mm-4469 === Subject: The Curve Space in Maths The Curve Space in Maths we all know, the force is multiplied by force is equal to work. It is abstracted to be maths problem, it becomes dot product of vector , namely the inner procudt of vector. namely : .a6磨.a6å=.a6 .98.a6ç.a6.98.a6.98.a6å.a6 .98cos<.a6ç,.a6å>. Also, the force is multiplied by moment of force, it also can be abstracted to be maths problem, it becomes the vector problem, it is the exterior product of vector. namely: .a6.98.a6çÁç.a6[Capi talAHat].a6.98=.a6.98.a6ç.a6.98.a6[OGr ave].a6å.a6.98sin<.a6ç,.a6[CapitalAHat ]>. Also, to the Coulomb's law: F=kq1q2/r^2.we also abstract it into a maths problem, and when we calculate it respective in a dot, a line, an area,or a sphere.we can conclude the same result with by using the Gauss's electric flux theorem.but from the maths principle,it is contradiction,because from the title meaning, it cann't get into the dot,the line (this can get the correct and the same result with by using the Gauss's electric flux theorem),an area or a sphere(we use the calculous -the double integral in maths to calculte it, we get the result that it can get into the area or the shpere,and this result is the same with using the Gauss's electric flux theorem).So all of it shows we must create a new maths field to resolve this problem, this is calculous in the curve space. At the Gauss's electric flux theorem: it is false all. So, the curve space in maths, we can defined it im maths as following: In right handed system in quadrature frame,namely in three dimensional coordinate space:in XÁ¢YÁ¢Z, r is the dot of function f(x) of vector, rÁæf(xÁ¢Y[DownExclamati on]¢Z).or is the vector that from the origin of coordinates O to r. If any function F(xÁ¢YÁ¢Z)£[CapitalAHat ]has the relation with the origin of coordinates, namely: F(xÁ¢YÁ¢Z)=f(x[DownExclamation ]¢YÁ¢Z)/or^2 £.9exÁ¢YÁ¢Z[Down Exclamation]æR£[YAcute]£Âcomes into existence,it says f(xÁ¢YÁ¢Z) is in right handed system coordinate, it means there is a only core in the origin coordinates and the three dimensional coordinate in this space with the core in origin coordinate is a curve sapce in maths. The integral with the function to the origin coordinate , ÁñF=Áñf(x[D ownExclamation]¢YÁ¢Z)/or^2d£¬x[Dow nExclamation]¢YÁ¢Z£© is the true calculous in curve sapce. I have found this question 20 years ago, but up to now, no one yet find and support me. sad for the knowledge achievement all over the world. caoyan 2007-5-2 http://thre-firewh2.home.sunbo.net/ === Subject: calculous in the curve space theorem 3 Cao's theorem 3 can conclude follow theorem 1, Á§sin dx=dx Á.88 Áñsin dx dx=Áñdxdx=1 2, Á§ edx-1=dx Á.88 Áñ(edx-1)dx=Á[CapitalOGrave ]dxdx=1 3, Á§ ln(1+dx)=dx Á.88 Áñln(1+dx)dx=Á[CapitalOGrav e]dxdx=1 4, Á§ (1+dx)^¤.84-1=¤.84dx Á.88 Áñ[(1+dx)^¤.84-1]dx=[D ownExclamation]ñ¤.84dxdx=¤[Cap italNTilde]Áñdxdx=¤.84 These all can show even if a very tiny digital such as dx in the integral formula, we cann't deal it with 0 and then calculate them again, that is incorrect. Because even if a very tiny digital such as dxÁ.9c0 , as after we calculate the integral formula , it is a number that cann't be ignored. The 4 can explain it throughly. caoyan 2007-10-31 http://thre-firewh2.home.sunbo.net/index.php?xname=AB6BP01 === Subject: Re: Third dimension... <18101346.1193840391486.JavaMail.jakarta@nitrogen.mathforum.org> <20071031102807.843$Gp@newsreader.com> <200710311344138930-kirakun@earthlinknet On 2007-10-31 12:52:01 -0400, jay1b...@aol.com said: > What is to the third dimension as a point is to the first dimension and as > a line is to the second dimension? > As I noted in my original response, the answer should be plain to see. > David Well put. Now ... borrowing that... What is to the fourth dimension > as a point is to the first dimension, > as a line is to the second dimension and > as a plain is to the third dimension? Jay Bala. The answer is an affine linear subspace of codimension 1 a.k.a. a hyperplane. This answer also works for all your other analogies in this pattern too. -- -kira This, I thought would be the 5th. but a funtion of time. Yes, time is always one of the aditional dimensions of first, second, third, etc. Let me hear some thoughts on this. Fourth? I believe is a curved surface of thinckness zero. Jay Bala. === Subject: Re: Third dimension... <18101346.1193840391486.JavaMail.jakarta@nitrogen.mathforum.org> <20071031102807.843$Gp@newsreader.com> <20071031131035.894$W2@newsreader.com ...object is plane, which happens to be pronounced just like plain. I wasnt paying attention. Jay. === Subject: Re: Complete Electronic (.pdf/doc) Solution Manuals. Get witihn 30 Minutes! Hey please send me the solution manual for Digital Image Processing : Gonzalez, woods, 2nd ed. === Subject: Re: Tetration h(z) of z=e^pi/2 <1193775528.799880@athprx04> <1193784304.628937@athprx03> <1193832774.962425@athprx04> <1193836771.23983@athprx04> I think Your ideas are brilliant. Not that I am any kind of expert in the details of tetration, but intuitively. 1) Especially about lasso dynamics of spirals. Would they be so called algebraic spirals, which has so called Kolmogorov dimension >1 while Hausdorf = 1 and topological = 1? Such appear in turbulence when explaining Kolmogorov spectra with nonisotropic turbulence. 2) For me , it also makes sense to have 2 values for sgrt(2) tetration in h(z) ( forgive me mistakes in symbols, please) because: sgrt (2) have 2 values, + - because of properties of exponentation, and is related to logarithmic infinity ( log having infinite periodic values for any number) . Now if we replace logarithmic infinity with tetration infinity , it is logical to expect that this property of sgrt(2) will be somehow preserved - the property to have 2 values attached to it. 3) Also very interestingly, while sgrt(2) is still within radius of convergence of h(z), - sgrt (2) is not(?) - so value 4 must be related to minus root of sgrt (2) - which leads to very interesting suggestions if extrapolated of how to interpret signs in different cases. 4) Also, as sgrt 3 is not inside the convergence zone, sgrt (3) h(z) will have 2 values, but complex. Now there migh lie the origin of fundamental difference between period 2 and period 3 means chaos. 5) Does 3rd root of 2 has 3 values then? 12th root of 2 -12 ? what are they? Ivars Fabriciuss === Subject: Re: Tetration h(z) of z=e^pi/2 Am 31.10.2007 20:44 schrieb ivars.fabriciuss@gmail.com: > > I think Your ideas are brilliant. Not that I am any kind of expert in > the details of tetration, but intuitively. :-) Unfortunately I never tended to receive a Ph.D. But - > > 1) Especially about lasso dynamics of spirals. Would they be so called > algebraic spirals, which has so called Kolmogorov dimension >1 while > Hausdorf = 1 and topological = 1? Such appear in turbulence when > explaining Kolmogorov spectra with nonisotropic turbulence. Here I knw nothing about. I'll use that as keywords today to see, what relation is there. > > 2) For me , it also makes sense to have 2 values for sgrt(2) tetration > in h(z) ( forgive me mistakes in symbols, please) because: > > sgrt (2) have 2 values, + - because of properties of exponentation, > and is related to logarithmic infinity ( log having infinite periodic > values for any number) . Yes ,that may be an interesting question. I always like the check of suitability of a generalization. But until now I did not consider negative bases. Perhaps you like to enter this path? Concerning the rest of the post: I hope I can answer later today. Gottfried Helms -- --- Gottfried Helms, Kassel === Subject: Re: Tetration h(z) of z=e^pi/2 <1193775528.799880@athprx04> <1193784304.628937@athprx03> <1193832774.962425@athprx04> <1193836771.23983@athprx04> I think Your ideas are brilliant. Not that I am any kind of expert in > the details of tetration, but intuitively. :-) Unfortunately I never tended to receive a Ph.D. But - That would not matter- it is quality of ideas that do. 1) Especially about lasso dynamics of spirals. Would they be so called > algebraic spirals, which has so called Kolmogorov dimension >1 while > Hausdorf = 1 and topological = 1? Such appear in turbulence when > explaining Kolmogorov spectra with nonisotropic turbulence. Here I knw nothing about. I'll use that as keywords today to > see, what relation is there. Look for this guy: http://www3.imperial.ac.uk/people/j.c.vassilicos/publications e.g this http://www3.imperial.ac.uk/portal/pls/portallive/docs/1/3265930.PDF But there was something more like a review. Unfortunately, I can not access those journals where really important publications are, pay for > 2) For me , it also makes sense to have 2 values for sgrt(2) tetration > in h(z) ( forgive me mistakes in symbols, please) because: sgrt (2) have 2 values, + - because of properties of exponentation, > and is related to logarithmic infinity ( log having infinite periodic > values for any number) . Yes ,that may be an interesting question. I always like the > check of suitability of a generalization. But until now > I did not consider negative bases. Perhaps you like to enter > this path? I am generalist by nature, I have not enough knowledge to perform rigorous studies, nor I know any programming tools:) What I think should be possible, is to generalize a bit a la Euler style on divergent sums, trying to shortcut around some rigid proofs/ numerical calculations via intuitive explotation of the easier, analyticaly interesting (like tetration of e^pi/2) values of h(z) and things about Lambert function that are kind of known - T function, Derivatives of Lambert function, integrals, inverse function. I will keep thinking about it a little, may be I get some concrete ideas. But anyhow, correct formalism of tetration is THE missing link in understanding the structure of mathematics- may be not the last one, but very important, as it may free us from need of imaginary and negative values or at least give understanding why we need them( as negative sign is just multiplication by i^4n-2 , in nature we do not have negative numbers, as we do not have 3/4 - we only have 1 and 1/2 and 1/3 and 1/5 and 1/7th - 1/4 th is just 1/2 of 1/2 and 3/4 is not existant as partition- it is 3 pieces of 1/2 of 1/2 of the whole). If it would be possible to have fractional tetration - not applied n times, but e.g n/7 times we might get into notion of fractional negative sign-> not - , but (- with index 1/7). Ivars Fabriciuss === Subject: Re: Tetration h(z) of z=e^pi/2 <1193775528.799880@athprx04> <1193784304.628937@athprx03> <1193832774.962425@athprx04> <1193836771.23983@athprx04> Interestingly, h( e^(-pi/2))= (2/pi)* W( pi/2) Proof: h( e^(-pi/2)) = - W( - ln (e^-pi/2)) / ln e^(-pi/2) = -W( pi/2) / - pi/ 2 = 2/pi * W( pi/2) Now we see that : h(e^pi/2) = - i = -2/pi* W( -pi/2) h(e-pi/2) = (2/pi)* W( pi/2) So h (e^pi/2)/h ( e^-pi/2) = - W(-pi/2)/W(pi/2) = -i*pi/2*W(pi/2) Could be defined irrespectively of divergence of h(e^pi/2). If we multiply h( e^pi/2) * h ( e^-pi/2) = -2/pi* W( -pi/2)*(2/pi)* W( pi/2) = -4/pi^2 W(-pi/2) * W(pi/2) = -i/2*pi * W(pi/2) defined again. If we look for power h(e^pi/2) ^2 = h(e^pi/2) * h (e^pi/2) =( h(e^-pi/2)* - i*pi/2* W(pi/ 2))^2 = ((2/pi)* W( pi/2)* -i*pi/2* W(pi/2))^2 = +W^4( pi/2) = -i^2 I must have made mistake somewhere......... Ivars Fabriuciuss === Subject: The Metric System Interested in hearing comments about the ramifications, past, present, future, on US failure to fully convert. Please expand your thoughts in === Subject: Re: The Metric System > Interested in hearing comments about the ramifications, past, present, > future, on US failure to fully convert. Hasn't been a problem for the UK. We do science in Metric/SI units then drive home in miles per hour and discuss fuel consumption in miles per gallon - even if knowbody knows the price per gallon because fuel it's priced and sold per litre. === Subject: Re: The Metric System <13ijah0ae6pa23f@corp.supernews.com Hasn't been a problem for the UK. We do science in Metric/SI units then > drive home in miles per hour and discuss fuel consumption in miles per > gallon - even if knowbody knows the price per gallon because fuel it's > priced and sold per litre. I always wondered about that. Do they display MPG ratings on new cars as well, or km/l? BTW, I believe the conversion factor is 1 mpg = 0.43 km/l 1 km/l = 2.35 mpg === Subject: Re: The Metric System > Hasn't been a problem for the UK. We do science in Metric/SI units then > drive home in miles per hour and discuss fuel consumption in miles per > gallon - even if knowbody knows the price per gallon because fuel it's > priced and sold per litre. I always wondered about that. Do they display MPG ratings on new > cars as well, or km/l? BTW, I believe the conversion factor is > 1 mpg = 0.43 km/l > 1 km/l = 2.35 mpg New cars in the UK are still in mpg (or at least mine is). The Belgian car we had until last year was in L/100KM. I dare say it might be possible to hack the computer in it to do either. === Subject: Re: The Metric System <13ijah0ae6pa23f@corp.supernews.com Interested in hearing comments about the ramifications, past, present, > future, on US failure to fully convert. Hasn't been a problem for the UK. We do science in Metric/SI units then > drive home in miles per hour and discuss fuel consumption in miles per > gallon - even if knowbody knows the price per gallon because fuel it's > priced and sold per litre. Speak for yourself! The fact that we're getting fuel in litres and distances in miles makes it hard