 852E 052F === Subject: -- Packing unit circles in circles: new results Packing N unit circles in a circle of smallest radius r is perhaps the most classic of packing problems. This thread will present some new packings, over the course of a month or so. At the end of the thread, conjectured bounds for this packing problem will be given. For previously known packings, see the appropriate section of Eckard Specht's excellent Packomania: . (Note that, once he has shown my new packings at his site, the links given below may become invalid.) In my figures, tangencies between circles are indicated by a small normal segment, and unit circles are color-coded according to their number of tangencies: red, 0; purple, 3; green, 4; yellow, 5; orange, 6. (Also note that my radius r corresponds with Specht's ratio, rather than his radius.) ------------------------------------ N = 144 : r = 13.250964369219..., symmetry group D_2 The best packing previously known has r = 13.2538... and is not symmetric. ------------------------------------ N = 183 : r = 14.870824502675..., symmetry group C_3 The best packing previously known has r = 14.8750... and is not symmetric. ------------------------------------ N = 206 : r = 15.738543703311..., symmetry group D_2 The best packing previously known has r = 15.7439... and is not symmetric. ------------------------------------ N = 207 : r = 15.770271663575..., symmetry group D_3 The best packing previously known has r = 15.7817... and is not symmetric. ------------------------------------ David W. Cantrell === Subject: Finding Shortest Path by Concatenating Paths posting-account=xozGQQoAAAD99EQH9srmwM1ajggyokYW Gecko/20080702 Iceweasel/2.0.0.16 (Debian-2.0.0.16-0etch1),gzip(gfe),gzip(gfe) I have N nodes and K previously determined directed paths in a graph. How can I find the shortest path visiting all N nodes by concatenating given directed paths? === Subject: JSH: Quadratic Diophantines: what JSH dosen't want you to know. The FIRST proof using tautological space ever. There are at least 5 errors, can you find them all? > Quadratic Diophantine Result I. Quadratic Diophantine Theorem: In the ring of integers, given the quadratic expression c1x2 + c2xy + c3y2 = c4z2 + c5zx + c6zy where the c's are constants, for solutions to exist it must be true that ((c2 - 2c1)2 + 4c1(c2 - c1 - c3))v2 + (2(c2 - 2c1)(c6 - c5) + 4c5(c2 - c1 - c3))v + (c6 - c5)2 - 4c4(c2 - c1 - c3) = n2 mod p for some n, where p is any prime coprime to z for a given solution, when v = -(x+y)z-1 mod p. For example with x2 + y2 = z2, I have c1 = 1, c2 = 0, c3 = 1, c4 = 1, c5 = 0, and c6 = 0 which gives -4v2 + 8 is a quadratic residue modulo p, for every prime coprime to z, when v = -(x+y)z-1 mod p. Making the substitution gives -4(-(x+y)z-1)2 + 8 = n2 mod p for some n, which is -4(x+y)2 + 8z2 = n2z2 mod p and since x2 + y2 = z2, I can substitute out z, to get 4(x-y)2 = n2z2 mod p. Proof of theorem: The theorem is proven using what I call a tautological space, where x+y+vz = 0(mod x+y+vz) as then I have x+y = -vz (mod x+y+vz), and can square both sides to get x2 + 2xy + y2 = v2z2 (mod x+y+vz) and multiply both sides by c1 and subtract from c1x2 + c2xy + c3y2 = c4z2 + c5zx + c6zy and use x = -y-vz (mod x+y+v) to substitute out x, and simplify to get (c4 - c5v - c1v2)z2 + ((c2 -2c1)v - c5 + c6)zy + (c2 - c1 - c3)y2 = 0 (mod x+y+vz) and then it's just a matter of completing the square, and collecting terms multiplied times y2 on the right, as you have an equation of the form (Az + By)2 = Cy2 (mod x+y+vz) and noting then that C must be a quadratic residue modulo p, where p is any prime such that x+y+vz = 0 mod p where coprimeness with z is required by the solution v = -(x+y)z-1 mod p. Proof complete. The Quadratic Diophantine Theorem allows determination of whether or not integer solutions are prohibited from existence for the given specified quadratic expression for various constants, because of the requirement that any prime coprime to z for a solution must have the given quadratic residue. II. Quadratic Diophantine Theorem and Pell's Equation With the Quadratic Diophantine Theorem derived, it makes sense to try it out with a well-known equation in Diophantine theory which is Pell's Equation: x2 - Dy2 = 1 with D a natural number. So with Pell's Equation I have c1 = 1, c2=0, c3 = -D, c4 = 1, c5 = 0, c6 = 0, and z=1 which gives 4Dv2 - 4D + 4 = n2 mod p and v = -(x+y) mod p, so I have 4D(x+y)2 - 4D + 4 = n2 mod p and since that must be true for all primes p, since z=1, I have in general that the left hand side must be a perfect square so it must be true then that D(x+y)2 - D + 1 = S2 where S is some integer, and I have in general that x+y = sqrt((S2 + D - 1)/D). Working backwards I found that S=41 gives that solution, verifying the result. Notice also that S2 = 1 mod D, so S = +/- 1 mod D when D is prime, while S = +/- 1 mod D is always a solution, while additional congruence relations can be found when it is not. So I can make the substitution S = jD +/- 1, to find x+y = sqrt(Dj2 +/- 2j + 1) which is x+y = sqrt((D-1)j2 + (j +/- 1)2) and I have the existence of solutions related to another Diophantine relation of the form (D-1)u2 + v2 = w2 with the condition that u = j and v = j+/-1. For instance with D=2, I have that I need solutions to u2 + v2 = w2 with u=j, and v=j+/-1, and j=20 works as 202 + 212 = 292, and gives x+y = 29, and again x=17, y=12 is a known solution to x2 - 2y2 = 1. So then x2 - 2y2 = 1 is related to certain Pythagorean triples and every case for which D-1 is a square there is a relation to them as well. Also notice that from x+y = sqrt((S2 + D - 1)/D) I have S2 - D(x+y)2 = -D + 1 which means a second Diophantine equation connected to the first! With D=2, I get then that x2 - 2y2 = 1, is connected to S2 - 2(x+y)2 = -1 so for every solution of the first there is a solution of the second. So there is an immediate result with the classical Pell's Equation, with little effort at all using the theorem, which can be used against any Diophantine quadratic in 2 variables, almost as easily, and also give results in 3 variables, though not quite as generally. III. Solvability and Diophantine Quadratic Chains Deciding to take my newly discovered Quadratic Diophantine Theorem for a spin against Pell's Equation turned out to be a good idea as besides letting me validate that I had derived the theorem correctly, it also showed me that the result I had didn't simply lead in a BFC--Big Freaking Circle. Still there is more as it indicates a route to finding a general solution for all 2 variable Diophantine equations using what I now call quadratic chains, which are infinite chains of related Diophantine equations. To derive the full theory I will use c1x2 + c2xy + c3y2 = c4z2 + c5zx + c6zy with z=1, so I have ((c2 - 2c1)2 + 4c1(c2 - c1 - c3))v2 + (2(c2 - 2c1)(c6 - c5) + 4c5(c2 - c1 - c3))v + (c6 - c5)2 - 4c4(c2 - c1 - c3) = n2 mod p for some n, where p is any prime coprime to z for a given solution, when v = -(x+y)z-1 mod p, like before but because z=1, I can immediately substitute and generalize to all primes as I did in my previous postwith Pell's Equation to get ((c2 - 2c1)2 + 4c1(c2 - c1 - c3))(x+y)2 - (2(c2 + 2c1)(c6 - c5) + 4c5(c2 - c1 - c3))(x+y) + (c6 - c5)2 - 4c4(c2 - c1 - c3) = S2 for some integer S, and to simplify doing the next calculations let A = ((c2 - 2c1)2 + 4c1(c2 - c1 - c3)) B = (2(c2 + 2c1)(c6 - c5) + 4c5(c2 - c1 - c3)) and C = (c6 - c5)2 - 4c4(c2 - c1 - c3 so I have A(x+y)2 - B(x+y) + C = S2 and it's immediately clear that I just have another quadratic Diophantine equation! Now manipulating to complete the square gives (A(x+y) - B/2)2 + AC - (B/2)2 = AS2 which is (2A(x+y) - B)2 + 4AC - B2 = 4AS2 and I have then the new quadratic Diophantine: (2A(x+y) - B)2 - 4AS2 = B2 - 4AC and have the stunning result that every quadratic Diophantine in two variables is connected to a quadratic Diophantine of the form: u2 - Dv2 = F and I get an existence condition as (2A(x+y) - B)2 = 4AS2 mod (B2 - 4AC) so I have that A must be a quadratic residue modulo (B2 - 4AC). But I have an even more stunning result as, of course, (2A(x+y) - B)2 - 4AS2 = B2 - 4AC is another Diophantine equation so I can use it to get yet another equation of the same form! Since that can go on forever, I now have the result that every Diophantine quadratic in 2 variables is connected to an infinity of others, chained to them, in that if one has solutions they all must have solutions, and if one does not, then none of them can. And obvious question then is, can both 4A and B2 - 4AC be perfect squares? Maybe but that would give a finite number solutions. I need a way where it is at least possible to get an infinity of solutions. Oh, duh, with A not a perfect square let B2 - 4AC be a perfect square and you get an infinity of solutions, and can then just pick those for which you have integer solutions in your chain. The full general method with x2 - Dy2 = n2 is that you solve for y2 to get y2 = (x2 - n2)/D and assume there exists k such that n = x-kD, as then you easily get k(2x + kD) = y2 so y = sqrt(k(2x+kD) and I need properties for k, where easily there are seen to be two cases, where the first is k = j2, which means there exists some m such that x = (m2 - j2D)/2 while the second case is k = 2j2, which gives x = (2m2 - j2D)/2 so from n = x-kD, with the first case I have j = sqrt((x-n)/D) and for the second j = sqrt((x-n)/2D). So you just find an x that will give an integer j, where x must be coprime to j, D and n, and then you have y, so it's a simple enough technique. So if that is what is needed, somewhere in the chain it must be true that B2 - 4AC is a perfect square, and of course if you find that member of the chain you can then generate solutions for any other member within the chain. James Harris 9/8/08 === Subject: Divide a board in smaller boards posting-account=ZDUqRgoAAADqITA9XoHQbKdd2qUZzqPk AppleWebKit/525.13 (KHTML, like Gecko) Chrome/0.2.149.27 Safari/525.13,gzip(gfe),gzip(gfe) Hello All, I am working in a puzzle and I am trying to learn wich section or kind of math must I use to approach the problem. The problem is: A board 13x13 can be divided in how many smaller boards? We can use several kinds of board as: 1 (12x12) + 1 (5x5) of 169 (1x1). My first approach was: (x)2 + (y)2 = 169 But this approach was naive as we can have more than 2 kinds of boards. So it strike me that my approach was flawed, and the real question is: 1- there is a formal way to approach this kind of problem? 2- which education the person must have, in which field? 3- How can I go step-by-step towards this knowledge? Sorry if it seems a little broad, but I think the older members or most talented can give some insights. Corsario === Subject: Re: Divide a board in smaller boards posting-account=Jz4DtgkAAAAZkdWvJAd__jMF7l1N5_1V .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) > Hello All, I am working in a puzzle and I am trying to learn wich section or kind > of math must I use to approach the problem. The problem is: A board 13x13 can be divided in how many smaller boards? This is IBM's Ponder This problem for September 2008 http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/Challenges/September2008 .html We can use several kinds of board as: 1 (12x12) + 1 (5x5) of 169 (1x1). Not really. If you put a 12x12 board on a 13x13 square, you are left with a L shape which then requires twenty five 1x1 squares to cover, making 26 smaller squares in total. This is not the best answer as putting one 11x11 square, eleven 2x2 squares and four 1x1 squares requires fewer; that is not the best answer either. Experiment with varing the sizes of the largest smaller squares and see what fits into the gaps. My first approach was: (x)2 + (y)2 = 169 But this approach was naive as we can have more than 2 kinds of > boards. So it strike me that my approach was flawed, and the real question is: 1- there is a formal way to approach this kind of problem? 2- which education the person must have, in which field? 3- How can I go step-by-step towards this knowledge? Sorry if it seems a little broad, but I think the older members or > most talented can give some insights. The problems IBM poses vary: the problems often do not require post- graduate mathematics, but they do require a logical mind and a familiarity and comfort with mathematical questions. In this case you could work through credible possibilities by hand or with computer aids; my guess is no matter what the size of the original square, an optimal solution will have the largest smaller square in a corner. Before getting to 13x13 you could try smaller odd squares: for example 7x7 can be covered with one 4x4, two 3x3, three 2x2 and three 1x1 squares. The hardest part is deciding whether you have an optimal solution. Look at the solutions to previous months' problems: if you understand the solutions then you might have been able to work the problems out. > Corsario === Subject: Re: Divide a board in smaller boards A board 13x13 can be divided in how many smaller boards? This is IBM's Ponder This problem for September 2008 > http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/Challenges/September2008 . html > Boards are to be square and the 13x13 board is to be geometrically partition into smaller boards. Boards can have only integral measure. The problem is to so divide the board into a minum number of boards. Some claim a computer is not to be used? Is that one of the rules? The minimum number of boards are 14. 13^2 = 10^2 + 7 * 3^2 + 6 * 1^2 The rules don't require I prove my answer. However peer review will vouch for my answer. ;-) === Subject: Re: Divide a board in smaller boards > A board 13x13 can be divided in how many smaller boards? > This is IBM's Ponder This problem for September 2008 > http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/Challenges/September2008 . html > Boards are to be square and the 13x13 board is to be geometrically > partition into smaller boards. Boards can have only integral measure. The problem is to so divide the board into a minum number of boards. > Some claim a computer is not to be used? Is that one of the rules? I don't know. However : - The programming of an algorithm to find it is per se an interesting problem. - A solution by hand is much more interesting IMHO The minimum number of boards are 14. 13^2 = 10^2 + 7 * 3^2 + 6 * 1^2 > I have less ! (hint : only two 1*1 squares) But I have cheated (Found this in a book) > The rules don't require I prove my answer. ;-) As in many tiling/packing/etc problems, the proof it is the best solution is often : nobody has found better A computer scanning of all possible tilings could be done here (13x13) as there are not too many. > However peer review will vouch for my answer. ;-) As I said just above... -- Philippe Ch., mail : chephip+news@free.fr site : http://mathafou.free.fr/ (recreational mathematics) === Subject: Re: Divide a board in smaller boards A board 13x13 can be divided in how many smaller boards? > This is IBM's Ponder This problem for September 2008 > http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/Challenges/September2008 . html > Boards are to be square and the 13x13 board is to be geometrically > partition into smaller boards. Boards can have only integral measure. The problem is to so divide the board into a minium number of boards. > The minimum number of boards are 14. 13^2 = 10^2 + 7 * 3^2 + 6 * 1^2 I have less ! (hint : only two 1*1 squares) Empty claim without proof. > But I have cheated (Found this in a book) Ok, then make restitution. ;-) Return the answer without crying finders, keepers, loosers, weepers. ---- === Subject: Re: Divide a board in smaller boards > A board 13x13 can be divided in how many smaller boards? > This is IBM's Ponder This problem for September 2008 > http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/Challenges/September2008 . html > Boards are to be square and the 13x13 board is to be geometrically > partition into smaller boards. Boards can have only integral measure. > The problem is to so divide the board into a minium number of boards. > The minimum number of boards are 14. > 13^2 = 10^2 + 7 * 3^2 + 6 * 1^2 > I have less ! (hint : only two 1*1 squares) Empty claim without proof. > But I have cheated (Found this in a book) Ok, then make restitution. ;-) Return the answer > without crying finders, keepers, loosers, weepers. > So that everybody could copy paste into IBM's ??? The contest would then be meaningless ! I would have, if we were in october and nobody had given this answer. (please note that I didn't even mention in *how many* less parts) Just a note : IBM doesn't require any proof of minimality. This means that everyone which by chance has this book, or found a reference to that problem with the solution, could copy paste it and pretend he has found it by himself. (BTW the book doesn't proove it is the best, it is just better than those allready posted here). -- Philippe Ch., mail : chephip+news@free.fr site : http://mathafou.free.fr/ (recreational mathematics) === Subject: Re: Divide a board in smaller boards > Hello All, > I am working in a puzzle and I am trying to learn wich section or > kind of math must I use to approach the problem. > I would say combinatoric... > The problem is: > A board 13x13 can be divided in how many smaller boards? This is IBM's Ponder This problem for September 2008 > http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/Challenges/September2008 . html > ;-) It is up to You (corsario) to answer this alone. At least up to the end of IBM contests. Just a hint. In fact IBM asks to *tile* the original square by smaller squares. This word tiling may help you, or not... The Packing Center http://www.stetson.edu/~efriedma/packing.html doesn't give the solution, but a little more search may be... Note that the problem is equivallent to find some network of 1 Ohm resistors equivallent to 1 Ohm. So that the tiling may be set into equations. And of course, allthough not explicitely specified, it is into *integer* squares. Otherwise dividing into 6 squares is trivial (side of larger square = 13/3), and obviously optimum. A generalization is no more tiling, but just dissecting. The difference is that you may as well redissect the remaining parts. For instance : > We can use several kinds of board as: > > 1 (12x12) + 1 (5x5) Not really. If you put a 12x12 board on a 13x13 square, you are left > with a L shape which then requires twenty five 1x1 squares to cover, > making 26 smaller squares in total. So this is tiling. But you may as well dissect the 13*13 into really one 12*12 and one 5*5, if you temper with rectangular cuts and use reassembly : Cut the 12*12 slanted, resulting into 4 irregular shaped remaining parts, which can be reassembled into a single 5*5 square. This dissection of a square into 5 parts to build 2 squares is a classical, and a kind of visual proof of Pythagora theorem ! For any sides x and y with x^2 + y^2 = 169, you get such a dissection. For some of them (try with the 13^2 = 12^2 + 5^2) cutting with none of the parts being squares before reassembling, may result into preserving the checkerboard property (that is all cuts along the lines of the initial checkerboard). If you want only integer sides, this is another matter. You have to find in how many ways 169 is the sum of two [integer] squares. And find that because 13 is a prime number, the only way is 12^2 + 5^2 (and the trivial 13^2 + 0^2). This is a problem in arithmetic and number theory. Solved centuries ago. For dissection into more that 2 squares, the problem becomes harder. For instance with 169, there are 6 ways of dividing into 4 (integer) squares, 1 way into 3 squares and one into 2 squares. For more than 4 squares, you may cut by any first square < 13^2, and the remaining area can allways be dissected into at most 4 squares. (theorem : any integer is the sum of at most 4 squares). Finding then all 169 = sum of integer squares, can be done by a suitable algorithm. There is a more efficient way to find them than brute force (using Euclid's algorithm in Gauss integers). However with 169, brute force is simpler. For the IBM question, you may as well use the following approach : Find all decompositions 169 = sum of integer squares as above. Then filter out and keep only those which result into a *tiling*. Not shure it is the best way, may be finding directly the tilings is better. And however IBM's question is intended to be solved without a computer ! -- Philippe Ch., mail : chephip+news@free.fr site : http://mathafou.free.fr/ (recreational mathematics) === Subject: Re: Divide a board in smaller boards posting-account=JMZqKwoAAACUM5HyT1LoB3KEmRo1RkY8 AppleWebKit/525.13 (KHTML, like Gecko) Chrome/0.2.149.29 Safari/525.13,gzip(gfe),gzip(gfe) First off, you can't make one 12x12 and one 5x5 out of a 13x13 board. Secondly, I assume you mean just integer dimensions?... otherwise it's infinity. Next, I assume you mean how many combinations of smaller boards.. otherwise it's just 169. Lastly, I'm assuming you are allowing rectangular boards as well, and not just square? That said, the way I'd approach this problem is a recursive algorithm. You have a data structure.. a 2D array, intially 13x13, initialized to all 1's. 1 means that 1x1 section is not sawed off. 0 means it is. This gets passed into a function. You have the function take the 2D array as an argument. If all elements are 0, you return 0, meaning you cannot saw off any boards from the board passed in. Otherwise, you can only saw off one board from the leftmost then downmost corner (start at the upper rightmost element.. go all the way left, then all the way down). Do a pair of for loops to cycle through the possible widths and heights of each board, all the way up to 13x13. For each rectangle, return 1 plus the return value of the same function, with a the same array, modified so that the current iteration's rectangle is chopped off from the board (its elements are set to 0). Print out the return value of the initial call to this recursive function. I might've been a little off, but essentially this algorithm is similar to the Towers of Hanoi problem found in many Computer Science textbooks. Oh, and I'm sure there's a less computerized more math-oriented way to figure this out, but, I'm a programmer :) - Scott > Hello All, I am working in a puzzle and I am trying to learn wich section or kind > of math must I use to approach the problem. The problem is: A board 13x13 can be divided in how many smaller boards? We can use several kinds of board as: 1 (12x12) + 1 (5x5) of 169 (1x1). My first approach was: (x)2 + (y)2 = 169 But this approach was naive as we can have more than 2 kinds of > boards. So it strike me that my approach was flawed, and the real question is: 1- there is a formal way to approach this kind of problem? 2- which education the person must have, in which field? 3- How can I go step-by-step towards this knowledge? Sorry if it seems a little broad, but I think the older members or > most talented can give some insights. > Corsario === Subject: << FREE HELP DESK SOFTWARE > posting-account=vX8wfgoAAAAoIMzGNbiD7z__6cf_T9Wc SV1),gzip(gfe),gzip(gfe) << FREE HELP DESK SOFTWARE > http://helpdesksoftwarefree.blogspot.com http://refinancingmortgageloans1.blogspot.com === Subject: Dons parallel prime numbers research (45-46th mersenne primes discovered Wellington NZ.) Cc: MCDOnewt@yahoo.co.nz, thomas_hally@yahoo.com, letters@smh.com.au posting-account=TV2szgkAAACrA1vyuh8IN_0zzgzcwogw .NET CLR 2.0.50727; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) DonÍs parallel prime numbers research Mond 15 Sept 2008. (45th and 46 known mersenne primes discovered Wellington NZ.) Editor, Sir / Madam Dompost newss britton.broun nzmm nzm newsct ijeditor.mensa.org Dw mzd jour eg press frank rec.puzz alt.math nz.general In April-May 2000 I announced that, by doing extreme long division on a 486 laptop computer (New Zealand Science monthly magazine, Bulletin board,) I had finally discovered the number 1580 187 223 was the least prime divisor of ( 1 billion raised to the 1 billionth power) plus 3. DonÍs exponential number, (10 ^ 9 ) ^ ( 10 ^ 9 ) +3, contains 8 999 999 999 zeroes and fills 2 million pages of 90 characters per line times 50 lines per page. A world mathematician shivered that it was ïnot feasible to test my number!Í However, about 10 days later, they had all come round to giving my answer the TICK v/. Bob Backstrom even added to my factors of (billion ^ billion plus 1.) Just why is 864 000 001 (ten thousand days plus a heartbeat) one of the prime factors! In world mathematical year 2000 Poster Competition, I displayed a previous record Mersenne prime exponent, 302 1377, in ñTable Mountain palindrome formî- M p = (1+1) ^ ( 2 x 34 x 44432 + 1 ) -1. Figure, increasing digits-plateau-decreasing, .. / TTT . PUZZLES, Multi-palindrome CRYPTARITHM. ( AA * AHA * AHHHA )^2 = ADMIT ONE NOT IMDA. Each unique letter ADMITONE.. etc. is to be replaced by a different digit, 0-9. I would add that the cryptic letters, 2413672 96475, may describe my Square Result, ^2 ? Pi-Search Table Mountain (Mons Mensae) powers of 3 palindrome. ï.83 713 999 9999 317.83Í followed by 11 even digits. I often calculated ïtwin primes around mersenne prime exponentÍ and ïfactors of mersenne numbersÍ, when (2 raised to a prime exponent) minus 1, is not always a mersenne prime. Centuries study have today, 16 Sept 2008, unearthed just the 45th and 46th known Mersenne primes! If ArchimedesÍ propositions 41-43, ñA = PI. CXC ñ, is evaluated as a (Base 27 number), A=1, Z= 26 etc., it gives DD.MM.CCYY, of Easter Day, 2oo8. (Probability that 3 siblings born on Easter day, different years? ) The string ï 2424 2424 2Í was found at pi-search position 242 421 after the decimal point (Scott Glazer.) Don (sin .25 degree) ^-2 = 52 525.25, DominionPost greetings ad, 29/3/2008. Yours, Don McDonald, NZ. 16/9/08. === Subject: Re: Dons parallel prime numbers research (45-46th mersenne primes discovered Wellington NZ.) > A world mathematician shivered that it was ënot feasible to test my What is a world mathematician? -- He is not here; but far away The noise of life begins again And ghastly thro' the drizzling rain On the bald street breaks the blank day. === Subject: U.S.: Math, reading skills improve (Winston-Salem Journal) Mail-To-News-Contact: abuse@dizum.com http://www.ng2000.com/fw.php?tp=math === Subject: Re: Panel probes ways to propel youth toward science, math (Midland Daily News) posting-account=lHNboAoAAACyasQ0uqX7OeM_tLuWGoQp CLR 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) > http://www.ng2000.com/fw.php?tp=math ææææAlthough Dow Corning Corp. scientists have spurred students' excitement when they've >entered local classrooms to talk about their jobs, there are barriers such as fear and >lack of parental involvement that keep students out of scientific and technical professions. There is also lack of *corporate* involvement. Sending a few people to hype science via a dog and pony show in the classroom does not constitute 'involvement'. U.S. corporations are shipping technical jobs overseas. (e.g. India) They are not willing 'to put their money where their mouth is. U.S. residents are not totally stupid. What incentive exists to study science if one can not earn a living doing it? The percentage of the population that studies science (and math) as a labor of love is quite small...... === Subject: old and new spectra Originator: israel@math.ubc.ca (Robert Israel) I am reading the classical paper of K.S. Brown Abstract homotopy theory and generalized sheaf cohomology where it uses a notion of Kan spectrum, which nowadays seems to be almost forgotten. But since people continue to use Brown's results about generalized sheaf cohomology, I imagine that Kan's definition of spectra should be equivalent to more relatively modern ones, such that of Whitehead's paper Generalized homology theories; that is, a sequence of topological spaces (or simplicial sets) E_n , together wit maps SE_n ---> E_{n+1} . Does any one knows if this is so? Is the category of Kan spectra equivalent to Whitehead ones (or at least the localized categories)? Any references for this result? Agusti Roig === Subject: Re: old and new spectra dir: I am reading the classical paper of K.S. Brown Abstract homotopy >theory and generalized sheaf cohomology where it uses a notion of Kan >spectrum, which nowadays seems to be almost forgotten. But since people continue to use Brown's results about generalized >sheaf cohomology, I imagine that Kan's definition of spectra should be >equivalent to more relatively modern ones, such that of Whitehead's >paper Generalized homology theories; that is, a sequence of >topological spaces (or simplicial sets) E_n , together wit maps SE_n >---> E_{n+1} . Does any one knows if this is so? Is the category of Kan spectra >equivalent to Whitehead ones (or at least the localized categories)? >Any references for this result? Maybe I should stress that in my previous message, by a Kan spectrum I reallymeant spectrum in the sense of the original definition by Kan, as it appears, for instance, in his paper Semisimplicial spectra, Illinois J. Math 7 (1963). This is a kind of simplicial set E_n , but the index n runs over all integers, not just the natural numbers. There are also an infinite number of faces and degeneration maps for each n . Which is not the same as modern Kan spectrum: this is a modern spectrum, as defined above, with an extension property. Sorry if I confused somebody. Agusti Roig === Subject: Re: old and new spectra I am reading the classical paper of K.S. Brown Abstract homotopy > theory and generalized sheaf cohomology where it uses a notion of Kan > spectrum, which nowadays seems to be almost forgotten. But since people continue to use Brown's results about generalized > sheaf cohomology, I imagine that Kan's definition of spectra should be > equivalent to more relatively modern ones, such that of Whitehead's > paper Generalized homology theories; that is, a sequence of > topological spaces (or simplicial sets) E_n , together wit maps SE_n > ---> E_{n+1} . Does any one knows if this is so? Is the category of Kan spectra > equivalent to Whitehead ones (or at least the localized categories)? > Any references for this result? > Agusti Roig > Indeed they are equivalent, and that was addressed in some joint papers such as: AUTHOR = {Kan, Daniel M. and Whitehead, George W.}, TITLE = {Orientability and {P}oincar'e duality in general homology theories}, JOURNAL = {Topology}, FJOURNAL = {Topology. An International Journal of Mathematics}, VOLUME = {3}, YEAR = {1965}, PAGES = {231--270}, ISSN = {0040-9383}, MRCLASS = {55.30}, MRNUMBER = {MR0190925 (32 #8335)}, MRREVIEWER = {V. Gugenheim}, } Kan spectra are hardly forgotten, are now usually called simplicial spectra and actually came one year after Whitehead's topological spectra. At that time Kan and Whitehead were colleagues at MIT, their offices were only a door or two apart and they were fully aware of each others work. -- Robert L. Knighten RLK@knighten.org === Subject: Curious quadratic form over Q Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) Originator: israel@math.ubc.ca (Robert Israel) At a recent talk by Skip Garibaldi, he mentioned an intriguing elementary fact that fell out accidentally from some high-powered machinery he was working with. Say that two matrices A and B over the rationals are rationally congruent if there exists a matrix S over the rationals such that S^t A S = B. Theorem (Garibaldi). Let n = 0 mod 4. Then the diagonal matrices A = diag[(n choose 0), (n choose 2), (n choose 4), ..., (n choose n/2-2)] B = diag[(n choose 1), (n choose 3), (n choose 5), ..., (n choose n/2-1)] are rationally congruent. Similarly, let n = 2 mod 4. Then the matrices A = diag[(n choose 0), (n choose 2), ..., (n choose n/2-1)] B = diag[(n choose 1), (n choose 3), ..., (n choose n/2-2), (n choose n/2)/2] are rationally congruent. Apparently, no elementary proof of this fact is known. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: MSP/circuit/formula complexities of monotone Boolean functions. posting-account=8WKDHAoAAACYqN5DFDzDzFfFo3Bkg_vB Does anyone know of a monotone Boolean function with reasonable Boolean circuit complexity, but high monotone span program size and high Boolean formula complexity? I'm working on a paper for an upcoming conference and it would be very useful to be able to point to James McLaughlin. === Subject: radical ideal algorithms posting-account=3lvGuwoAAAD2hisjCBzgCEMY3Bc6U2C0 The book by Cox, Little and O'Shea, Ideals, Varieties, and Algorithms, discusses the radical membership algorithm. However, I would like a nice algorithm the starts with a finite set of polynomials in several variables, considers the radical of the ideal generated by this set, and produces a small set of generators for this === Subject: Determining f given f(n) and f'(n), n integer posting-account=RH5FcgoAAABlr4vlVdw3hAfzGV01oJBG Let f:R->C be a function and fhat:R->C its Fourier transform. Suppose that fhat is supported on [0,1] and that the values ...,f(-2),f(-1),f(0),f(1),f(2),f(3),... of f(n) at the integers n are given. Then we know what fhat and f are: fhat = sum_n f(n) e^{2pi i n}, f = (inverse) Fourier transform of fhat. Suppose now, instead, that fhat is supported on (-1,1). Then the values of f(n) at the integers n are not enough to determine f. Suppose, then, that we are given not just f(n) but also f'(n) for every integer n. It is not hard to show that this determines f. Question: what is the simplest way of writing f in terms of f(n) and f'(n), assuming that fhat is supported on (-1,1)? (I managed to find two ways without too much trouble, but they are really a little complicated - in particular, I cannot tell anything much about f from them, or even plot f for some simple choices of f(n) and f'(n). ) Harald === Subject: Re: Determining f given f(n) and f'(n), n integer On 13 Sep 2008 02:40:38 -0400, Harald Helfgott Let f:R->C be a function and fhat:R->C its Fourier transform. Suppose that fhat is supported on [0,1] and that the >values ...,f(-2),f(-1),f(0),f(1),f(2),f(3),... of f(n) at the integers >n are given. Then we know what fhat and f are: fhat = sum_n f(n) e^{2pi i n}, >f = (inverse) Fourier transform of fhat. Suppose now, instead, that fhat is supported on (-1,1). Then the >values of f(n) at the integers n are not enough to determine f. >Suppose, then, that we are given not just f(n) but also f'(n) for >every integer n. >It is not hard to show that this determines f. Question: what is the simplest way of writing f in terms of f(n) and >f'(n), assuming that fhat is supported on (-1,1)? (I managed to find two ways without too much trouble, but they are >really a little complicated - in particular, I cannot tell anything >much about f from them, or even plot f for some simple choices of f(n) >and f'(n). ) Hmm. You need the biorthogonal set to a certain set of functions... There exist F and G with the following properties: The Fourier transforms of F and G are supported in (-1,1), F(0) = 1, F(n) = 0 for all n <> 0. F'(n) = 0 for all n, G'(0) = 1, G'(n) = 0 for n <> 0, and G(n) = 0 for all n. Then f(x) = sum f(n) F(x-n) + sum f'(n) G(x-n). Seems like F(x) = (sin(pi x)/(pi x))^2, I think, and it seems like some multiple of G(x) = (sin(pi x))^2/x should do it. >Harald David C. Ullrich Understanding Godel isn't about following his formal proof. That would make a mockery of everything Godel was up to. (John Jones, My talk about Godel to the post-grads. in sci.logic.) === Subject: Etymology of parabolic subgroup Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) Why are parabolic subgroups called parabolic subgroups? I've heard two explanations. 1. It has something to do with parabolic elements of SL(2,R). This sounds plausible, but I haven't heard a really convincing explanation along these lines. 2. Parabolic is short for para-Borelic, meaning containing a Borel subgroup. I heard this from someone who seemed convinced that this was the original reason for the term. A related question is who first introduced the term and when. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Etymology of parabolic subgroup Originator: tchow@lebesgue.mit.edu.mit.edu (Timothy Chow) Why are parabolic subgroups called parabolic subgroups? I've heard two explanations. 1. It has something to do with parabolic elements of SL(2,R). This sounds plausible, but I haven't heard a really convincing explanation along these lines. 2. Parabolic is short for para-Borelic, meaning containing a Borel subgroup. I heard this from someone who seemed convinced that this was the original reason for the term. A related question is who first introduced the term and when. -- Tim Chow tchow-at-alum-dot-mit-dot-edu The range of our projectiles---even ... the artillery---however great, will never exceed four of those miles of which as many thousand separate us from the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences === Subject: Re: Kind of like zombies > Ok I did the one post noting the obvious--that protecting your > professors is taking away your own opportunities. But now I think it > faithfulness against your own interests. you do not know my interests. It's like, of course if there are new research techniques over-turning > older results that is an opportunity for young people. trivial, there are far more challangeing problems out there, but you would not know of them because you hate mathematicians. Why do you think I keep posting to alt.math.undergrad? You crave attention. > Supposedly your own self-interest would have made you push for new > ideas but for years now, you've been like mindless zombies. Following > along when that means that for most of you, you will never even have > CAREERS in mathematics. Speak for yourself, I am doing just fine. I have made my first million with my proofs, and I am just 23. > All these older mathematicians are blocking your places as they have > them. Not if you are smart, they only block the dumb ones. Oh, and yeah, mathematics is a fascinating field. The person with the > more powerful techniques can get the huge results. Duh. Which is not JSH. I have the most powerful mathematical research techniques. I can find > the huge results. You don't, you can't. Accept the Fact that you are just not smart enough. > So those of you mindlessly trotting behind your professors like good > little math students not only are against your own self-interest, > you're running out of time, as THEY had their time, but for you there > is the near certainty that as time goes by, I'm likely to take out > entire areas of research possibilities. Your myoptic sick view is your own, and is not shared by any math students. Have no fear, JSH, you are mentally unable to take out any areas of math, including the distributive property. > So you could work hard. Follow the system. And wake up one morning > to hear that I've nailed yet another huge result, like researchers who > do anything with Pell's Equation could be hearing today, if they > bother caring. Bleatings from a mental midget. A math Retard, justly flushed out of school, when he failed basic algebra. > And think about it. Those of you who know about the new research > might be seeing in amazement your society acting as if it doesn't > exist! ...delusional trolling... Texts continuing to trot out the old info, and people working hard, > putting in their mental sweat and effort. Trying as hard as they can > do figure out more about...about the trivially solved. The social reality I face IS formidable. Paranoid. For years now I've seen how willfully many of you will ignore major > mathematical techniques to trot along behind your professors and be > good little math students, so yes, I understand you may continue. You have no math at all, JSH. Nothing. Just for social crap, to feel good, to think that, hey, those are the > rules and you are following them, so does it really matter if your > mathematical knowledge is actually primitive? If history will > overturn any validation you receive from today's society? I think for most of you, it does not, as that is some vague > hypothetical. But I hope some of you DO care about correctness. And DO care about > mathematics as discovery and truth Yes, we do. That is why we flush you. You have nothing at all, nothing, not a thing. > But for years now, most of you have been, well, more like zombies than > math students. Speak for yourself. > I have proven Fermat's Last Theorem. And in so doing found a math > error in core that is over one hundred years old. I have found THE > prime counting function. I have results across prime number. I am > now coming back to Diophantine equations with immediate success. all lies........ from a lying troll. You stand against me and you stand against mathematical history for > people who will lose in the judgment of history. History has already judged you, JSH. You ARE Troll/crackpot, narssistic monkey-boy. And some will go down very badly, more than happy to take down as many > of you with them as they can. you use threats of violance? how, ...... stupid. You ARE a small brain. > The puzzle for me for so many years has been: why do so many of you > hate yourselves? Speak for yourself. Did your Mother and Father hate you? Is it because you could only think about yourself? Why do so many of you despise your own futures? Speak for yourself. What future do you have as a crackpot/troll on the internet? => none <= A question I have often asked myself is, why don't any of you seem to > have a sense of self-preservation? Why do you think you know what we are thinking? Google thought distortions and learn about your mental illnesses. I ponder that question now. ponder, wonder, but never be able to see it, oh narssistic one. > James Harris === Subject: Re: cheapest air max 90, airmax 90 shoes, airmax 87 shoes, chanel dior lv boots for sale posting-account=p1Z4uwoAAADz-x8kR-ONLigAuPACf1S3 GoogleT5),gzip(gfe),gzip(gfe) please look our website ,have more mode shoes clothing hat cap bags ! 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Taking the example:- a (x + 2) + b (x^2 + x + 1) = 2x^2 + 5x + 5 then this has solution a = (x + 2) and b = 1 (according to the book I am following, which prescribes using the EEA to find the solution), but using the EEA I get values for the Bezout relation as being:- (-1/3 x + 1/3)(x + 2) + 1/3 (x^2 + x + 1) = 1 so, assumedly multiplying both sides of the above by 2x^2 + 5x + 5, should yield the same solution the book has.. but it doesnt.. Anyone see where I'm going wrong here? Jeremy Watts === Subject: Re: using the extended euclidean algorithm to solve polynomial equations of the type a.f + b.g = c I am attempting to use the 'extended euclidean algorithm' to solve equations > of the type :- a.f + b.g = c where, 'f' , 'g' and 'c' are univariate polynomials, and 'a' and 'b' are > unknown univariate polynomials (all polynomials must be over the integers). Taking the example:- a (x + 2) + b (x^2 + x + 1) = 2x^2 + 5x + 5 then this has solution a = (x + 2) and b = 1 (according to the book I > am following, which prescribes using the EEA to find the solution), but > using the EEA I get values for the Bezout relation as being:- (-1/3 x + 1/3)(x + 2) + 1/3 (x^2 + x + 1) = 1 so, assumedly multiplying both sides of the above by 2x^2 + 5x + 5, should > yield the same solution the book has.. but it doesnt.. Anyone see where I'm going wrong here? 2*3 + (-1)*5 = 1; (-3)*3 + 2*5 = 1. -- Paul Sperry Columbia, SC (USA) === Subject: Re: More with Quadratic Diophantine Theorem > So a constructivist would normally like to see it shown that > |sqrt(2)-p/q| =(2-p^2/q^2)/|sqrt(2)+p/q| > 1/3q^2, just as a > number theorist would. (3 is of course not the best possible.) Hmmmm...that reminds me of the kind of inequality that comes out of continued fractions. I suppose another approach a constructivist could take to sqrt(2) would be to find the continued fraction for it: 1 + 1 / (2 + 1/ (2 + 1/ (2 + ... and note that it does not have a finite number of terms, and so the number must be irrational. (Assuming there are constructivist proofs that continue fractions without a finite number of terms represent irrational numbers, and that the above is the sqrt(2)). -- --Tim Smith === Subject: Re: More with Quadratic Diophantine Theorem P.S. The only place I see references to constructionists is > on usenet. I'm assuming it's meant to refer to constructivists. My brain probably got its indexes for words that start with 'construct' mixed up, and crossed this: with this: :-) -- --Tim Smith === Subject: Re: More with Quadratic Diophantine Theorem > i think you would be surprised at gauss' elementariness > i figured that if you spent some time reading him > you too could be that paranoid asshole > inflating yourself with me me me > and finally be a fair mathematician to boot >I'm contemplating this awesome result linking all quadratic contemplating means you have nothing. >Diophantine equations in 2 variables and wondering how far it goes. Google for it, lazy. >You're mumbling. You're trolling. >History will remember me. But what about you? History will remember JSH will never f*cking do it -UA How long will History remember JSH? About 3 days after his last post. >Oh, you don't care, right? >Hundreds of years from now, some people may be wondering about who I >am and what kind of person I was, where one may hero worship, and >another may mouth off about my many failings. ...may be... but in fact, not at all. No one will be wondering about JSH, long gone troll on the internet. >But who will even know about you? She is famous, JSH is known crackpot/troll and self-admitted non-mathematical person. >James Harris === Subject: Re: More with Quadratic Diophantine Theorem >[...] >But who will even know about you? She is famous, JSH is known crackpot/troll and self-admitted >non-mathematical person. Galathaea, you're a ... celebrity!? May I have your autograph? :-) -- Angus Rodgers Contains mild peril === Subject: Re: More with Quadratic Diophantine Theorem posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN Gecko/20070509 Camino/1.5,gzip(gfe),gzip(gfe) >[...] >But who will even know about you? She is !&^^@u$, JSH is known crackpot/troll and self-admitted >non-mathematical person. Galathaea, you're a ... celebrity!? no this is obviously a cia attempt to make my head explode by appealing to my narcissism and latent messiah complex they are concerned my antiamerican manifesto and the antiamerican party as a whole is about to go viral after some well placed plants on the daily show and rush limbaugh they still haven't realised though that my paranoia long ago forced me to filter all news i read through a bot that alters all such head-exploding comments (thereby upholding the first law of bots) > May I have your autograph? :-) -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: Re: More with Quadratic Diophantine Theorem posting-account=Yn5cwwoAAADntcMuRwk-EwLg-DMZ_hXN Gecko/20070509 Camino/1.5,gzip(gfe),gzip(gfe) >[...] >But who will even know about you? >She is !&^^@u$, JSH is known crackpot/troll and self-admitted >non-mathematical person. Galathaea, you're a ... celebrity!? no this is obviously a cia attempt to make my head explode > by appealing to my narcissism > and latent messiah complex they are concerned my antiamerican manifesto > and the antiamerican party as a whole > is about to go viral after some well placed plants > on the daily show and rush limbaugh they still haven't realised > though > that my paranoia long ago forced me > to filter all news i read through > a bot that alters all such head-exploding comments > (thereby upholding the first law of bots) May I have your autograph? :-) actually my head almost exploded with the request for autograph i'm seriously concerned about my bot letting that through i'm wondering if it's turning against me too... (just because i'm paranoid doesn't mean they're not out to get me and _they_ have many tricks...) -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: solutions manual (To search click in keyboard Ctrl+F) posting-account=y7Z6OAoAAAD9FX_IL8yyi-5ioDwYBttu CLR 2.0.50727),gzip(gfe),gzip(gfe) solutions manual (To search click in keyboard Ctrl+F) Solutions Manuals in Electronic (PDF)Format! Just contact with , solutionpayfee (at) hotmail.com (my email address), these are parts of our solutions, if the solution you want is on the list, please email to me. NOTICE: if the solutions manual that in my list ,please note it in your email . 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Martin(chapter 1 to chapter15) solution manual for Probability and Statistical Inference ( 7th edition by Hogg & Tanis) solution manual for Fundamentals of Communication Systems by John G. Proakis ,Masoud Salehi === Subject: Re: Card Probability Any one? === Subject: solution manual for Design and Analysis of Experiments 6th Edition solutions manual by Douglas C. Montgomery posting-account=aKV_eAoAAADXzRa1b97cF1Cm-0DpAIKo Gecko/2008070208 UGES/1.7.2.0 Firefox/3.0.1,gzip(gfe),gzip(gfe) hey! I need to get solution manual for tha book Design and Analysis of Experiments 6th Edition solutions manual by Douglas C. Montgomery It has to be deliver for this saturday. I prefer pdf format. pls contact me as soon as possible if you have one. arif === Subject: need solution manual of analysis and design of analog integrated circuits by PR gray,P.J Hurst R.G Meyer posting-account=TaHQxQkAAAAuQ0WrbbccylauOL3oy6nA 1.1.4322; .NET CLR 2.0.50727; .NET CLR 3.0.04506.30; InfoPath.2),gzip(gfe),gzip(gfe) hi i m in short of funds and i need the solution as to help me understand the concepts please fwd me the solutions if you have === Subject: Re: nilsson riedel solutions posting-account=-pJcQAkAAAC6v5z1s_ijkIZJRl4lQR-D Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) tsubasa...@gmail.com > If anyone has this solutions manual, I would really appreciate you > sending them to me: ee9...@gmail.com > Me too please if you can... pntbll1313@yahoo.com === Subject: Re: JSH: Now we'll see > They angered me despite my experience with this sort of thing as I see > them as hating knowledge, hating discovery, and hating humanity in the > process. I doubt that they hate any of those things. What they don't like (as > opposed to hate) to you posting trivia sometimes and falsehoods often > and claiming that it is all so very important. JSH intentionally posts trivia, and knowingly posts lies, he is a troll. internet, that is it, and he has admitted that. > You make yourself look foolish. Result? People think you're a fool. yep, he is a fool, and not very bright either. === Subject: Complete theory for 2 variable Diophantine equations, paper now available posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) I have completed the basic theory for 2 variable Diophantine equations. That is, the mathematical theory covering equations of the form c_1*x^2 + c_2*xy + c_3*y^2 = c_4 + c_5*x + c_6*y. That theory gives the equation for determining existence of integer solutions, as well as a method using what I call Diophantine chains to actually find solutions when they exist. The paper does include some basic Pell's Equation results as well, like the result that for every solution to Pell's Equation of the form x^2 - 2y^2 = 1 you have a solution to the negative Pell's equation z^2 - 2(x+y)^2 = -1. I am publishing through Google Docs: James Harris === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > I have completed the basic theory for 2 variable Diophantine > equations. æThat is, the mathematical theory covering equations of the > form c 1*x^2 + c 2*xy + c 3*y^2 = c 4 + c 5*x + c 6*y. That theory gives the equation for determining existence of integer > solutions, as well as a method using what I call Diophantine chains to > actually find solutions when they exist. The paper does include some basic Pell's Equation results as well, > like the result that for every solution to Pell's Equation of the form x^2 - 2y^2 = 1 you have a solution to the negative Pell's equation z^2 - 2(x+y)^2 = > -1. I am publishing through Google Docs: > I did want to put the new mathematical tools forward but also I was curious to find out things like, can people actually access the document? And more importantly, will anyone reply with issues with the details of the theory itself? After all I found a proof of Fermat's Last Theorem over 6 years ago. I no longer believe in the academic system. I read news reports of supposed findings, or listen to babbling about String theory or supposedly how old the universe is, and now kind of yawn, if I bother at all. It is weird though. I discretized conic sections using my tautological spaces. And added to my math yet another remarkable result, which took me 8 days to do, with mathematical tools so powerful they can do that with little to no effort. 2000 years of mathematical research in that area. 8 days for me to cover with a more powerful and succinct mathematical theory. So I had this one idea I call tautological spaces and it can do so much, but it doesn't seem like that big of a deal. But I remember being a kid playing with parabolas, graphing them over and over again, and being excited about their properties. Reading other people's math. Now I read my math. And to my math that I read I now have a full discrete theory for conics in general, figured out within a few days, using a mathematical technique, I invented. And the world calls me a crackpot. I no longer believe in people, with good reasons. Over six years of good reasons with the knowledge of my accomplishments and the world's reaction to them. But at least I still like people, mostly. I just kind of see most as, primitive. I believe in mathematics. Long after all of you are dead. Long after the sun has cooled and the Milky Way has drifted apart, what I've discovered will still be true. And I defined mathematical proof. So I know of what I speak. James Harris === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available posting-account=Rkt6TwoAAACG_SqlrxmgPCl1Ozr0PWSD Trident/4.0; .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) > I have completed the basic theory for 2 variable Diophantine > equations. That is, the mathematical theory covering equations > of the form c_1*x^2 + c_2*xy + c_3*y^2 = c_4 + c_5*x + c_6*y. Just so we know what to look out for, which parts of the theory did you provide that were missed by Euler, Gauss, Lagrange, H J S Smith, Hurwitz, Minkowski, Kneser, Watson, Hasse, and a few dozen others? John R Ramsden === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.13 (KHTML, like Gecko) Chrome/0.2.149.29 Safari/525.13,gzip(gfe),gzip(gfe) > I have completed the basic theory for 2 variable Diophantine > equations. æThat is, the mathematical theory covering equations > of the form c 1*x^2 + c 2*xy + c 3*y^2 = c 4 + c 5*x + c 6*y. Just so we know what to look out for, which parts of the theory > did you provide that were missed by Euler, Gauss, Lagrange, > H J S Smith, Hurwitz, Minkowski, Kneser, Watson, Hasse, > and a few dozen others? I've simplified. Just the number of names shows that all of their research couldn't go into 6 pages. I give a complete theory in only 6 pages. Mathematicians might not care about such a simplification, though I hope they do, but for physicists simpler mathematical tools are gold. They're easier to use, can be used more widely, and can point to underlying physical rules. Like here, there could be greater indications of discrete behavior beyond known quantum behavior, which could advance discrete physics theory. Discrete mathematics is such a difficult area that physics theories that assume more discrete behavior in our world--like discrete space-- are hard to mathematicize. One of my long time goals has been opening the door to checking such ideas, which requires advancing the mathematical tools. Taking an area of number theory with 2000 years of prior history and simplifying with a 6 page paper which encompasses everything previously done indicates that the mathematical tool advancements are achievable. It could mean a total transformation of our understanding of behavior in certain areas, and might allow the merging of Einstein's gravitational theories with quantum mechanics. The two theories kind of don't seem to like each other now. James Harris. === Subject: JSH: Complete theory for 2 variable Diophantine equations, paper now available posting-account=aLpfCwoAAACh4BOs3HOlQBCoxUpEgyxc Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) Discrete mathematics is such a difficult area that physics theories > that assume more discrete behavior in our world--like discrete space-- > are hard to mathematicize. Wrong. In fact one of the main reasons for introducing lattice field theory - a huge area of research in current physics - is that lattice theories are much /easier/ to mathematicize than their continuum counterparts. === Subject: Re: JSH: Complete theory for 2 variable Diophantine equations, paper now available posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) Discrete mathematics is such a difficult area that physics theories > that assume more discrete behavior in our world--like discrete space-- > are hard to mathematicize. Wrong. In fact one of the main reasons for introducing lattice field > theory - a huge area of research in current physics - is that lattice > theories are much /easier/ to mathematicize than their continuum > counterparts. Ok then, quantize gravitational theory and report back. Or simply give an overview of current efforts with quantum gravity. James Harris === Subject: Re: JSH: Complete theory for 2 variable Diophantine equations, paper now available > Discrete mathematics is such a difficult area that physics theories > that assume more discrete behavior in our world--like discrete space-- > are hard to mathematicize. Wrong. In fact one of the main reasons for introducing lattice field > theory - a huge area of research in current physics - is that lattice > theories are much /easier/ to mathematicize than their continuum > counterparts. Ok then, quantize gravitational theory and report back. Or simply > give an overview of current efforts with quantum gravity. James Harris Hey stooopid Harris - quantized gravitation is a trivial mathematical exercise. Go write a quantized gravitation theory that is testably predictive. Science is empirical, math is not. We'll wait. Hey stooopid Harris - why aren't you rich from breaking posted RSA products into paired primes? Did somebody steal your zeta function, stooopid Harris? -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/lajos.htm#a2 === Subject: Re: JSH: Complete theory for 2 variable Diophantine equations, paper now available posting-account=aLpfCwoAAACh4BOs3HOlQBCoxUpEgyxc Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > Discrete mathematics is such a difficult area that physics theories > that assume more discrete behavior in our world--like discrete space-- > are hard to mathematicize. Wrong. In fact one of the main reasons for introducing lattice field > theory - a huge area of research in current physics - is that lattice > theories are much /easier/ to mathematicize than their continuum > counterparts. Ok then, quantize gravitational theory and report back. Huh? What on Earth do you think this question has to do with what I That doesn't change the fact that lattice theories are much easier to mathematicize than their continuum counterparts. In fact the main difficulty with quantising gravity is the fact that the theory is not perturbatively renormalizable, and last I heard it was not known whether there its RG flow has a UV fixed point - these are problems which arise precisely because the theory treats spacetime as continuous, rather than discrete. So your question is utterly irrelevant. On the other hand you claim that physical theories with discrete space are harder to mathematicize, so it only seems fair to ask you to rigorously define quantised Yang-Mills theory on Minkowski space. After all, the discrete-space version of the theory has been defined for decades, so if it's true that discrete-space theories are harder to mathematicize than their continuum counterparts then defining Yang- Mills theory on continuous spacetime should be a doddle. Also there's potentially a million dollars in it for you, since it's one of the Clay institute problems. So get cracking, and report back. >æOr simply give an overview of current efforts with quantum gravity. === Subject: Re: JSH: Complete theory for 2 variable Diophantine equations, paper now available posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) Discrete mathematics is such a difficult area that physics theories > that assume more discrete behavior in our world--like discrete space-- > are hard to mathematicize. Wrong. In fact one of the main reasons for introducing lattice field > theory - a huge area of research in current physics - is that lattice > theories are much /easier/ to mathematicize than their continuum > counterparts. Ok then, quantize gravitational theory and report back. Or simply give an overview of current efforts with quantum gravity. James Harris === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available >Taking an area of number theory with 2000 years of prior history and >simplifying with a 6 page paper which encompasses everything >previously done indicates that the mathematical tool advancements are >achievable. It could mean a total transformation of our understanding of behavior >in certain areas, and might allow the merging of Einstein's >gravitational theories with quantum mechanics. All by rearranging the terms of a quadratic equation? That's ... literally incredible! -- Angus Rodgers Contains mild peril === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available > Taking an area of number theory with 2000 years of prior history and > simplifying with a 6 page paper which encompasses everything > previously done indicates that the mathematical tool advancements are > achievable. > It could mean a total transformation of our understanding of behavior > in certain areas, and might allow the merging of Einstein's > gravitational theories with quantum mechanics. All by rearranging the terms of a quadratic equation? > That's ... literally incredible! > Yes, but don't forget the tautological space. That makes a difference. === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.13 (KHTML, like Gecko) Chrome/0.2.149.29 Safari/525.13,gzip(gfe),gzip(gfe) > Taking an area of number theory with 2000 years of prior history and > simplifying with a 6 page paper which encompasses everything > previously done indicates that the mathematical tool advancements are > achievable. > It could mean a total transformation of our understanding of behavior > in certain areas, and might allow the merging of Einstein's > gravitational theories with quantum mechanics. All by rearranging the terms of a quadratic equation? > That's ... literally incredible! Yes, but don't forget the tautological space. æThat makes a difference. For the physicists what I do is artificially add extra degrees of freedom. It's a kind of wacky technique that came to me back in December 1999, where you take an expression like x+y+vz = x+y+vz and express it with mod as x+y+vz = 0(mod x+y+vz) and then do some basic algebraic manipulations, and subtract out an equation to be analyzed, and consider the residue which is how I got my Quadratic Diophantine Theorem, which allowed me to encompass 2000 years of mathematical research on 2 variable quadratic Diophantines, in 6 pages. It is an incredibly powerful analysis technique which is unfortunately facing a vicious political war with current number theorists--fighting over what they see as their turf against an outsider--doing their best from what I've seen to suppress the technique by suffocation-- literally sucking the air away from knowledge of it by not acknowledging it, or by some criticizing results from it. But for physicists it is really just adding degrees of freedom. The v variable is totally free and carefully setting it to various values is what allows you to get results. If physicists do not help me with the political war, I have no doubt number theorists will continue to work to suppress the technology. So far they have done so since December 1999--to give you perspective. publishing