for most people to do a proper fuel consumption calculation and most stick with mpg because it's what they're used to. You then compound the problem because, as you say, nobody knows the prices of a gallon and on that basis it's harder to get a handle on how much it costs you to run your car! I switched to using L/100km a couple of years ago and haven't looked back. It is possible - even here in the UK! === Subject: Re: The Metric System > Interested in hearing comments about the ramifications, past, present, > future, on US failure to fully convert. Hasn't been a problem for the UK. We do science in Metric/SI units then > drive home in miles per hour and discuss fuel consumption in miles per > gallon - even if knowbody knows the price per gallon because fuel it's > priced and sold per litre. Speak for yourself! The fact that we're getting fuel in litres and > distances in miles makes it hard for most people to do a proper fuel > consumption calculation and most stick with mpg because it's what > they're used to. You then compound the problem because, as you say, > nobody knows the prices of a gallon and on that basis it's harder to > get a handle on how much it costs you to run your car! I switched to using L/100km a couple of years ago and haven't looked > back. It is possible - even here in the UK! That's what I mean you worked the problem and found a solution. The mixture hasn't caused the UK to grind to a halt? As it happens I agree we should switch over properly. Road signs and cars first perhaps. Sun readers won't like it though :-) === Subject: Re: The Metric System <13ijah0ae6pa23f@corp.supernews.com > Interested in hearing comments about the ramifications, past, present, > future, on US failure to fully convert. Hasn't been a problem for the UK. We do science in Metric/SI units then > drive home in miles per hour and discuss fuel consumption in miles per > gallon - even if knowbody knows the price per gallon because fuel it's > priced and sold per litre. Speak for yourself! The fact that we're getting fuel in litres and > distances in miles makes it hard for most people to do a proper fuel > consumption calculation and most stick with mpg because it's what > they're used to. You then compound the problem because, as you say, > nobody knows the prices of a gallon and on that basis it's harder to > get a handle on how much it costs you to run your car! I switched to using L/100km a couple of years ago and haven't looked > back. It is possible - even here in the UK! If the metric convention had been set to km/L, maybe the switch would have been easier. It seems to me that people used to think how far they will travel on one gallon of fuel tend to more easily relate to how far they can travel on 1 liter. The only way they can do this now is by doing some extra figuring. Andr? Michaud === Subject: Re: The Metric System > Interested in hearing comments about the ramifications, past, present, > future, on US failure to fully convert. > Hasn't been a problem for the UK. We do science in Metric/SI units then > drive home in miles per hour and discuss fuel consumption in miles per > gallon - even if knowbody knows the price per gallon because fuel it's > priced and sold per litre. > Speak for yourself! The fact that we're getting fuel in litres and > distances in miles makes it hard for most people to do a proper fuel > consumption calculation and most stick with mpg because it's what > they're used to. You then compound the problem because, as you say, > nobody knows the prices of a gallon and on that basis it's harder to > get a handle on how much it costs you to run your car! > I switched to using L/100km a couple of years ago and haven't looked > back. It is possible - even here in the UK! > > If the metric convention had been set to km/L, maybe the switch would > have been easier. It seems to me that people used to think how far > they > will travel on one gallon of fuel tend to more easily relate to how > far they > can travel on 1 liter. The only way they can do this now is by doing > some extra figuring. > > Andr.8e Michaud > I'm not sure that would be the case... the issue here is that because of 30+ years of goverment dithering, each time I fill my car I do so in litres but the odometer tells me I've travelled X miles. Most Brits, even those educated in metric, will go for mpg (using either 4.5 or 5 as a rough number of litres per gallon). The whole idea of metrication is that we all use the same systems and L/100km is the recognised standard. I'll admit that it was a little confusing when I first started using it, but after a few weeks it just seemed a more logical method of doing things. When we someday make the move to km on our roads some people will still try to use mpg but how many will convert litres to gallons, km to miles, then get the figure and how many will do the calculation in metric and look at a conversion chart? Either way people will eventually just forget mpg altogether, but I don't think it would be right if we as a nation decided to unilaterally start to use km/l. === Subject: Re: The Metric System Nntp-Posting-Host: hera.cwi.nl > Interested in hearing comments about the ramifications, past, present, > future, on US failure to fully convert. Please expand your thoughts in What do you want? The US system is since the late 1800's soundly based on the metric system. That they do not wish to *use* the metric system itself, but only derived units, they share with only two other countries in the world: Liberia and Birma. Anecdote. Once upon a time in a German magazine there was an advertisement for 88.9 mm floppy disks. They did use the proper metric value for 3.5 inch floppies. The only problem was that true 3.5 inch floppies do not exist, the specification is 90 mm, so where had that 1.1 mm gone? -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: The Metric System > Interested in hearing comments about the ramifications, past, present, > future, on US failure to fully convert. Please expand your thoughts in Would you care to expand your cross-posting in the direction of the news group ? Ken Pledger. === Subject: Re: The Metric System > > Interested in hearing comments about the ramifications, past, present, > future, on US failure to fully convert. Please expand your thoughts in Trolling idiot. 20% of the US population is supported by charity ripped from your wallet. The rub with victimology and rule of the disempowered is that there is always somebody even less qualified, a worse victim, and more screwed up than you are. Why should any reproductive, non-productive, and counter-productive segment of the US economy not climb aboard the gravy train? Look how well NASA did mixing English and metric unts on a $billion trip to Mars. -- 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: Sea change > Narrow minded people never believe it is possible until it happens. > > What I am looking for is a revolution within the academic community > worldwide where mathematicians are just a tool to get to EVERY > academic, worldwide. > > So even English professors will feel the impact though many of them > will probably wonder what in the hell is going on. > > My hypothesis is that the current academic system is not only broken > but it is a safe haven and wanted hideout for parasitic types who rely ^^^^^^ I think that was meant to be wanton. Jimbo's prose is beginning to deteriorate. -- Michael Press === Subject: Fermat's Last Theorem simple proof impossible? Hi. I'm wondering. Has it been proven that it is impossible to prove Fermat's Last Theorem using only the mathematics Fermat would have had available at his time? Did Fermat himself have a real proof like he claimed? Just because we don't know how to do it does not mean it is impossible to do. Obviously a way to settle one of the questions, namely that of Fermat having a proof, would be to find what he claimed to have as a proof and see if it was valid. === Subject: Re: Fermat's Last Theorem simple proof impossible? Nntp-Posting-Host: hera.cwi.nl Apart from the other responses... > Did Fermat himself have a real proof like he > claimed? to others that they did show something for which he claimed to have a proof (this clearly shows his background, i.e. not mathematics, he was just an amateur). He had pretty good ideas, but there are not many actual proofs by Fermat known. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: Fermat's Last Theorem simple proof impossible? > Hi. I'm wondering. Has it been proven that it is impossible to prove > Fermat's Last Theorem using only the mathematics Fermat would have had > available at his time? No. How could you prove such a thing? The complexity of the Wiles proof has caused most people to be pessimistic on this question though. > Did Fermat himself have a real proof like he > claimed? How can we know? We can only make educated guesses, based on the centuries of unsuccessful efforts. I would guess that he had a subtle fallacy and did not have an actual proof. Even Wiles' monster proof had a subtle gap in its first release. > Just because we don't know how to do it does not mean it is > impossible to do. Of course not. > Obviously a way to settle one of the questions, > namely that of Fermat having a proof, would be to find what he claimed > to have as a proof and see if it was valid. How do you recommend we do that? - Randy === Subject: Re: Fermat's Last Theorem simple proof impossible? Fermat's Last Theorem using only the mathematics Fermat would have had > available at his time? No. How could you prove such a thing? Perhaps one can formulate a Liouville theorem for number theoretical conjectures, for example, limiting steps in a proof to finite operations of arithmetic and exponential functions, representing exponentiation and powers, and thus keeping elliptical functions out. Maybe that would satisfy Marilyn Vos Savant's criticism of Wiles' proof based on non-Euclidean geometry (snicker). === Subject: Re: Fermat's Last Theorem simple proof impossible? |Perhaps one can formulate a Liouville theorem for number theoretical |conjectures, for example, limiting steps in a proof to finite |operations of arithmetic and exponential functions, representing |exponentiation and powers, and thus keeping elliptical functions out. I dimly recall having read that the kind of descent argument favored by Fermat only works when a certain kind of cohomological obstruction doesn't exist, but that the Fermat curve for some primes has a nontrivial such cohomology. Take this with a grain of salt. Keith Ramsay === Subject: Re: Fermat's Last Theorem simple proof impossible? > > I dimly recall having read that the kind of descent argument > favored by Fermat only works when a certain kind of cohomological > obstruction doesn't exist, but that the Fermat curve for some primes > has a nontrivial such cohomology. Take this with a grain of salt. You are probably thinking of the Tate-Shafarevich group. A search on Tate (Shafarevich OR Safarevic) obstruction should help. Be forewarned it involves fairly deep concepts. --Bill Dubuque === Subject: Re: Fermat's Last Theorem simple proof impossible? I dimly recall having read that the kind of descent argument > favored by Fermat only works when a certain kind of cohomological > obstruction doesn't exist, but that the Fermat curve for some primes > has a nontrivial such cohomology. Take this with a grain of salt. You are probably thinking of the Tate-Shafarevich group. > A search on Tate (Shafarevich OR Safarevic) obstruction > should help. Be forewarned it involves fairly deep concepts. yes the tate-shafarevich group measures the cohomological obstruction to the infinite descent argument that fermat used to solve the quartic case whenever the tate-shafarevich group is nontrivial the hasse principle does not hold in general this group and the selmers constrain many descent arguments and structure the rational points on varieties -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: Re: Fermat's Last Theorem simple proof impossible? I dimly recall having read that the kind of descent argument > favored by Fermat only works when a certain kind of cohomological > obstruction doesn't exist, but that the Fermat curve for some primes > has a nontrivial such cohomology. Take this with a grain of salt. You are probably thinking of the Tate-Shafarevich group. > A search on Tate (Shafarevich OR Safarevic) obstruction > should help. Be forewarned it involves fairly deep concepts. yes the tate-shafarevich group > measures the cohomological obstruction > to the infinite descent argument > that fermat used to solve the quartic case whenever the tate-shafarevich group is nontrivial > the hasse principle does not hold in general > this group and the selmers > constrain many descent arguments > and structure the rational points on varieties It is also an obstruction to Minkowski's theorem that enables one to lift results from a local or finite field to Q. Thus, proofs based on working over Z/pZ or GF(p^n) and then lifting to Q can not work either. I once heard Larry Washington give a talk on this subject. He is a terrific lecturer. === Subject: Re: Fermat's Last Theorem simple proof impossible? days. My association with the Department is that of an alumnus. >I'm wondering. Has it been proven that it is impossible to prove >Fermat's Last Theorem using only the mathematics Fermat would have had >available at his time? No. > Did Fermat himself have a real proof like he >claimed? Barring a time machine, it seems