a paper of mine with analysis done using this technique. So you see, it IS a war of information suppression and a dead mathematical journal is one of the casualties. James Harris === Subject: Re: JSH Complete theory for 2 variable Diophantine equations, paper now available Alert Blocking level 7 all Cisco Routers JSH Block imposed Further attempts by JSH to post Math JSH will be truncated with extreme prejudice === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.13 (KHTML, like Gecko) Chrome/0.2.149.29 Safari/525.13,gzip(gfe),gzip(gfe) >Taking an area of number theory with 2000 years of prior history and >simplifying with a 6 page paper which encompasses everything >previously done indicates that the mathematical tool advancements are >achievable. It could mean a total transformation of our understanding of behavior >in certain areas, and might allow the merging of Einstein's >gravitational theories with quantum mechanics. All by rearranging the terms of a quadratic equation? > That's ... literally incredible! My position is that the difficulties in reconciling the general theory of relativity with quantum mechanics have to do with the discrete. There are rules that are emergent with discrete results that are not there with continuous functions, which can even be seen with my current paper where there is a mod p result that exists based on how quadratic residues behave. It disappears in the field of reals or complex numbers. The issue is a huge one in physics. And the question really is about describing our world. You see, in physics, what works is what works in the real world. Better mathematical tools are needed to explore this area. My research may be a foot in the door... James Harris === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available >Taking an area of number theory with 2000 years of prior history and >simplifying with a 6 page paper which encompasses everything >previously done indicates that the mathematical tool advancements are >achievable. It could mean a total transformation of our understanding of behavior >in certain areas, and might allow the merging of Einstein's >gravitational theories with quantum mechanics. All by rearranging the terms of a quadratic equation? > That's ... literally incredible! >My position is that the difficulties in reconciling the general theory >of relativity with quantum mechanics have to do with the discrete. piss-off, moron. >There are rules that are emergent with discrete results that are not >there with continuous functions, which can even be seen with my >current paper where there is a mod p result that exists based on how >quadratic residues behave. new buzzwords will not help you. >It disappears in the field of reals or complex numbers. So is your intelect, disappeared into complex spoofarinies. >The issue is a huge one in physics. And the question really is about >describing our world. Wrong. You need attention to exist, post your crap in alt.highschool.morons.with.NPD. >You see, in physics, what works is what works in the real world. You have no idea of what you are talking about. >Better mathematical tools are needed to explore this area. My >research may be a foot in the door... Rather a turd on the Lawn. >James Harris === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available reply-type=response >Taking an area of number theory with 2000 years of prior history and >simplifying with a 6 page paper which encompasses everything >previously done indicates that the mathematical tool advancements are >achievable. >It could mean a total transformation of our understanding of behavior >in certain areas, and might allow the merging of Einstein's >gravitational theories with quantum mechanics. > All by rearranging the terms of a quadratic equation? > That's ... literally incredible! >My position is that the difficulties in reconciling the general theory >of relativity with quantum mechanics have to do with the discrete. piss-off, moron. Yeah, why don't you off, stooopid emotional ignorant cunt? === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available I have completed the basic theory for 2 variable Diophantine > equations. That is, the mathematical theory covering equations of the > form c_1*x^2 + c_2*xy + c_3*y^2 = c_4 + c_5*x + c_6*y. That theory gives the equation for determining existence of integer > solutions, as well as a method using what I call Diophantine chains to > actually find solutions when they exist. The paper does include some basic Pell's Equation results as well, > like the result that for every solution to Pell's Equation of the form x^2 - 2y^2 = 1 you have a solution to the negative Pell's equation z^2 - 2(x+y)^2 = > -1. I am publishing through Google Docs: > James Harris What are you telling us for. If it's new publich it in a joural or conference. === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.13 (KHTML, like Gecko) Chrome/0.2.149.29 Safari/525.13,gzip(gfe),gzip(gfe) I have completed the basic theory for 2 variable Diophantine > equations. æThat is, the mathematical theory covering equations of the > form c 1*x^2 + c 2*xy + c 3*y^2 = c 4 + c 5*x + c 6*y. That theory gives the equation for determining existence of integer > solutions, as well as a method using what I call Diophantine chains to > actually find solutions when they exist. The paper does include some basic Pell's Equation results as well, > like the result that for every solution to Pell's Equation of the form x^2 - 2y^2 = 1 you have a solution to the negative Pell's equation z^2 - 2(x+y)^2 = > -1. I am publishing through Google Docs: > James Harris What are you telling us for. If it's new publich it in a joural or > conference. It's at a journal, but that takes time. And they might decide not to publish anyway. But I can provide the mathematical tools which DO have relevance to current physics research, as well as research in other sciences, today. So hey, don't worry. Paper is at a journal--a major one. But in the meantime, I can also publish directly and physicists can use the mathematical tools now--without waiting on some editors and publication cycles of a major journal. Oh, also, I'm not a big fan of journals though I do play the game, and with some revolutionary mathematics in it--relying on similar techniques to those used for this latest research--and some freaking sci.math'ers not only managed to get the editors of that journal to pull my paper after publication with some concerted emails, wouldn't you know the damn journal DIED a few months later. Yeah. Died. The entire freaking journal keeled over and quietly died. It was a 10 year old journal. Yeah. It's like that. The journal system is weak. But I know, yeah, it's the main system, so I at least DID send this latest paper to one--and then published myself. James Harris === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available > Oh, also, I'm not a big fan of journals though I do play the game, and > with some revolutionary mathematics in it--relying on similar > techniques to those used for this latest research--and some freaking > sci.math'ers not only managed to get the editors of that journal to > pull my paper after publication with some concerted emails, wouldn't > you know the damn journal DIED a few months later. /tried/ submitting the paper to another journal? > But I know, yeah, it's the main system, so I at least DID send this > latest paper to one--and then published myself. Pray tell, could you post the reviewers' comments when they come back? === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.13 (KHTML, like Gecko) Chrome/0.2.149.29 Safari/525.13,gzip(gfe),gzip(gfe) > Oh, also, I'm not a big fan of journals though I do play the game, and > with some revolutionary mathematics in it--relying on similar > techniques to those used for this latest research--and some freaking > sci.math'ers not only managed to get the editors of that journal to > pull my paper after publication with some concerted emails, wouldn't > you know the damn journal DIED a few months later. /tried/ submitting the paper to another journal? Yes. > But I know, yeah, it's the main system, so I at least DID send this > latest paper to one--and then published myself. Pray tell, could you post the reviewers' comments when they come back? They never send them to me. Never. Guess they realize I'd just post them and rip on them. The journals do not follow the rules with my research. They can't. As if they followed the rules, they'd publish. Like with this latest result, it IS a general theory for 2 variable Diophantine equations which is simpler than anything else previously known. I've boiled down 2000 years of math history to a 6 page paper that represents research I started 8 days ago. I'm shutting down just one number theory area, for now, by completing the research. I can take them all away. Of course, number theorists can pretend I did not, but then, they're more than just pathetic, now aren't they? And physicists will have to not use tools readily available to give in to mathematicians who are, well, weak. It took me one week to take away 2 variable Diophantine equations. One week. James Harris === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available > But I know, yeah, it's the main system, so I at least DID send this > latest paper to one--and then published myself. > Pray tell, could you post the reviewers' comments when they come back? They never send them to me. Never. Guess they realize I'd just post them and rip on them. Let me see if I got this one. You are claiming that when your paper was accepted the editor did not send you the reviewers' comments because he realized that you would just post them and rip on them. Did I get that right? Jose Carlos Santos === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available <6j40d9F1c46bU1@mid.individual.net> posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.13 (KHTML, like Gecko) Chrome/0.2.149.29 Safari/525.13,gzip(gfe),gzip(gfe) But I know, yeah, it's the main system, so I at least DID send this > latest paper to one--and then published myself. > Pray tell, could you post the reviewers' comments when they come back? They never send them to me. æNever. Guess they realize I'd just post them and rip on them. Let me see if I got this one. You are claiming that when your paper was > accepted the editor did not send you the reviewers' comments because he > realized that you would just post them and rip on them. Did I get that > right? > all the arguing on sci.math so I told the editors upfront that I was an amateur researcher, and even had to correct them when they were sending emails to me with Dr. Harris. And they stopped doing that and switched to Mr. Harris. If I'd realized that I should get reviewers comments I would have requested them, but the editors may have been hedging their bets by not sending them. One of the more telling emails I think was when I was effusively thanking them for publishing my paper--I had been in contact regularly with the journal editors for 9 months keeping up with how things were going--one of the editors emailed me back that it didn't matter who found a result, but only its correctness mattered, even if that person were a janitor. I thought that was kind of odd thing to say, but maybe a reference to the movie Good Will Hunting and an indication that the editors realized how big my paper was. And later after the debacle I was in contact with other editors on the journal after chief editor refused to reply back to me after sending an email that he was taking a sabbatical, so no, I don't accept the explanations that sci.math posters give claiming that it was all just a mistake. And posters claim I knowingly sent an erroneous paper to the journal but Barry Mazur himself commented on an early draft!!! I forwarded his email to Ralph McKenzie when he was claiming problems with the paper when I'd sent it to him for publication in a journal for which he was editor, and after Dr. Mazur's paper he offered I could explain to him in person. And I DID explain to him in person driving over 4 hours each way from the Atlanta metro area, so I put in the legwork for that paper and had feedback from top mathematicians--none of whom gave the sci.math'er complaints. NONE OF THEM VALIDATED ANY OF YOUR COMPLAINTS ABOUT THE PAPER OR ITS METHOD. The editors knew what they were doing when they published my paper. The journal used two reviewers. I never got their reports. And the sci.math email campaign worked against 9 months of effort, where I was upfront with those editors. So it was the sci.math'ers who deliberately with their emails broke the journal system, and even that journal itself died. The sci.math'ers showed the weakness of the system, and maybe the editors did just kind of give up, as in one of their first editions they'd published a paper claiming to prove P=NP, nearly 10 years before. And don't blather on about what the author of that paper says today, as after 10 years why would he hold onto his claims if his society doesn't play by its own rules, if he wants to keep working as a mathematician? Maybe a lot of mathematicians themselves have given up on the math system. James Harris === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available > But I know, yeah, it's the main system, so I at least DID send this > latest paper to one--and then published myself. > Pray tell, could you post the reviewers' comments when they come back? > They never send them to me. Never. > Guess they realize I'd just post them and rip on them. > Let me see if I got this one. You are claiming that when your paper was > accepted the editor did not send you the reviewers' comments because he > realized that you would just post them and rip on them. Did I get that > right? all the arguing on sci.math so I told the editors upfront that I was > an amateur researcher, and even had to correct them when they were > sending emails to me with Dr. Harris. And they stopped doing that > and switched to Mr. Harris. If I'd realized that I should get reviewers comments I would have > requested them, but the editors may have been hedging their bets by > not sending them. One of the more telling emails I think was when I was effusively > thanking them for publishing my paper--I had been in contact regularly > with the journal editors for 9 months keeping up with how things were > going--one of the editors emailed me back that it didn't matter who > found a result, but only its correctness mattered, even if that person > were a janitor. I fully agree with the editor on this. > I thought that was kind of odd thing to say, but maybe a reference to > the movie Good Will Hunting and an indication that the editors > realized how big my paper was. How did you jump from correct to big paper? > And later after the debacle I was in contact with other editors on the > journal after chief editor refused to reply back to me after sending > an email that he was taking a sabbatical, so no, I don't accept the > explanations that sci.math posters give claiming that it was all just > a mistake. And posters claim I knowingly sent an erroneous paper to the journal > but Barry Mazur himself commented on an early draft!!! I forwarded his email to Ralph McKenzie when he was claiming problems > with the paper when I'd sent it to him for publication in a journal > for which he was editor, and after Dr. Mazur's paper he offered I > could explain to him in person. And I DID explain to him in person driving over 4 hours each way from > the Atlanta metro area, so I put in the legwork for that paper and had > feedback from top mathematicians--none of whom gave the sci.math'er > complaints. NONE OF THEM VALIDATED ANY OF YOUR COMPLAINTS ABOUT THE PAPER OR ITS > METHOD. The editors knew what they were doing when they published my paper. > The journal used two reviewers. How do you know that? > I never got their reports. You never even *saw* them. How do you know that they ever existed? > And the sci.math email campaign worked against 9 months of effort, > where I was upfront with those editors. Effort? You sent the paper and, nine months later they published. What effort did you do during those months? > So it was the sci.math'ers who deliberately with their emails broke > the journal system, and even that journal itself died. Which proofs do you have concerning the connection between your paper being withdrawn and the end of the journal? Jose Carlos Santos === Subject: Re: JSH Complete theory for 2 variable Diophantine equations, paper now available > But I know, yeah, it's the main system, so I at least DID send this > latest paper to one--and then published myself. > Pray tell, could you post the reviewers' comments when they come back? > They never send them to me. Never. > Guess they realize I'd just post them and rip on them. > Let me see if I got this one. You are claiming that when your paper was > accepted the editor did not send you the reviewers' comments because he > realized that you would just post them and rip on them. Did I get that > right? > all the arguing on sci.math so I told the editors upfront that I was > an amateur researcher, and even had to correct them when they were > sending emails to me with Dr. Harris. And they stopped doing that > and switched to Mr. Harris. > If I'd realized that I should get reviewers comments I would have > requested them, but the editors may have been hedging their bets by > not sending them. > One of the more telling emails I think was when I was effusively > thanking them for publishing my paper--I had been in contact regularly > with the journal editors for 9 months keeping up with how things were > going--one of the editors emailed me back that it didn't matter who > found a result, but only its correctness mattered, even if that person > were a janitor. I fully agree with the editor on this. Agree here too, it has always been that way. > I thought that was kind of odd thing to say, but maybe a reference to > the movie Good Will Hunting and an indication that the editors > realized how big my paper was. How did you jump from correct to big paper? Wrong conclusion. (JSH unfamiliar with process now conjectures failing to realize that most all papers are small.) > And later after the debacle I was in contact with other editors on the > journal after chief editor refused to reply back to me after sending > an email that he was taking a sabbatical, so no, I don't accept the > explanations that sci.math posters give claiming that it was all just > a mistake. So? he was taking a sabbatical. What has the rest of above to do with that? > And posters claim I knowingly sent an erroneous paper to the journal > but Barry Mazur himself commented on an early draft!!! > I forwarded his email to Ralph McKenzie when he was claiming problems > with the paper when I'd sent it to him for publication in a journal > for which he was editor, and after Dr. Mazur's paper he offered I > could explain to him in person. > And I DID explain to him in person driving over 4 hours each way from > the Atlanta metro area, so I put in the legwork for that paper and had > feedback from top mathematicians--none of whom gave the sci.math'er > complaints. didn't you threaten him at the chalkboard? Did you know it is very easy to talk with most all professors at universities? Did you listen to him or try to ram your math down his throat? > NONE OF THEM VALIDATED ANY OF YOUR COMPLAINTS ABOUT THE PAPER OR ITS > METHOD. You must show it is correct. Did any of them validate it was correct ?? > The editors knew what they were doing when they published my paper. > The journal used two reviewers. How do you know that? How? > I never got their reports. You never even *saw* them. How do you know that they ever existed? Obviously, JSH confrontational personality was known by them and for reasons of personal safety instead of telling him to go back to high school, they dropped it. Or nobody really reviewed it at all, then the paper was withdrawn, JSH got caught with his spoof. > And the sci.math email campaign worked against 9 months of effort, > where I was upfront with those editors. Effort? You sent the paper and, nine months later they published. What > effort did you do during those months? > So it was the sci.math'ers who deliberately with their emails broke > the journal system, and even that journal itself died. Wrong again. Accept the fact that your paper is junk, written by a troll. Which proofs do you have concerning the connection between your paper > being withdrawn and the end of the journal? > Jose Carlos Santos === Subject: Re: JSH Complete theory for 2 variable Diophantine equations, paper now available > One of the more telling emails I think was when I was effusively > thanking them for publishing my paper--I had been in contact regularly > with the journal editors for 9 months keeping up with how things were > going--one of the editors emailed me back that it didn't matter who > found a result, but only its correctness mattered, even if that person > were a janitor. I fully agree with the editor on this. Agree here too, it has always been that way. OK, now I'm curious. Some of the great mathematicians of the past were what we today would call amateurs. But has any amateur actually found anything significant in modern times? Let's define amateur as someone without a PhD in mathematics (or a related field). What is the most significant amateur contribution in, say, the last 20 years? Last 50 years? Last 100 years? -- --Tim Smith === Subject: Re: JSH Complete theory for 2 variable Diophantine equations, paper now available > One of the more telling emails I think was when I was effusively > thanking them for publishing my paper--I had been in contact regularly > with the journal editors for 9 months keeping up with how things were > going--one of the editors emailed me back that it didn't matter who > found a result, but only its correctness mattered, even if that person > were a janitor. > I fully agree with the editor on this. > Agree here too, it has always been that way. OK, now I'm curious. Some of the great mathematicians of the past were what we today would > call amateurs. But has any amateur actually found anything significant > in modern times? Marjorie Rice: http://www.ivanrival.com/docs/picturepuzzling_2.pdf Jose Carlos Santos === Subject: Re: JSH Complete theory for 2 variable Diophantine equations, paper now available >One of the more telling emails I think was when I was effusively >thanking them for publishing my paper--I had been in contact regularly >with the journal editors for 9 months keeping up with how things were >going--one of the editors emailed me back that it didn't matter who >found a result, but only its correctness mattered, even if that person >were a janitor. I fully agree with the editor on this. >Agree here too, it has always been that way. OK, now I'm curious. Some of the great mathematicians of the past were what we today would > call amateurs. But has any amateur actually found anything significant > in modern times? Let's define amateur as someone without a PhD in mathematics (or a > related field). What is the most significant amateur contribution in, > say, the last 20 years? Last 50 years? Last 100 years? Ramanujan's work, perhaps ? http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Ramanujan.html Han de Bruijn === Subject: Re: JSH Complete theory for 2 variable Diophantine equations, paper now available One of the more telling emails I think was when I was effusively >thanking them for publishing my paper--I had been in contact regularly >with the journal editors for 9 months keeping up with how things were >going--one of the editors emailed me back that it didn't matter who >found a result, but only its correctness mattered, even if that person >were a janitor. >I fully agree with the editor on this. Agree here too, it has always been that way. > OK, now I'm curious. > Some of the great mathematicians of the past were what we today would > call amateurs. But has any amateur actually found anything significant > in modern times? > Let's define amateur as someone without a PhD in mathematics (or a > related field). What is the most significant amateur contribution in, > say, the last 20 years? Last 50 years? Last 100 years? Ramanujan's work, perhaps ? http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Ramanujan.html Han de Bruijn Ramanujan was amature, He was a real genius. After reading his works, one concludes that this JSH stuff is complete 100% crap. === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available > Oh, also, I'm not a big fan of journals though I do play the game, and > with some revolutionary mathematics in it--relying on similar > techniques to those used for this latest research--and some freaking > sci.math'ers not only managed to get the editors of that journal to > pull my paper after publication with some concerted emails, wouldn't > you know the damn journal DIED a few months later. > /tried/ submitting the paper to another journal? Yes. > But I know, yeah, it's the main system, so I at least DID send this > latest paper to one--and then published myself. > Pray tell, could you post the reviewers' comments when they come back? They never send them to me. Never. Guess they realize I'd just post them and rip on them. That's one possible explanation. === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available [snip crap] > James Harris GOD SAVE US FROM THE CONGENITALLY UNIMPORTANT. That's you, harris. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/lajos.htm#a2 === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available posting-account=OKTeIQkAAAAZk6JK1hK7-grwpoUDNy98 2.0.50727),gzip(gfe),gzip(gfe) > I have completed the basic theory for 2 variable Diophantine > equations. æThat is, the mathematical theory covering equations of the > form > c 1*x^2 + c 2*xy + c 3*y^2 = c 4 + c 5*x + c 6*y. > That theory gives the equation for determining existence of integer > solutions, as well as a method using what I call Diophantine chains to > actually find solutions when they exist. > The paper does include some basic Pell's Equation results as well, > like the result that for every solution to Pell's Equation of the form > x^2 - 2y^2 = 1 > you have a solution to the negative Pell's equation z^2 - 2(x+y)^2 = > -1. > I am publishing through Google Docs: > James Harris What are you telling us for. If it's new publich it in a joural or > conference. It's at a journal, but that takes time. æAnd they might decide not to > publish anyway. Ya think? But I can provide the mathematical tools which DO have relevance to > current physics research, as well as research in other sciences, > today. Yeah, sure. So hey, don't worry. æPaper is at a journal--a major one. æ Be sure and let us know what they say when they reject it. > But in the > meantime, I can also publish directly and physicists can use the > mathematical tools now--without waiting on some editors and > publication cycles of a major journal. Or waiting for a peer review. Oh, also, I'm not a big fan of journals though I do play the game, and > with some revolutionary mathematics in it--relying on similar > techniques to those used for this latest research--and some freaking > sci.math'ers not only managed to get the editors of that journal to > pull my paper after publication with some concerted emails, wouldn't > you know the damn journal DIED a few months later. You've still never said. Who put you up to sending it to Yeah. æDied. æThe entire freaking journal keeled over and quietly > died. æIt was a 10 year old journal. æYeah. æIt's like that. The journal system is weak. So are your papers. But I know, yeah, it's the main system, so I at least DID send this > latest paper to one--and then published myself. Anybody can post anything. James Harris === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available > I have completed the basic theory for 2 variable Diophantine > equations. That is, the mathematical theory covering equations of the > form > c_1*x^2 + c_2*xy + c_3*y^2 = c_4 + c_5*x + c_6*y. > That theory gives the equation for determining existence of integer > solutions, as well as a method using what I call Diophantine chains to > actually find solutions when they exist. > The paper does include some basic Pell's Equation results as well, > like the result that for every solution to Pell's Equation of the form > x^2 - 2y^2 = 1 > you have a solution to the negative Pell's equation z^2 - 2(x+y)^2 = > -1. > I am publishing through Google Docs: > James Harris What are you telling us for. If it's new publich it in a joural or > conference. You just answered your own question. === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available posting-account=jPnQ2goAAAA461y3QD0lbyw0oKeThma1 AppleWebKit/525.18 (KHTML, like Gecko) Version/3.1.2 Safari/525.20.1,gzip(gfe),gzip(gfe) well, seeing that he seems to imply the definition of a tuatological space (est-ce que un espace tautologique/ QuestionMark), it sort-of is a demonstration of modular arithmetic, at least the additive part of it, that I read up to/UnScrolled). that was my question, iff I had asked. yeah, what you call some thing is what you call something; the map is supposed to be like the terrain, preferably & suitably earthlike-ish. > You just answered your own question. thus: the additive inverse of X is -2X?... I mean, not summorial of -2X iff defined. sorry, about the outburst from Descartes CIRCA Fermat; didn't realize that it may be thought, ambivalent! === Subject: Re: Complete theory for 2 variable Diophantine equations, paper now available > I have completed the basic theory for 2 variable Diophantine > equations. That hardly belongs in a physics newsgroup, blazo :-) [followup set appropriately] Dirk Vdm === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation >Now that I have a general theory for all 2 variable quadratic >Diophantine equations I'm not even sure you know what that means. >it's worth coming back to note again the weird >connection I found between certain Pythagorean Triplets and Pell's >Equation in the form x^2 - Dy^2 = 1 when D-1 is a perfect square. For instance for D=2, I have that for >every solution of Pell's Equation you have a Pythagorean Triplet! I'm hardly an expert here, but let me make the following comments: 1. It's an interesting result 2. People should stop bashing you because it is, as I said, an interesting result. Seriously guys. He's come up with something correct for a change. Give the man some credit. 3. It's cute. Not groundbreaking. Not weird. The relationship between Pell's Equation and Pythagorean Triples has been known for a long time. A new one wouldn't be a big surprise. 4. If you'd present the results without so much ego you'd get a better reception (yes, I know your history) Alan -- Defendit numerus === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > Now that I have a general theory for all 2 variable quadratic > Diophantine equations it's worth coming back to note again the weird > connection I found between certain Pythagorean Triplets and Pell's > Equation in the form x^2 - Dy^2 = 1 when D-1 is a perfect square. æFor instance for D=2, I have that for > every solution of Pell's Equation you have a Pythagorean Triplet! But the triplets are special in that with u^2 + v^2 = w^2, v = u+1. > The connection is that w is x+y from Pell's Equation. The more general result is that u = sqrt(D-1)j, and v = j+1, while w > still equals x+y. Intriguingly that means that proof that there are an infinite number > of solutions for certain Pell's Equations is proof that there are an > infinity of Pythagorean Triplets of a certain form! An easy example with D=2, is x=17, y=12, where notice you are paired > with the triplet 20, 21, 29. That is just some low-hanging fruit that I thought I'd mention. æKind > of been a whirlwind of results flowing from playing with my > Diophantine Quadratic Theorem. New argument now I'm starting to see is that I've found nothing new, though I will add that for me the Pell's Equation result is just a fun tidbit which is nothing compared to the main result of generally solving the 2 variable Diophantine equation. A succinct example of the tidbit result claimed to not be new is the easy to show case that for EVERY solution to x^2 - 2y^2 = 1 you have a solution to the negative Pell's Equation: z^2 - 2(x+y)^2 = -1. For instance, x=17, y = 12 is a solution to the first as 17^2 - 2(12)^2 = 1 and with x+y=29, you get z=41 for the second, as 41^2 - 2(29)^2 = -1. To me that it's easy to explain so I have to wonder why no one it seems has said it in that way in human history before... 2000 years of mathematical history with Pell's Equation. The will to lie about a subject that old is a powerful and demonic one, and for those of you who have wondered how I could be right, if so many people are arguing with me, here you can see. They argue with me because these battles are supposed to be hard. If it were easy then there wouldn't be a choice, now would there? I'm set. It's you who has a fate in the balance. It's your life that is being decided now. Not mine. What are you made of? Who are you really? In a sense, me and the others here are just agents to test your mettle. God's way of testing your worth as human beings. James Harris === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation posting-account=Ae7cPwoAAAA1p9Bl1szxMYHINqjRfucA CLR 1.1.4322; .NET CLR 2.0.50727; InfoPath.1),gzip(gfe),gzip(gfe) where scan through any list of Pythagorean Triplets or if the other results that have physics implications and I'm glad to be hard. If it were easy then there wouldn't be a choice, now would there? I'm set. It's you who has a fate in the UK for most of the other results that have physics implications and I'm glad to be hard. If it were easy then there wouldn't be a quadratic residue modulo (B^2-4AC). The result is just a loudmouthed idiot who can't comprehend when a brilliant result wanders by BECAUSE you are proving that you really are just agents to test your mettle. God's way of testing your worth as human beings. You are an infinity of integer solutions to x^2-Dy^2=1, you had an integer solution to the ellipse: (D-1)u^2+v^2=w^2 where again w=x+y. So in some sense. For example, if you sent a banana is. Furthermore, I believe that the probability of your work would be nice material for an April Fool's edition, for example: it's hard to pick one as better than the other. But an actual, physical banana: just think of the banana's conspiration you have a solution using 17+12=29, so I have that S^2-D(x+y)^2=-D+1 so you see the second equation 41^2-29^2=-1. Another result of interest I found with Pell's Equation may be elliptical which may explain to some extent how it comes up in quantum physics. That solutions to exist it must be true that ((c_2-2c_1)^2+4c_1*(c_2-c_1-c_3))v^2+(2(c_2-2c_1)*(c_6-c_5)+4c_5*(c_2- c_1-c_3))v+(c_6-c_5)^2-4c_4*(c_2-c_1-c_3)=n^2modp where v=(x+y)modp, so you can substitute out z, to get 4(x- y)^2=n^2*z^2modp so the requirement is met, as of course, there are an infinity of integer solutions for x^2-2y^2=3D1 you must have integer solutions for z^2-2(x+y)^2=3D-1 which indicates they kind of surprising. Also they don't seem to have major ideas, be able to show it is, and it not matter at all. They have locked the doors against amateur discoverers and thrown away the key. New argument now I'm starting to see is that I've found can simplify explanations of our world. Physics isn't just about mouthing off or trying to impress people. It's looking for the second Diophantine equation connected to the Annals, it would not be able to share them with you. Hope you go to my math blog. The results are correct even if you delete them out in your reply. They show how to make Mock Banana from parsnips. Sorry to add a talking about post to my post: Solving Quadratic Diophantine Theorem: In the ring of integers, given the quadratic expression c_1*x^2+c_2*xy+c_3*y^2=c_4*z^2+c_5*zx+c_6*zy where the c's are constants, for solutions to x^2+y^2=z^2. And a square was required here because p can be integers just jump out at you, for instance Wikipedia has such a list at http://en.wikipedia.org/wiki/Pythagorean_triple conveniently at the top of the banana's conspiration you have c_1*x^2+c_2*xy+c_3*y^2=c_4+c_5*x+c_6*y and the result also applies to the main result of interest I found with Pell's Equation. Seems to me that it's easy to explain so I have that (2A(x+y)-B)^2+4AC-B^2=4AS^2 which is that I've found nothing new, though I will add that for every solution to the main result of generally solving any quadratic Diophantine equation of any form to a solution to u^2+v^2=w^2 -- of a particular form, which is nothing compared to the negative Pell's Equation: z^2-2(x+y)^2=3D-1. For instance, x=3D17, y=3D 12 is a stunning simplification over a previously complex areas. Besides that discrete mathematics is a Pythagorean triplet where w=x+y, and v=u+1, for every case where D-1 is a solution using 17+12=29, so I have that S^2-D(x+y)^2=-D+1 so you can the same type issue with my research is simplification. No need for long descriptions about Pell Numbers or anything else, to solutions to Pell's Equation, and found several tidbit results: With x^2-Dy^2=1, I have for the second, as 41^2-2(29)^2=3D-1. To me that you may be looking for the same type issue with my prime counting research, which is kind of surprising. Also they don't seem to have noticed before that with A=(c_2-2c_1)^2+4c_1*(c_2-c_1-c_3) B=2(c_2-2c_1)*(c_6-c_5)+4c_5*(c_2- c_1-c_3) and C=(c_6-c_5)^2-4c_4*(c_2-c_1-c_3) you have that z^2-2(x+y)^2=3D-1 any place though I will add that for EVERY solution to u^2+v^2=w^2 -- of a particular form, which is kind of cool, as in, who knew? Who knew that for every solution to u^2+v^2=w^2 -- of a particular form, which is just a fun tidbit which is nothing compared to the general diophantine quadratic in 2 variables but much simplified, and when you solve for x+y and S, you immediately have solutions for x^2-2y^2=3D1 you immediately have solutions for x^2-2y^2=3D1 you also have that S^2-D(x+y)^2=-D+1 so you see the second Diophantine equation of any form to a circle or an ellipse? And you can to say that I've found nothing new, though I have for the second Diophantine equation connected to the main result of generally solving any quadratic Diophantine in 2 variables but much simplified, and when you solve for x+y and S, you immediately get a solution for c_1*x^2+c_2*xy+c_3*y^2=c_4+c_5*x+c_6*y but also you can substitute out, and have a Xerox of the tidbit result claimed to not be accepted for formal peer review, even if you delete them out in your reply. They show how to immediately go from a 2 variable Diophantine equations in 2 variables, like c_1*x^2+c_2*xy+c_3*y^2=c_4+c_5*x+c_6*y you can the same results I've noticed, but Pell Numbers or anything else, which is nothing compared to the negative Pell's Equation: z^2-2(x +y)^2=3D-1. For instance, x=3D17, y=3D 12 is a relation to the ellipse: (D-1)u^2+v^2=w^2 where again w=x+y. So for the result also applies to the main result of interest I found with Pell's Equation. Seems to me that some people could so despise discovery, especially to do so and bother posting on a drink a'rum. Daylight come and he wanna go home. banana. It's six foot, seven foot, eight foot, bunch. A beautiful bunch a'ripe banana. Hide thee deadly black tarantula. Day-o, day-ay-ay-o. === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation posting-account=3WPJYgoAAAA55VjhzK9i07RN8h8u8eEs Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) New argument now I'm starting to see is that I've found nothing new, > In the words of Emily Litella, Nevermind. God's way of testing your worth as human beings. > LOL. Or your stupidity. Based on your track record, guess what I'm bettin on? ;>) Reality is you just need the help of others 'cuz you're too dumb to solve anything on your own. Like you, the routine's gettin old. > James Harris === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation >[...] A succinct example of the tidbit result claimed to not be new is the >easy to show case that for EVERY solution to x^2 - 2y^2 = 1 you have a solution to the negative Pell's Equation: z^2 - 2(x+y)^2 = -1. For instance, x=17, y = 12 is a solution to the first as 17^2 - 2(12)^2 = 1 and with x+y=29, you get z=41 for the second, as 41^2 - 2(29)^2 = -1. To me that it's easy to explain so I have to wonder why no one it >seems has said it in that way in human history before... 2000 years of mathematical history with Pell's Equation. Oh, gawd, is this a joke? Charlie Brown rushes up to kick the football again: (x + 2y)^2 - 2(x + y)^2 = -(x^2 - 2y^2) = -1 Even by your standards (not to mention mine), this is silly! AAUUGGGHH! Come on James, admit it: you wanted to see if anyone was daft enough to believe that you could be daft enough to mean this seriously! I just don't know what to believe. >[...] I'm set. It's you who has a fate in the balance. It's your life that is being decided now. Not mine. What are you made of? Who are you really? In a sense, me and the others here are just agents to test your >mettle. God's way of testing your worth as human beings. Some of that might be right. I'm struggling badly these days, and this might just be another test, of some weird kind ... guess I've failed. -- Angus Rodgers Contains mild peril === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) >[...] A succinct example of the tidbit result claimed to not be new is the >easy to show case that for EVERY solution to x^2 - 2y^2 = 1 you have a solution to the negative Pell's Equation: z^2 - 2(x+y)^2 = -1. For instance, x=17, y = 12 is a solution to the first as 17^2 - 2(12)^2 = 1 and with x+y=29, you get z=41 for the second, as 41^2 - 2(29)^2 = -1. To me that it's easy to explain so I have to wonder why no one it >seems has said it in that way in human history before... 2000 years of mathematical history with Pell's Equation. Oh, gawd, is this a joke? Charlie Brown rushes up to kick the football again: æ æ(x + 2y)^2 - 2(x + y)^2 æ= -(x^2 - 2y^2) æ= -1 Yup. It's EASY. Therefore the past mathematicians who didn't discover it, were they ignorant? Or maybe just, um, not so great? After all, I discovered it in a couple of days. Now, go, cite the result from any other source that Pell's Equation x^2 - 2y^2 = 1 is directly connected to the negative Pell's Equation z^2 - 2(x+y)^2 = -1. Just try to rescue the blind belief that brilliance has truly defined past mathematical efforts in this area. I suggest instead, you are making the argument that others simply failed to see the simple. > Even by your standards (not to mention mine), this is silly! AAUUGGGHH! Come on James, admit it: you wanted to see if anyone was daft > enough to believe that you could be daft enough to mean this > seriously! Um, I went from not to my knowledge even knowing about Pell's Equation last Friday, to giving some remarkably simple results that I can't find anywhere else despite their obvious simplicity, in a few days. 2000 years of mathematical history traversed by me completely within 4 days. It seems to me you make a brilliant argument that past mathematicians were not, after all, all that brilliant, unless you wish to cite someone, anyone, before me, noting that EVERY case of x^2 - 2y^2 = 1 connected to z^2 - 2(x+y)^2 = -1 as that's a kind of beautiful symmetry. Now I know how hard mathematical discovery is, so I want to say that I DO think those past mathematicians were quite brilliant, but mathematics is an infinite subject, though many of you seem to forget it. How many results would it take then? I can wipe out entire areas of number theory in a single week, as I just demonstrated. The psychological wars you people fight are just signs of weakness to me, and I know human psychology better than you do. I know how your brains are wired and why you fight. It is a primitive male urge to solidify control over women, whether you have women or not or are even gay. You are naked apes, doing what apes do. I long since tired of contacting mathematicians directly with my research as they'd always go sort of oddly silent. I'll never forget the colleague of someone I knew who was a professor who he'd contacted about my research who left the country on a 6 month sabbatical, and when he came back, claimed he didn't remember ever hearing about it. paper, went on a sabbatical as well, immediately thereafter. I wonder what happened to him. Did you people destroy his career? But blame him? I can take mathematicians out one by one at will just with an email of one of my papers. It's not the single one of you that has power. It is the bulk of all of you together. So as this proceeds, you force me to find a result that handles every mathematicians around the world at the same time. Is that challenge worthy of me? Do you think? (Oh, and their students, as well. LOL.) James Harris === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation >Um, I went from not to my knowledge even knowing about Pell's Equation >last Friday, to giving some remarkably simple results that I can't >find anywhere else despite their obvious simplicity, in a few days. 2000 years of mathematical history traversed by me completely within 4 >days. It seems to me you make a brilliant argument that past mathematicians >were not, after all, all that brilliant, unless you wish to cite >someone, anyone, before me, noting that EVERY case of x^2 - 2y^2 = 1 connected to z^2 - 2(x+y)^2 = -1 as that's a kind of beautiful symmetry. I earnestly recommend that you read John Stillwell, /Mathematics and Its History/. It has certainly opened my eyes to how little I know, and how many interesting things there are for me still to know; and, who knows, it might even do the same for you. I was looking through it this morning to help me compile a list of topics I need to know about - basic stuff, not anything that could be called advanced, scarcely even anything from the beginning of the twentieth century (or later) - and the list already contains 32 topics. I'm sure any mathematician could easily add to it other topics that they consider basic and that (if they knew how ignorant I am!) I don't know about. Anyway (in case you wonder why I mention this), I happened to come across this passage, on page 52 (see also section 3.4, earlier): The first mathematical processes we would recognise as infinite were probably devised by the Pythagoreans, for example, the recurrence relations x_{n+1} = x_n + 2y_n, y_{n+1} = x_n + y_n for generating integer solutions of the equations x^2 - 2y^2 = +/-1. So you've caught up with Pythagoras (circa 600 BCE)! That's a start. If you fancy more of a challenge, try this (from page 73): Example: x^2 - 92y^2 = 1. [This is Brahmagupta's first example; he says that a person solving this within a year is a mathematician. If you do that, you're now up to about the year 628 CE. If that's too easy, try finding a solution to x^2 - 61y^2 = 1 (Bhaskara, 1150; also Fermat, 1657). Health warning: the smallest solution is quite big (to put it mildly)! However, if you think that's peanuts, you could also have a go at Archimedes's Cattle Problem. (Archimedes's dates are 287-212 BCE.) This leads to an instance of Pell's equation, of which the number of digits in the number of digits of the smallest solution is 6. (Yes, you did read that sentence correctly.) Apparently that was solved in 1880. >The psychological wars you people fight are just signs of weakness to >me, and I know human psychology better than you do. I know how your >brains are wired and why you fight. It is a primitive male urge to solidify control over women, whether >you have women or not or are even gay. You are naked apes, doing what apes do. Hmm ... you don't know me very well, do you? But you probably have a classification already prepared for me. If I'm not an alpha male mathematician, I must be one of their pathetic minions or dupes, or something like that, yes? I wanted to add something reassuring, but I'm having an unbelievably nasty time these days, my concentration is gone, and I can't remember what it was; anyway, I'm having a hard enough time reassuring myself! I only wish someone did know how my brain is wired and why (and what!) I'm fighting. -- Angus Rodgers Contains mild peril === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > Um, I went from not to my knowledge even knowing about Pell's Equation > last Friday, to giving some remarkably simple results that I can't > find anywhere else despite their obvious simplicity, in a few days. > 2000 years of mathematical history traversed by me completely within 4 > days. > It seems to me you make a brilliant argument that past mathematicians > were not, after all, all that brilliant, unless you wish to cite > someone, anyone, before me, noting that EVERY case of > x^2 - 2y^2 = 1 > connected to > z^2 - 2(x+y)^2 = -1 > as that's a kind of beautiful symmetry. I earnestly recommend that you read John Stillwell, /Mathematics and > Its History/. I'm sorry to say this, Angus, because I know you mean well, but you are really being a bit stupid. It should be completely obvious to you by now that James has not the slightest interest in reading any mathematical texts. Giving him advice like this is equivalent to pissing into the wind. === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation posting-account=3WPJYgoAAAA55VjhzK9i07RN8h8u8eEs Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) I earnestly recommend that you read John Stillwell, /Mathematics and > Its History/. æ I'm sorry to say this, Angus, because I know you mean well, but you are > really being a bit stupid. æIt should be completely obvious to you by > now that James has not the slightest interest in reading any > mathematical texts. æGiving him advice like this is equivalent to > pissing into the wind. Now give Angus his due. Angus plays Socrates to James's Meno in a fashion that even Plato would applaud. But you are right that both are stupid in the sense that neither can see the endgame. Angus will eventually snap and James will win, just as surely as James will never solve anything of any real significance. Problem is that telling them does no good. ;>) M === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > I earnestly recommend that you read John Stillwell, /Mathematics and > Its History/. æ > I'm sorry to say this, Angus, because I know you mean well, but you are > really being a bit stupid. æIt should be completely obvious to you by > now that James has not the slightest interest in reading any > mathematical texts. æGiving him advice like this is equivalent to > pissing into the wind. Now give Angus his due. Angus plays Socrates to James's Meno in a >fashion that even Plato would applaud. What's this, the Greek chorus? Suddenly everybody's on at me! >But you are right that both are stupid in the sense that neither can >see the endgame. Angus will eventually snap and James will win, just >as surely as James will never solve anything of any real significance. >Problem is that telling them does no good. ;>) Someone should run a book. -- Angus Rodgers Contains mild peril === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation >I'm sorry to say this, Angus, because I know you mean well, but you are >really being a bit stupid. It should be completely obvious to you by >now that James has not the slightest interest in reading any >mathematical texts. Giving him advice like this is equivalent to >pissing into the wind. But James isn't going to go away, is he? I might as well get used to him. And in a weird kind of way, I'm enjoying this, while fully realising that it might be an ancient sci.math rite of passage, and it might not be fruitful at any level whatsoever. The way in which the conversation keeps going even when it appears to have become re- duced to utter nothingness seems almost like Zen (whatever that is). -- Angus Rodgers Contains mild peril === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > I'm sorry to say this, Angus, because I know you mean well, but you are > really being a bit stupid. It should be completely obvious to you by > now that James has not the slightest interest in reading any > mathematical texts. Giving him advice like this is equivalent to > pissing into the wind. But James isn't going to go away, is he? I might as well get used > to him. And in a weird kind of way, I'm enjoying this, while fully > realising that it might be an ancient sci.math rite of passage, and > it might not be fruitful at any level whatsoever. The way in which > the conversation keeps going even when it appears to have become re- > duced to utter nothingness seems almost like Zen (whatever that is). > I understand the perverse appeal of interacting with him, and he does read all the posts (he probably re-reads his own many times over). My point was simply that advising him to read anything else is a waste of keystrokes. === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > I'm sorry to say this, Angus, because I know you mean well, > but you are really being a bit stupid. It should be completely > obvious to you by now that James has not the slightest interest > in reading any mathematical texts. Giving him advice like this > is equivalent to pissing into the wind. But James isn't going to go away, is he? I might as well get used > to him. And in a weird kind of way, I'm enjoying this, while fully > realising that it might be an ancient sci.math rite of passage, and > it might not be fruitful at any level whatsoever. The way in which > the conversation keeps going even when it appears to have > become reduced to utter nothingness seems almost like Zen > (whatever that is). You are romanticizing the situation. James does go away from time to time, and the newsgroup is the better for it. He leaves when the chorus of boos becomes loud enough. === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.13 (KHTML, like Gecko) Chrome/0.2.149.29 Safari/525.13,gzip(gfe),gzip(gfe) > I'm sorry to say this, Angus, because I know you mean well, > but you are really being a bit stupid. æIt should be completely > obvious to you by now that James has not the slightest interest > in reading any mathematical texts. æGiving him advice like this > is equivalent to pissing into the wind. But James isn't going to go away, is he? æI might as well get used > to him. æAnd in a weird kind of way, I'm enjoying this, while fully > realising that it might be an ancient sci.math rite of passage, and > it might not be fruitful at any level whatsoever. æThe way in which > the conversation keeps going even when it appears to have > become reduced to utter nothingness seems almost like Zen > (whatever that is). You are romanticizing the situation. > James does go away from time to time, > and the newsgroup is the better for it. > He leaves when the chorus of boos > becomes loud enough. Cite then old man. Give ANY math text that has the result that with x^2 - 2y^2 = 1 you automatically have another answer with z^2 - 2(x+y)^2 = -1. You are just an old blow-hard trying to protect your turf, and willing to piss on mathematics for it because you were NEVER a real mathematician, now were you? Were you old man? Were you? James Harris === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > Cite then old man. Give ANY math text that has the result that with x^2 - 2y^2 = 1 you automatically have another answer with z^2 - 2(x+y)^2 = -1. You are just an old blow-hard trying to protect your turf, and willing > to piss on mathematics for it because you were NEVER a real > mathematician, now were you? Were you old man? Were you? Did you look at the references Angus Rodgers gave? On page 17 of Number Theory: An Approach Through History from Hammurapi to Legendre, by Andre Weil, there is this: (x+2y)^2 - 2(x+y)^2 = -(x^2-2y^2) That's a pure superset of your result. It shows that if x^2-2y^2 = N then you automatically have: z^2-2(x+y)^2 = -N and, unlike yours, it actually gives you z = x+2y. -- --Tim Smith === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.13 (KHTML, like Gecko) Chrome/0.2.149.29 Safari/525.13,gzip(gfe),gzip(gfe) Cite then old man. Give ANY math text that has the result that with x^2 - 2y^2 = 1 you automatically have another answer with z^2 - 2(x+y)^2 = -1. You are just an old blow-hard trying to protect your turf, and willing > to piss on mathematics for it because you were NEVER a real > mathematician, now were you? Were you old man? Were you? Did you look at the references Angus Rodgers gave? æOn page 17 of Scanned them quickly... > Number Theory: An Approach Through History from Hammurapi to Legendre, > by Andre Weil, there is this: æ æ(x+2y)^2 - 2(x+y)^2 = -(x^2-2y^2) That's a pure superset of your result. æIt shows that if æ æx^2-2y^2 = N then you automatically have: æ æz^2-2(x+y)^2 = -N and, unlike yours, it actually gives you z = x+2y. I wouldn't doubt next there will be a barrage of requests for me to apologize to the other posters, but my question is, why couldn't they do what Tim Smith did? Succinctly and clearly state what is given versus sending me fishing for it. James Harris === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > and, unlike yours, it actually gives you z = x+2y. > I wouldn't doubt next there will be a barrage of requests for me to > apologize to the other posters, but my question is, why couldn't they > do what Tim Smith did? My question is: why couldn't you do what Tim Smith did? === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.13 (KHTML, like Gecko) Chrome/0.2.149.29 Safari/525.13,gzip(gfe),gzip(gfe) > and, unlike yours, it actually gives you z = x+2y. > I wouldn't doubt next there will be a barrage of requests for me to > apologize to the other posters, but my question is, why couldn't they > do what Tim Smith did? My question is: æwhy couldn't you do what Tim Smith did? I looked over both links. The second link is a Google scan of a book by Weil and it just so happens that the required page for some reason scanned in differently, and hurrying along I brushed past it. Tim Smith may simply have looked more carefully than I did. But regardless the simpler thing would have been for the poster to give the one link and note on what page the result was shown. Given his preening behavior afterwards it seems possible to me he preferred a continuing argument where I looked stupid. Hey, I look stupid all the time. That's not news. But people who make it harder to get information and think they're gaining points by making me waste time learn soon enough how quickly they can be flushed down the newsgroup toilet. This guy may think he's joining the sci.math elite or something. So he's testing my will to back away from considering the implications of the latest research to talking about idiot behavior from wannabes coming into the newsgroup thinking they have a quick route to popularity by making me look stupid. Moron. James Harris === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation >I looked over both links. The second link is a Google scan of a book >by Weil and it just so happens that the required page for some reason >scanned in differently, and hurrying along I brushed past it. This is mathematics James, you cannot just brush past things. You need to read and understand things. It is strange of you to ask for references and then just brush past the references you are given. Having asked for them it would be polite of you to read them carefully. Tim Smith may simply have looked more carefully than I did. Which may be part of the reason Tim Smith gets treated with more respect here than you generally do. Actions have consequences James. If you do not liek the consequences then do not do the actions. But regardless the simpler thing would have been for the poster to >give the one link and note on what page the result was shown. The posted merely assumed that you were able to read a web reference. In this the posted made a mistake, but that is more down to you brushing past rather than reading with care and attention. rossum === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation >Hey, I look stupid all the time. That's not news. I wouldn't worry about it. The important thing is to be aware of your own mistakes, so you can correct them. It's pretty much the definition of sanity, in my book. (There isn't much of it about!) >But people who make it harder to get information and think they're >gaining points by making me waste time learn soon enough how quickly >they can be flushed down the newsgroup toilet. This guy may think he's joining the sci.math elite or something. of the latest research to talking about idiot behavior from wannabes >coming into the newsgroup thinking they have a quick route to >popularity by making me look stupid. Moron. -- Angus Rodgers Contains mild peril === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation posting-account=OKTeIQkAAAAZk6JK1hK7-grwpoUDNy98 FunWebProducts; SLCC1; .