unlikely that this question can be given a final, definitive answer. The general consensus, however, is that it is unlikely. Keep in mind that the claim was a personal note made on the margin of his copy of the book, a note that he probably never imagined someone else reading. Years after making the note he did publicly discuss a special case (he gave the full proof in the case n=4, a rarity for him), and related problems, but never once even hinted in public at the general statement. As such, it is not unreasonable to think that he may have later realized he was mistaken; why not make a correction then? Because the original statement was not public; it was a note to himself in a personal book. There was nobody to correct. >Just because we don't know how to do it does not mean it is >impossible to do. Obviously a way to settle one of the questions, >namely that of Fermat having a proof, would be to find what he claimed >to have as a proof and see if it was valid. Unless you discover previously unknown material written by Fermat himself, this is impossible. Even if you found an elementary proof that used nothing but the machinery that we know existed at the time of Fermat, you would have no way of knowing whether Fermat had considered that proof or not. -- 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: Irrational number from an infinite sum <200710311752.l9VHqDYJ107572@walkabout.empros.comFirst the question, then the details: How is it that the following sum is an irrational number? e = 1/0! + 1/1! + 1/2! + 1/3! + ad infinitum I purposely didn't use an ellipsis above. By ad infinitum, I mean >an actual infinite number of terms in the series. There is no such thing as an infinite number of terms in the series. Hmmm. My philosophical stance seems more and more to be a minority view. Do you really mean to say that in the expression e = sum(k=0,inf) a_k there are not an infinite number of a_k? What there is is the *limit* of the sum as the number of terms increases > without bound. In other words, look at the sequence: 1/0! > 1/0! + 1/1! > 1/0! + 1/1! + 1/2! > .. > 1/0! + 1/1! + 1/2! + ... + 1/n! Every term in this sequence is the sum of rationals, and is hence rational > itself. However, the limit of this sequence as n increases without bound is > an irrational number, e. And it is impossible to discuss that limit process without implying that there are in fact infinitely many terms in the sequence {1/0!, 1/1!, 1/2!, ... } > As you note in what I've trimmed, the sum of rationals is rational. However, > the limit of a sequence of rationals is not necessarily a rational. For > more information, see: Going to that page, I follow the link to converges, where I find the usual language: ... there exists an N such that |S_n - S| < epsilon for n > N If there are only a finite number of S_n, this does not make sense as written. - Randy === Subject: Re: Irrational number from an infinite sum >First the question, then the details: >How is it that the following sum is an irrational number? > e = 1/0! + 1/1! + 1/2! + 1/3! + ad infinitum >I purposely didn't use an ellipsis above. By ad infinitum, I mean >an actual infinite number of terms in the series. > There is no such thing as an infinite number of terms in the series. Hmmm. My philosophical stance seems more and more to >be a minority view. Do you really mean to say that in the expression e = sum(k=0,inf) a_k there are not an infinite number of a_k? There are no a_k at all in the _expression_; in the _expression_ there is exactly one a_k. There are certainly infinitely many a_k in the universe where the object denoted by the expression lives. But the object denoted by the expression is not literally the sum of infinitely many a_k. > What there is is the *limit* of the sum as the number of terms increases > without bound. > In other words, look at the sequence: > 1/0! > 1/0! + 1/1! > 1/0! + 1/1! + 1/2! > .. > 1/0! + 1/1! + 1/2! + ... + 1/n! > Every term in this sequence is the sum of rationals, and is hence rational > itself. However, the limit of this sequence as n increases without bound is > an irrational number, e. And it is impossible to discuss that limit >process without implying that there are in fact >infinitely many terms in the sequence >{1/0!, 1/1!, 1/2!, ... } > As you note in what I've trimmed, the sum of rationals is rational. However, > the limit of a sequence of rationals is not necessarily a rational. For > more information, see: > Going to that page, I follow the link to converges, >where I find the usual language: ... there exists an N such that |S_n - S| < >epsilon for n > N If there are only a finite number of S_n, this >does not make sense as written. - Randy ****** David C. Ullrich === Subject: Re: Irrational number from an infinite sum >What might we say to someone who declares that they can produce a >number that is exactly equal to the quotient 1/3 using only the >mechanical process of long division? Why does it matter what we might say to someone who declares >that? I was under the impression that you wanted to >talk about mathematics. I have been trying to sort out some terminology, which seems like it might be a useful exercise in an environment where the proper use of symbols can be so important. I think that I have come to an adequate resolution (for my purposes) below. Perhaps it will be helpful to others. This has been my problem: The actual infinite string 0.333(ad infinitum) is a completed set. There are many ways to construct that string, but to construct it by means of infinite long division implies that the following supposed-sum (which is intended to exist apart from the notion of limits) is also a completed set: 3/10^1 + 3/10^2 + 3/10^3 + ad infinitum Based on what I understand about infinite sums, this latter completed set either: 1. Has no defined meaning, or 2. Is impossible to construct because adding an infinite number of terms is not defined. If the set which one builds with the ad-infinitum sum is either undefined or impossible, then the infinite string 0.333(ad infinitum) which represents it would seem to be undefined as a consequence -- which led me to assert that it is not a number. One might assign a meaning to that string (as we assign the value of pi to a single glyph), but its meaning wasn't derived completely from the series. [One might note at this point that its meaning may be derived from the supposed-sum _plus_ additional information -- which is the gist of a paragraph later in this post.] But all symbols ultimately have their meanings assigned. So why can't 0.333(ad infinitum) be a number? I suppose that it can be a number in the same sense that the glyph which represents pi is a number -- the symbol may be manipulated (intact) algebraically. Difficulties may arise when one starts changing the appearance of a symbol and declares that they are modifying the number in like manner. For instance, doubling the font size for the pi glyph isn't usually interpreted as 2*pi. One seems to get away with manipulating the appearance of the symbol by performing the following multiplication using third-grade mechanics: 3 * 0.333... = 0.999... But purely mechanical manipulation of the symbol doesn't work in trying to calculate: 4 * 0.333... = 1.333... The string 0.333(ad infinitum) is a completed set. The supposed-sum 3/10^1 + 3/10^2 + 3/10^3 + ad infinitum is not defined and may not be useful in constructing a set. But the limit 3/10^1 + 3/10^2 + 3/10^3 + ... is defined. So where is the problem in associating 0.333(ad infinitum) with the limit? There isn't one. It may be comparable to using more significant digits than necessary. Apples are discrete objects. They can be counted with integers: 1, 2, 3, ... They can also be counted with floating-point numbers: 1.0, 2.0, 3.0, ... 1.0 isn't an integer (in the sense often used by computer programmers), but it is still a number -- and it is more specific than necessary when counting apples. 1.0 is more specific than 1 in that it explicitly declares more significant digits. That an infinite number of significant digits may be implied by the integer is a separate issue. It makes (perhaps erroneous) sense to me that the completed set 0.333(ad infinitum) may be more defined than the limit -- because: 1. The string is more defined than the supposedly-actual-infinite-sum which was used to generate it mechanically, and 2. One never needs to actually construct the series to obtain the limit. Thus the label 0.333... seems like it could be more precise than necessary. I realize that one shouldn't speak of one infinite object being more precise than another. Perhaps it is better to say that the infinite string is _as_ distinct from other symbols as the limit is from other values. For my purposes, that is probably the essence of a symbol being a number. This strikes me as a pretty good argument and satisfies me enough to lay the issue aside for the foreseeable future. An essential feature of a label is that it be _distinct_ (unambiguous), not that it be _finite_. 0.333... is a completed set. It is a distinct thing. Therefore, it can be a valid label/symbol/number. So I have to concede that, as unwieldy as it is, the actual infinite string of characters represented by 0.333... can be a number. How a number is generated is irrelevant. It doesn't matter whether it was generated mechanically by one who is oblivious to the notion of limits and doesn't understand the limitations of its use. The generator of the number might make erroneous claims about how that number (in the form generated) might be used, but that is a different matter. == begin side bar == The apparent contradiction in rational + rational + ... = irrational was but one manifestation of my confusion about terminology. And it seemed like a good place to gain clarity because others have apparently come to terms with it. This actually helped a lot: >There's no such thing as an actual sum with an actual >infinite number of terms. == end side bar == Adam -- === Subject: Re: 1^2 =3, Discovered I consider your honesty a monument. Stay glorious, -Aiya-Oba. === Subject: Re: 1^2 =3, Discovered <13300060.1193860976586.JavaMail.jakarta@nitrogen.mathforum.org> On Oct 31, 1:02 pm, Anthony A. Aiya-Oba You still don't get it? > I consider your honesty a monument. > Stay glorious, > -Aiya-Oba. === Subject: need solutions manual for introduction to cryptography Hi guys, I need solutions manual to introduction to cryptography with coding theory Wade Trappe, Lawrence C. Washington / Prentice Hall I would highly appreciate if anyone who has the manual could contact me at tylerdurden2000m at yahoo dot com === Subject: Re: need solutions manual for introduction to cryptography > Hi guys, > I need solutions manual to introduction to cryptography with coding theory > Wade Trappe, Lawrence C. Washington / Prentice Hall I would highly appreciate if anyone who has the manual could contact me at tylerdurden2000m at yahoo dot com There is no solution manual, the answers are encoded in the text. === Subject: calculous in the curve space theorem 3 Cao's theorem 3 can conclude follow theorem 1, Á§sin dx=dx Á.88 Áñsin dx dx=Áñdxdx=1 2, Á§ edx-1=dx Á.88 Áñ(edx-1)dx=Á[CapitalOGrave ]dxdx=1 3, Á§ ln(1+dx)=dx Á.88 Áñln(1+dx)dx=Á[CapitalOGrav e]dxdx=1 4, Á§ (1+dx)^¤.84-1=¤.84dx Á.88 Áñ[(1+dx)^¤.84-1]dx=[D ownExclamation]ñ¤.84dxdx=¤[Cap italNTilde]Áñdxdx=¤.84 These all can show even if a very tiny digital such as dx in the integral formula, we cann't deal it with 0 and then calculate them again, that is incorrect. Because even if a very tiny digital such as dxÁ.9c0 , as after we calculate the integral formula , it is a number that cann't be ignored. The 4 can explain it throughly. caoyan 2007-10-31 http://thre-firewh2.home.sunbo.net/index.php?xname=AB6BP01 === Subject: Re: sum of three squares > I would like to know if there is known how to solve equation > x^2+y^2+z^2=s^2 in integers. Probably there is no solution because i > didn't find anything on web, but maybe there is some reference i can If the number s^2 does not have the form 4r.(8k + 7) it can be expressed as a sum of three squares. In this case subtract a square, call it z^2, from s^2 such that the difference is expressible as a sum of two squares. There is a method for expressing n := x^2 + y^2 = s^2 - z^2 as the sum of two squares. A number n is a expressible as a sum of two squares if and only if all prime factors of n of the form 4m+3 have even exponent in the prime factorization of n. -- Michael Press === Subject: Re: Quartic equation I am working a problem which results in a quartic equation of the > form: ax^4 - bx + c = 0 Due to the physical nature of the problem, only real and positive > solutions of x will have meaning. All coefficients are known to be > positive. No concrete statement about their relative magnitudes can > be made at this time. Is there a cleaned-up / shortcut form of the quartic formula for this > special case? Seeing this thread again, it's clear that in this case the best strategy seems to be the opposite of what I said before: Rather than worry about how a, b, c are composed of other variables, package them up even more! If a and/or b is zero then it's easy to classify the real/positive solutions (although, as you said the coefficients are all positive, that case doesn't arise). Otherwise, multiplying throughout by a^3 / (a^2.b)^(4/3) reduces the equation to: ( F(X) := ) X^4 - X + A = 0 [*] where: A, X = (a/b)^(1/3) . (c/b), (a/b)^(1/3) . x If a, b, c are all positive then A is positive and X, x have the same sign. Clearly [*] is easier to work with than your original quartic, as you only need worry about varying one coefficient. Obviously F, being large & positive for large |X| with X of either sign, has at least one minimum. So, since dF/dx = 0 has exactly one real root T := 2^(1/3) / 2, it must have exactly one minimum. A necessary condition for F(X) to have at least one real root is that this minimum be non-positive, i.e. F(T) <= 0. If F(T) < 0 then F has two real roots (the maximum number it can ever have), and one is positive. Finally, the limiting condition for the other root to be positive is when it is zero, which occurs when B = 0. In summary, the necessary & sufficient conditions are as follows: * No real roots when F(T) > 0 * One real (double) root, T, positive, when F(T) = 0 * Two real roots, one positive, when F(T) < 0 < B * Two real roots, both positive, when F(T) < 0 < B.F(T) John R Ramsden === Subject: Re: Quartic equation Hi Rob, the roots of your quartic: x^4 - 1/CD0*C1*x + 4*W^2*K/(rho^2*S^2*CD0)=0 are : > x1= I*( sqrt(y1)+sqrt(y2)+sqrt(y3)) > x2= I*( sqrt(y1)-sqrt(y2)-sqrt(y3)) > x3= I*(-sqrt(y1)+sqrt(y2)-sqrt(y3)) > x4= I*(-sqrt(y1)-sqrt(y2)+sqrt(y3)) (I=the imaginary unit) And y1^2,y2^2,y3^2 are the roots of the cubic : y^3 - W^2*K/(rho^2*S^2*CD0)*y + 1/(64*CD0^2)*C1^2=0 Let : b1=- W^2*K/(rho^2*S^2*CD0) > b0=1/(64*CD0^2)*C1^2 and c0= (-b0/2+((b0/2)^2+(b1/3)^3)^(1/2))^(1/3) > c1= (-b0/2-((b0/2)^2+(b1/3)^3)^(1/2))^(1/3) then the roots y1,y2,y3 of the cubic are: y1= c0+c1 > y2=(-1+sqrt(3)*I)/2*c0+(-1-sqrt(3)*I)/2*c1 > y3=(-1-sqrt(3)*I)/2*c0+(-1+sqrt(3)*I)/2*c1 Example: W=10 > K=1 > rho=1 > S=1 > CD0=12 > C1=16 The Cubic is: x^3 - 25/3*x + 1/36 and the roots : y1=2.885083234 > y2=-2.888416571 > y3=0.003333337778 The Quartic is: x^4 - 4/3*x + 100/3 and the roots : x1=1.699534222 + 1.756288342*I > x2=-1.699534222 + 1.640818211*I > x3=1.699534222 - 1.756288342*I > x4=-1.699534222 - 1.640818211*I Of course you will need to specify the ranges > of the variables so they have a real meaning. I'm not sure if you expected this kind of a result?;-) I'm sure this will prove useful, but it will take some time for me to > be able to sit down and play with it. However, I expect there to be > one meaningful positive real root. Let me try to throw together an example with reasonable numbers based > roughly on a Cessna 172. I've included a short Matlab code below > where I copied your equations. ... hack hack hack .... Unfortunately, all four roots are still imaginary. Fortunately, for this problem, solving the other-way-round is much > easier. So, we can check our answers very easily. I have done this at the bottom of the included Matlab code. For 150 > lbf of fuel burn, the velocity result should be about 171 ft/sec. Or > about 1.5% increase. Maybe not enough to worry about, but it seems > reasonable. Have I done something wrong in implementing your solutions? Rob clear all > format compact Winit=2450; % Initial weight lbf > K=0.058; > rho=0.002377; % slug/ft^3 Sea Level Standard > S=174; % ft^2 > CD0=0.0319; Vinit=168.78; % 100kts in ft/s qinit = 0.5 * rho * Vinit^2; CLinit=Winit/(qinit * S); > CDinit=CD0+K*CLinit^2; C1=CDinit*Vinit^3; W=Winit-150; % 150 lb of fuel burn. b1=-W^2*K/(rho^2*S^2*CD0); > b0=1/(64*CD0^2)*C1^2; c0= (-b0/2+((b0/2)^2+(b1/3)^3)^(1/2))^(1/3); > c1= (-b0/2-((b0/2)^2+(b1/3)^3)^(1/2))^(1/3); I=sqrt(-1); y1= c0+c1; > y2=(-1+sqrt(3)*I)/2*c0+(-1-sqrt(3)*I)/2*c1; > y3=(-1-sqrt(3)*I)/2*c0+(-1+sqrt(3)*I)/2*c1; x1= I*( sqrt(y1)+sqrt(y2)+sqrt(y3)); > x2= I*( sqrt(y1)-sqrt(y2)-sqrt(y3)); > x3= I*(-sqrt(y1)+sqrt(y2)-sqrt(y3)); > x4= I*(-sqrt(y1)-sqrt(y2)+sqrt(y3)); % Check solution. V=1.02*Vinit; % Guess at post-accelerated speed. W=sqrt((C1*V - V^4*CD0)*(rho^2*S^2/(4*K))) vrat=linspace(0.9,1.1); for i=1:length(vrat); > V=vrat(i)*Vinit; > W2(i)=sqrt((C1*V - V^4*CD0)*(rho^2*S^2/(4*K))); > end plot(vrat,Winit-W2,[1 1], [-1000 2500], [.9 1.1], [0 0])- Hide quoted text - - Show quoted text - Hi Rob, > Have I done something wrong in implementing your solutions? i don't think so, i noticed at one point that chances to get real solutions are slim and i don't have much time to verify. maybe in two weeks again. Gerry === Subject: ACA, ACA_0, and their ordinals The proof theoretic ordinal of ACA_0 is epsilon_0. The proof theoretic ordinal of ACA is -- I believe -- epsilon_(epsilon_0). Can anyone point me to a proof -- or an arm-waving plausibility argument -- for the second claim??? === Subject: Re: ACA, ACA_0, and their ordinals > The proof theoretic ordinal of ACA_0 is epsilon_0. The proof theoretic > ordinal of ACA is -- I believe -- epsilon_(epsilon_0). Can anyone point me to a proof -- or an arm-waving plausibility > argument -- for the second claim??? I'll give you a reference (my) tomorrow morning, about 16 hours from now. All my stuff is at home, so I'll look it up when I get home tonight. I have several expository papers by Simpson, Friedman, etc. that discuss the ordinal strengths of various subsystems of analysis. Most of the ordinals are way beyond gamma_0 (which is way beyond epsilon_(epsilon_0), as I'm sure you know), by the way, but I do seem to recall that epsilon_(epsilon_0) is on at least one of the ordinal charts I've seen. Dave L. Renfro === Subject: Re: ACA, ACA_0, and their ordinals . > The proof theoretic ordinal of ACA 0 is epsilon 0. The proof > theoretic ordinal of ACA is -- I believe -- epsilon (epsilon 0). > Can anyone point me to a proof -- or an arm-waving plausibility > argument -- for the second claim??? . . > I'll give you a reference (my) tomorrow morning, about > 16 hours from now. All my stuff is at home, [...] I'm surprised no one else has commented yet, seeing as how your post was cross-posted to sci.logic. Drake [3] has an ordinal chart on p. 15. ACA is not listed, but among the several handwritten additions I've made on my copy (made back in 1991 or 1992) are |ACA| = epsilon (epsilon 0) and |ATR| = gamma (epsilon 0). Sch?tte [5] has an ordinal chart on p. 42 which lists 'elementary analysis' as $theta 1 epsilon {0}$, credited to W. Tait. The top of p. 39 says $theta 1 beta$ is equal to epsilon beta. On pp. 41-42, 'elementary analysis' is defined as the formal system of second order arithmetic where comprehension is restricted to arithmetical formulas that means to formulas which do not contain bound set variables (there seems to be a typo or something, as that means to does not seem to fit grammatically). No publications by W. Tait are listed in the bibliography. Avigad/Sommer [1] has an ordinal chart on p. 28 that lists the ordinal for ACA as epsilon (epsilon 0). Of the 11 ordinals in the chart, they say the first 5 will be proved in the present paper and the remaining (which includes ACA) will be proved in a later paper. I couldn't find a later paper by them in my stuff, but an internet search just now revealed Avigad/Sommer [2], which might be the paper in which the other proofs appear. I don't have access to JSTOR, so I can't see more than the first page (what the URL I've provided takes you to), or Math. Reviews, but if you do then this is probably where you want to start. Feferman [4] makes some comments in Sections 8.2.2-8.2.3 (pp. 958-959) about the role of epsilon beta numbers for proof-theoretic ordinals. I hardly know anything about this subject, but it seems to me that these comments might be something to look at if the other things above don't tell you what you want. Finally, although I imagine you've already looked in these books, for completeness I'll mention that you may try looking in the well known texts by Sch?tte (1977), Takeuti (1987), Pohler (1989), and Simpson (1999). http://www.math.psu.edu/simpson/sosoa/ [Simpson's book info.] [1] Jeremy Avigad and Richard Sommer, A model-theoretic approach to ordinal analysis, Bulletin of Symbolic Logic 3 (1997), 17-52. [2] Jeremy Avigad and Richard Sommer, A model-theoretic Ordinal Analysis of Theories of Predicative Strength, Journal of Symbolic Logic 64 (1999), 327-349. http://tinyurl.com/35j5ho [3] Frank Drake, On the foundations of mathematics in 1987, pp. 11-25 in H.-D. Ebbinghaus et al (editors), LOGIC COLLOQUIUM '87, North-Holland, 1989. [4] Solomon Feferman, Theories of finite type related to mathematical practice, pp. 913-971 in Jon Barwise (editor), HANDBOOK OF MATHEMATICAL LOGIC, North-Holland, 1977. [5] Kurt Sch?tte, Proof theory, pp. 37-43 in Evandro Agazzi (editor), MODERN LOGIC -- A SURVEY, D. Reidel Publishing Company, 1981. Dave L. Renfro === Subject: turn $6 into $6000 no strings attached YOU KNOW THAT YOU SPEND AT LEAST $6.00 EVERY PAY PERIOD ON USELESS STUFF, ME TOO. SO I THOUGHT, WHAT THE HECK, I'M ALL THE WAY TO THE BANK WEEK AFTER WEEK WITH My PILES OF 1$ BILLS. I SOONER! THIS IS LONG, SO IF YOU DON'T WANT TO READ IT ALL NOW, JUST COPY AND PASTE, IT IS SOOO WORTH IT! DON'T TAKE MY WORD FOR IT, JUST TRY IT! How to turn $6 into $6,000! READING THIS COULD CHANGE YOUR LIFE! SO JUST DO IT! This really works! financial woes and I decided to try something new. If it works for me then I will be able to get myself out of a very difficult financial situation. Please read and see what results another got, it's pretty exciting! It REALLY CAN MAKE YOU EASY MONEY!! IT WORKS!!! BUT YOU HAVE TO FOLLOW IT TO THE LETTER FOR IT TO WORK!!!! 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Simply put your cursor at the beginning of this letter and drag your cursor to the bottom of this document, and select 'copy' from the edit menu. This will copy the entire letter into the computer's memory. Step 2) Open a blank 'notepad' file and place your cursor at the top paste a copy of the letter into notepad so that you can add your name to the list. Step 3) Save your new notepad file as a .txt file. If you want to do your postings in different settings, you'll always have this file to go back to. Step 4) Use Netscape or Internet explorer and try searching for various newsgroups (on-line forums, message boards, chat sites, discussions.) message by highlighting the text of this letter and selecting paste from the edit menu. Fill in the Subject, this will be the header that everyone sees as they scroll through the list of postings in a particular group, click the post message button. You're done with your first one! Congratulations...THAT'S IT! All you have to do is jump to different newsgroups and post away, after you get the hang of it, it will take about 30 seconds for each newsgroup! **REMEMBER, THE MORE NEWSGROUPS YOU POST IN, THE MORE MONEY YOU WILL MAKE!! BUT YOU HAVE TO POST A MINIMUM OF 200** That's it! You will begin receiving money from around the world within days! You may eventually want to rent a P.O.Box due to the large amount of mail you will receive. If you wish to stay anonymous, you can invent a name to use, as long as the postman will deliver it. **JUST MAKE SURE ALL THE ADDRESSES ARE CORRECT. ** HOW IT WORKS: Out of 200 postings, say I receive only 5 replies (a very low example). So then I made $5.00 with my name at #6 on the letter. Now, each of the 5 persons who just sent me $1.00 make the MINIMUM 200 postings, each with my name at #5 and only 5 persons respond to each of the original 5, that is another $25.00 for me, now those 25 each make 200 MINIMUM posts with my name at #4 and only 5 replies each, I will bring in an additional $125.00! Now, those 125 persons turn around and post the MINIMUM 200 with my name at #3 and only receive 5 replies each, I will make an additional $625.00! OK, now here is the fun part, each of those 625 persons post a MINIMUM 200 letters with my name at #2 and they each only receive 5 replies, that just made me $3,125.00!!! Those 3,125 persons will all deliver this message to 200 newsgroups with my name at #1 and if still 5 persons per 200 newsgroups react I will receive $15,625,00! With an original investment of only $6.00! latest posting in the newsgroups, and send out another $6.00 to names on the list, putting your name at number 6 again. And start posting again. The thing to remember is: do you realize that thousands of people all over the world are YOU are now!! So, can you afford $6.00 and see if it really works?? I think so... People have said, what if the plan is played out and no one sends you the money? So what! What are the chances of that happening when there are tons of new honest users and new honest people who are joining the Internet and newsgroups everyday and are willing to give it a try? Estimates are at 20,000 to 50,000 new users, every day, with thousands of those joining the actual Internet. Remember, play FAIRLY and HONESTLY and this will really work. God bless you! === Subject: Re: Software to create math lessons und Deine freundlichen Gr??e erhellen den oft etwas > bleiernen Himmel in sci.math erheblich. Im namen aller dort Beteiligten (hier: ungefragt ;-) ) - What i always wanted to say: when one gets contradiction as a reply, you might be a bit disappointed, when someone swears towards You, one might be angry - but nothing is more bitter, as not getting any reply at all. So we should try to answer all sincere posts at least once by one of us. sci.math is such an emotional usenet-group, why not making it a place of positive emotions, most of the times. And we should not forget, to give these hard-working mathematicians of never ending patience, like Robert Israel, Lynn Kurtz, Arturo Magidin, David C. Ullrich, Randy Poe, Dave l.Renfro, Jose Carlos Santos, Kira praise so now and then. I hope they stay enjoying these discussions in here, especially