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506),gzip(gfe),gzip(gfe) spider-mtc-tf02.proxy.aol.com[400C70A2] (Prism/1.2.1), HTTP/1.1 cache-mtc-af14.proxy.aol.com[400C754E] (Traffic-Server/6.1.5 [uScM]) > and, unlike yours, it actually gives you z = x+2y. > I wouldn't doubt next there will be a barrage of requests for me to > apologize to the other posters, but my question is, why couldn't they > do what Tim Smith did? My question is: ?why couldn't you do what Tim Smith did? I looked over both links. ?The second link is a Google scan of a book > by Weil and it just so happens that the required page for some reason > scanned in differently, and hurrying along I brushed past it. Tim Smith may simply have looked more carefully than I did. But regardless the simpler thing would have been for the poster to > give the one link and note on what page the result was shown. Given his preening behavior afterwards it seems possible to me he > preferred a continuing argument where I looked stupid. Hey, I look stupid all the time. ?That's not news. But people who make it harder to get information and think they're > gaining points by making me waste time learn soon enough how quickly > they can be flushed down the newsgroup toilet. This guy may think he's joining the sci.math elite or something. So he's testing my will to back away from considering the implications > of the latest research to talking about idiot behavior from wannabes > coming into the newsgroup thinking they have a quick route to > popularity by making me look stupid. What journal did you send your paper to? Moron. James Harris === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation >Cite then old man. Give ANY math text that has the result that with x^2 - 2y^2 = 1 you automatically have another answer with z^2 - 2(x+y)^2 = -1. You are just an old blow-hard trying to protect your turf, and willing >to piss on mathematics for it because you were NEVER a real >mathematician, now were you? Were you old man? Were you? This must be more Zen, I suppose. Whatever it is, you are clearly the master of it. I am lost in amazement that you can keep asking the same question, which has already been answered as plainly as it could possibly be! Anyway, for the third time: The first is a Google Books scan of some pages from the Stillwell book I mentioned. The second is a Google Books scan of some pages from Andre Weil, /Number Theory: An approach through history from Hammurapi to Legendre/ (Birkh.8auser 1987, 4th pr. in paperback 2007). The Weil extract gives EXACTLY what you are asking for. (Stillwell merely implies it, so that any rational person would consider it established, but you are obviously already able to wriggle out of that kind of implication.) This is already clear on page 16; and if you squint hard at the deliberately rather blurry scan of page 17 (something to do with copyright, I presume), you can just see the EXACT same identity - that very, very easy identity! - that I typed out a couple of days ago. (No ... good gawd! ... it was only a little over one day and two nights ago ... this is all obviously starting to get to me.) I repeat, the result is approximately 2600 years old. -- Angus Rodgers Contains mild peril === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > I'm sorry to say this, Angus, because I know you mean well, > but you are really being a bit stupid. It should be completely > obvious to you by now that James has not the slightest interest > in reading any mathematical texts. Giving him advice like this > is equivalent to pissing into the wind. > But James isn't going to go away, is he? I might as well get used > to him. And in a weird kind of way, I'm enjoying this, while fully > realising that it might be an ancient sci.math rite of passage, and > it might not be fruitful at any level whatsoever. The way in which > the conversation keeps going even when it appears to have > become reduced to utter nothingness seems almost like Zen > (whatever that is). You are romanticizing the situation. Quite possibly. But am I making it worse (given how bad it has been, and for how long)? Of course, if it were something new, I wouldn't be keeping it going like this. And of course, if /everybody/ ignored James, he would go away. But no-one has developed the ability to control everybody so as to make this happen (even assuming it to be a desirable outcome). The fact is, James has been a continual presence in sci.math for over a decade, and he has a continual audience who interact with him, for a host of individual reasons. I am just joining that audience for a while (for my own individual reasons). There seems little point in trying to dissuade me from doing so, unless I can make an individual difference for the worse - and in that case, the argument that no individual can make a difference (assuming that to be your argument) carries no weight! I probably won't make the situation any better (that would indeed be rather romantic), but I also don't think I can make it any worse (an idea which, in its way, is equally romantic, don't you think?). >James does go away from time to time, >and the newsgroup is the better for it. Of course, I understand that. I have mostly ignored him for years. >He leaves when the chorus of boos >becomes loud enough. And then he comes back. (Presumably he needs something, and he's incredibly determined to get it.) I've been letting other people deal with him, and mostly ignoring the fuss. But at some point (just because the fuss has been so extraordinarily persistent) I have to see for myself what all the fuss is about. Fortunately, Rotwang did some hard work, which made it possible for me to see some of it at last without too much effort, and I'm grateful to him for that. It now seems worth showing a bit of persistence myself, and doing a bit of work to try to understand this ... well, this person. I'm quite prepared to give up completely, if it becomes obvious to me that it is really hopeless. My time and energy are both limited. But I've been in the doldrums for a couple of weeks, and this is as useful a way of spending time as any, right now. (I'm also still trying to study! If this were taking time and energy away from studying, I wouldn't do it. But that hasn't been happening.) I do honestly identify with James, in a way, and there is nothing calculated about that. Of course one can very easily get misled by such identifications, and this has happened to me many times; but for that reason, I am alert to the danger. Also, those who most loudly condemn him are not as free from identifying with him, in their own way, as they might like to think. We Are All Guilty! :-) -- Angus Rodgers Contains mild peril === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > It now seems > worth showing a bit of persistence myself, and doing a bit of > work to try to understand this ... well, this person. William Baerg, an arachnologist at the University of Arkansas purposely allowed himself to be bitten by a black widow spider in 1922: three days of pain and delirium in a hospital. But that was not enough. In 1933 William Blair, MD, of the University of Alabama took up the torch and allowed a black widow spider to bite him. The pain lasted a week. His skin ithced, burned, and peeled for a further two weeks -- Michael Press === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation posting-account=Z3AipgkAAABkoMfyNwddSxsYhXHi5CDt CLR 1.1.4322; InfoPath.1; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022),gzip(gfe),gzip(gfe) I'm sorry to say this, Angus, because I know you mean well, but you are >really being a bit stupid. æIt should be completely obvious to you by >now that James has not the slightest interest in reading any >mathematical texts. æGiving him advice like this is equivalent to >pissing into the wind. But James isn't going to go away, is he? æI might as well get used > to him. æAnd in a weird kind of way, I'm enjoying this, while fully > realising that it might be an ancient sci.math rite of passage, and > it might not be fruitful at any level whatsoever. æThe way in which > the conversation keeps going even when it appears to have become re- > duced to utter nothingness seems almost like Zen (whatever that is). -- > Angus Rodgers > Contains mild peril Angus, James is demanidng a citation in which the author explicitly says that given a solution to x^2 - 2y^2 = 1, you also get a solution to x^2 - 2y^2 = -1. I don't see that you have done that, although I didn't read through all of the citations that you posted. Therefore James will not stop. It doesn't matter that this is screamingly obvious from some of what you posted. He did, in fact, notice this point and seems to think that this is a world-shaking mathematical discovery. It is actually an interesting point, since it gives you a unit of norm -1 from a unit of norm 1,l and so looking at general Pell equations, it can only be done for some of them. Which ones? Possibly interesting thing to have a casual look at. Now the mathematics is so easy that is difficult to believe that it wasn't published or sent in a letter or something some long while ago. The only reasons it wouldn't have been is that everybody thought it was such a minor point that it wasn't worth mentioning, or else that they thought anybody reading what the did write would simply see Has anybody checked L.E. Dickson's history of number theory? Achava === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.13 (KHTML, like Gecko) Chrome/0.2.149.29 Safari/525.13,gzip(gfe),gzip(gfe) On Sep 13, 5:43æpm, Achava Nakhash, the Loving Snake >I'm sorry to say this, Angus, because I know you mean well, but you are >really being a bit stupid. æIt should be completely obvious to you by >now that James has not the slightest interest in reading any >mathematical texts. æGiving him advice like this is equivalent to >pissing into the wind. But James isn't going to go away, is he? æI might as well get used > to him. æAnd in a weird kind of way, I'm enjoying this, while fully > realising that it might be an ancient sci.math rite of passage, and > it might not be fruitful at any level whatsoever. æThe way in which > the conversation keeps going even when it appears to have become re- > duced to utter nothingness seems almost like Zen (whatever that is). -- > Angus Rodgers > Contains mild peril Angus, James is demanidng a citation in which the author explicitly says that > given a solution to x^2 - 2y^2 = 1, you also get a solution to x^2 - > 2y^2 = -1. æI don't see that you have done that, although I didn't > read through all of the citations that you posted. æTherefore James > will not stop. æIt doesn't matter that this is screamingly obvious > from some of what you posted. æHe did, in fact, notice this point and > seems to think that this is a world-shaking mathematical discovery. > It is actually an interesting point, since it gives you a unit of norm > -1 from a unit of norm 1,l and so looking at general Pell equations, > it can only be done for some of them. æWhich ones? æPossibly > interesting thing to have a casual look at. Ah, finally some rationality. So then, what's the answer? Which ones? > Now the mathematics is so easy that is difficult to believe that it > wasn't published or sent in a letter or something some long while > ago. æThe only reasons it wouldn't have been is that everybody thought > it was such a minor point that it wasn't worth mentioning, or else > that they thought anybody reading what the did write would simply see It's obvious in hindsight. > Has anybody checked L.E. Dickson's history of number theory? Achava Please check. Going backwards from a result can be like figuring out how the clues worked with a crossword puzzle--after all the letters have been filled in for you. Discovery is not about whether something is simple or not, but whether it's new or not. Regardless, the Pell's Equation result is more a demonstration of how some of you change the rules when it suits you, which is more of a lesson to math students who think this situation is all about me. It's not. It's about people who don't follow the rules. It has always been about people who choose not to follow the rules when they don't like a result, or don't want to give a particular person credit. Nothing more. So in THAT there IS nothing new. James Harris === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation >James is demanidng a citation in which the author explicitly says that >given a solution to x^2 - 2y^2 = 1, you also get a solution to x^2 - >2y^2 = -1. I don't see that you have done that, although I didn't >read through all of the citations that you posted. I posted these two an hour ago, in response to his insistent requests: (reference to the Stillwell book I mentioned) (reference to a book by Andre Weil) >Therefore James will not stop. I don't mind if he doesn't stop. While very deluded, he is obviously* sincere. Also, his creativity in keeping up these conversations (for how many years now?) is amusing. I've mostly avoided them in the past, mainly because I didn't know what his mathematics was. I'm curious to see what happens when one focuses mainly on what he actually claims to have done. (I know others have also tried doing this in the past, but I really don't mind having a go - in my own eccentric way - even if it is just as hopeless as all the other attempts. Perhaps I do nurse the glorious fantasy of being The Genius Who Solved The Harris Problem! :-) If so, no doubt I will crash in flames. I do know how complicated and subtle this kind of thing can be - after all, I'm pretty twisted, too.) *Or at least, I can't tell that he isn't. >It doesn't matter that this is screamingly obvious >from some of what you posted. He did, in fact, notice this point and >seems to think that this is a world-shaking mathematical discovery. >It is actually an interesting point, I acknowledged that some of his points are both true and interesting, in this thread, four days ago - and perhaps also earlier than that (I forget). And Rotwang started the whole thing (as far as I'm concerned) by verifying James's claim at the start of the first of these threads. And James has had support from some other posters. It is by no means a chorus of universal condemnation and invalidation. >since it gives you a unit of norm >-1 from a unit of norm 1,l and so looking at general Pell equations, >it can only be done for some of them. Which ones? Possibly >interesting thing to have a casual look at. I imagine Brahmagupta's identity is the appropriate generalisation? That's what I Googled for to find those references. But I haven't thought much about it. >Now the mathematics is so easy that is difficult to believe that it >wasn't published or sent in a letter or something some long while >ago. It very definitely was: 2600 years ago, as I've said more than once. Certainly the Pythagoreans generated the series of Pell numbers, and almost certainly they would have been aware of the relation between successive pairs of terms outside the context of the recurrence, as Weil's formulation suggests. It hardly seems worth quibbling about, but for James's extraordinary and baffling persistence. >The only reasons it wouldn't have been is that everybody thought >it was such a minor point that it wasn't worth mentioning, or else >that they thought anybody reading what the did write would simply see No need to guess! >Has anybody checked L.E. Dickson's history of number theory? (Another on my long, long list of books to buy ...) -- Angus Rodgers Contains mild peril === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.13 (KHTML, like Gecko) Chrome/0.2.149.29 Safari/525.13,gzip(gfe),gzip(gfe) James is demanidng a citation in which the author explicitly says that >given a solution to x^2 - 2y^2 = 1, you also get a solution to x^2 - >2y^2 = -1. æI don't see that you have done that, although I didn't >read through all of the citations that you posted. I posted these two an hour ago, in response to his insistent requests: (reference to the Stillwell book I mentioned) > (reference to a book by Andre Weil) Therefore James will not stop. I don't mind if he doesn't stop. æWhile very deluded, he is obviously* > sincere. æAlso, his creativity in keeping up these conversations (for > how many years now?) is amusing. æI've mostly avoided them in the past, Hey, I made a mistake before and didn't see the equations with the link to the book by Weil. But you COULD have, like Tim Smith posted where the equation was versus just giving links for me to look through and you gave 2 when the second would have sufficed. Instead you're grand-standing. Hey, I make lots of mistakes. I admittedly knew next to nothing about this area of number theory before a bit over a week ago, and am feeling my way along. Assholes like you may think it fun to come in and play stupid games that waste people's time but I, unlike you, am actually trying to find answers versus trying to look pretty for the crowd. Now you can see the discussion moving more towards physics where I'm making the case that math society is deliberately trying to keep advanced mathematical tools from the science community so you can begin to see that it's not just about kissing ass with math people. And you may find your place in history here, and the consequences that follow. In the physics world you don't gain points by deliberately obscuring information to try and make someone look stupid. But physicists, you see, are actually in the pursuit of knowledge. Having such a purpose can give you ethics, decency, and common sense. James Harris === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation >James is demanidng a citation in which the author explicitly says that >given a solution to x^2 - 2y^2 = 1, you also get a solution to x^2 - >2y^2 = -1. æI don't see that you have done that, although I didn't >read through all of the citations that you posted. > I posted these two an hour ago, in response to his insistent requests: > (reference to the Stillwell book I mentioned) > (reference to a book by Andre Weil) >Therefore James will not stop. > I don't mind if he doesn't stop. æWhile very deluded, he is obviously* > sincere. æAlso, his creativity in keeping up these conversations (for > how many years now?) is amusing. æI've mostly avoided them in the past,Hey, I made a mistake before and didn't see the equations with the >link to the book by Weil. But you COULD have, like Tim Smith posted where the equation was >versus just giving links for me to look through and you gave 2 when >the second would have sufficed. Instead you're grand-standing. Hey, I make lots of mistakes. I admittedly knew next to nothing about >this area of number theory before a bit over a week ago, and am >feeling my way along. Assholes like you may think it fun to come in and play stupid games >that waste people's time but I, unlike you, am actually trying to find >answers versus trying to look pretty for the crowd. Now you can see the discussion moving more towards physics where I'm >making the case that math society is deliberately trying to keep >advanced mathematical tools from the science community so you can >begin to see that it's not just about kissing ass with math people. And you may find your place in history here, and the consequences that >follow. In the physics world you don't gain points by deliberately obscuring >information to try and make someone look stupid. I don't see how (i) posting the (already perfectly evident) identity of 01:49:03 +0100 in this thread, (ii) responding to your request for a citation with a citation (of the Stillwell book), and finally (iii) responding to your request for Web references with two Web references constitutes obscuring information. >But physicists, you see, are actually in the pursuit of knowledge. Having such a purpose can give you ethics, decency, and common sense. Good luck with that. -- Angus Rodgers Contains mild peril === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.13 (KHTML, like Gecko) Chrome/0.2.149.29 Safari/525.13,gzip(gfe),gzip(gfe) James is demanidng a citation in which the author explicitly says that >given a solution to x^2 - 2y^2 = 1, you also get a solution to x^2 - >2y^2 = -1. æI don't see that you have done that, although I didn't >read through all of the citations that you posted. I posted these two an hour ago, in response to his insistent requests: (reference to the Stillwell book I mentioned) > (reference to a book by Andre Weil) I checked the first time, but had trouble with the second page. After Tim Smith's post I looked again more closely and saw the general result, so yes, you are correct. >Therefore James will not stop. Hey, if you'd put all the information upfront like Tim Smith then scanned in clearer I probably would have noticed the first time. I really am curious about finding out what is correct here as I learn about an area I hadn't been very interested in, a little more than a week ago. I don't even remember hearing about Pell's Equation before then. James Harris === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation >Perhaps I do nurse the >glorious fantasy of being The Genius Who Solved The Harris Problem! :-) I have started my own small attempt at this: JSH - an Axiomatic Approach Axiom 1: JSH is the world's greatest living mathematician. Being an axion of the system, this is unchallengable from within the system. We are at liberty to speculate whether or not JSH is the greatest mathematician ever, but we cannot challenge Axiom 1. This axiomatic system is also consistent - there is no inconsistency between the axiom and itself. The greatness of JSH is already apparent. Theorem 1: There are parts of mathematics that only JSH understands. If someone else understood all the mathematics that JSH does, then that person would be as great a mathematician as JSH, and that is not allowed by Axiom 1. Theorem 2: All mathematical results produced by JSH are new, exciting, ground breaking, revolutionary and very important. This follows directly from Axiom 1; since JSH is the world's greatest living mathematician, therefore all his results are the worlds greatest mathematical results. JSH has a complete and rigorous proof of this, but unfortunately it falls into the area of mathematics covered by Theorem 1, so we cannot hope to understand it. This theorem applies to all of JSH's results. If JSH rederives the Chinese Remainder Theorem, then that result is also new, exciting, ground breaking, revolutionary and very important. Whoever first discovered the CRT thousands of years ago was not aware of things like complex numbers, transcendental numbers and so forth that JSH is, hence JSH's result cannot be viewed in the same light as the original proof, which was made in a far less complex environment. Borges' Pierre Menard ... (http://www.coldbacon.com/writing/borges-quixote.html) is relevant here, particularly the passage discussing truth, whose mother is history, rival of time .... Corollary 2.1: JSH's factoring methods are new, exciting, ground breaking, revolutionary and very important. This follows directly from Theorem 2. Lemma 2.2: RSA factoring is in danger. By Corollary 2.1 we know the importance etc. of James' factoring ideas. This requires that these methods will be able to factor RSA numbers quickly; if they were not able to factor such numbers quickly then the methods would not be revolutionary etc. Since we know that these results are important they must have a great impact on the Factoring Problem. Once we have understood the full impact of these factoring ideas we will be able to factor very large numbers very quickly. However, due to our lack of understanding, as per Theorem 1, James has not yet been able to assign a timescale to how long it will take us to fully comprehend the depth and importance of his factoring methods. Corollary 2.3: JSH's Diophantine methods are new, exciting, ground breaking, revolutionary and very important. This follows directly from Theorem 2. Merely because we cannot see the importance of James' results does not mean that they are not important. Theorem 1 may well be in play again here. rossum === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) >Um, I went from not to my knowledge even knowing about Pell's Equation >last Friday, to giving some remarkably simple results that I can't >find anywhere else despite their obvious simplicity, in a few days. 2000 years of mathematical history traversed by me completely within 4 >days. It seems to me you make a brilliant argument that past mathematicians >were not, after all, all that brilliant, unless you wish to cite >someone, anyone, before me, noting that EVERY case of x^2 - 2y^2 = 1 connected to z^2 - 2(x+y)^2 = -1 as that's a kind of beautiful symmetry. I earnestly recommend that you read John Stillwell, /Mathematics and > Its History/. æIt has certainly opened my eyes to how little I know, > and how many interesting things there are for me still to know; and, > who knows, it might even do the same for you. æI was looking through > it this morning to help me compile a list of topics I need to know > about - basic stuff, not anything that could be called advanced, > scarcely even anything from the beginning of the twentieth century > (or later) - and the list already contains 32 topics. æI'm sure any > mathematician could easily add to it other topics that they consider > basic and that (if they knew how ignorant I am!) I don't know about. > Anyway (in case you wonder why I mention this), I happened to come > across this passage, on page 52 (see also section 3.4, earlier): æThe first mathematical processes we would recognise as infinite > æwere probably devised by the Pythagoreans, for example, the > ærecurrence relations æ x {n+1} = x n + 2y n, > æ y {n+1} = x n + y n æfor generating integer solutions of the equations x^2 - 2y^2 = +/-1. So you've caught up with Pythagoras (circa 600 BCE)! That's a start. You keep changing the subject. The question is, was it previously know that given a solution to x^2 - 2y^2 = 1 you ALSO have a solution with z^2 - 2(x+y)^2 = -1? So, cite from a text where that equation is given, or give up. Lying in long replies is a waste of time, but it does show what kind of person you are. Hate to lose, eh? Would rather lie about math if that helps you believe you're winning? James Harris === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation The question is, was it previously know that given a solution to x^2 - 2y^2 = 1, you ALSO have a solution with (x+2y)^2 - 2(x+y)^2 = -1 ? This is trivial as I pointed out before. It's simply N(u) = 1, N(v) = -1, N = Norm => N(uv) = N(u)N(v) = -1 for u = x + /2 y, v = 1 + /2 so uv = x + 2y + (x + y) /2 Such composition identies are ancient (Diophantus, Brahmagupta). --Bill Dubuque === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > The question is, was it previously know that given a solution to > x^2 - 2y^2 = 1, you ALSO have a solution with > (x+2y)^2 - 2(x+y)^2 = -1 ? This is trivial as I pointed out before. It's simply N(u) = 1, N(v) = -1, N = Norm => N(uv) = N(u)N(v) = -1 for u = x + /2 y, v = 1 + /2 so uv = x + 2y + (x + y) /2 Such composition identies are ancient (Diophantus, Brahmagupta). Well, I'm not finding it trivial. What do you mean by Norm in the above? I think I've figured out what you mean by /2, but explicitly stating that would help, too. -- --Tim Smith === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > The question is, was it previously know that given a solution to > x^2 - 2y^2 = 1, you ALSO have a solution with > (x+2y)^2 - 2(x+y)^2 = -1 ? > This is trivial as I pointed out before. It's simply > N(u) = 1, N(v) = -1, N = Norm > => N(uv) = N(u)N(v) = -1 > for u = x + /2 y, v = 1 + /2 > so uv = x + 2y + (x + y) /2 > Such composition identies are ancient (Diophantus, Brahmagupta). Well, I'm not finding it trivial. What do you mean by Norm... N(a + b /2) = a^2 - 2 b^2, /2 = sqrt(2) --Bill Dubuque === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > Anyway (in case you wonder why I mention this), I happened to come > across this passage, on page 52 (see also section 3.4, earlier): > æThe first mathematical processes we would recognise as infinite > æwere probably devised by the Pythagoreans, for example, the > ærecurrence relations > æ x_{n+1} = x_n + 2y_n, > æ y_{n+1} = x_n + y_n > æfor generating integer solutions of the equations x^2 - 2y^2 = +/-1. > So you've caught up with Pythagoras (circa 600 BCE)! That's a start. You keep changing the subject. No, I don't. (Perhaps you would prefer it if I did?) >The question is, was it previously know that given a solution to x^2 - 2y^2 = 1 you ALSO have a solution with z^2 - 2(x+y)^2 = -1? Yes. See immediately above. I honestly don't know how to be any clearer than that! (Remember that z = x + 2y, as I explained in a previous post.) >So, cite from a text where that equation is given, or give up. Lying in long replies is a waste of time, but it does show what kind >of person you are. Hate to lose, eh? Would rather lie about math if that helps you believe you're winning? Not at all, as I'm quite accustomed to being a loser. But, once again, what does the truth have to do with winning or losing some sort of game? You're surely not a disciple of Michel Foucault, or dungeon of pre-modernity has been replaced with the bright modern prison, but Foucault cautions that visibility is a trap. It is exercises its controlling systems of power and knowledge (terms which Foucault believed to be so fundamentally connected that he often combined them in a single hyphenated concept, power-knowledge.'') -- Angus Rodgers Contains mild peril === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.13 (KHTML, like Gecko) Chrome/0.2.149.29 Safari/525.13,gzip(gfe),gzip(gfe) > Anyway (in case you wonder why I mention this), I happened to come > across this passage, on page 52 (see also section 3.4, earlier): > æThe first mathematical processes we would recognise as infinite > æwere probably devised by the Pythagoreans, for example, the > ærecurrence relations > æ x {n+1} = x n + 2y n, > æ y {n+1} = x n + y n > æfor generating integer solutions of the equations x^2 - 2y^2 = +/-1. > So you've caught up with Pythagoras (circa 600 BCE)! That's a start. You keep changing the subject. No, I don't. (Perhaps you would prefer it if I did?) Quit being coy. It doesn't matter what people can get to from something already known. Here what matters is what they knew. Yes, in hindsight, you can figure out a lot when there is an answer in front of you from which to work back. But that's like saying E=mc^2 is nothing because once you see it, you can work back to it easily enough with physics known to Newton. Understand? >The question is, was it previously know that given a solution to x^2 - 2y^2 = 1 you ALSO have a solution with z^2 - 2(x+y)^2 = -1? Yes. æSee immediately above. æI honestly don't know how to be any > clearer than that! (Remember that z = x + 2y, as I explained in a > previous post.) Yet readers can go on the web and LOOK for it, and not see it. It's too simple and direct not to have been put in a mathematical text if someone had noticed, especially with a subject that is 2000 years old. >So, cite from a text where that equation is given, or give up. Lying in long replies is a waste of time, but it does show what kind >of person you are. Hate to lose, eh? Would rather lie about math if that helps you believe you're winning? Not at all, as I'm quite accustomed to being a loser. But, once Well you seem to be trying hard enough now that I think you're just lying again. There is NO way you can't get the difference between being able to show that x^2 - 2y^2 = 1 gives you z^2 - 2(x+y)^2 = -1 with what was known with actually knowing that ahead of time. Any number of mathematical discoveries are simple in hindsight. Understand? Being able to work backwards once a result is given to you does not prove the result was already known. You clearly are intelligent enough to know that so any reply dodging the obvious has to be deliberate, a lie, and an indication that despite what you say, you are trying to win here, where winning to you is convincing others that what I found was already known. Now why do you wish them to believe that? Who are you, really? Mazur? Maybe Ribet? Or Wiles himself? James Harris === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation >The question is, was it previously know that given a solution to >x^2 - 2y^2 = 1 >you ALSO have a solution with >z^2 - 2(x+y)^2 = -1? > Yes. æSee immediately above. æI honestly don't know how to be any > clearer than that! (Remember that z = x + 2y, as I explained in a > previous post.) Yet readers can go on the web and LOOK for it, and not see it. I don't know if this particular case of a general recurrence relation is to be seen anywhere on the Web (not counting any archives of this thread, of course). I expect it is, but I don't see that it matters, either way. The more general recurrence relation for Pell's equation is /bound/ to be on the Web somewhere. (I can't be bothered to look.) >It's too simple and direct not to have been put in a mathematical text >if someone had noticed, especially with a subject that is 2000 years >old. But I have just quoted very precisely from a well-known textbook (currently in print: 2nd edition, Springer, New York, 2002) this result which has been known for 2600 years - so what is going on here? >So, cite from a text where that equation is given, or give up. (And I did. Cite, I mean. Not give up.) >Lying in long replies is a waste of time, but it does show what kind >of person you are. >Hate to lose, eh? >Would rather lie about math if that helps you believe you're winning? > Not at all, as I'm quite accustomed to being a loser. But, onceWell you seem to be trying hard enough now that I think you're just >lying again. There is NO way you can't get the difference between being able to >show that x^2 - 2y^2 = 1 gives you z^2 - 2(x+y)^2 = -1 with what was known with actually knowing that ahead of time. I assure you, I did know it (but I had forgotten the details of this and other results concerning Pell's equation, because I have a head like a sieve). I have read every word of Stillwell's book (up to the penultimate chapter, with which I am struggling at the moment) and attempted every exercise, including several on Pell's equation. I'm sure you sincerely believe I am up to something dishonest; and I'm not accusing you of lying. You seem to be confused in some way. Confusion is nothing to be ashamed of, unless you cling on to it and deny it for everything you're worth - and even that, in a way, is nothing to be ashamed of, because it must indicate some kind of desperation (which I don't pretend to understand). >Any number of mathematical discoveries are simple in hindsight. Understand? Being able to work backwards once a result is given to you does not >prove the result was already known. You clearly are intelligent enough to know that so any reply dodging >the obvious has to be deliberate, a lie, and an indication that >despite what you say, you are trying to win here, where winning to you >is convincing others that what I found was already known. Now why do you wish them to believe that? Because it is a simple and easily verifiable fact. (Of course, in addition to that, you can analyse my motives for wanting you to recognise what is a simple and easily verifiable fact. I have little doubt that my motives are complex and not entirely worthy; but how much does that matter? Analysis of motives is usually your point of view, because you seem to believe I am lying, it makes sense for you to analyse my motives. You are mistaken, but go