with their most charming pupil 'hot girl'. Gru? - Gottfried Have fun Hero PS sorry for all those i did not mention l === Subject: Re: #216 in fact a circle does not even obey associativity or commutative addition; new textbook: Mathematical-Physics <47202978.7020004@hotmail.com> <47217B9F.3080503@hotmail.com> <4722D1E5.3070008@hotmail.com> <4722FD90.1040002@hotmail.com> If you read Dik's idea closely, you'll see that the algebra is defined > so that all the sums and products are done modulo 2 pi (360Á). > So adding two arcs that sum to greater than 2 pi results in an > arc that wraps around the zero point of the unit circle, and > likewise for multiplication. > David, modulo or no modulo, how do you reconcile these facts? > Using the North Pole as 0 degrees and thus Toronto is 47, > Pittsburgh is 50 and Miami is 65 > (Toronto + Pittsburgh) + Miami > 47 + 3 + 15 = 65 > (Miami + Toronto) + Pittsburgh > 65 + 342 + 3 = 410 which in modulo is 50 > So the one addition lands in Miami but the second addition lands in Pittsburgh. > As for the Commutative of addition > Miami + South Pole > 65 + 115 = 180 > South Pole + Miami > 180 + 245 = 425 which in modulo is 65 > So if I airplaned using this arithmetic one would land on the South Pole > but the other addition would land in Miami. > Care to explain why both the Commutative and Associative breakdown, David? > You're doing it wrong. I don't see why you say that Totonto is 47Á, but then you use 47 in one equation but 342 in the other. Likewise, you say Pittsburgh is 50Á, but then you use 3 and 410 in your equations. Do things like that and of course you'll get wrong answers. I get this: Miami = 25Á N = 65Á from N Pole South Pole = 90Á S = 180Á from N pole Adding: Miami + South Pole = 65Á + 180Á (mod 360Á) = 245Á (mod 360Á) = 245Á And: South Pole + Miami = 180Á + 65Á (mod 360Á) = 245Á (mod 360Á) = 245Á So Miami + South Pole = South Pole + Miami (in the ring) I just don't see the problem. > Frankfurt and Zurich are approx on the same line of longitude and they > are approx 300 Km apart. And the Earth circumference is approx 40,000 Km So, now, does the circle obey Commutative addition as per Dik's arclength? Do we have A + B = B + A Here we use Frankfurt = A and Zurich = B > So we have A + B = 300 km > And we have B + A = 39,700 km So obviously we do not have Commutative because although we can get a > B + A to equal 300 km we can go circumnavigate around the globe to > travel 39,700 km to reach Frankfurt starting from Zurich. So as long as addition offers two choices (unless the points are > antipodal) do the numbers vary. Except that you forgot to do all the operations as they were actually defined, using modulo 360Á. Or in this case, mod 40,000 km, since you're now using km instead of degrees. I get: A + 300km = B (mod 40,000km) A = B - 300km (mod 40,000km) and: A - 39,700km = B (mod 40,000km) A = B + 39,700km (mod 40,000km) as well as: A + 40,300km = B (mod 40,000km) A = B - 40,300km (mod 40,000km) Again, I just don't see the problem, as long as you do the addition and multiplication operations *as they are defined in the ring*. > The reason points on a circle are not obeying Commutative addition is > because we have two choices, we can go all the way around or we can take > the smaller arc. But only one choice when you apply the modulus, which is how the operations are defined in the ring. === Subject: Re: #216 in fact a circle does not even obey associativity or commutative addition; new textbook: Mathematical-Physics > > I just don't see the problem. > David, I condensed this problem to the simple case of Frankfurt to Zurich. Dik's system does not address the problem that Frankfurt to Zurich has two choices, either 300 km or 39,700 km. So that system always has choices, whether you go clockwise or counterclockwise, whether you use the major arc or the minor arc. So every operation has this problem of choices. And thus, Dik's system is noncommutative, nonassociative and nondistributive. And there is noway of removing those choices and thus never a ring or field. === Subject: Re: #216 in fact a circle does not even obey associativity or commutative Nntp-Posting-Host: hera.cwi.nl > I just don't see the problem. > > David, I condensed this problem to the simple case of Frankfurt to > Zurich. Dik's system does not address the problem that Frankfurt to > Zurich has two choices, either 300 km or 39,700 km. So that system > always has choices, whether you go clockwise or counterclockwise, > whether you use the major arc or the minor arc. So every operation > has this problem of choices. And thus, Dik's system is noncommutative, > nonassociative and nondistributive. And again you fail to see that in my system the distance between Frankfurt and Zurich is *not* addition, but subtraction. And there you indeed do have two choices, and subtraction obviously is *not* commutative. > And there is noway of removing those choices and thus never a ring or > field. You just can't read or understand my system. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: #234 in fact a circle does not even obey associativity or commutative <47294A5D.5020701@hotmail.com> Zurich. Dik's system does not address the problem that Frankfurt to > Zurich has two choices, either 300 km or 39,700 km. So that system > always has choices, whether you go clockwise or counterclockwise, > whether you use the major arc or the minor arc. So every operation > has this problem of choices. And thus, Dik's system is noncommutative, > nonassociative and nondistributive. And again you fail to see that in my system the distance between Frankfurt > and Zurich is *not* addition, but subtraction. And there you indeed do > have two choices, and subtraction obviously is *not* commutative. And there is noway of removing those choices and thus never a ring or > field. You just can't read or understand my system. > -- > dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 > home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ Wrong Dik, it is you who is unable to understand your mistakes. So you defined the minor arc as addition and the major arc as subtraction. But now what do you do for podal and antipodal points where minor arc equals major arc? Do you roll the dice or flip a coin to see which direction or clockwise or counterclockwise. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: Re: #216 in fact a circle does not even obey associativity or commutative addition; new textbook: Mathematical-Physics On 2007-10-31 17:30:04 -0400, David R Tribble said: > If you read Dik's idea closely, you'll see that the algebra is defined > so that all the sums and products are done modulo 2 pi (360Á). > So adding two arcs that sum to greater than 2 pi results in an > arc that wraps around the zero point of the unit circle, and > likewise for multiplication. > > > David, modulo or no modulo, how do you reconcile these facts? > > Using the North Pole as 0 degrees and thus Toronto is 47, > Pittsburgh is 50 and Miami is 65 > > (Toronto + Pittsburgh) + Miami > 47 + 3 + 15 = 65 > > (Miami + Toronto) + Pittsburgh > 65 + 342 + 3 = 410 which in modulo is 50 > > So the one addition lands in Miami but the second addition lands in Pitt > sburgh. > > As for the Commutative of addition > Miami + South Pole > 65 + 115 = 180 > > South Pole + Miami > 180 + 245 = 425 which in modulo is 65 > > So if I airplaned using this arithmetic one would land on the South Pole > but the other addition would land in Miami. > > Care to explain why both the Commutative and Associative breakdown, Davi > d? > > > You're doing it wrong. > > I don't see why you say that Totonto is 47Á, but then you use 47 in > one equation but 342 in the other. Likewise, you say Pittsburgh > is 50Á, but then you use 3 and 410 in your equations. > Do things like that and of course you'll get wrong answers. > > I get this: > Miami = 25Á N = 65Á from N Pole > South Pole = 90Á S = 180Á from N pole > > Adding: > Miami + South Pole > = 65Á + 180Á (mod 360Á) > = 245Á (mod 360Á) > = 245Á > And: > South Pole + Miami > = 180Á + 65Á (mod 360Á) > = 245Á (mod 360Á) > = 245Á > So > Miami + South Pole = South Pole + Miami (in the ring) > > I just don't see the problem. Suppose you've defined a direction from the north pole (there are two possible directions) as the std 'positive' direction. Suppose going in that direction you add 65 + 105 + 210 = 380 = 20 mod 360. a1 a2 a3 Using the other direction as canonical the same 'points' add 295 + 255 + 150 = 700 = 340 mod 360. b1 b2 b3 If you mix and match directions, you get for one possibility: 65+255+210 = 530 = 170 mod 360. a1 b2 a3 It would seem you need to specify a canonical 'direction' to measure angles from the origin and ensure consistent results. Is that right? > > > Frankfurt and Zurich are approx on the same line of longitude and they > are approx 300 Km apart. And the Earth circumference is approx 40,000 Km > > So, now, does the circle obey Commutative addition as per Dik's arclength? > > Do we have A + B = B + A > > Here we use Frankfurt = A and Zurich = B > So we have A + B = 300 km > And we have B + A = 39,700 km > > So obviously we do not have Commutative because although we can get a > B + A to equal 300 km we can go circumnavigate around the globe to > travel 39,700 km to reach Frankfurt starting from Zurich. > > So as long as addition offers two choices (unless the points are > antipodal) do the numbers vary. > > Except that you forgot to do all the operations as they were actually > defined, using modulo 360Á. Or in this case, mod 40,000 km, > since you're now using km instead of degrees. > > I get: > A + 300km = B (mod 40,000km) > A = B - 300km (mod 40,000km) > and: > A - 39,700km = B (mod 40,000km) > A = B + 39,700km (mod 40,000km) > as well as: > A + 40,300km = B (mod 40,000km) > A = B - 40,300km (mod 40,000km) > > Again, I just don't see the problem, as long as you do the addition > and multiplication operations *as they are defined in the ring*. > > > The reason points on a circle are not obeying Commutative addition is > because we have two choices, we can go all the way around or we can take > the smaller arc. > > But only one choice when you apply the modulus, which is how the > operations are defined in the ring. === Subject: Triangle with more than 180 degrees- In non euclidean geometry, is it possible for a triangles inside angles to add up to more than 180 degrees? === Subject: Re: Triangle with more than 180 degrees- > In non euclidean geometry, is it possible for a triangles inside > angles to add up to more than 180 degrees? > Of course. Try drawing a triangle on a sphere. === Subject: Re: Triangle with more than 180 degrees- <4728f446$0$17021$9a6e19ea@news.newshosting.com > In non euclidean geometry, is it possible for a triangles inside > angles to add up to more than 180 degrees? Of course. Try drawing a triangle on a sphere. These are triangles with curved sides. I can draw triangles with curved and not straight sides in a planar plane, which have a sum of angles exceeding 180 degrees, just as well. With friendly greetings Hero === Subject: Re: Triangle with more than 180 degrees- Nntp-Posting-Host: hera.cwi.nl > > In non euclidean geometry, is it possible for a triangles inside > angles to add up to more than 180 degrees? > > Of course. Try drawing a triangle on a sphere. > > These are triangles with curved sides. I can draw triangles with > curved and not straight sides in a planar plane, which have a sum of > angles exceeding 180 degrees, just as well. With that definition you cannot draw a triangle on a sphere. What you are doing is to apply Euclidean geometry here, while the question was about Non-Euclidean geometry. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: Re: Triangle with more than 180 degrees- <4728f446$0$17021$9a6e19ea@news.newshosting.com> In non euclidean geometry, is it possible for a triangles inside angles to add up to more than 180 degrees? Of course. Try drawing a triangle on a sphere. These are triangles with curved sides. I can draw triangles with curved and not straight sides in a planar plane, which have a sum of angles exceeding 180 degrees, just as well. On a sphere, straight lines are curved. That's the difference, the curved lines aren't straight. On a sphere, they are. To put it another way: In Euclidean geometry, the things called lines are modeled by straight lines in 3-d space, and the things called points are modeled by points in 3-d space. In spherical geometry, the things called lines are modeled by great circles in a sphere, and the things called points are modeled by diametrically opposite pairs of points on the surface of the sphere. Using the spherical model, the sum of a triangles angles are always greater than 180 degrees. about Hero's. > These are triangles with curved sides. I can draw triangles with > curved and not straight sides in a planar plane, which have a sum of > angles exceeding 180 degrees, just as well. With that definition you cannot draw a triangle on a sphere. What you are doing is to apply Euclidean geometry here, while the question was about Non-Euclidean geometry. ............................................................................ .......... I often read about tangent space and tangent bundle and Riemann math and i never grasped the essence up to now. So my question: in hyperbolic geometry of 3D one has tangents, or not? There must be a mathematical space in hyperbolic geometry with both, with hyperbolic surfaces and with their tangent planes - is this a hyperbolic 3D? Are in hyperbolic geometry these tangents straight, is a tangent plane a plane or can it be sometimes a curved surface? Is the tangent plane a hyperbolic plane or not? Is the tangent plane a Lobachevsky plane or not? Is in hyperbolic geometry every geodesic straight? Think of hyperbolic paraboloid or the hyperboloid of one sheet, where there are straight geodesics and not straight ones. In fact they are generated as ruled surfaces from straight lines. Is this valid for non-euclidian too? Is there for the non-euclidian mathematician no difference between straight geodesics and not straight geodesics? As Euler and some other mathematicians devoloped differential geometry and especially investigated the curvature of curves and of surfaces before the advance of hyperbolic geometry, does hyperbolic geometry has a different or a modified concept of curvature? With friendly greetings Hero PS Actually, are there spheres in hyperbolic geometry, as this seems to be, when i look at Your answers? === Subject: Re: Triangle with more than 180 degrees- <4728f446$0$17021$9a6e19ea@news.newshosting.com In non euclidean geometry, is it possible for a triangles inside > angles to add up to more than 180 degrees? Of course. Try drawing a triangle on a sphere. These are triangles with curved sides. On a sphere, straight lines are curved. > I can draw triangles with > curved and not straight sides in a planar plane, which have a sum of > angles exceeding 180 degrees, just as well. That's the difference, the curved lines aren't straight. On a sphere, they are. With friendly greetings > Hero === Subject: Re: Triangle with more than 180 degrees- > > . > > In non euclidean geometry, is it possible for a triangles inside > angles to add up to more than 180 degrees? > > Of course. Try drawing a triangle on a sphere. > > These are triangles with curved sides. > > On a sphere, straight lines are curved. > > I can draw triangles with > curved and not straight sides in a planar plane, which have a sum of > angles exceeding 180 degrees, just as well. > > That's the difference, the curved lines aren't straight. > On a sphere, they are. To put it another way: In Euclidean geometry, the things called lines are modeled by straight lines in 3-d space, and the things called points are modeled by points in 3-d space. In spherical geometry, the things called lines are modeled by great circles in a sphere, and the things called points are modeled by diametrically opposite pairs of points on the surface of the sphere. Using the spherical model, the sum of a triangles angles are always greater than 180 degrees. --Mark === Subject: Re: Null sequences in l_oo > > >Is there an elementary proof of this: >If (x_n) is a zero-converging sequence in the > space > l_oo (of all real bounded sequences, endowed with > the > sup-norm), then there is some x* in l_oo such that > > ||x* + x_n|| = ||x*|| + (x*)_n for all n ? >(of course, here x_n is a vector, hence a bounded > sequence itself, while (x*)_n denotes the nth > coordinate of the vector x*) > > Are you certain you stated the problem correctly? > >Thx in advance >Ady. > > > ****** > > David C. Ullrich Yes. Why? > > No good reason - I wondered for example if you might > have meant to include the condition (x*)_n >= 0. > > Do you happen to know that this is actually true, > for some non-elementary reason? > > > ****** > > David C. Ullrich Let us consider c=(||x_n||) as a non-negative element of c_0, and let Q=[-c,c] be the corresponding order interval in the Banach lattice c_0. Then Q is compact, convex, and nonvoid. Now, define the (nonlinear) operator K:Q-->c_0 by Kx=(||x+x_n||-||x||). It is well-defined, because (x_n) is a null sequence. Moreover, K(Q) is a subset of Q. Remark that K is Lipschitz, hence continuous. Then K has at least one fixed point, say x*, via the Schauder Fixed Point Theorem. Of course, x* belongs to l_oo. I cannot assume x*>=0, since the sequence (x_n) is given, and one cannot control its behaviour. However, I would be very grateful to you if you can provide me with a proof based only on Linear Functional Analysis/Real Analysis, for some teaching purposes. Ady. === Subject: Re: Null sequences in l_oo > > >Is there an elementary proof of this: If (x_n) is a zero-converging sequence in the > space > l_oo (of all real bounded sequences, endowed with > the > sup-norm), then there is some x* in l_oo such that > > ||x* + x_n|| = ||x*|| + (x*)_n for all n ? (of course, here x_n is a vector, hence a bounded > sequence itself, while (x*)_n denotes the nth > coordinate of the vector x*) > > Are you certain you stated the problem correctly? > >Thx in advance >Ady. > > > ****** > > David C. Ullrich >Yes. Why? > > No good reason - I wondered for example if you might > have meant to include the condition (x*)_n >= 0. > > Do you happen to know that this is actually true, > for some non-elementary reason? > > > ****** > > David C. Ullrich Let us consider c=(||x_n||) as a non-negative element of c_0, and let Q=[-c,c] be the corresponding order interval in the Banach lattice c_0. Then Q is compact, convex, and nonvoid. Now, define the (nonlinear) operator K:Q-->c_0 by Kx=(||x+x_n||-||x||). It is well-defined, because (x_n) is a null sequence. Moreover, K(Q) is a subset of Q. Remark that K is Lipschitz, hence continuous. Then K has at least one fixed point, say x*, via the Schauder Fixed Point Theorem. Of course, x* belongs to l_oo. Hmm - that's interesting. >I cannot assume x*>=0, since the sequence (x_n) is given, and one cannot control its behaviour. >However, I would be very grateful to you if you can provide me with a proof based only on Linear Functional >Analysis/Real Analysis, for some teaching purposes. Evidently the students do know some functional analysis, then. I don't see why you couldn't give the argument above, including a simple ad hoc version of the fixed-point theorem you need - it's not that hard. oh. It's not hard, _assuming_ the Brower fixed-point theorem in R^N, which I suppose is not elementary. >Ady. ****** David C. Ullrich === Subject: Re: I need Classical Mechanics Solutions Manual (Goldstein) > Hi > I need Classical Mechanics Solutions Manual (Goldstein). > Please email me Luke.I...@gmail.com > Luke I have the solution manual, but for 2nd edition. Many of the problems are recycled for the 3rd. Hard copy only, I can make copies, but there is 280 pages of it. Contact me and we can arrange something. === Subject: Re: I need Classical Mechanics Solutions Manual (Goldstein) > Hi > I need Classical Mechanics Solutions Manual (Goldstein). > Please email me Luke.I...@gmail.com > Luke I have the solution manual, but for 2nd edition. Many of the problems are recycled for the 3rd. Hard copy only, I can make copies, but there is 280 pages of it. Contact me and we can arrange something. === Subject: Re: Converting deg to grads > Hi folks, > How can i convert degs and radians to grads . What is > the formula. Sunil > 100 grades = Pi/2 radians. Grad is short form for grades. Try on your calculator sin(Pi/2)=1=sin(100 grad) -- Mohan Pawar www.mpClasses.com US Central Time: 5:10 PM 10/31/2007 === Subject: Re: Converting deg to grads > Hi folks, > How can i convert degs and radians to grads . What > is > the formula. > Sunil 100 grades = Pi/2 radians. Grad is short form for grades. Generally grades has been abandoned for grad instead (not really much of a short form is it?). 1/100 of a grad or grade would be a centigrade causing enough confusion to be one reason Celsius was adopted for what used to be temperature centigrade. Similary, most adopted grad for grade. === Subject: Re: Converting deg to grads > Hi folks, > How can i convert degs and radians to grads . What is > the formula. Sunil 1. http://www.convertworld.com/en/angle/Grad.html 2. http://www.onlineconversion.com/angles.htm 3. http://online.unitconverterpro.com/unit-conversion/convert-alpha/angle.html === Subject: Re: Converting deg to grads > Hi folks, > How can i convert degs and radians to grads . What is > the formula. > > 1. http://www.convertworld.com/en/angle/Grad.html > > 2. http://www.onlineconversion.com/angles.htm > > 3. > http://online.unitconverterpro.com/unit-conversion/convert-alpha/ angle.html None of those sites tells you what a grad is. I've seen them on my calculator and I surmise that a grad is a hundredth of a right angle. Since that is approximately a degree it would appear to be a useless unit. -- Jeremy Boden 64 bits good, 32 bits bad === Subject: Re: Converting deg to grads <13ihrk53ph5tpfb@corp.supernews.com> Hi folks, > How can i convert degs and radians to grads . What is > the formula. 1.http://www.convertworld.com/en/angle/Grad.html 2.http://www.onlineconversion.com/angles.htm 3. >http://online.unitconverterpro.com/unit-conversion/convert-alpha/ angle.html None of those sites tells you what a grad is. I've seen them on my > calculator and I surmise that a grad is a hundredth of a right angle. > Since that is approximately a degree it would appear to be a useless unit. -- > Jeremy Boden > 64 bits good, 32 bits bad I can then use to convert x degrees as a multiplying factor. If you want grads to degrees, from any of the sites, I get: 1 grad = 0.9 degree So, I am not sure what you mean that the site does not tell you what a grad is. Can you please say what is missing? ~A === Subject: Re: Converting deg to grads > 1. http://www.convertworld.com/en/angle/Grad.html None of those sites tells you what a grad is. http://www.convertworld.com/en/angle/Grad.html The grad is a unit of plane angle, equivalent to 1/400 of a full circle, dividing a right angle in 100. One grad equals 9/10 of a degree or p/200 of a radian. That explains what enough for me. >I've seen them on my calculator and I surmise that a grad >is a hundredth of a right angle. That seems to be correct surmising. >Since that is approximately a degree it would appear to be a useless unit. I'll leave the why to others, as I don't recall using it myself. That the unit may be seen on many calculators suggests that others find frequent use for it. -- Adam -- === Subject: Re: Converting deg to grads Nntp-Posting-Host: hera.cwi.nl ... >Since that is approximately a degree it would appear to be a useless unit. > > I'll leave the why to others, as I don't recall using it myself. > > That the unit may be seen on many calculators suggests that others > find frequent use for it. I understand that geometers frequently use the unit. But Jeremy's comment that the grad is approximately a degree, and thus appears to be useless applies equally well to the yard, which is approximately a metre and so appears to be useless. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: intro to chi squared? Can anybody suggest some introductory material to chi squared reliability calculations? I've got a paper my boss has asked me to review. It is about the reliability of a component. The component gets tested on a particular schedule, and has never shown a failure in 5 years of testing. So the question to be asked is: Does this level of testing meet the requirement that failures happen less than . And the paper's author has just written down a formula for the reliability estimate based on the existing data. This formula talked about degrees of freedom and I don't really get what those are in this context. Any pointers appreciated. Socks === Subject: Re: intro to chi squared? > Can anybody suggest some introductory material to > chi squared reliability calculations? > .... You may like to try posting your question to the news group. Ken Pledger. === Subject: Re: Marilyn vos Stupid is at it again Sylvain Croussette > , On Oct 28, 6:54 pm, mensana...