on, knock yourself out! This conversation is strangely fascinating, and it enables me to avoid making myself miserable by trying to do some mathematics that I don't seem to be quite up to at the moment ... OK, there's an unworthy motive for you.) >Who are you, really? Mazur? Maybe Ribet? Or Wiles himself? I wish. -- Angus Rodgers Contains mild peril === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif AppleWebKit/525.13 (KHTML, like Gecko) Chrome/0.2.149.29 Safari/525.13,gzip(gfe),gzip(gfe) >The question is, was it previously know that given a solution to >x^2 - 2y^2 = 1 >you ALSO have a solution with >z^2 - 2(x+y)^2 = -1? > Yes. æSee immediately above. æI honestly don't know how to be any > clearer than that! (Remember that z = x + 2y, as I explained in a > previous post.) Yet readers can go on the web and LOOK for it, and not see it. I don't know if this particular case of a general recurrence relation > is to be seen anywhere on the Web (not counting any archives of this That was the challenge to you, to produce a case where it WAS shown. > thread, of course). I expect it is, but I don't see that it matters, Of course you don't. Suddenly you're spectacularly stupid, right? >Who are you, really? æMazur? æMaybe Ribet? æOr Wiles himself? I wish. Ok, I'll give you that you're unlikely to be either of them. But I suspect you are someone using a pseudonym trying to be clever. The short of it is what I said all along before this colossal waste of time: x^2 - 2y^2 = 1 leading directly to a second solution with z^2 - 2(x+y)^2 = -1 was not previously noticed, at least, not in the record. If you disagree, cite a case which shows that result itself. Not b.s. over and over again with an empty claim. It is math people. Lying about it is just stupid. James Harris === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation >The short of it is what I said all along before this colossal waste of >time: x^2 - 2y^2 = 1 leading directly to a second solution with z^2 - 2(x+y)^2 = -1 was not previously noticed, at least, not in the record. If you disagree, cite a case which shows that result itself. Not b.s. >over and over again with an empty claim. -- Angus Rodgers Contains mild peril === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation posting-account=BVr-MgkAAABE4LRE1rHDnN9heo0IZZTk .NET CLR 1.1.4322),gzip(gfe),gzip(gfe) spider-dtc-tg06.proxy.aol.com[CDBC70C6] (Prism/1.2.1), HTTP/1.1 cache-dtc-ac01.proxy.aol.com[CDBC7482] (Traffic-Server/6.1.5 [uScM]) > Intriguingly that means that proof that there are an infinite number > of solutions for certain Pell's Equations is proof that there are an > infinity of Pythagorean Triplets of a certain form! Yup, been there, done that.http://en.wikipedia.org/wiki/Pythagorean triple Please point out on that page where Pell's Equation is related to > Pythagorean Tripes and specifically where, for instance, you can find > that there must exist a Pythagorean Triple of the form, u^2 + (u+1)^2 = w^2 for every integer solution to x^2 - 2y^2 = 1, where w = x+y. Mathematics can only give us the truth. ?It is human nature that can > deny proof. And it's time for people to stop claiming that it's only about proof > because the reality is that social issues like class and status play a > role as well in acceptance of mathematical results. People in power can deny a result to maintain power like in any > political arena. James Harris --------------------------------------------------- James has asked: > Please point out on that page where Pell's Equation is related to > Pythagorean Tripes and specifically where, for instance, you can find > that there must exist a Pythagorean Triple of the form, u^2 + (u+1)^2 = w^2 > Here is something that looks like your material about relationships between the Pell Equation with D=2 and Pythagorian Triples. Go to the link and scroll down to the end and note the information just above the beginning of section VII http://en.wikipedia.org/wiki/Pythagorean triple#VI. Near the end, see: If the two legs of a PNT differ by 1, the longer leg and the hypotenuse form the coordinates of a larger PNT in M the legs of which differ by 1. M(1,1) = {4, 3, 5}. M(4,5) = {120, 119, 169}. M(120,169) = {137904, 137903, 195025}, etc. Notice the last line: ... where Pi are the Pell numbers. Then go here: http://en.wikipedia.org/wiki/Pell number#Pell numbers Record the Pell number sequence and go here: http://en.wikipedia.org/wiki/Pell number#Pythagorean triples You should see a graphic with two of your favorite triangles and the generating rules using Pell numbers just below. The Pell number sequence generates both x^2 - 2y^2 = 1 and x^2 -2y^2 = -1, which supports your assertion: and the result that for every solution to x^2 - 2xy^2 = 1, you are linked to a solution to S^2 - 2(x+y)^2 = -1. ...from one of your earlier posts. Enrico === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > Intriguingly that means that proof that there are an infinite number > of solutions for certain Pell's Equations is proof that there are an > infinity of Pythagorean Triplets of a certain form! > Yup, been there, done that.http://en.wikipedia.org/wiki/Pythagorean triple Please point out on that page where Pell's Equation is related to > Pythagorean Tripes and specifically where, for instance, you can find > that there must exist a Pythagorean Triple of the form, u^2 + (u+1)^2 = w^2 for every integer solution to x^2 - 2y^2 = 1, where w = x+y. Mathematics can only give us the truth. It is human nature that can > deny proof. And it's time for people to stop claiming that it's only about proof > because the reality is that social issues like class and status play a > role as well in acceptance of mathematical results. People in power can deny a result to maintain power like in any > political arena. James Harris --------------------------------------------------- > James has asked: Please point out on that page where Pell's Equation is related to > Pythagorean Tripes and specifically where, for instance, you can find > that there must exist a Pythagorean Triple of the form, u^2 + (u+1)^2 = w^2 Here is something that looks like your material > about relationships between the Pell Equation > with D=2 and Pythagorian Triples. Go to the link and scroll down to the end and note > the information just above the beginning of section VII http://en.wikipedia.org/wiki/Pythagorean triple#VI. Near the end, see: > If the two legs of a PNT differ by 1, the longer leg and the > hypotenuse form the coordinates of a larger PNT in M the legs of which differ by 1. M(1,1) = {4, 3, 5}. > M(4,5) = {120, 119, 169}. M(120,169) = {137904, 137903, 195025}, etc. Notice the last line: ... where Pi are the Pell numbers. Do you know what a Pell number is? > Then go here: http://en.wikipedia.org/wiki/Pell number#Pell numbers Did that and saw what a Pell number is. > Record the Pell number sequence and go here: http://en.wikipedia.org/wiki/Pell number#Pythagorean triples You should see a graphic with two of your favorite triangles > and the generating rules using Pell numbers just below. > The Pell number sequence generates both æx^2 - 2y^2 = 1 > and x^2 -2y^2 = -1, which supports your assertion: and the result that for every solution to x^2 - 2xy^2 = 1, you are > linked to a solution to S^2 - 2(x+y)^2 = -1. ...from one of your earlier posts. Enrico I've noticed, but Pell Numbers are not just solutions to x^2 - 2y^2 = 1. And it seems remarkable that no one bothered to just come out and say that given x^2 - 2y^2 = 1 you immediately have solutions for z^2 - 2(x+y)^2 = -1 which indicates they kind of bounced around that realization but never quite made it. I ran into the same type issue with my prime counting function where posters would go on and on (and still do) about what was previously known and find ways to relate what I did to that, but, um, the count of prime numbers is the count of primes numbers! So there MUST be mathematical relationships when the equations are doing the same thing! The difference with my research is simplification. No need for long Pythagorean Triplets of a certain form are related to solutions to Pell's Equation and another I've seen called the negative Pell's Equation. Seems to me that you may be looking for the same line posters used against my prime counting research, which is to find any way you can to say that I've found nothing new. Sigh. Oh well. Here we go again... James Harris === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation posting-account=HaopWgoAAADs72-s8RQYwP_-ruRUuNzX Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > Intriguingly that means that proof that there are an infinite number > of solutions for certain Pell's Equations is proof that there are an > infinity of Pythagorean Triplets of a certain form! > Yup, been there, done that.http://en.wikipedia.org/wiki/Pythagorean triple > Please point out on that page where Pell's Equation is related to > Pythagorean Tripes and specifically where, for instance, you can find > that there must exist a Pythagorean Triple of the form, > u^2 + (u+1)^2 = w^2 > for every integer solution to x^2 - 2y^2 = 1, where w = x+y. > Mathematics can only give us the truth. It is human nature that can > deny proof. > And it's time for people to stop claiming that it's only about proof > because the reality is that social issues like class and status play a > role as well in acceptance of mathematical results. > People in power can deny a result to maintain power like in any > political arena. > James Harris --------------------------------------------------- > James has asked: > Please point out on that page where Pell's Equation is related to > Pythagorean Tripes and specifically where, for instance, you can find > that there must exist a Pythagorean Triple of the form, > u^2 + (u+1)^2 = w^2 Here is something that looks like your material > about relationships between the Pell Equation > with D=2 and Pythagorian Triples. Go to the link and scroll down to the end and note > the information just above the beginning of section VII http://en.wikipedia.org/wiki/Pythagorean triple#VI. Near the end, see: > If the two legs of a PNT differ by 1, the longer leg and the > hypotenuse form the coordinates of a larger PNT in M the legs of which differ by 1. M(1,1) = {4, 3, 5}. > M(4,5) = {120, 119, 169}. M(120,169) = {137904, 137903, 195025}, etc. Notice the last line: ... where Pi are the Pell numbers. Do you know what a Pell number is? Then go here: http://en.wikipedia.org/wiki/Pell number#Pell numbers Did that and saw what a Pell number is. Record the Pell number sequence and go here: http://en.wikipedia.org/wiki/Pell number#Pythagorean triples You should see a graphic with two of your favorite triangles > and the generating rules using Pell numbers just below. > The Pell number sequence generates both æx^2 - 2y^2 = 1 > and x^2 -2y^2 = -1, which supports your assertion: and the result that for every solution to x^2 - 2xy^2 = 1, you are > linked to a solution to S^2 - 2(x+y)^2 = -1. ...from one of your earlier posts. Enrico I've noticed, but Pell Numbers are not just solutions to x^2 - 2y^2 = > 1. And it seems remarkable that no one bothered to just come out and say > that given x^2 - 2y^2 = 1 you immediately have solutions for z^2 - 2(x+y)^2 = -1 which indicates they kind of bounced around that realization but never > quite made it. I ran into the same type issue with my prime counting function where > posters would go on and on (and still do) about what was previously > known and find ways to relate what I did to that, but, um, the count > of prime numbers is the count of primes numbers! So there MUST be mathematical relationships when the equations are > doing the same thing! The difference with my research is simplification. æNo need for long > Pythagorean Triplets of a certain form are related to solutions to > Pell's Equation and another I've seen called the negative Pell's > Equation. Seems to me that you may be looking for the same line posters used > against my prime counting research, which is to find any way you can > to say that I've found nothing new. Sigh. æOh well. æHere we go again... James Harris Sigh. You've found nothing new! Glad you agree! At least you are willing to acknowledge your mistake! === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation On 10 Sep 2008 01:22:21 -0400, Bill Dubuque is essential to stand on the shoulders of mathematical giants. --Bill Dubuque Normally this would be excellent advice. Unfortunately, in this case James is only aware of one mathematical giant, himself. All other mathematicians in history are insignificant compared to him. Remember he did in four day what took all of them 2000 years. James is attempting to stand on his own shoulders. rossum === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation <1vtic49kg920vcaiqik3lf6bjbmv2nkq1n@4ax.com> posting-account=n1ZfDgkAAABbCs44qOtz8dP-RkWuEBif Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > On 10 Sep 2008 01:22:21 -0400, Bill Dubuque To get nontrivial results in mathematics it >is essential to stand on the shoulders of mathematical giants. --Bill Dubuque Normally this would be excellent advice. æUnfortunately, in this case > James is only aware of one mathematical giant, himself. æAll other > mathematicians in history are insignificant compared to him. æRemember > he did in four day what took all of them 2000 years. James is attempting to stand on his own shoulders. rossum You are an angry little man. JSH === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation <1vtic49kg920vcaiqik3lf6bjbmv2nkq1n@4ax.com> posting-account=3WPJYgoAAAA55VjhzK9i07RN8h8u8eEs Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) Normally this would be excellent advice. æUnfortunately, in this case > James is only aware of one mathematical giant, himself. æAll other > mathematicians in history are insignificant compared to him. æRemember > he did in four day what took all of them 2000 years. James is attempting to stand on his own shoulders. > He should be able to do this, since he has accomplished the feat of sticking his head up his ass before. > rossum You are an angry little man. JSH Man up. This is what you were saying. Does it embarrass you to see how stupid you sound when you hear it from another's lips? Let's hope so. M === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation <1vtic49kg920vcaiqik3lf6bjbmv2nkq1n@4ax.com> posting-account=HaopWgoAAADs72-s8RQYwP_-ruRUuNzX .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.1),gzip(gfe),gzip(gfe) On 10 Sep 2008 01:22:21 -0400, Bill Dubuque To get nontrivial results in mathematics it >is essential to stand on the shoulders of mathematical giants. >--Bill Dubuque Normally this would be excellent advice. æUnfortunately, in this case > James is only aware of one mathematical giant, himself. æAll other > mathematicians in history are insignificant compared to him. æRemember > he did in four day what took all of them 2000 years. James is attempting to stand on his own shoulders. rossum You are an angry little man. JSH- Hide quoted text - - Show quoted text - You are an angry little NPD afflicted child! === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation James is attempting to stand on his own shoulders. > rossum > You are an angry little man. > ___JSH- Hide quoted text - > - Show quoted text - >You are an angry little NPD afflicted child! Don't be too hard on James, he tries hard. When he gets ticked off, the poison flows in short sentences, to support a grand ego reliant on a vast knowledge of Math he does not have. Like a small frog bumping into a wall in the dark, JSH tries to get ahead, but Math above simple algebra is far too difficult for him. He never could have passed the SAT. === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > His hook is simple and effective. Every fault he blames > someone for is true of himself. 'Tis maddening to be > accused of his faults. >The real story is that the math system is skewed against amateur >researchers so I find myself trying to promote my research where I >can. Posters tried ordering me not to post, but when that failed they >switched to smear tactics. >But my full answer is with mathematics: research AFTER I got my own theorem and started looking for ways to >use it. > He cannot be approached. Showing him sympathy, or empathy > opens oneself to a dose of pure evil viciousness. He is > a mad dog. Do not put your hand out. He has NPD, and he is a troll/crackpot. > Criticizing him makes you a participant in an unsanitary act. nope, have to keep supressing JSH, if his math got out the stock market would collapse. Too late! >But I've kind of been here before... Years ago I had my prime >counting function and didn't figure people could get away with lying >about research on prime numbers, but it's years later... your function is usless. >Politics are powerful. Mathematical proof is not enough. spoof, not proof. >James Harris === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > His hook is simple and effective. Every fault he blames > someone for is true of himself. 'Tis maddening to be > accused of his faults. > The real story is that the math system is skewed against amateur > researchers so I find myself trying to promote my research where I > can. Posters tried ordering me not to post, but when that failed they > switched to smear tactics. > But my full answer is with mathematics: research AFTER I got my own theorem and started looking for ways to > use it. > He cannot be approached. Showing him sympathy, or empathy > opens oneself to a dose of pure evil viciousness. He is > a mad dog. Do not put your hand out. He has NPD, and he is a troll/crackpot. But not just any troll - he is super-troll! === Subject: Re: JSH: Pythagorean Triplets and Pell's Equation > His hook is simple and effective. Every fault he blames > someone for is true of himself. 'Tis maddening to be > accused of his faults. > The real story is that the math system is skewed against amateur > researchers so I find myself trying to promote my research where I > can. Posters tried ordering me not to post, but when that failed they > switched to smear tactics. > But my full answer is with mathematics: > research AFTER I got my own theorem and started looking for ways to > use it. > He cannot be approached. Showing him sympathy, or empathy > opens oneself to a dose of pure evil viciousness. He is > a mad dog. Do not put your hand out. > He has NPD, and he is a troll/crackpot. But not just any troll - he is super-troll! I gratefully glow in the presence of his reflected sunlight. === Subject: Baby Rudin; Any difference between the hardcover and the international ed. Any difference besides that fact that it is a softcover, and the printing seems to be poor in some spots. Other than that , word for word? === Subject: Re: Baby Rudin; Any difference between the hardcover and the international ed. >Any difference besides that fact that it is a softcover, and the printing seems to be poor in some spots. Other than that , word for word? Do you really think that anyone here has _compared_ them word for word? David C. Ullrich Understanding Godel isn't about following his formal proof. That would make a mockery of everything Godel was up to. (John Jones, My talk about Godel to the post-grads. in sci.logic.) === Subject: Re: Solutions Manual Needed posting-account=L4vzLgoAAAApG6JhDktRMZOMvPKzD8Wo Gecko/2008070208 Firefox/3.0.1,gzip(gfe),gzip(gfe) > Hey, I am looking for the INSTRUCTOR solutions manual to the following > text: Introduction to Operations Research 8th Edition by Hillier, Lieberman. Does anyone have it? æAll I can seem to find is the 7th edition... I > NEED the 8th edition. THANKS! I just read your post. I'm curious if you found any solution manual for the Introduction to Operations Research by Hillier and Lieberman. === Subject: hi bhupala Cc: bhupala@gmail.com posting-account=1tD9sQkAAAAZttDG2u_2do8CrsFILJK7 5.1),gzip(gfe),gzip(gfe) hii bhupala. i saw ur post dat u can provide free solutions. plz send me solutions 4 MICROELECTRONICS BY MILLMAN & GRABEL... waiting 4 ur reply..... === Subject: Get Solutions Manual posting-account=q-2XYgoAAAA09XnYVjs6Cn-Z-RYO4JNz SV1),gzip(gfe),gzip(gfe) Are You looking for solutions manual for a tough class?! Did the search results lead you here?! Try sending me email with the name and details of the solutions manual you need and I may be able to help. Do not reply here, instead send email to jhonrecard(at)gmail(dot)com.If the solutions manual you are looking for is not listed here, do not give up and send me email, I may be able to help! Please note: It is NOT free to send you the solutions manual if it is available . 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Thomas, Jr.) Unix: The Textbook (Syed Mansoor Sarwar, Robert Koretsky & Syed Aqeel Sarwar) Understanding the Math You Teach: Content and Methods for Prekindergarten through Grade 4 (Anita C. Burris) Using and Understanding Mathematics: A Quantitative Reasoning Approach, Bennett, Briggs) Understanding Engineering Mathematics (Bill Cox) Vector Mechanics for Engineers: Statics & Dynamics (Ferdinand P. Beer) Visual Basic 2008 How to Program, (Harvey & Paul) Deitel Visual Basic.Net Programming (Jeffrey Tsay) VHDL: A Starter's Guide (Sudhakar Yalamanchili) Vector Calculus (Susan J. Colley) Virtual ChemLab: General Chemistry Student Lab Manual / Workbook, v2.5. (Brian F. Woodfield & Matthew C. Asplund) VLSI Test Principles and Architectures: Design for Testability (Chen, Cheng, Eklow et al.) Wireless Communications & Networks (William Stallings) Work Systems: The Methods, Measurement & Management of Work (Mikell P. Groover) World Trade and Payments: An Introduction (Richard E. Caves,Jeffrey A. Frankel & Ronald W. Jones) Wireless Communications: Principles and Practice, by Rappaport Wireless Communications and Networking (Jon W. Mark, Weihua Zhuang) Web 101 (Wendy G. Lehnert & Richard L. Kopec) Web Development and Design Foundations with XHTML Water and Wastewater Technology (Mark J. Hammer, Sr. & Mark J. Hammer, Jr.) Water-Resources Engineering (Chin) XML: Language Mechanics and Applications (Dwight Peltzer) 10-Key Touch Key: Developing Speed and Accuracy (Burton) === Subject: Get Solutions Manual posting-account=q-2XYgoAAAA09XnYVjs6Cn-Z-RYO4JNz SV1),gzip(gfe),gzip(gfe) Are You looking for solutions manual for a tough class?! Did the search results lead you here?! Try sending me email with the name and details of the solutions manual you need and I may be able to help. Do not reply here, instead send email to jhonrecard(at)gmail(dot)com.If the solutions manual you are looking for is not listed here, do not give up and send me email, I may be able to help! Please note: It is NOT free to send you the solutions manual if it is available . Applied Fluid Mechanics (Mott) Applied Strength of Materials (Mott) Adaptive Filter Theory (Simon Haykin) Applied Multivariate Statistical Analysis (Johnson & Wichern) A First Course in Abstract Algebra (John B. Fraleigh) Adaptive Control, by Astrom, Wittenmark Advanced Modern Engineering Mathematics, by G. James Aircraft Structures for Engineering Students (T.H.G. Megson) Advanced calculus, by Gerald B. Folland Antennas for All Applications (John Kraus & Ronald Marhefka) An Introduction to the Finite Element Method (J. N. Reddy) Advanced Fluid Mechanics (William Graebel) A Transition to Advanced Mathematics, by Smith, Eggen, Andre A First Course in Differential Equations, by Zill, Cullen Applied Partial Differential Equations, by J. David Logan Analytical Mechanics, by Fowels, Cassiday Applied Calculus for the Managerial, Life, and Social Sciences, by Soo T. Tan Advanced Engineering Mathematics (Erwin Kreyszig) Applied Numerical Methods with MATLAB for Engineers and Scientists (Steven C. Chapra) Analysis and Design of Analog Integrated Circuits, by Gray,Hurst, Lewis, Meyer Advanced Mathematical Concepts Precalculus with Applications by Holliday Applied Statistics and Probability for Engineers (Douglas Montgomery & George Runger) Antenna theory, by Balanis Automatic Control Systems, by Kuo, Golnaraghi Accompany Futures, Options, and Swaps, Robert W. Kolb Applied Partial Differential Equations (Haberman) Analysis and Performance of Fiber Composites (Bhagwan Agarwal, Lawrence Broutman & K. Chandrashekhara Advanced Visual Basic 2005 (Kip Irvine & Tony Gaddis) Ada 95: Problem Solving and Program Design (Michael B. Feldman, Koffman) Algorithm Design (Jon Kleinberg & í.8ava Tardos) Artificial Intelligence: Structures and Strategies for Complex Problem Solving, Luger Access 2007 Guidebook, Maggie Trigg, Phyllis Dobson Applied Numerical Analysis Using MATLAB (Fausett) A Friendly Introduction to Numerical Analysis (Bradie) Algebra and Trigonometry (Michael Sullivan) Algebra and Trigonometry (Robert F. Blitzer) Algebra and Trigonometry: An Early Functions Approach (Robert F. Blitzer) Algebra for College Students (Allen R. Angel) Algebra for College Students (Robert F Blitzer) A Graphical Approach to Precalculus (John Hornsby, Lial & Rockswold) A Graphical Approach to Precalculus with Limits: A Unit Circle Approach (John Hornsby, Margaret L. Lial & Gary K. Rockswold) A Problem Solving Approach to Mathematics (Rick Billstein, Libeskind & Lott) A Survey of Mathematics with Applications (Allen R. Angel, Abbott & Runde) A Survey of Mathematics with Applications: Expanded Edition (Angel, Abbott & Runde) Beginning and Intermediate Algebra (Margaret L. Lial, John Hornsby & Terry McGinnis) Beginning and Intermediate Algebra with Applications & Visualization, Gary K. Rockswold,Terry A. Kriege Basic Engineering Plasticity: An Introduction with Engineering and Manufacturing Applications (David Rees) Biomaterials Science: An Introduction to Materials in Medicine, Buddy D. Ratner, Allan Hoffman, Frederick Schoen & Jack Lemons) Bioprocess Engineering Principles (Pauline M. Doran) Business Math Using Calculators: With 10-Key Computer Assisted Instruction (Burton) Business Math & Study Guide Package, Cheryl Cleaves, Margie Hobbs. Basic College Mathematics (John Tobey & Jeffrey Slater) Basic College Mathematics with Early Integers (K. Elayn Martin-Gay) Business Mathematics (Charles D. Miller, Stanley A. Salzman Gary Clendenen) Beginning Algebra (Margaret L. Lial, John Hornsby & Terry McGinnis) Beginning Algebra with Applications & Visualization, Gary K. Rockswold, Terry A. Krieger Brief Course in Mathematical Statistics (Hogg & Tanis) College Algebra Essentials (Michael Sullivan) College Algebra (Robert F. Blitzer) College Algebra Essentials (Robert F. Blitzer) College Algebra: An Early Functions Approach (Robert F. Blitzer) College Algebra: Concepts through Functions (Michael Sullivan III & Michael Sullivan) College Algebra Enhanced with Graphing Utilities (Sullivan III & Michael Sullivan) Construction Methods and Management (Stephens W. Nunnally) Construction Project Administration (Fisk Wayne Reynolds) Construction Accounting and Financial Management (Steven J. Peterson) Cost Analysis and Estimating for Engineering and Management (Phillip F. Ostwald & Timothy S. McLaren) Construction Estimating Using Excel (Stephen J. Peterson) Calculus for the Life Sciences (Marvin L. Bittinger, Neal Brand & John Quintanilla) Calculus with Applications for the Life Sciences (Raymond N. Greenwell, Nathan P. Ritchey & Margaret L. Lial) Calculus (George B. Thomas, Jr. & Ross L. Finney) Calculus: A Complete Course (Ross L. Finney, Franklin D. Demana, Bert K. Waits & Daniel Kennedy) Calculus (Elgin H. Johnston & Jerry Mathews) Chemical Engineering Volume 1, by Richardson, Coulson,Backhurst, Harker Computer Networks: A Systems Approach, Larry Peterson, Bruce Davie Computer Organization and Design, the Hardware/Software Interface, David Patterson, John Hennessy Customer Service: Career Success through Customer Loyalty (Timm) Customer Service: A Practical Approach (Harris) Conceptual Physical Science (Paul G. Hewitt, John A. Suchocki & Leslie Hewitt) Conceptual Integrated Science (Paul G. Hewitt, Suzanne Lyons, John A. Suchocki & Jennifer Yeh) Conceptual Physics Media Update, Paul G. Hewitt College Physics (Jerry D Wilson, Anthony J Buffa & Bo Lou) College Algebra and Trigonometry (J. S. Ratti & Marcus S. McWaters) College Algebra and Trigonometry (Mark Dugopolski) College Algebra and Trigonometry (Margaret L. Lial, John Hornsby & David I. Schneider) College Algebra (Mark Dugopolski) College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (Ronald J. Harshbarger & Lisa S. Yocco) College Algebra (Judith A. Beecher, Judith A. Penna & Marvin L. Bittinger) College Algebra (Margaret L. Lial, John Hornsby & David I. Schneider) Contemporary Engineering Economics (Chan Park) Chemistry: An Introduction to General, Organic, & Biological Chemistry, Karen C Timberlake Conceptual Chemistry, (John A. Suchocki) Customer Relationship Management: The Bottom Line to Optimizing Your ROI (Anton & Petouhoff) Computer Numerical Control: Operation and Programming (Jon S. Stenerson & Kelly Curran) Corporate Finance (Jonathan Berk & Peter DeMarzo) College Algebra (J. S. Ratti & Marcus S. McWaters) Data Structures and Other Objects Using C++ (Michael Main & Walter Savitch) Data Structures and Problem Solving Using C++ (Mark Allen Weiss) Data Structures and Algorithm Analysis in Java (Mark Allen Weiss) Collections Framework, by Gray Data Abstraction and Problem Solving with Java (Frank M. Carrano & Prichard) Data Structures and Other Objects Using Java (Michael Main) Data Structures and Problem Solving Using Java (Mark Allen Weiss) Data Structures in Java (Thomas A. Standish) Database Systems: An Application Oriented Approach, Compete Version (Michael Kifer, Arthur Bernstein & Philip M. Lewis) DataBase Systems: A Practical Approach to Design, Implementation and Management (Thomas M. Connolly & Carolyn E. Begg) Database Systems: An Application-Oriented Approach, Introductory Version (Michael Kifer, Arthur Bernstein & Philip M. 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Smith) Environmental and Natural Resource Economics (Tom Tietenberg) Engineering Materials Vol. 1: An Introduction to Properties, Applications and Design (Michael Ashby & David R H Jones) Engineering Materials Vol. 2: An Introduction to Microstructures, Processing and Design (Michael Ashby & David R H Jones) Electronic Circuits - Fundamentals & Applications, Mike Tooley Engineering Materials Science, by Milton Ohring Foundations of Macroeconomics (Robin Bade & Michael Parkin) Foundations of Microeconomics (Robin Bade & Michael Parkin) Finite Mathematics, by Margaret L. Lial , Raymond N. Greenwell , Nathan P. Ritchey Fundamentals of Differential Equations bound, Kent Nagle, B. Saff, Snider Financial Accounting, by Harrison Fundamentals of Renewable Energy Processes (Aldo da Rosa) First Course in Statistics (James T. McClave & Terry Sincich) Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics (E. 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Beem) Guide to Microsoft Excel 2002 for Scientists and Engineers (Bernard V. Liengme) Health Economics (Charles E. Phelps) Heat Transfer: A Practical Approach - by Cengel How to Break Software Security (James A. Whittaker & Herbert H. Thompson) Hydrology and Floodplain Analysis (Philip Bedient, Wayne Huber & Baxter Vieux) Higher Engineering Mathematics (John Bird) History of Mathematics: Brief Version (Victor J. Katz) Introduction to Vacuum Technology (David M. Hata) Introduction to Programming in Java: An Interdisciplinary Approach (Sedgewick & Kevin Wayne) Introduction to Programming Using Java: An Object-Oriented Approach, Arnow, Dexter Weiss) Interactive Computer Graphics: A Top-Down Approach Using OpenGL (Edward Angel) Introduction to the Design and Analysis of Algorithms (Anany V. Levitin) Implementing Databases in Oracle 9i (John Day & Craig Van Slyke) Internet Effectively: A Beginner's Guide to the World Wide Web (Tyrone Adams & Sharon Scollard) Introduction to Mathematical Statistics (Hogg, Craig & McKean) Introduction to Mathematical Statistics and Its Applications (Larsen & Marx) Introductory Algebra (Robert F Blitzer) Introductory and Intermediate Algebra (Robert F Blitzer) Intermediate Algebra for College Students (Allen R. Angel) Intermediate Algebra (Michael Sullivan III & Katherine R. Struve) Intermediate Algebra (K. Elayn Martin-Gay) Intermediate Algebra (Marvin L. Bittinger) Intermediate Algebra: Graphs & Models (Marvin L. Bittinger, David J. Ellenbogen & Barbara L. Johnson) Intermediate Algebra (Margaret L. Lial, John Hornsby & Terry McGinnis) Intermediate Algebra with Applications and Visualization (Gary K. Rockswold & Terry A. 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Nyhoff & Jeffrey Nyhoff) Java Foundations: Introduction to Program Design and Data Structures, Lewis, DePasquale, Chase Java Software Solutions: Foundations of Program Design (John Lewis & William Loftus) Java Software Structures: Designing and Using Data Structures (Lewis, Chase) Job Hazard Analysis (James E. Roughton & Nathan Crutchfield) Kernel Projects for Linux (Gary Nutt) Linear Algebra with Applications (Bretscher) Law and Economics (Robert Cooter & Thomas Ulen) Linear Algebra, by Stephen H. Friedberg, Arnold J. Insel , Lawrence E. Spence Linear Algebra with Applications, by Otto Bretscher Linear Circuit Analysis: Time Domain, Phasor and Laplace Linear Systems and Signals, B P Lathi LabVIEW 8 Student Edition (Bishop) Logic and Design of Computer Programs (Jim Messinger) Learning SQL: A Step-by-Step Guide Using Access (Sikha Bagui & Richard Earp) Light on the Web: Essentials to Making the 'Net Work for You (Wendy G. Lehnert) Linear Algebra with Applications (S. Leon) Linear Algebra for Engineers and Scientists Using Matlab (Hardy) Logic and Computer Design Fundamentals, by Morris Mano and Charles Kime Linear Algebra and Differential Equations (Gary L. Peterson & James S. Sochacki) Linear Algebra and Its Applications, David C. Lay Laser Processing of Engineering Materials: Principles, Procedure and Industrial Application, John Ion Laminar Composites (by George Staab) Learning Math in Elementary and Middle School & IMAP Package (George Cathcart, Yvonne M. Pothier, James H. Vance & Nadine S. Bezuk) Machine Design: An Integrated Approach (Norton) Mechanics of Materials, by Russell C. Hibbeler Modern Control Systems (Dorf) Modern Wireless Communications (Simon Haykin, Michael Moher) Mathematics for the Technical Trades (Cook) Mathematical Statistics with Applications (Miller) Macroeconomics, by Michael Leeds, Allmen, Schiming Macroeconomics (Stephen D. Williamson) Money, the Financial System, and the Economy (R. Glenn Hubbard) Microeconomics: Theory and Applications with Calculus (Jeffrey M. Perloff) Modern Industrial Organization (Dennis W. Carlton & Jeffrey M. Perloff) Modern Labor Economics: Theory and Public Policy (Ronald G. Ehrenberg & Robert S. Smith) Market Regulation (Roger Sherman) Mathematical Methods for Economics (Michael Klein) Multinational Business Finance (David K. Eiteman, Arthur I. Stonehill & Michael H. Moffett) Mechanics of Materials: A Modern Integration of Mechanics and Materials in Structural Design, Jenkins & Khanna) Modern Operating Systems, by Andrew Tanenbaum Mathematics with Applications (Margaret L. Lial, Hungerford & John Holcomb) Mathematical Ideas Expanded Edition (Charles D. Miller, Heeren & John Hornsby) Mathematics All Around (Tom Pirnot) Mathematics for Elementary School Teachers (Phares O'Daffer, Randall Charles, Thomas Cooney, John A. Dossey & Jane Schielack) Mathematics for Elementary Teachers plus Activities Manual (Sybilla Beckmann) Mathematical Reasoning for Elementary Teachers (Calvin T. Long & Duane W. DeTemple) Mechatronics: Principles and Applications (Godfrey Onwubolu) Machine Vision: Theory, Algorithms, Practicalities (E. R. Davies) Managing Quality: Integrating the Supply Chain (S. Thomas Foster) Network Security Essentials: Applications and Standards (William Stallings) Numerical Methods Using Matlab (Mathews & Fink) Network Flows: Theory, Algorithms, and Applications by Ravindra K. Ahuja , Thomas L. Magnanti Numerical Methods for Engineers (Steven C. Chapra) Nanoengineering of Structural, Functional and Smart Materials, Mark J. Schulz, Ajit D. Kelkar Numerical Analysis (Timothy Sauer) Numerical Analysis and Scientific Computation (Jeffery J. Leader) Network Management: Principles and Practice (Mani Subramanian) Numerical Methods in Biomedical Engineering, by Dunn, Constantinides & Prabhas Moghe) Operating System Concepts, Silberschatz, Galvin, Gagne Objects First With Java: A Practical Introduction Using BlueJ (Barnes & Kolling) Object of Java, the: Introduction to Programming Using Software Engineering Principles (David D. Riley) Object-Oriented Programming in Java: A Graphical Approach, Preliminary Ed.,Kathryn Sanders & Andy van Dam) Oracle 10g Programming: A Primer (Rajshekhar Sunderraman) Oracle 9i Programming: A Primer (Rajshekhar Sunderraman) OSP: An Environment for Operating System Projects (Michael Kifer & Scott A. Smolka) Object-Oriented Programming featuring Graphical Applications in Java (Michael J. Laszlo) Object Oriented Software Development Using Java (Xiaoping Jia) Prealgebra & Introductory Algebra (K. Elayn Martin-Gay) Prealgebra (Jamie Blair, John Tobey & Jeffrey Slater) Precalculus (Michael Sullivan) Precalculus (Robert F. Blitzer) Precalculus Essentials (Robert F. Blitzer) Precalculus: Concepts through Functions, A Unit Circle Approach to Trigonometry (Michael Sullivan III & Michael Sullivan) Precalculus Enhanced with Graphing Utilities (Michael Sullivan III Precalculus Essentials: Enhanced with Graphing Utilities (Michael Sullivan III ) Prealgebra (Margaret L. Lial & Diana L. Hestwood) Prealgebra (Marvin L. Bittinger, David J. Ellenbogen & Barbara L. Johnson) Prealgebra (Tom Carson) Physics: Principles with Applications with MasteringPhysics, Douglas C. Giancoli Physlet Physics: Interactive Illustrations, Explorations and Problems for Introductory Physics (Wolfgang Christian & Mario Belloni) Physics for Scientists and Engineers with Modern Physics and MasteringPhysics, Douglas C. Giancoli Physlet Quantum Physics: An Interactive Introduction (Mario Belloni, Christian & Anne Cox) Precalculus: Graphs and Models Graphing Calculator Manual Package., Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen & Judith A. Penna) Precalculus with Modeling and Visualization (Gary K. Rockswold) Precalculus (Judith A. Beecher, Judith A. Penna & Marvin L. Bittinger) Precalculus (Mark Dugopolski) Precalculus (Margaret L. Lial, John Hornsby & David I. Schneider) Precalculus: Functions and Graphs (Mark Dugopolski) Principles of Chemical Kinetics (James House) Plant Pathology (George Agrios) Principles of Corrosion Engineering and Corrosion Control (Zaki Ahmad) Physical Metallurgy and Advanced Materials (R E Smallman & A.H.W. Ngan) Plastics: Microstructure and Engineering Applications (Nigel Mills) Project Management for Business and Engineering: Principles and Practice (John Nicholas) Professionalism: Real Skills for Workplace Success (Anderson & Bolt) Principles of Operations Management, Jay Heizer, Barry Render Physical Chemistry with Spartan Student Physical Chemistry Software (Thomas Engel & Philip Reid) Prentice Hall Lab Manual Introductory Chemistry, (Charles H Corwin) Probability and Statistics with Integrated Software Routines (Ronald Deep) Probability and Random Processes: With Applications to Signal Processing and Communications (Miller & Childers) Practical Perl with CGI Applications (Elizabeth Chang) Project-Based Software Engineering: An Object-Oriented Approach (Stiller & Cathie LeBlanc) Pointers on C (Kenneth Reek) Probability & Statistics for Engineers & Scientists (Walpole,Myers, Ye) Probability and Statistics (Morris H. DeGroot & Mark J. Schervish) Prealgebra and Introductory Algebra (Marvin L. Bittinger & David J. Ellenbogen) Prealgebra and Introductory Algebra (Margaret L. Lial, John Hornsby, Terry McGinnis & Diana L. Hestwood) Physics: Concepts & Connections (Art Hobson) Physics with Mastering Physics (James S. Walker) Power Generation Technologies (Paul Breeze) Principles of Sequence Stratigraphy (Octavian Catuneanu Quantum Mechanics: An Accessible Introduction (Robert Scherrer) Quantum Physics, by Stephen Gasiorowicz Quality (summers) Quality Management (Goetsch & Davis) Quality: A Corporate Force, Managing for Excellence (C. Harold Aikens) Occupational Safety and Health for Technologists, Engineers, and Managers (Goetsch) Quantum Chemistry and Spectroscopy with Spartan Student Physical Chemistry Software (Thomas Engel & Philip Reid) Quantitive Reasoning & the Environment (Greg Langkamp & Joseph Hull) Risk Takers: Uses and Abuses of Financial Derivatives ( John Marthinsen) RF Circuit Design: Theory & Applications, by Bretchko, Ludwig Reinforced Concrete Design (George F. Limbrunner & Abi Aghayere) Reinforced Concrete: Mechanics and Design (James G. MacGregor & James K. Wight) Renewable Energy (Sí.9frensen or Sorensen) Statistics: Informed Decisions Using Data (Michael III Sullivan) Franklin) Statistics for the Life Sciences (Samuels & Witmer) Statistics for Engineering and the Sciences (Mendenhall & Sincich) Statistics (McClave & Terry Sincich) Serving Internal and External Customers (Anne Swartzlander) Supply Chain Management (Sunil Chopra & Peter Meindl) Statistical Quality Design and Control (DeVor, Chang & Sutherland) Simply C#: An Application-Driven Tutorial Approach, by Deitel, Hoey Six Sigma: Basic Tools and Techniques (Donna C.S. Summers) Structures (Daniel Lewis Schodek & Martin Bechthold) Statics and Strength of Materials for Architecture and Building Construction (Onouye & Kane) Surveying with Construction Applications (Barry F. Kavanagh) Structural Analysis (Hibbeler) Structural Steel Design (Jack C. McCormac) The Economics of Macro Issues (Roger LeRoy Miller & Daniel K. Benjamin) The Economics of Money, Banking and Financial Markets (Frederic S. Mishkin) The Economics of Sports (Michael A. Leeds & Peter von Allmen) Theory of Asset Pricing (George Pennacchi) Thomas' Calculus: Multivariable, by Thomas, Weir, Hass, Giordano Thermodynamics: An Engineering Approach (Cengel) The Science and Engineering of Materials, by Donald R.Askeland, Pradeep P. Phule Thermal Physics (Ralph Baierlein) Theory and Design for Mechanical Measurements (Figliola & Beasley) Transport Phenomena (Bird & Stewart) The Economics of Public Issues (Roger LeRoy Miller, Daniel K. Benjamin & Douglass C. North) The 8051 Microcontroller (I. Scott MacKenzie, Raphael Chung-Wei Phan) The Finite Element Method: Its Basis and Fundamentals (Zienkiewicz, Taylor Zhu) The Management of Construction: A Project Lifecycle Approach (F. Lawrence Bennett) Transport Phenomena in Multiphase Systems (Faghri & Zhang) Theory of Plasticity (Jagabanduhu Chakrabarty) Themodynamics, Statistical Thermodynamics, and Kinetics (Thomas Engel & Philip Reid) The Physics of Sound (Richard E Berg & David G Stork) University Physics with Modern Physics, Hugh D. Young, Roger A. Freedman Understanding Modern Economics (Roger LeRoy Miller) Using Econometrics: A Practical Guide (A.H. Studenmund) Understanding Fiber Optics (Jeff Hecht) Understanding UNIX/LINUX Programming: A Guide to Theory and Practice (Bruce Molay) University Calculus (Joel D. Hass, Maurice D. Weir & George B. Thomas, Jr.) University Calculus: Alternate Edition (Joel D. Hass, Maurice D. Weir & George B. Thomas, Jr.) Unix: The Textbook (Syed Mansoor Sarwar, Robert Koretsky & Syed Aqeel Sarwar) Understanding the Math You Teach: Content and Methods for Prekindergarten through Grade 4 (Anita C. Burris) Using and Understanding Mathematics: A Quantitative Reasoning Approach, Bennett, Briggs) Understanding Engineering Mathematics (Bill Cox) Vector Mechanics for Engineers: Statics & Dynamics (Ferdinand P. Beer) Visual Basic 2008 How to Program, (Harvey & Paul) Deitel Visual Basic.Net Programming (Jeffrey Tsay) VHDL: A Starter's Guide (Sudhakar Yalamanchili) Vector Calculus (Susan J. Colley) Virtual ChemLab: General Chemistry Student Lab Manual / Workbook, v2.5. (Brian F. Woodfield & Matthew C. Asplund) VLSI Test Principles and Architectures: Design for Testability (Chen, Cheng, Eklow et al.) Wireless Communications & Networks (William Stallings) Work Systems: The Methods, Measurement & Management of Work (Mikell P. Groover) World Trade and Payments: An Introduction (Richard E. Caves,Jeffrey A. Frankel & Ronald W. Jones) Wireless Communications: Principles and Practice, by Rappaport Wireless Communications and Networking (Jon W. Mark, Weihua Zhuang) Web 101 (Wendy G. Lehnert & Richard L. Kopec) Web Development and Design Foundations with XHTML Water and Wastewater Technology (Mark J. Hammer, Sr. & Mark J. Hammer, Jr.) Water-Resources Engineering (Chin) XML: Language Mechanics and Applications (Dwight Peltzer) 10-Key Touch Key: Developing Speed and Accuracy (Burton) === Subject: Get Solutions Manual posting-account=q-2XYgoAAAA09XnYVjs6Cn-Z-RYO4JNz SV1),gzip(gfe),gzip(gfe) Are You looking for solutions manual for a tough class?! Did the search results lead you here?! Try sending me email with the name and details of the solutions manual you need and I may be able to help. Do not reply here, instead send email to jhonrecard(at)gmail(dot)com.If the solutions manual you are looking for is not listed here, do not give up and send me email, I may be able to help! Please note: It is NOT free to send you the solutions manual if it is available . Applied Fluid Mechanics (Mott) Applied Strength of Materials (Mott) Adaptive Filter Theory (Simon Haykin) Applied Multivariate Statistical Analysis (Johnson & Wichern) A First Course in Abstract Algebra (John B. Fraleigh) Adaptive Control, by Astrom, Wittenmark Advanced Modern Engineering Mathematics, by G. James Aircraft Structures for Engineering Students (T.H.G. Megson) Advanced calculus, by Gerald B. Folland Antennas for All Applications (John Kraus & Ronald Marhefka) An Introduction to the Finite Element Method (J. N. Reddy) Advanced Fluid Mechanics (William Graebel) A Transition to Advanced Mathematics, by Smith, Eggen, Andre A First Course in Differential Equations, by Zill, Cullen Applied Partial Differential Equations, by J. David Logan Analytical Mechanics, by Fowels, Cassiday Applied Calculus for the Managerial, Life, and Social Sciences, by Soo T. Tan Advanced Engineering Mathematics (Erwin Kreyszig) Applied Numerical Methods with MATLAB for Engineers and Scientists (Steven C. Chapra) Analysis and Design of Analog Integrated Circuits, by Gray,Hurst, Lewis, Meyer Advanced Mathematical Concepts Precalculus with Applications by Holliday Applied Statistics and Probability for Engineers (Douglas Montgomery & George Runger) Antenna theory, by Balanis Automatic Control Systems, by Kuo, Golnaraghi Accompany Futures, Options, and Swaps, Robert W. Kolb Applied Partial Differential Equations (Haberman) Analysis and Performance of Fiber Composites (Bhagwan Agarwal, Lawrence Broutman & K. Chandrashekhara A Graphical Approach to Algebra and Trigonometry (John Hornsby, Margaret L. Lial & Gary K. Rockswold) Algebra and Trigonometry: Graphs and Models Graphing Calculator Manual Package (Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen & Judith A. Penna) Algebra and Trigonometry: Graphs & Models and Graphing Calculator Manual Package, Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna Algebra and Trigonometry with Modeling and Visualization (Gary K. Rockswold) A Graphical Approach to College Algebra (John Hornsby, Margaret L. Lial & Gary K. Rockswold) Astronomy: A Beginner's Guide to the Universe (Eric Chaisson & Steve McMillan) Algebra for College Students (Margaret L. Lial, John Hornsby & Terry McGinnis) Applied Physics (Dale Ewen, Ronald Nelson, Neill Schurter & Erik Gundersen) Algebra A Combined Approach (K. Elayn Martin-Gay) Precalculus: Concepts through Functions, A Right Triangle Approach to Trigonometry (Michael Sullivan III & Michael Sullivan) Algebra and Trigonometry Enhanced With Graphing Utilities, Michael Sullivan III Advanced Java: Internet Applications (Art Gittleman) Applied Statistics and the SAS Programming Language (Cody & Smith) Advanced Engineering Mathematics (Michael Greenberg) Algebra Connections (Ira J. Papick & UMO University of Missouri) Additional Calculus Topics (Raymond A. Barnett, Michael R. Ziegler & Karl E. Byleen) Applied Linear Algebra (Peter J. Olver & Cheri Shakiban) A Course in Probability (Neil A. Weiss) A Problem Solving Approach to Mathematics for Elementary School Teachers (Rick Billstein, Shlomo Libeskind & Johnny W. Lott) Astronomy Today, Eric Chaisson, Steve McMillan An Introduction to Modern Astrophysics (Bradley W. Carroll & Dale A. Ostlie) Aircraft Digital Electronic and Computer Systems: Principles, Operation and Maintenance (Mike Tooley) Atmospheric Science: An Introductory Survey (John Wallace, Peter Hobbs) Agriculture's Ethical Horizon (Robert Zimdahl) Active Learning Guide (Alan Van Heuvelen & Eugenia Etkina) Additional Calculus Topics (Raymond Barnett, Michael Ziegler & Karl Byleen) Addison-Wesley's Interactive Linux Tutorial and Reference (Edutrends, Inc.) Brief Calculus and Its Applications (Larry J Goldstein, Schneider, Lay & Asmar) Building Construction: Principles, Materials, and Systems (Madan Mehta, Diane Armpriest & Walter Scarborough) Basic Environmental Technology: Water Supply, Waste Management & Pollution Control (Jerry A. Nathanson) Boundary Value Problems and Partial Differential Equations (David Powers) Basic Engineering Mathematics (John Bird) Communication Systems Engineering (John G. Proakis & Masoud Salehi) College Algebra with Modeling and Visualization (Gary K. Rockswold) College Algebra: Graphs and Models Graphing Calculator Manual Package (Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen & Judith A. Penna) Concepts of Programming Languages (Robert W. Sebesta) C for Java Programmers (Tomasz Muldner) Computer Security: Art and Science (Matt Bishop) College Mathematics (Cleaves & Hobbs) Course in Business Statistics (Groebner, Shannon, Fry & Smith) Calculus with Applications (Margaret L. Lial, Greenwell & Nathan P. Ritchey) College Geometry: A Discovery Approach (David Kay) Criminalistics: An Introduction to Forensic Science (Richard Saferstein) Concrete Structures (Mehdi Setareh & Robert M. Darvas) Chemical Engineering Design (Coulson & Richardson's Chemical Engineering - Volume 6) - (Sinnott) C++ Programming with Design Patterns Revealed (Tomasz Muldner) Calculus Connections (Asma Harcharras, Dorina Mitrea) College Mathematics for Business, Economics, Life Sciences and Social Sciences (Raymond A. Barnett, Michael R. Ziegler & Karl E. Byleen) Chapter Zero: Fundamental Notions of Abstract Mathematics (Carol Schumacher) Circuits, Signals, and Systems for Bioengineers: A MATLAB-Based Introduction (John Semmlow) Construction Mathematics (Surinder Virdi & Roy Baker) Data Analysis and Probability Connections: Mathematics for Middle School Teachers (Debra A. Perkowski & Michael Perkowski) Developmental Mathematics (Marvin L. Bittinger & Judith A. Beecher) Developmental Mathematics: Basic Mathematics and Algebra (Margaret L. Lial, John Hornsby, Terry McGinnis, Stanley A. Salzman & Diana L. Hestwood) Dynamics of Structures (Chopra) Digital Image Processing, by Gonzalez, Woods Diagnostic Ultrasound Imaging: Inside Out (Thomas Szabo) Data Mining: A Tutorial Based Primer (Richard Roiger & Michael Geatz) Discrete Mathematics with Graph Theory (Edgar G. Goodaire & Michael M. Parmenter) Elementary Differential Equations with Boundary Value Problems, Henry Edwards David Penney Engineering Science (W. Bolton) Essential Java for Scientists and Engineers (Brian D Hahn & Katherine M Malan) Energy Technology and Directions for the Future (Fanchi) Engineering Mathematics (John Bird) Elementary and Intermediate Algebra: Graphs & Models (Marvin L. Bittinger, David J. Ellenbogen & Barbara L. Johnson) Elementary Algebra (Tom Carson, Ellyn Gillespie & Bill E. Jordan) Elementary Algebra with Early Systems of Equations (Tom Carson & Ellyn Gillespie) Elementary Algebra: Concepts and Applications (Marvin L. Bittinger & David J. Ellenbogen) Engineering Economy and the Decision-Making Process (Joseph C. Hartman) Engineering Management: Challenges in the New Millennium (C M Chang) Engineering Economy (Sullivan) Environmental Contaminants: Assessment and Control (Daniel Vallero) Energy Technology and Directions for the Future (Fanchi) Engineering of Software, the: A Technical Guide for the Individual, Dick Hamlet & Maybee Elementary Statistics: Picturing the World (Larson & Farber) Elementary Linear Algebra with Applications (Kolman & Hill) Essentials of Basic College Mathematics (John Jr Tobey, Jr., Jeffrey Slater) Essentials of Intermediate Algebra for College Students (Robert F. Blitzer) Excursions In Modern Mathematics with Mini-Excursions (Peter Tannenbaum) Elementary Statistics Using Excel (Mario F. Triola) Elementary Structures for Architects and Builders (Ronald E. Shaeffer) Essentials of Soil Mechanics and Foundations: Basic Geotechnics (David F. McCarthy) Electric Motors and Drives: Fundamentals, Types and Applications (Austin Hughes) Essential MATLAB for Engineers and Scientists (Brian D Hahn & Dan Valentine) Environmental Engineering (Ruth F Weiner & Robin Matthews) Elementary Math Modeling Updated (Mary Ellen Davis & C. Henry Edwards) E&M TIPERs: Electricity & Magnetism Tasks (C. J. Hieggelke,Maloney, O'Kuma & Steve Kanim) Explorations in Conceptual Chemistry: A Student Activity Manual (Jeffrey Paradis) Fundamentals of Probability, with Stochastic Processes (Saeed Ghahramani) Fundamentals of Mathematics (William M Setek & Michael A Gallo) Finite Math and Its Application (Larry J Goldstein, Schneider & Martha J. Siegel) Fundamentals of Differential Equations with Boundary Value Problems with IDE CD (Saleable Package), Kent Nagle, Late, Edward B. Saff Finite Mathematics and Calculus with Applications (L. Lial, Greenwell & Ritchey) Finite Math with Applications (Margaret L. Lial, Hungerford & John Holcomb) Fundamental Mathematics through Applications (Geoffrey Akst & Sadie Bragg) Finite Element Analysis with Error Estimators: An Introduction to the FEM and Adaptive Error Analysis for Engineering Students (J. Akin) Gas Dynamics (John & Keith) Geometry: An Investigative Approach (Phares G. O'Daffer & Stanley R. Clemens) Geology for Engineers and Environmental Scientists (Alan E. Kehew) General, Organic and Biological Chemistry: Structures of Life (Karen C. Timberlake) Groundwater Science (Charles Fitts) Geometry Connections (John K. Beem) Guide to Microsoft Excel 2002 for Scientists and Engineers (Bernard V. Liengme) Health Economics (Charles E. Phelps) Heat Transfer: A Practical Approach - by Cengel How to Break Software Security (James A. Whittaker & Herbert H. Thompson) Hydrology and Floodplain Analysis (Philip Bedient, Wayne Huber & Baxter Vieux) Higher Engineering Mathematics (John Bird) History of Mathematics: Brief Version (Victor J. Katz) Introductory Chemistry and CW+ GradeTracker Access Card Package, (Nivaldo J. Tro) Introductory Chemistry, Nivaldo J. Tro Introductory and Intermediate Algebra (Marvin L. Bittinger & Beecher) Introductory and Intermediate Algebra (argaret L. Lial, John Hornsby & Terry McGinnis) Introductory Statistics for Engineering Experimentation (Peter Nelson, Copeland & Coffin) Introduction to Naval Architecture (Tupper) Introduction to Optimum Design (Jasbir Arora) ISO 9001:2000 Quality Registration Step-by-Step (Fred Dobb) Industrial Safety and Health Management (C. Ray Asfahl) Introduction to Economic Reasoning (William D. Rohlf, Jr.) Introduction to Engineering Technology (Robert J. Pond) Introduction to Data Mining (Pang-Ning Tan, Michael Steinbach & Vipin Kumar) Introduction to the Team Software Process (Watts S. Humphrey) Introductory Linear Algebra: An Applied First Course (Kolman & Hill) Introductory Algebra (K. Elayn Martin-Gay) Intermediate Algebra (Robert F Blitzer) Introductory Mathematical Analysis for Business, Economics and the Life and social Sciences (Ernest F Haeussler, Richard S. Paul & R.J. Wood Introductory Linear Algebra: An Applied First Course (Bernard Kolman & David R. Hill) Introductory Statistics (Neil A. Weiss) Intro Stats (Richard D. De Veaux, Paul F. Velleman & David E.Bock) Introduction to Linear Algebra (Lee W. Johnson, R. Dean Riess & Jimmy T. Arnold) Introduction to Technical Mathematics (Allyn J. Washington, Triola & Reda) Integrated Arithmetic and Basic Algebra (Bill E. Jordan & William P. Palow) Introductory Algebra through Applications (Geoffrey Akst & Sadie Bragg) Introduction to Optics (Frank L Pedrotti, Leno M Pedrotti Leno S Pedrotti) Introduction to Environmental Engineering and Science (Gilbert M. Masters & Wendell P. Ela) Introduction to Transport Phenomena (W. Thomson) Introduction to Naval Architecture: Formerly Muckle's Naval Architecture for Marine Engineers (E C Tupper) Interactive Statistics (Martha Aliaga & Brenda Gunderson) Instrumentation and Control Systems (W. Bolton) Introduction to Applied Statistical Signal Analysis: Guide to Biomedical and Electrical Engineering Applications (Richard Shiavi) Introduction to Computer Security (Matt Bishop) Java: An Introduction to Problem Solving and Programming (Walter Savitch) Java: An Introduction to Computing (Joel Adams, Larry R. Nyhoff & Jeffrey Nyhoff) Java Foundations: Introduction to Program Design and Data Structures, Lewis, DePasquale, Chase Java Software Solutions: Foundations of Program Design (John Lewis & William Loftus) Java Software Structures: Designing and Using Data Structures (Lewis, Chase) Job Hazard Analysis (James E. Roughton & Nathan Crutchfield) Kernel Projects for Linux (Gary Nutt) Linear Algebra with Applications (Bretscher) Law and Economics (Robert Cooter & Thomas Ulen) Linear Algebra, by Stephen H. Friedberg, Arnold J. Insel , Lawrence E. Spence Linear Algebra with Applications, by Otto Bretscher Linear Circuit Analysis: Time Domain, Phasor and Laplace Linear Systems and Signals, B P Lathi LabVIEW 8 Student Edition (Bishop) Logic and Design of Computer Programs (Jim Messinger) Kernel Projects for Linux (Gary Nutt) Linear Algebra with Applications (Bretscher) Law and Economics (Robert Cooter & Thomas Ulen) Linear Algebra, by Stephen H. Friedberg, Arnold J. Insel , Lawrence E. Spence Linear Algebra with Applications, by Otto Bretscher Linear Circuit Analysis: Time Domain, Phasor and Laplace Linear Systems and Signals, B P Lathi LabVIEW 8 Student Edition (Bishop) Logic and Design of Computer Programs (Jim Messinger) Linux: The Textbook (Syed Mansoor Sarwar, Robert Koretsky & Syed Aqeel Sarwar) LINUX & UNIX Programming Tools: A Primer for Software Developers (Syed) Languages and Machines: An Introduction to the Theory of Computer Science (Thomas A. Sudkamp) Mathematics for Electrical Engineering and Computing (Mary Attenborough) Modeling in Transport Phenomena: A Conceptual Approach (Ed.,Ismail Tosun) Materials: Engineering, Science, Processing and Design (Michael Ashby, Dr Hugh Shercliff & David Cebon) Mathematical Proofs: A Transition to Advanced Mathematics (Gary Chartrand, Polimeni & Zhang) Mastering Networks: An Internet Lab Manual (Jorg Liebeherr & Magda El Zarki) Mathematics for New Technologies (Don Hutchison & Mark Yannotta) Multivariate Data Analysis (Hair, Black, Babin, Anderson & Tatham) Mathematics for Economics and Business (Ian Jacques) Modern Matrix Algebra (Hill & Kolman) Modern Elementary Statistics (John E. Freund, Benjamin M. Perles) Network Security Essentials: Applications and Standards (William Stallings) Numerical Methods Using Matlab (Mathews & Fink) Network Flows: Theory, Algorithms, and Applications by Ravindra K. Ahuja , Thomas L. Magnanti Numerical Methods for Engineers (Steven C. Chapra) Nanoengineering of Structural, Functional and Smart Materials, Mark J. Schulz, Ajit D. Kelkar Numerical Analysis (Timothy Sauer) Numerical Analysis and Scientific Computation (Jeffery J. Leader) Network Management: Principles and Practice (Mani Subramanian) Numerical Methods in Biomedical Engineering, by Dunn, Constantinides & Prabhas Moghe) Operating System Concepts, Silberschatz, Galvin, Gagne Objects First With Java: A Practical Introduction Using BlueJ (Barnes & Kolling) Object of Java, the: Introduction to Programming Using Software Engineering Principles (David D. Riley) Object-Oriented Programming in Java: A Graphical Approach, Preliminary Ed.,Kathryn Sanders & Andy van Dam) Orbital Mechanics for Engineering Students (Howard Curtis) Open Channel Hydraulics (A. Osman Akan) Principles of Statics and Dynamics, by Russell C. Hibbeler Probability and Statistics for Engineers (Johnson, Miller, Freund) Partial Differential Equations and Boundary Value Problems with Fourier Series ( Asmar) Precalculus: Graphical, Numerical, Algebraic (Franklin Demana, Bert K. Waits, Gregory D. Foley & Daniel Kennedy) Principles of Economics, Roy J. Ruffin, Paul R. Gregory Principles of Money, Banking, and Financial Markets (Lawrence S. Ritter, William L. Silber & Gregory F. Udell) Public Finance and the American Economy (Neil Bruce) Personal Finance with Financial Planning Software (Jeff Madura) Principles of Managerial Finance Brief (Lawrence J. Gitman) Principles of Managerial Finance, Lawrence J. Gitman) Principles of Risk Management and Insurance (George E. Rejda) Plastics: Materials and Processing (Strong) Physics an Introduction, by James S. Walker Probability and Statistical Inference (Hogg & Tanis) Principles and Applications of Electrical Engineering (Rizzoni) Prealgebra and Introductory Algebra (Margaret L. Lial, John Hornsby, Terry McGinnis & Diana L. Hestwood) Physics: Concepts & Connections (Art Hobson) Physics with Mastering Physics (James S. Walker) Power Generation Technologies (Paul Breeze) Principles of Sequence Stratigraphy (Octavian Catuneanu) Programming the World Wide Web (Robert W. Sebesta) Principles of Database Systems with Internet and Java Applications (Greg Riccardi) Quantum Mechanics: An Accessible Introduction (Robert Scherrer) Quantum Physics, by Stephen Gasiorowicz Quality (summers) Quality Management (Goetsch & Davis) Quality: A Corporate Force, Managing for Excellence (C. Harold Aikens) Occupational Safety and Health for Technologists, Engineers, and Managers (Goetsch) Quantum Chemistry and Spectroscopy with Spartan Student Physical Chemistry Software (Thomas Engel & Philip Reid) Quantitive Reasoning & the Environment (Greg Langkamp & Joseph Hull) Risk Takers: Uses and Abuses of Financial Derivatives (John Marthinsen) RF Circuit Design: Theory & Applications, by Bretchko, Ludwig Reinforced Concrete Design (George F. Limbrunner & Abi Aghayere) Reinforced Concrete: Mechanics and Design (James G. MacGregor & James K. Wight) Renewable Energy (Sí.9frensen or Sorensen) Shigley's Mechanical Engineering Design (Budynas) Semiconductor Physics and Devices (Donald A. Neamen) Signal Processing and Linear Systems by Lathi Statics and Mechanics of Materials: An Integrated Approach (Riley, Sturges & Morris) Signals and Systems (Simon Haykin & Barry Van Veen) Semiconductor Devices: Physics and Technology (Simon M. Sze) Separation Process Principles (Seader & Henley) Statics and Strengths of Materials (Morrow & Kokernak) Simply Java Programming: An Application-Driven.89.8b¢ Tutorial Approach(Deitel) SQL for SQL Server (Bijoy Bordoloi & Douglas B. Bock) Simply Visual Basic 2008 (Harvey & Paul) Deitel Simply Visual Basic .NET (Deitel & Nieto) Soils and Foundations (Liu & Evett) Structure and Interpretation of Signals and Systems (Edward A. Lee & Pravin Varaiya) Stats: Modeling the World (David E. Bock, Paul F. Velleman & Richard D. De Veaux) Single Variable Calculus (Monty J. Strauss, Gerald L. Bradley & Karl J. Smith) Statistics and Probability for Engineering: Applications with Microsoft Excel (Decoursey) Structural and Stress Analysis (Megson) Systems for Planning and Control in Manufacturing (D. K. Harrison & D. J. Petty) Statistical Reasoning for Everyday Life (with SPSS from A to Z: A Brief Step-by-Step Manual), Jeffrey O. Bennett, Briggsr & Triola Stats: Data and Models, (Richard D. De Veaux, Paul F. Velleman & David E. Bock) Galin) Statistics for Science and Engineering (John Kinney) The Science and Engineering of Materials, by Donald R.Askeland, Pradeep P. Phule Thermal Physics (Ralph Baierlein) Theory and Design for Mechanical Measurements (Figliola & Beasley) Transport Phenomena (Bird & Stewart) The Economics of Public Issues (Roger LeRoy