@aol.compost ... > I must say Marylin's explanation seems very plausible > to me, as most people did wear swords on the left. In > any case, wouldn't a right-hander naturally be inclined > to put their best foot forward, i.e. their right foot > first in the stirrup, and want to swing into the saddle > from the right? It may not be applicable, but stirrups are a relatively > recent invention. ~600 year. -- > Michael Press > > Actually I remember reading that stirrups were invented in China about > 2000 years ago, and made their way to Europe around 700-800 AD. They > were certainly around in 1066 because you can see them on the Bayeux > tapestry (battle of Hastings). > > Sometimes when I watch let's say on television something about ancient > Rome or whatever, just for fun I look for the actors on horseback to > see if they ride with stirrups, if so that's an anachronism. I > suppose it would cost more in production to train the actors to ride > without them. > > As for mounting a horse without stirrups, I suppose you jump on it, > like in the film Troy with Brad Pitt in the role of Achilles. That's > a big budget movie, they didn't use stirrups, probably because they > wanted to make every detail as historically acurate as possible (the > war of Troy is supposed to have happened around 1200-1300 BC). I > remember a scene after Achilles kills Hector, he ties the body to his > horse and then jumps on it by putting his hands on the back leg, you > know like the game children play jumping over sheep. And I think he > did it from the left side of the horse. But it doesn't explain why > the left side, because you also jump from the right. Crikey. My 600 years is wrong for Europe and the world. Sorry for the misinformation. I am right handed and prefer to vault a hurdle right side forward. -- Michael Press === Subject: Solutions manuals I have the solutions manual in electronic format for the follwing textbooks. Paypal, debit, and credit cards are acceptable methods of payments. Analysis and Design of Analog Integrated Circuits, 4th Ed., by Gray,Hurst, Lewis, Meyer Analytical Mechanics, 7th Edition, by Fowels, Cassiday An Interactive Introduction to Mathematical Analysis, by Jonathan Lewin An Introduction to the Mathematics of Financial Derivatives, 2nd Ed.,by Neftci [ISBN:0125153929] Antenna Theory, 2nd Ed., by Balanis Antennas all Applications, 3rd Edition, Kraus, Marhefka Applied Linear Statistical Models, 5th Ed., by Neter (Selected Sol.) Applied Numerical Analysis, 6th Edition, by Gerald, Wheatley Applied Numerical Methods with MATLAB Engineers and Scientists,1st Ed,. by Chapra Applied Statistics and Probability Engineers, 3rd Ed., by Montgomery, Runger (Selected Solutions) Applied Strength of Materials, 4th Edition, by Mott A Transition to Advanced Mathematics, 5th Edition, by Smith, Eggen,Andre Automatic Control Systems, 8th Edition, by Kuo, Golnaraghi A Course in Game Theory by Osborne, Rubinstein A Course in Algebraic Number Theory by Cohen Adaptive Filter Theory, 4th Edition, by Haykin Adaptive Control, 2nd. Ed., by Astrom, Wittenmark Advanced Engineering Mathematics, 8th Editoin, by Erwin Kreyszig (even solutions) Advanced Engineering Mathematics, 9th Edition, by Erwin Kreyszig (even solutions) Advanced Macroeconomics, 1st Ed., by David Romer Advanced Mathematical Concepts Precalculus With Applications by Holliday [ISBN: 0028341759] Advanced Modern Engineering Mathematics, 3rd Ed., by G. James A First Course In Differential Equations, 7th Edition, by Zill, Cullen Analog Integrated Circuit Design, 1st Ed., by Johns, Martin (text ebook and solution manual) Basic Business Statistics: Concepts and Applications, 10th Ed., by Berenson, Krehbiel, Levine (chap1-18) Basic Engineering Circuit Analysis, 7th Ed., by J. David Irwin Basic Engineering Circuit Analysis, 8th Ed., by J. David Irwin, Nelms (Missing a chapter or 2) Bioprocess Engineering Principles by Doran Calculus: Study and Solutions Guide, Vol. 1, 7th Ed., by Larson,Hostetler, Edwards Chemical and Engineering Thermodynamics, 3rd Ed., Stanley I. Sandler Chemical Engineering Volume 1, 6th Edition, by Richardson, Coulson,Backhurst, Harker Thornton College Physics, Volume 1: 7th Edition, by Serway, Faugh College Physics, Volume 2: 7th Edition, by Serway, Faughn Communications Systems, 4th Ed., by Haykin Communications Systems Engineering, 2nd Edition, by Proakis Computational Techniques Fluid Dynamics by Srinivas, Fletcher Computer Networks, 4th Ed., by Andrew S. Tanenbaum Computer Networks: A Systems Approach, 3rd Edition, by Davie Control Systems Engineering, 4th Ed., by Norman Nise Corporate Finance, 6th Edition, by Ross C++ How to Program: Intro Object-Oriented Design with the UML, 3rd Ed., by Deitel, Nieto Calculus Early Transcendental, 5th Ed., by James Stewart Calculus - Early Transcendentals, 7th Ed., by Anton, Bivens, Davis Calculus: Graphical, Numerical, Algebraic, 3rd Ed., Waits, Finney,Demana, Kennedy Calculus: Multivariable, 5th Edition, by James Stewart Calculus: Single Variable, Early Transcendental, 5th Edition, by James Stewart Calculus, Single and Multivariable, 3rd Ed., by Hughes- Hallett,McCallum Integrated Circuits 3rd Edition by Muller Differential Equations with Boundary Value Problems, 2nd Ed., by Polking, Arnold Digital And Analog Communication Systems 7th Ed., Leon W. Couch Digital Communications, 4th Edition, by Proakis Digital Communications: Fundamentals and Applications, 2nd Ed, Skylar Digital Design, 4th Edition, by Mano, Ciletti Digital Image Processing, 2nd Edition, by Gonzalez, Woods Digital Integrated Circuits, 2nd Ed., by Rabaey (Solutions ONLY Chapters 3, 5, 6, 10) Digital Signal Processing: A Computer Based Approach, 1st Ed., by Mitra Digital Signal Processing: A Computer Based Approach, 2nd Ed., by S.Mitra Digital Signal Processing: A Computer Based Approach, 3rd Ed., by S.Mitra Digital Signal Processing: Principles, Algorithms and Applications, 3rd Edition, by Proakis Discrete Time Signal Processing, 2nd Edition, Oppenheim Dynamics of Mechanical Systems by C.T.F. Ross Data and Computer Communications, 8th Edition by Stallings Database Management Systems, 3rd Ed., by Ramakrishnan, Gehrke (Sol. Chapters 2-21, odd only) Design of Analog CMOS Integrated Circuits, 1st Edition, by Razavi Design of Analysis of Experiments, 6th Edition, Montgomery (missing chapter 6-8) Design of Machinery, 3rd Ed by Robert L. Norton Design With Operational Amplifiers and Analog Integrated Circuits, 2nd Ed., by Sergio Franco Design With Operational Amplifiers and Analog Integrated Circuits, 3rd Ed., by Sergio Franco Elementary Principles of Chemical Processes, 3rd Ed., by Felder,Rousseau Elements of Chemical Reaction Engineering, 3rd Ed., by H. Scott Fogler Engineering and Chemical Thermodynamics, by Koretsky [ISBN: 0471385867] (No sol. chapt 6) Engineering Circuit Analysis, 6th Edition, Hyat Engineering Electromagnetics, 6th Ed W. Hayt, J. Buck Engineering Electromagnetics, 7th Ed., Hayt, Buck Engineering Fluids Mechanics 7th Edition by Crowe Engineering Fluids Mechanics 8th Edition by Crowe Engineering Mathematics, 4th Ed., by John Bird Engineer Mechanics: Dynamics, 4th Ed., by Bedd Engineering Mechanics: Dynamics, 10th Ed., by Russell C. Hibbeler Engineering Mechanics: Dynamics 11th Ed. by Hibbeler Engineering Mechanics: Dynamics 5th Ed. by Meriam, Kraige Engineering Mechanics: Statics, 4th Edition - A. Bedd, Wallace Fowler Engineering Mechanics: Statics, 5th Ed., Meriam, Kraige Engineering Mechanics: Statics, 6th Ed., Meriam, Kraige Engineering Mechanics: Statics, 10th Ed., by Russell C. Hibbeler Engineering Mechanics: Statics 11th Ed. by Hibbeler Experiments with Economic Principles by Bergstrom, Miller Econometric Analysis, 5th Edition, by Greene Wooldridge Econometrics of Financial Markets, by Adamek, Cambell, Lo, MacKinlay, Viceira Electrical Properties of Materials, 7th Ed., by D. Walsh, L. Solymar Electric Circuits 6th Ed. by Nilsson Electric Circuits 7th Ed. by Nilsson Electric Machinery, 6th Ed., Fitzgerald, Kingsley, Umans Electric Machinery Fundamentals, 4th Ed by Chapman Electromagnetic Fields and Waves by Iskander Electronic Circuit Analysis, 2nd Ed., by Donald Neamen Electronics, 2nd Ed., by Allan R. Hambley Elementary Differential Equations, 8th Edition, by Boyce, DiPrima(some odd/even) Fundamentals of Applied Electromagnetics, 5th Ed., 2008 Media Edition,by Ulaby Fundamentals of Digital Logic with Verilog Design, 1st Edition, by Brown, Vranesic Fundamentals of Electric Circuits, 2nd Edition, by Alexander Fundamentals of Electromagnetics with Engineering Appls by Wentworth Fundamentals of Fluid Mechanics, 5th Ed. by Munson, Young.. Fundamentals of Heat and Mass Transfer, 4th Ed by Incropera... Fundamentals of Heat and Mass Transfer, 5th Ed by Incropera... Fundamentals of Heat and Mass Transfer, 6th Ed by Incropera... Fundamentals of Logic Design, 5th Ed., by Roth Jr. Fundamentals of Machine Component Design, 3rd Ed., by Juvinall Fundamentals of Machine Component Design, 4th Ed., by Juvinall Fundamentals of Machine Elements, 2nd Ed., Hamrock, Jacobson, Schmid Fundamentals of Physics by Halliday, 7th Ed., Walker, Resnick Fundamentals of Semiconductor Devices, 1st Edition by Anderson Fundamentals of Structural Analysis, 2nd Ed., Chia-Ming Uang, Kenneth Leet Fundamentals of Thermal-Fluid Sciences, 2nd Ed. by Cengel Fundamentals of Thermal-fluid Sciences, Int'l 2nd Ed. by Cengel Fundamentals of Engineering Thermodynamics, 5th Ed. by Shapiro Fundamentals of Thermodynamics, 5th Ed., by Sonntag, Borgnakke... Fundamentals of Thermodynamics, 6th Ed., by Sonntag Facilities Planning, 3rd Edition, by Tompkins, White, Bozer, Tanchoco Feedback Control of Dynamic Systems, 4th Edition, by Powell, Emami- Naeini Financial Accounting, 4th Ed., by Libby, Short (Chap1-14) Financial Accounting: An International Introduction, 2nd Ed., by Alexander, Nobes Finite Element Techniques in Structural Mechanics by Ross Fluid Mechanics - 5th Edition by Frank M. White Fluid Mechanics and Thermodynamics of Turbomachinery, 5th Ed., by S. L. Dixon [ISBN: 0750678704] Essentials of Fluid Mechanics: Fundamentals and Applications, 1st Ed., by Cengel & Cimbala Fluid Mechanics with Engineering Applications, 10th Edition, by Finnemore Fundamentals of Aerodynamics, 3rd Edition, by J. D. Anderson, Jr. Fundamentals of Applied Electromagnetics, 1st Ed., 2001 Media Edition, by Ulaby Geometry, 04 Edition, by McGraw-Hill [ISBN: 0078296374] Guide to Energy Management, 5th Edition, by Pawlik Heat Transfer: A Practical Approach - 2nd Edition by Cengel Hydraulics in Civil and Environmental Engineering, 4th Ed., by Andrew Chadwick Introduction to Algorithms, 2nd Ed by Cormen, Leiserson (Selected Sol.) Introduction To Chemical Engineering Thermodynamics, 7th Ed., by Van Ness, Smith, Abbott Introduction to Electric Circuits, 6th Ed., by Dorf, Svoboda Introduction to Electric Circuits, 7th Ed., by Dorf, Svoboda Introduction to Electrodynamics, 3rd Ed. by David Griffiths Introduction to Fluid Mechanics - 5th Ed. by Fox.. Introduction to Fluid Mechanics - 6th Ed by Fox, McDonald... Introduction to Linear Algebra, 3rd Ed., by Gilbert Strang Introduction to Linear Algebra, 5th Ed., Arnold, Johnson, Riess Introduction to Probability by Grinstead, Snell (odd solutions only, not just answers but step by step solutions) Introduction to Quantum Mechanics, 2nd Ed. by Griffiths Introdution to Solid State Physics, 8th Edition by Kittel Introduction to Statistical Quality Control, 4th Edition, by Montgomery Introduction to Thermal Systems Engineering: Thermodynamics, Fluid Mechanics, and Heat Transfer by Moran, Shapiro, Munson, DeWitt Introduction to Thermal Systems Engineering, by Moran, Shapiro Linear Algebra, by J. Hefferon Linear Algebra And Its Applications, 3rd Ed., by David C. Lay Linear Algebra with Applications, 2nd Edition - by Otto Bretscher Linear Algebra with Applications, 3rd Edition - by Otto Bretscher Linear Circuit Analysis: Time Domain, Phasor and Laplace.., 2nd Ed, Lin Machine Design: An Integrated Approach, 2nd Ed., by Robert L. Norton Machine Design: An Integrated Approach, 3rd Ed., by Robert L. Norton Managerial Accounting, 11th Ed., by Noreen, Brewer, Garrison Materials Science and Engineering: An Introduction, 6th Ed. by Callister Matrix Analysis and Applied Linear Algebra by Carl Meyer MC68HC11: An Introduction: Software/Hardware Interf, 2nd Ed, by Huang Mechanical Engineering Design, 7th Ed. by Mischke, Shigley Mechanical Vibrations, 3rd Edition, by S. S. Rao (99% same as 4th Edition, No Solutions Chapters 6, 9, and 12) Mechanics of Fluids, 8th Ed., by Bernard Massey Mechanics of Fluids, 4th Ed., Irving H. Shames Mechanics of Fluids, 8th Ed., by Bernard Massey Mechanics of Materials - 3rd Ed. by Beer, Johnston, Dewolf Mechanics of Materials - 6th Ed. by Hibbeler Mechanics of Materials, 6th Edition by James M. Gere (missing small portion, section 8.5) Mechanics of Materials, 6th Ed., by Sturges, Morris, Riley (part of Chapt 2 is missing but only #1 thru #60) Mechanics of Solids by C.T.F. Ross Microeconomic Analysis, 3rd Ed., by H. Varian (Ans. to Exercises: Ch. 1- Ch.25) Microeconomic Theory, by Mas-Colell, Whinston, Green Microelectronic Circuit Analysis and Design, 3rd Edition, by D. Neamen Microelctronic Circuits, 5th Ed. by Sedra and Smith Microelectronic Circuit Design, 2nd Edition by Jaeger, Blalock Microelectronic Circuit Design, 3rd Edition by Jaeger, Blalock Microelectronics: Digital and Analog Circuits and Systems by Millman Microwave and Rf Design of Wireless Systems, 1st Edition, by Pozar Microwave Engineering, 3rd Ed., by David M. Pozar Microwave Transistor Amplifiers: Analysis and Design, 2nd Ed., by Guillermo Gonzalez Miller & Freund's Probability and Statistics Engineers, 7th Edition, Johnson, Miller Modern Compressible Flow, 3rd Edition, by Anderson Modern Control Engineering, 3rd Edition, by Ogata Modern Control Engineering, 4th Edition, by Ogata Modern Digital and Analog Communication Systems, 3rd Ed., by Lathi Modern Control Systems, 9th Ed., by Richard C. Dorf, Robert H Bishop (98% same as the 10th Ed.) Modern Operating Systems,2nd Ed., by Andrew Tanenbaum Modern Physics 4th Edition by Tipler Monetary Theory and Policy, 2nd Edition, by Walsh Multivariable Calculus, 5th Edition, by James Stewart Operating Systems: Internals and Design Principles, 4th Edition, by Stallings Operating System Concepts, 7th Ed., Silberschatz, Galvin, Gagne Options, Futures and Other Derivatives, 4th Ed., by John Hull Options, Futures and Other Derivatives, 5th Ed., by John Hull (Chapters 1 thru 18 ONLY) Orbital Mechanics: Engineering Students by Howard Curtis (includes matlab scripts) Organic Chemistry, 4th Ed., by Carey, Atkins (Student Study Guide and Sol. Man.) Partial Differential Equations with Fourier Series and Boundary Value ) Physical Chemistry - 7th Edition - by Julio de Paula, Peter Atkins Physics, 6th Edition, by John Cutnell Physics, 5th Edition, Vol 2 by Halliday, Resnick, Krane (Chap 25-52) Physics Scientist and Engineers by Knight (No Chapt 36-42) Physics Scientist and Engineers, 6th Ed., by Serway Physics Scientists and Engineers-Vol 1, 5th Edition, Serway, Beichner (Chap. 1 - 22) Physics Scientists and Engineers-Vol 2, 5th Edition, Serway, Beichner (Chap. 23 - 46) Physics Scientists and Engineers, 3rd Ed., by Douglas C. Giancoli Physics Scientist and Engineers, 5th Edition, by Tipler, Mosca Physics: Principles with