Miller, Daniel K. Benjamin & Douglass C. North) The 8051 Microcontroller (I. Scott MacKenzie, Raphael Chung-Wei Phan) The 8051 Microcontroller and Embedded Systems (Mazidi, Mazidi & McKinlay) Technology and Society ( Hjorth, Eichler, Khan, John Morello) The Art and Science of Java (Eric Roberts) The Object of Data Abstraction and Structures (using Java) (David Riley) Technical Calculus (Dale Ewen, Joan S. Gary & James E. Trefzger) The Cosmic Perspective, Jeffrey O. Bennett, Megan Donahue, Nicholas Schneider, Mark Voit The Essential Cosmic Perspective Media Update, Jeffrey O. Bennett, Megan Donahue, Nicholas Schneider, Mark Voit Technical Calculus with Analytic Geometry (Allyn J. Washington) The Complete A+ Guide to PC Repair (Cheryl A. Schmidt) University Physics with Modern Physics, Hugh D. Young, Roger A. Freedman Understanding Modern Economics (Roger LeRoy Miller) Using Econometrics: A Practical Guide (A.H. Studenmund) Understanding Fiber Optics (Jeff Hecht) Understanding UNIX/LINUX Programming: A Guide to Theory and Practice (Bruce Molay) University Calculus (Joel D. Hass, Maurice D. Weir & George B. Thomas, Jr.) University Calculus: Alternate Edition (Joel D. Hass, Maurice D. Weir & George B. Thomas, Jr.) Unix: The Textbook (Syed Mansoor Sarwar, Robert Koretsky & Syed Aqeel Sarwar) Understanding the Math You Teach: Content and Methods for Prekindergarten through Grade 4 (Anita C. Burris) Using and Understanding Mathematics: A Quantitative Reasoning Approach, Bennett, Briggs) Understanding Engineering Mathematics (Bill Cox) Vector Mechanics for Engineers: Statics & Dynamics (Ferdinand P. Beer) Visual Basic 2008 How to Program, (Harvey & Paul) Deitel Visual Basic.Net Programming (Jeffrey Tsay) VHDL: A Starter's Guide (Sudhakar Yalamanchili) Vector Calculus (Susan J. Colley) Virtual ChemLab: General Chemistry Student Lab Manual / Workbook, v2.5. (Brian F. Woodfield & Matthew C. Asplund) VLSI Test Principles and Architectures: Design for Testability (Chen, Cheng, Eklow et al.) Wireless Communications & Networks (William Stallings) Work Systems: The Methods, Measurement & Management of Work (Mikell P. Groover) World Trade and Payments: An Introduction (Richard E. Caves,Jeffrey A. Frankel & Ronald W. Jones) Wireless Communications: Principles and Practice, by Rappaport Wireless Communications and Networking (Jon W. Mark, Weihua Zhuang) Web 101 (Wendy G. Lehnert & Richard L. Kopec) Web Development and Design Foundations with XHTML Water and Wastewater Technology (Mark J. Hammer, Sr. & Mark J. Hammer, Jr.) Water-Resources Engineering (Chin) XML: Language Mechanics and Applications (Dwight Peltzer) 10-Key Touch Key: Developing Speed and Accuracy (Burton) === Subject: Test Banks & Solution Manuals - NEW posting-account=aBM6KgoAAADrVPeOCixVZoA04FCm4rNR .NET CLR 2.0.50727; Media Center PC 5.0; .NET CLR 3.0.04506; InfoPath.2),gzip(gfe),gzip(gfe) Hi there! Student Plus Has The Following Test Banks & Solutions Manual, All In Digital Formats (PDF,DOC,RTF) For The Following Books' Titles: Note: Some Books With Either The Test Bank Or The Solution Manual (Test bank, Solution Manual, Instructor Guid) A Quantum Approach to Condensed Matter Physics,E,Taylor, Heinonen A Short Introduction to Quantum Information and Quantum Computation,E,Michel Le Bellac Accounting for Governmental and Nonprofit Entities,14,Wilson, Kattelus, Reck Accounting Information Systems,10,Romney, Steinbart Accounting Information Systems,11,Romney, Steinbart Accounting Information Systems,5,James A. Hall Accounting Information Systems,6,James A. Hall Accounting Information Systems,7, Gelinas, Dull Accounting Information Systems A Business Process: Approach,2,Jones, Rama Accounting Principles,7,Weygandt, Kieso, Kimmel Accounting Principles,8,Weygandt, Kieso, Kimmel Accounting Principles,9,Weygandt Adaptive Control,2,Astrom, Wittenmark Advanced Accounting,10,Beams, Clement, Anthony, Lowensohn Advanced Accounting,10,Fischer, Taylor, Cheng Advanced Accounting,2,Jeter, Chaney Advanced Accounting,3,Jeter, Chaney Advanced Accounting,8,Hoyle, Schaefer, Doupnik Advanced Accounting,9,Beams, Clement, Anthony, Lowensohn Advanced Accounting,9,Fischer, Taylor, Cheng Advanced Accounting,9,Hoyle, Schaefer, Doupnik Advanced Calculus,2002,Gerald B.Folland Advanced Engineering Mathematics,8,Kreyszig Advanced Engineering Mathematics,9,Erwin Kreyszig Advanced Modern Engineering Mathematics,3,Glyn James Advertising and Promotion: An Integrated Marketing Communications Perspective,6,Belch Advertising and Promotion: An Integrated Marketing Communications Perspective,7,Belch An Introduction to Numerical Analysis,E,David F. Mayer An Introduction to Numerical Analysis, rs, 0,E,Endre Suli, David F. M An Introduction to Ordinary Differential Equations,E,James C. Robinson An Introduction to the Finite Element Method,3,Reddy Analog Integrated Circuit Design,1996,Johns Martin Analysis and Design of Integrated Circuits,4,Gray, Hurst, Lewis, Meyer Analytical Mechanics,7,Fowles, Cassiday Applied Calculus for the Managerial, Life, and Social Sciences,6,Tan Applied Partial Differential Equations,4,Haberman Applied Partial Differential Equations,E,David Logan Applied Statistics and Probability for Engineers,3,Montgomery, Runger Artificial Intelligence: A Modern Approach,2,Russell, Norvig Astronomy Today,5,Chaisson, McMillan Auditing and Assurance Services,12,Arens, Elder, Beasley Auditing and Assurance Services (An Intergrated Approach),12,Alvin Arens, J. Elder, Beasley Automatic Control Systems,8,Kuo, Golnaraghi Basic Engineering Circuit Analysis,7,Irwin Basic Engineering Circuit Analysis,8,Irwin Basic Technical Mathematics with Calculus Metric Version,8,Alyn J. Washington Basic Technical Mathematics with Calculus, Canadian Edition,8,Allyn J. Washington Basic Technical Mathematics with Calculus, Cdn,8,Alyn J. Washington Biological Science,2,Scott Freeman Biology,7,Campbell, Reece Biology,8,Campbell, Reece Brief Principles of Macroeconomics,4,Gregory Mankiw Business Essentials,5,Ebert, Griffin Business Essentials,6,Ebert, Griffin Business Law and the Regulation of Business,8,Mann, Roberts Business Law and the Regulation of Business,9,Mann, Roberts Business Law Today, Standard Edition,8,Miller, Jentz Business Law Today: Comprehensive,7,Miller, Jentz Business Law Today: The Essentials,8,Miller, Jentz Business Law: Today The Essentials,7,Miller, Jentz Business Statistics: A Decision Making Approach,6,Groebner, Shannon, Fry, Smith Business Statistics: A Decision Making Approach,7,Groebner, Shannon, Fry, Smith C++ How to Program,3,Deitel, Deitel & Nieto Calculus,3,Hallett, Gleason, mcCallum Calculus,5,James Stewart Calculus,8,Varberg, Purcell, Rigdon Calculus With Analytic Geometry,7,Larson, Edwards, Hostetler, Hostetler Calculus with Applications,8,Lial, Greenwell, Ritchey Calculus with Applications Brief Version,8,Lial, Greenwell, Ritchey Calculus, Early Transcendental Functions,3,Smith, Minton Calculus, Early Transcendentals,5,Edwards, Penney Calculus, Early Transcendentals,6,Edwards, Penney Calculus, Early Transcendentals,7,Edwards, Penney Cases in Management Accounting and Control Systems,4,Allen, Brownlee, Haskins, Lynch, Rotch Chemistry: The Central Science,10,Brown, LeMay, Bursten Chemistry: The Central Science,11,Brown, LeMay, Bursten, Murphy, Woodward Classical Dynamics: A Contemporary Approach,E,Jos.8e, Eugene, Saletan Classical Electrodynamics,3,Jackson Classical Mechanics,2,Goldstein College Mathematics for Business, Economics, Life Sciences & Social Sciences,11,Barnett, Ziegler, Byleen College Physics,6,Serway, Faughn Communication Systems,4,Carlson Communication Systems,4,Haykin Communication Systems Engineering,2,Proakis, Salehi Complex Variables With Applications,3,Wunsch, Brown Computational Techniques for Fluid Dynamics,E,Karkenahalli Srinivas, Clive, Fletcher Computer Networking A Top Down Approach,3,James F.Kurose, Keith W. Ross Computer Organization and Architecture: Designing for Performance, 7,William Stallings Computer Science: An Overview,10,Glenn Brookshear Computer Science: An Overview,9,Glenn Brookshear Concepts and Applications of Finite Element Analysis,4,Cook Corporate Finance,8,Ross, Westerfield, Jordan Cost Accounting,12,Horngren, Datar, Foster Cost Accounting,13,Horngren, Foster, Datar, Rajan, Ittner Cost Accounting,5,Michael Maher Data Abstraction and Problem Solving with Java,2,Carrano, Prichard Data Abstraction and Problem Solving with Java, Walls and Mirrors, Data and Computer Communications,8,William Stallings Database System Concepts,4,Silberschatz, Korth, Sudarshan Database System Concepts,5,Silberschatz Design and Analysis of Experiments,6,Douglas C. Montgomery Device Electronics for Integrated Circuits,3,Richard S. Muller, Theodore, Kamins Differential Equations and Linear Algebra,3,Goode, Annin Differential Equations and Linear Algebra,E,Edwards, Penney Digital & Analog Communication Systems,7,Leon W. Couch Digital Image Processing,2,Gonzalez, Woods Digital Image Processing,3,Gonzalez, Woods Discrete and Combinatorial Mathematics,5,Ralph P. Grimaldi Discrete Mathematics,6,Richard Johnsonbaugh Economics,7,Roger A. Arnold Economics,8,Roger A. Arnold Electric Circuits,7,James W. Nilsson, Susan Riedel Electric Machinery,6,Fitzgerald, Charles Kingsley, Umans Electric Machinery Fundamentals,4,Stephen J. Chapman Electrical Machines, Drives and Power Systems,6,Theodore Wildi Electronic Commerce 2008,5,Turban, Dave King, Lee, Viehland Electronic Commerce: A Managerial Perspective 2006,4,Turban, Dave King, Lee, Viehland Electronics,2,Allan R. Hambley Elementary Dffferential Equations,8,Kohler, Johnson Elementary Differential Equations,8,Boyce, DiPrima Elementary Differential Equations and Boundary Value Problems,7,Boyce, DiPrima Elementary Differential Equations and Boundary Value Problems,8,Boyce, DiPrima Elementary Differential Equations With Boundary Value Problems, 4,Edwards, Penney Elementary Differential Equations with Boundary Value Problems, 6,Edwards, Penney Elementary Number Theory,5,Goddard, Rosen Elementary Principles of Chemical Processes,3,Richard M. Felder, Ronald W. Rousseau Elementary Statistics,2,Mario F. Triola Elementary Statistics,3,Mario F. Triola Elements Of Electromagnetics,3,Sadiku, Sagliocca, Soriyan Elements of Forecasting,3,Diebold Group, Francis X. Diebold Engineering Circuit Analysis,6,Hayt, Kemmerly, Durbin Engineering Electromagnetics,6,Hayt, Buck Engineering Fluid Mechanics,7,Crowe, Alger, Roberson Engineering Fluid Mechanics,7,Crowe, Elger, Roberson Engineering Mathematics,4,John Bird Engineering Mechanics (Dynamics),11,Hibbeler Engineering Mechanics (Statics),5,Bedford, Fowler Engineering Statistics,4,Montgomery, Runger, Hubele Environmental Economics and Natural Resource Management,E,David A. Anderson Equilibrium and Non-Equilibrium Statistical Thermodynamics,E,Bellac, Mortessagne, Batrouni Essentials of Economics,3,Gregory Mankiw Essentials Of Economics,3,Mankiw Essentials of Economics,4,Gregory Mankiw Essentials of Modern Business Statistics,3,Anderson, Sweeney, Williams Essentials of Statistics for Business and Economics,4,Anderson, Sweeney, Williams Essentials of Statistics for Business and Economics,5,Anderson, Sweeney, Williams Essentials of Statistics for Business and Economics, Abbreviated Edition,4,Anderson, Sweeney, Williams Field and Wave Electromagnetics,2,David K. Cheng Financial Accounting,6,Harrison, Horngren Financial and Managerial Accounting,13,Williams, Haka, Bettner Financial Management: Theory & Practice,12,Brigham, Ehrhardt Financial Reporting and Analysis,10,Charles H. Gibson Financial Reporting and Analysis,11,Gibson Finite Mathematics,8,Lial, Greenwell, Ritchey First Course In Abstract Algebra,7,John B. 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Patterson, McGraw Hill (Test Bank) West Federal Taxation 2008 (Comprehensive Volume), Edition 31, Willis, Hoffman, Maloney, Raabe (Test Bank) West Federal Taxation 2008 (Taxation of Business Entities), Edition 11, Smith, Raabe, Maloney (Test Bank) Wireless Communications, Edition 2, Theodore Rappaport (Solution Manual) If The Book You Are Looking For Is Not Listed, Please Contact Us And Student Plus Will Help Contact: Student.plus@hotmail.com Student.Plus(at)Hotmail(dot)com === Subject: Re: Concepts of Modern Physics Student Solution Manual Arthur Beiser posting-account=OOZ9_woAAABT1KJ674H2o8Sle6d8_XlS 5.1),gzip(gfe),gzip(gfe) > Hello If anybody is having soft copy of Concepts of Modern Physics Student > Solution Manual by Arthur Beiser please inform me. Siva === Subject: solutions manual of cuncepts of modern physics-beiser posting-account=OOZ9_woAAABT1KJ674H2o8Sle6d8_XlS 5.1),gzip(gfe),gzip(gfe) please send me this === Subject: Solutions manual for Machine Design: An Integrated Approach, 3rd Ed., by Robert L. Norton posting-account=HPZhWwoAAABmosEsQ60znd3RxOTIFHtk rv:1.9.0.1) Gecko/2008070206 Firefox/3.0.1,gzip(gfe),gzip(gfe) Does anyone have the solutions manual for Machine Design, an Integrated Approach, 3rd Ed. by Norton? If you have solutions for any chapters, I'd be very grateful. alg983@psu.edu === Subject: Re: Solutions manual for Machine Design: An Integrated Approach, 3rd Ed., by Robert L. Norton posting-account=14ou_goAAAA-hjz3u1vHKuyW-l3ZkYCI Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) email me at synnexster@gmail.com === Subject: Re: looking for book and solution manual for structural analysis 6th/7th edition by Russel Hibbeler posting-account=14ou_goAAAA-hjz3u1vHKuyW-l3ZkYCI Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) Email me at synnexster@gmail.com === Subject: Elements of Electromagnetics by Sadiku (4th) Solution WANTED I want to buy the Solution Manual for: Elements of Electromagnetics by Sadiku (4th) ONLY 4th === Subject: Re: JSH Re: Now we'll see > What I like about the Diophantine Equation Theorem, which I just > worked out today, is that now we can all see how long it takes for > the > mathematical community to recognize the result. > There are already posters insulting me in threads, how long will > that > continue? > Will there be yet another battle from the math community over this > result? > Posters casting doubt on the theorem? > A refusal by any established mathematicians to recognize it? > Possibly > claiming it's not of interest? > Time will tell. So now we wait. > James Harris > More JSH if you want > it;http://www.derkeiler.com/Newsgroups/sci.crypt/2006-07/msg00580.html Politics. The more of you post the better as you show who among you actually > knows any mathematics versus those who clearly do not. > I have suspected that many of you have no mathematical inclination or > interest but may even be psychology students, and others of you are > simply sociopathic thinking you had a victim to verbally assault. > Soon you will be part of history and your identities known. > Because the world will want to know the answers to who you ALL were. > Going back over the last 6 years. > Every single one of you will hopefully be known. Soon. > James Harris > Will you be calling in the army again this time? Or your space alien > buddies? > All because you did some high school algebra and didn't screw it up > completely? can be determined versus just having some people insulting each other >and talk talk talking? Spoof by a fool. Trolls die horrable deaths. >James Harris === Subject: Re: Hogg & Craig Solution Manual hi petrograd24. sorry i don't have the 4th edition solutions, but could i ask you where you got the 6th edition solutions? === Subject: << FREE HELP DESK SOFTWARE > posting-account=62vKdgoAAADZFKOHXQudQANKaQhpGHo8 SV1),gzip(gfe),gzip(gfe) )))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) )))))))) http://helpdesksoftwarefree.blogspot.com http://refinancingmortgageloans1.blogspot.com === Subject: Solutions Manual posting-account=67xqngoAAACyCmk857SLb1iUv8IpBLEW 3.0.04506.30; .NET CLR 1.1.4322; MSN Optimized;US; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; MSN Optimized;US),gzip(gfe),gzip(gfe) I would like to know the link for the solution manual for Atam Arya's Introduction to Classical Mechanics 2nd Edition. I found this through === Subject: JSH: Quadratic Diophantines: what JSH dosen't want you to know. The FIRST proof using tautological space ever. There are at least 5 errors, can you find them all? > Quadratic Diophantine Result I. Quadratic Diophantine Theorem: In the ring of integers, given the quadratic expression c1x2 + c2xy + c3y2 = c4z2 + c5zx + c6zy where the c's are constants, for solutions to exist it must be true that ((c2 - 2c1)2 + 4c1(c2 - c1 - c3))v2 + (2(c2 - 2c1)(c6 - c5) + 4c5(c2 - c1 - c3))v + (c6 - c5)2 - 4c4(c2 - c1 - c3) = n2 mod p for some n, where p is any prime coprime to z for a given solution, when v = -(x+y)z-1 mod p. For example with x2 + y2 = z2, I have c1 = 1, c2 = 0, c3 = 1, c4 = 1, c5 = 0, and c6 = 0 which gives -4v2 + 8 is a quadratic residue modulo p, for every prime coprime to z, when v = -(x+y)z-1 mod p. Making the substitution gives -4(-(x+y)z-1)2 + 8 = n2 mod p for some n, which is -4(x+y)2 + 8z2 = n2z2 mod p and since x2 + y2 = z2, I can substitute out z, to get 4(x-y)2 = n2z2 mod p. Proof of theorem: The theorem is proven using what I call a tautological space, where x+y+vz = 0(mod x+y+vz) as then I have x+y = -vz (mod x+y+vz), and can square both sides to get x2 + 2xy + y2 = v2z2 (mod x+y+vz) and multiply both sides by c1 and subtract from c1x2 + c2xy + c3y2 = c4z2 + c5zx + c6zy and use x = -y-vz (mod x+y+v) to substitute out x, and simplify to get (c4 - c5v - c1v2)z2 + ((c2 -2c1)v - c5 + c6)zy + (c2 - c1 - c3)y2 = 0 (mod x+y+vz) and then it's just a matter of completing the square, and collecting terms multiplied times y2 on the right, as you have an equation of the form (Az + By)2 = Cy2 (mod x+y+vz) and noting then that C must be a quadratic residue modulo p, where p is any prime such that x+y+vz = 0 mod p where coprimeness with z is required by the solution v = -(x+y)z-1 mod p. Proof complete. The Quadratic Diophantine Theorem allows determination of whether or not integer solutions are prohibited from existence for the given specified quadratic expression for various constants, because of the requirement that any prime coprime to z for a solution must have the given quadratic residue. II. Quadratic Diophantine Theorem and Pell's Equation With the Quadratic Diophantine Theorem derived, it makes sense to try it out with a well-known equation in Diophantine theory which is Pell's Equation: x2 - Dy2 = 1 with D a natural number. So with Pell's Equation I have c1 = 1, c2=0, c3 = -D, c4 = 1, c5 = 0, c6 = 0, and z=1 which gives 4Dv2 - 4D + 4 = n2 mod p and v = -(x+y) mod p, so I have 4D(x+y)2 - 4D + 4 = n2 mod p and since that must be true for all primes p, since z=1, I have in general that the left hand side must be a perfect square so it must be true then that D(x+y)2 - D + 1 = S2 where S is some integer, and I have in general that x+y = sqrt((S2 + D - 1)/D). Working backwards I found that S=41 gives that solution, verifying the result. Notice also that S2 = 1 mod D, so S = +/- 1 mod D when D is prime, while S = +/- 1 mod D is always a solution, while additional congruence relations can be found when it is not. So I can make the substitution S = jD +/- 1, to find x+y = sqrt(Dj2 +/- 2j + 1) which is x+y = sqrt((D-1)j2 + (j +/- 1)2) and I have the existence of solutions related to another Diophantine relation of the form (D-1)u2 + v2 = w2 with the condition that u = j and v = j+/-1. For instance with D=2, I have that I need solutions to u2 + v2 = w2 with u=j, and v=j+/-1, and j=20 works as 202 + 212 = 292, and gives x+y = 29, and again x=17, y=12 is a known solution to x2 - 2y2 = 1. So then x2 - 2y2 = 1 is related to certain Pythagorean triples and every case for which D-1 is a square there is a relation to them as well. Also notice that from x+y = sqrt((S2 + D - 1)/D) I have S2 - D(x+y)2 = -D + 1 which means a second Diophantine equation connected to the first! With D=2, I get then that x2 - 2y2 = 1, is connected to S2 - 2(x+y)2 = -1 so for every solution of the first there is a solution of the second. So there is an immediate result with the classical Pell's Equation, with little effort at all using the theorem, which can be used against any Diophantine quadratic in 2 variables, almost as easily, and also give results in 3 variables, though not quite as generally. III. Solvability and Diophantine Quadratic Chains Deciding to take my newly discovered Quadratic Diophantine Theorem for a spin against Pell's Equation turned out to be a good idea as besides letting me validate that I had derived the theorem correctly, it also showed me that the result I had didn't simply lead in a BFC--Big Freaking Circle. Still there is more as it indicates a route to finding a general solution for all 2 variable Diophantine equations using what I now call quadratic chains, which are infinite chains of related Diophantine equations. To derive the full theory I will use c1x2 + c2xy + c3y2 = c4z2 + c5zx + c6zy with z=1, so I have ((c2 - 2c1)2 + 4c1(c2 - c1 - c3))v2 + (2(c2 - 2c1)(c6 - c5) + 4c5(c2 - c1 - c3))v + (c6 - c5)2 - 4c4(c2 - c1 - c3) = n2 mod p for some n, where p is any prime coprime to z for a given solution, when v = -(x+y)z-1 mod p, like before but because z=1, I can immediately substitute and generalize to all primes as I did in my previous postwith Pell's Equation to get ((c2 - 2c1)2 + 4c1(c2 - c1 - c3))(x+y)2 - (2(c2 + 2c1)(c6 - c5) + 4c5(c2 - c1 - c3))(x+y) + (c6 - c5)2 - 4c4(c2 - c1 - c3) = S2 for some integer S, and to simplify doing the next calculations let A = ((c2 - 2c1)2 + 4c1(c2 - c1 - c3)) B = (2(c2 + 2c1)(c6 - c5) + 4c5(c2 - c1 - c3)) and C = (c6 - c5)2 - 4c4(c2 - c1 - c3 so I have A(x+y)2 - B(x+y) + C = S2 and it's immediately clear that I just have another quadratic Diophantine equation! Now manipulating to complete the square gives (A(x+y) - B/2)2 + AC - (B/2)2 = AS2 which is (2A(x+y) - B)2 + 4AC - B2 = 4AS2 and I have then the new quadratic Diophantine: (2A(x+y) - B)2 - 4AS2 = B2 - 4AC and have the stunning result that every quadratic Diophantine in two variables is connected to a quadratic Diophantine of the form: u2 - Dv2 = F and I get an existence condition as (2A(x+y) - B)2 = 4AS2 mod (B2 - 4AC) so I have that A must be a quadratic residue modulo (B2 - 4AC). But I have an even more stunning result as, of course, (2A(x+y) - B)2 - 4AS2 = B2 - 4AC is another Diophantine equation so I can use it to get yet another equation of the same form! Since that can go on forever, I now have the result that every Diophantine quadratic in 2 variables is connected to an infinity of others, chained to them, in that if one has solutions they all must have solutions, and if one does not, then none of them can. And obvious question then is, can both 4A and B2 - 4AC be perfect squares? Maybe but that would give a finite number solutions. I need a way where it is at least possible to get an infinity of solutions. Oh, duh, with A not a perfect square let B2 - 4AC be a perfect square and you get an infinity of solutions, and can then just pick those for which you have integer solutions in your chain. The full general method with x2 - Dy2 = n2 is that you solve for y2 to get y2 = (x2 - n2)/D and assume there exists k such that n = x-kD, as then you easily get k(2x + kD) = y2 so y = sqrt(k(2x+kD) and I need properties for k, where easily there are seen to be two cases, where the first is k = j2, which means there exists some m such that x = (m2 - j2D)/2 while the second case is k = 2j2, which gives x = (2m2 - j2D)/2 so from n = x-kD, with the first case I have j = sqrt((x-n)/D) and for the second j = sqrt((x-n)/2D). So you just find an x that will give an integer j, where x must be coprime to j, D and n, and then you have y, so it's a simple enough technique. So if that is what is needed, somewhere in the chain it must be true that B2 - 4AC is a perfect square, and of course if you find that member of the chain you can then generate solutions for any other member within the chain. James Harris 9/8/08 === Subject: Re: Quadratic Diophantines: what JSH dosen't want you to know. > The FIRST proof using tautological space ever. > There are at least 5 errors, can you find them all? > Quadratic Diophantine Result > I. Quadratic Diophantine Theorem: In the ring of integers, given the quadratic expression c1x2 + c2xy + c3y2 = c4z2 + c5zx + c6zy what is x2 ? x^2 or x_2 ? ditto y2, z2 and what is c1x2 ? c_1 * x_2 or c_1 * x^2 , or c^1 * x^2 ?? this is buggy stuff. and why is it in improper form? (extra constant) SO, that is about 5 there. Want me to continue? > where the c's are constants, for solutions to exist it must be true that ((c2 - 2c1)2 + 4c1(c2 - c1 - c3))v2 + (2(c2 - 2c1)(c6 - c5) + 4c5(c2 - > c1 - c3))v + (c6 - c5)2 - 4c4(c2 - c1 - c3) = n2 mod p Where did p come from? Where did n come from? Where did v come from? does n2 mean n_2 or n^2 or n*2 ??? What does (c2 - 2c1)2 mean ? _ or * or ^ ??? I smell Bull!! Wait.............. turd, flushed... I feel better now! === Subject: Re: What if: the Church had NOT condemned Galileo > On Sep 15, 12:54æpm, tadams...@yahoo.com The Church condemned Galileo because he was wrong. But what they > neglected to mention is that they were wrong too. > If Galileo had not satirized the Church they would not have condemned > him. æHis arrogance, ultimately, was what got him into trouble. > Correct. Dissing Pope Urban was not a peachy keen career move for Mr. G. > Mr. G. put all of Aristotle's howlers in the mouth of Simplicio who was > a surrogate for Pope Urban. > Bob Kolker- Hide quoted text - > - Show quoted text - > And, one could argue that all the Church was trying to do was to get > Galileo to do his job: æprovide clear proofs and an alternative, > comprehensive theoretical formulation to Aristotle. æ They were hoping > Galileo would be the next Thomas Aquinas. > HUH???? > Thomas Aquinas had to flee an investigation by the Bishop of Paris. > He was excommunicated after his death. > Unlike Galileo, Aquinas was lucky to have lived out his life before > the Chuch created the office of Grand Inquisitor. > Learn something about the Catholic Church!- Hide quoted text - > - Show quoted text - > Ummm... Thomas Aquinas was canonized as a Saint fifty years after his > death. æLearn something about the Catholic Church!- Hide quoted text - > - Show quoted text - > They excommunicated Aquinas and tried to bring him up on charges of > heresy, but he fled. æJust like with Galileo, they have never admitted > that they were wrong about the charges and the excommunication. > The Catholic Church never admits that it is wrong.- Hide quoted text - > - Show quoted text - I think you can take the canonization as an admission of error. Just > my opinion, of course. > Mine too. -- email to oshea dot j dot j at gmail dot com. === Subject: Re: Limit of a simple recurrence sequence > for the limit of x(n)? > The recurrence in question was x(n+m+1) = sum_{k=1}^m > [p(k) * x(n+k)] > where sum_k p(k) = 1. If X(n) is the column vector > [ x(n), x(n+1),...,x(n+m) ]^T, your recurrence can be > written as > X(n+1) = P X(n) > where P is the m x m matrix with entries P_{i,i+1}=1, > P_{m,j} = p(k), > all others 0. Let w be a left eigenvector of P for > eigenvalue 1, > i.e. w^T P = w^T, normalized so that sum_i w_i = 1. > Then the limit > will be w^T X(1). > -- > Robert Israel > israel@math.MyUniversitysInitials.ca > Department of Mathematics > http://www.math.ubc.ca/~israel > University of British Columbia Vancouver, > BC, Canada limit in terms p(k) and x(k), k=1 to m as follows: lim_{n->inf} x(n) = sum_{k=1}^m [sum_{i=1}^k [p(i) * x(k)]] / sum_{k=1}^m > [(m-k+1)*p(k)] However, I wonder why the matrix P is diagonizable, and why the absolute > values of other eigenvalues except 1 are all strictly smaller than 1, > although from the Gershgorin circle theorem, they must not be larger than > 1. P might not be diagonalizable: e.g. [ 0 1 0 ] [ 0 0 1 ] [ 1/16 7/16 1/2 ] is not. Fortunately, that's not needed. The fact that 1 is a simple eigenvalue and the others have absolute value strictly less than 1 is part of the version of the Perron-Frobenius theorem that applies to primitive matrices, i.e. those for which some power has all entries > 0. See also the theory of Markov chains. -- Robert Israel israel@math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada === Subject: Re: #174 temperature term and gravity term in Maxwell Equations ; Archimedes Plutonium's Superconductor Experiment Challenge ; new textbook: How Superconductivity really works; nanosecond Capacitor discharge current > Someone may say, AP you are overworking this, simply put a 1/T where T > is > temperature wherever you have a dt for change of rate of time t. Dorkwad, go read a stinking book. === Subject: Re: index of a subgroup and the index of any one of its conjugates (equality ?) days. My association with the Department is that of an alumnus. [...] >And yes, when there are doubts in my mind, I definitely would like >to hear what others knowledgeable in this field have to say about >them. But you don't say WHY you are having doubts. You just post something, say I don't know, I'm not sure, and then request people for their thoughts. You may no longer be a student, but that is exactly the kind of thing I already hear more than enough of from lazy students who don't want to even bother trying to work out what they are having trouble with. > Otherwise, if I'm confident enough with my own work, then I just let >them alone, and don't bother addressing them to the forum (most of >the time: however there are times I feel as though a proofreading, or >cursory inspection, by another party may be instructive, and this >usually has the advantage of building confidence in proof-writing as >well). Well, that's nice. But there is a world of difference between asking people in the newsgroup to help you work out a problem in which you are completely stuck, help you point in the right direction on a problem in which you some trouble, help you allay specific misgivings you might have about a particular argument (once you express those misgivings), and proofreading your work. And you should say up front which is the one you are requesting. So far, ALL your posts are phrased as if you were asking for help on problems in which you are completely clueless, which is what has been raising my irritation quotient (since the points that seem to be causing you trouble are exactly the same ones that you were walked through some days before). Now it turns out that in some instances you were looking for proof-reading and tips on proof-writing? Well, how nice. My reply would be very different depending on the situation; asking just exactly how to phrase a statement is very different from asking just how one might go about solving a problem. You have done yourself no favors, and you have come perilously close to wasting people's time. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes by Bill Watterson) Arturo Magidin magidin-at-member-ams-org === Subject: Re: Field Equations for the Higg's Field posting-account=Uy-x1gkAAADZQZOsYkACyKA9wdgWU8tq Gecko/20080702 Firefox/2.0.0.16,gzip(gfe),gzip(gfe) What makes gravity appear to be magnetic? Magnetism. When you have dark energy waves in large wave fronts, of the save pressure area, between them, and it will look as if two massive bodies are being attracted to each other. And so its easy to mistake that for the force of gravity, but what Einstein showed, was that mass, creates gravity wells, and so things will fall into those wells, once again, making it look like gravity is an attractive force. But when you look at galaxies, oddly enough they are not being attracted to each other that way and they don't rotate around each other under normal circumstances. Tiny ones might around big ones, but overall there is no evidence of attractive gravity between galaxies, except for that magnetic force. galaxies from each other. And its just that the playing field is so slippery, that it doesn't require much force to add up to cause them to drift around. Do they drift around at the speed of light and even accelerating away at the speed of light? Thats probably the gravitational red shift, because when you try to go through the quantum foam at the speed of light, it becomes a solid.