Applications, 6th Ed. by Giancoli Power System Analysis and Design, 3rd Ed., by Glover, Sarma Principles and Applications of Electrical Engineering 4th (Revised) Edition by Rizzoni Principles and Practices of Automatic Process Control, 3rd Edition by Smith, Corripio [ISBN: 0471431907] Principles of Communication: Systems, Modulation Noise, 5th Ed., Ziemer Principles of Physics, 3rd Edition, by Serway Principles of Physics, 4th Edition, by Serway Principles of Statics, 10th Ed., by Russell C. Hibbeler [ISBN: 0131866745] Probability and Statistics Engineers and Scientists, 3rd Edition, Hayter Probability and Statistics Engineering and the Sciences, 6th Ed., by Jay L. Devore Probability Random Variables, and Stochastic Processes, 4th Ed., by Papoulis, Pillai Quantum Mechanics: An Accessible Introduction, 1st Ed., by Robert Scherrer Recursive Macroeconomic Theory, 1st Ed., by Ljungqvist, Sargent Recursive Methods in Economic Dynamics, (2002) by Irigoyen, Rossi- Hansberg, Wright RF Circuit Design: Theory & Applications, by Bretchko, Ludwig Sears and Zemansky's University Physics 11th Edition by Young.. Semiconductor Device Fundamentals by Pierret Semiconductor Devices: Physics and Technology, 2nd Ed., S.M. Sze Semiconductor Physics And Devices -3rd Ed. by D. Neamen Separation Process Principles, 2nd Ed., Seader, Henley Signal Processing and Linear Systems by Lathi Signals and Systems, 2nd Edition, by Haykin, Van Veen Signals and Systems, 2nd Edition, Oppenheim, Willsky, Hamid, Nawab Signals and Systems: Analysis Using Transm Methods and MATLAB, 1st Ed., by M. J. Roberts Signals, Systems, and Transms, 3rd Ed., by Charles L. Phillips, Eve A. Riskin, John M. Parr Shigley's Mechanical Engineering Design, 8th Ed. by Budynas, Nisbett (No Sol. Chapt 18 & 19) Simply C#: An Application-Driven Tutorial Approach, by Deitel, Hoey (Chapters 1-32) Soil Mechanics: Concepts and Applications, 2nd Ed., by Powrie Solid State Electronic Devices - 5th Ed by Streetman Solid State Electronic Devices - 6th Ed by Streetman Statics and Mechanics of Materials: An Integrated Approach, 2nd Ed., by Riley, Sturges, Morris Structural Analysis, 5th Edition, by Hibbeler University Physics 11th Edition by Young.. Vector Mechanics: Statics 7th Edition by Beer Vector Mechanics: Dynamics, 7th Ed., by Beer, Johnston, Staab, Clausen Vibrations and Stability: Advanced Theory, Analysis, and Tools, 7th Ed., by Thomsen Wireless Communications: Principles and Practice, 2nd Ed, by Rappaport Theory and Design Mechanical Measurements, 4th Ed., Beasley, Figliola Thermal Physics, 2nd Edition, by Charles Kittel Thermal Physics, by Ralph Baierlein Thermodynamics: An Engineering Approach, 5th Ed., by Cengel, Boles (Missing solutions #118-149 of Chapter 7) Thermodynamics: An Engineering Approach, 6th Ed., by Cengel, Boles The Science and Engineering of Materials, 4th Ed., by Donald R. Askeland, Pradeep P. Phule Thomas' Calculus, Early Trans., Part 1, 10th Ed. by Thomas, Weir, Hass, Giordano Thomas' Calculus: Part 2, 10th Ed. (Multivariable, chs. 8-13), by Thomas, Weir, Hass, Giordano Thomas' Calculus, Early Trans., Part 1, 11th Ed. by Thomas, Weir, Hass, Giordano Thomas' Calculus: Part 2, 11th Ed. (Multivariable, chs. 11-16), by Thomas, Weir, Hass, Giordano Transport Phenomena, 1st Edition, by R. Byron Bird Transport Phenomena, 2nd Ed., by Bird. === Subject: Re: Ellipse Distance / Intersection Distance/Intersection between ellipse and ellipse > Stephan I recently asked about minimum distance between two non-intersecting > conic sections, not lucky in this particular aspect. > Narasimham Using transversality conditions f(x) and g(x) in addition the the Euler - Bernoulli equations on functional F(x,y,y') in variational calculus this can be solved, I believe. The Euler- Bernoulli equations using standard notation are: F + ( f' - y') Fy' = 0 and F + ( g' - y') Fy' = 0 whre f and g appear as some additional 'attachments'. See e.g., Calculus of Variations I.M.Gelfand & S.V.Fomin, Moscow State Univ. Prentice-Hall English edition LCCCN 63- 18806. Narasimham === Subject: Solutions Manuals Analysis and Design of Analog Integrated Circuits, 4th Ed., by Gray,Hurst, Lewis, Meyer Analytical Mechanics, 7th Edition, by Fowels, Cassiday An Interactive Introduction to Mathematical Analysis, by Jonathan Lewin An Introduction to the Mathematics of Financial Derivatives, 2nd Ed.,by Neftci [ISBN:0125153929] Antenna Theory, 2nd Ed., by Balanis Antennas all Applications, 3rd Edition, Kraus, Marhefka Applied Linear Statistical Models, 5th Ed., by Neter (Selected Sol.) Applied Numerical Analysis, 6th Edition, by Gerald, Wheatley Applied Numerical Methods with MATLAB Engineers and Scientists,1st Ed,. by Chapra Applied Statistics and Probability Engineers, 3rd Ed., by Montgomery, Runger (Selected Solutions) Applied Strength of Materials, 4th Edition, by Mott A Transition to Advanced Mathematics, 5th Edition, by Smith, Eggen,Andre Automatic Control Systems, 8th Edition, by Kuo, Golnaraghi A Course in Game Theory by Osborne, Rubinstein A Course in Algebraic Number Theory by Cohen Adaptive Filter Theory, 4th Edition, by Haykin Adaptive Control, 2nd. Ed., by Astrom, Wittenmark Advanced Engineering Mathematics, 8th Editoin, by Erwin Kreyszig (even solutions) Advanced Engineering Mathematics, 9th Edition, by Erwin Kreyszig (even solutions) Advanced Macroeconomics, 1st Ed., by David Romer Advanced Mathematical Concepts Precalculus With Applications by Holliday [ISBN: 0028341759] Advanced Modern Engineering Mathematics, 3rd Ed., by G. James A First Course In Differential Equations, 7th Edition, by Zill, Cullen Analog Integrated Circuit Design, 1st Ed., by Johns, Martin (text ebook and solution manual) Basic Business Statistics: Concepts and Applications, 10th Ed., by Berenson, Krehbiel, Levine (chap1-18) Basic Engineering Circuit Analysis, 7th Ed., by J. David Irwin Basic Engineering Circuit Analysis, 8th Ed., by J. David Irwin, Nelms (Missing a chapter or 2) Bioprocess Engineering Principles by Doran Calculus: Study and Solutions Guide, Vol. 1, 7th Ed., by Larson,Hostetler, Edwards Chemical and Engineering Thermodynamics, 3rd Ed., Stanley I. Sandler Chemical Engineering Volume 1, 6th Edition, by Richardson, Coulson,Backhurst, Harker Thornton College Physics, Volume 1: 7th Edition, by Serway, Faugh College Physics, Volume 2: 7th Edition, by Serway, Faughn Communications Systems, 4th Ed., by Haykin Communications Systems Engineering, 2nd Edition, by Proakis Computational Techniques Fluid Dynamics by Srinivas, Fletcher Computer Networks, 4th Ed., by Andrew S. Tanenbaum Computer Networks: A Systems Approach, 3rd Edition, by Davie Control Systems Engineering, 4th Ed., by Norman Nise Corporate Finance, 6th Edition, by Ross C++ How to Program: Intro Object-Oriented Design with the UML, 3rd Ed., by Deitel, Nieto Calculus Early Transcendental, 5th Ed., by James Stewart Calculus - Early Transcendentals, 7th Ed., by Anton, Bivens, Davis Calculus: Graphical, Numerical, Algebraic, 3rd Ed., Waits, Finney,Demana, Kennedy Calculus: Multivariable, 5th Edition, by James Stewart Calculus: Single Variable, Early Transcendental, 5th Edition, by James Stewart Calculus, Single and Multivariable, 3rd Ed., by Hughes- Hallett,McCallum Integrated Circuits 3rd Edition by Muller Differential Equations with Boundary Value Problems, 2nd Ed., by Polking, Arnold Digital And Analog Communication Systems 7th Ed., Leon W. Couch Digital Communications, 4th Edition, by Proakis Digital Communications: Fundamentals and Applications, 2nd Ed, Skylar Digital Design, 4th Edition, by Mano, Ciletti Digital Image Processing, 2nd Edition, by Gonzalez, Woods Digital Integrated Circuits, 2nd Ed., by Rabaey (Solutions ONLY Chapters 3, 5, 6, 10) Digital Signal Processing: A Computer Based Approach, 1st Ed., by Mitra Digital Signal Processing: A Computer Based Approach, 2nd Ed., by S.Mitra Digital Signal Processing: A Computer Based Approach, 3rd Ed., by S.Mitra Digital Signal Processing: Principles, Algorithms and Applications, 3rd Edition, by Proakis Discrete Time Signal Processing, 2nd Edition, Oppenheim Dynamics of Mechanical Systems by C.T.F. Ross Data and Computer Communications, 8th Edition by Stallings Database Management Systems, 3rd Ed., by Ramakrishnan, Gehrke (Sol. Chapters 2-21, odd only) Design of Analog CMOS Integrated Circuits, 1st Edition, by Razavi Design of Analysis of Experiments, 6th Edition, Montgomery (missing chapter 6-8) Design of Machinery, 3rd Ed by Robert L. Norton Design With Operational Amplifiers and Analog Integrated Circuits, 2nd Ed., by Sergio Franco Design With Operational Amplifiers and Analog Integrated Circuits, 3rd Ed., by Sergio Franco Elementary Principles of Chemical Processes, 3rd Ed., by Felder,Rousseau Elements of Chemical Reaction Engineering, 3rd Ed., by H. Scott Fogler Engineering and Chemical Thermodynamics, by Koretsky [ISBN: 0471385867] (No sol. chapt 6) Engineering Circuit Analysis, 6th Edition, Hyat Engineering Electromagnetics, 6th Ed W. Hayt, J. Buck Engineering Electromagnetics, 7th Ed., Hayt, Buck Engineering Fluids Mechanics 7th Edition by Crowe Engineering Fluids Mechanics 8th Edition by Crowe Engineering Mathematics, 4th Ed., by John Bird Engineer Mechanics: Dynamics, 4th Ed., by Bedd Engineering Mechanics: Dynamics, 10th Ed., by Russell C. Hibbeler Engineering Mechanics: Dynamics 11th Ed. by Hibbeler Engineering Mechanics: Dynamics 5th Ed. by Meriam, Kraige Engineering Mechanics: Statics, 4th Edition - A. Bedd, Wallace Fowler Engineering Mechanics: Statics, 5th Ed., Meriam, Kraige Engineering Mechanics: Statics, 6th Ed., Meriam, Kraige Engineering Mechanics: Statics, 10th Ed., by Russell C. Hibbeler Engineering Mechanics: Statics 11th Ed. by Hibbeler Experiments with Economic Principles by Bergstrom, Miller Econometric Analysis, 5th Edition, by Greene Wooldridge Econometrics of Financial Markets, by Adamek, Cambell, Lo, MacKinlay, Viceira Electrical Properties of Materials, 7th Ed., by D. Walsh, L. Solymar Electric Circuits 6th Ed. by Nilsson Electric Circuits 7th Ed. by Nilsson Electric Machinery, 6th Ed., Fitzgerald, Kingsley, Umans Electric Machinery Fundamentals, 4th Ed by Chapman Electromagnetic Fields and Waves by Iskander Electronic Circuit Analysis, 2nd Ed., by Donald Neamen Electronics, 2nd Ed., by Allan R. Hambley Elementary Differential Equations, 8th Edition, by Boyce, DiPrima(some odd/even) Fundamentals of Applied Electromagnetics, 5th Ed., 2008 Media Edition,by Ulaby Fundamentals of Digital Logic with Verilog Design, 1st Edition, by Brown, Vranesic Fundamentals of Electric Circuits, 2nd Edition, by Alexander Fundamentals of Electromagnetics with Engineering Appls by Wentworth Fundamentals of Fluid Mechanics, 5th Ed. by Munson, Young.. Fundamentals of Heat and Mass Transfer, 4th Ed by Incropera... Fundamentals of Heat and Mass Transfer, 5th Ed by Incropera... Fundamentals of Heat and Mass Transfer, 6th Ed by Incropera... Fundamentals of Logic Design, 5th Ed., by Roth Jr. Fundamentals of Machine Component Design, 3rd Ed., by Juvinall Fundamentals of Machine Component Design, 4th Ed., by Juvinall Fundamentals of Machine Elements, 2nd Ed., Hamrock, Jacobson, Schmid Fundamentals of Physics by Halliday, 7th Ed., Walker, Resnick Fundamentals of Semiconductor Devices, 1st Edition by Anderson Fundamentals of Structural Analysis, 2nd Ed., Chia-Ming Uang, Kenneth Leet Fundamentals of Thermal-Fluid Sciences, 2nd Ed. by Cengel Fundamentals of Thermal-fluid Sciences, Int'l 2nd Ed. by Cengel Fundamentals of Engineering Thermodynamics, 5th Ed. by Shapiro Fundamentals of Thermodynamics, 5th Ed., by Sonntag, Borgnakke... Fundamentals of Thermodynamics, 6th Ed., by Sonntag Facilities Planning, 3rd Edition, by Tompkins, White, Bozer, Tanchoco Feedback Control of Dynamic Systems, 4th Edition, by Powell, Emami- Naeini Financial Accounting, 4th Ed., by Libby, Short (Chap1-14) Financial Accounting: An International Introduction, 2nd Ed., by Alexander, Nobes Finite Element Techniques in Structural Mechanics by Ross Fluid Mechanics - 5th Edition by Frank M. White Fluid Mechanics and Thermodynamics of Turbomachinery, 5th Ed., by S. L. Dixon [ISBN: 0750678704] Essentials of Fluid Mechanics: Fundamentals and Applications, 1st Ed., by Cengel & Cimbala Fluid Mechanics with Engineering Applications, 10th Edition, by Finnemore Fundamentals of Aerodynamics, 3rd Edition, by J. D. Anderson, Jr. Fundamentals of Applied Electromagnetics, 1st Ed., 2001 Media Edition, by Ulaby Geometry, 04 Edition, by McGraw-Hill [ISBN: 0078296374] Guide to Energy Management, 5th Edition, by Pawlik Heat Transfer: A Practical Approach - 2nd Edition by Cengel Hydraulics in Civil and Environmental Engineering, 4th Ed., by Andrew Chadwick Introduction to Algorithms, 2nd Ed by Cormen, Leiserson (Selected Sol.) Introduction To Chemical Engineering Thermodynamics, 7th Ed., by Van Ness, Smith, Abbott Introduction to Electric Circuits, 6th Ed., by Dorf, Svoboda Introduction to Electric Circuits, 7th Ed., by Dorf, Svoboda Introduction to Electrodynamics, 3rd Ed. by David Griffiths Introduction to Fluid Mechanics - 5th Ed. by Fox.. Introduction to Fluid Mechanics - 6th Ed by Fox, McDonald... Introduction to Linear Algebra, 3rd Ed., by Gilbert Strang Introduction to Linear Algebra, 5th Ed., Arnold, Johnson, Riess Introduction to Probability by Grinstead, Snell (odd solutions only, not just answers but step by step solutions) Introduction to Quantum Mechanics, 2nd Ed. by Griffiths Introdution to Solid State Physics, 8th Edition by Kittel Introduction to Statistical Quality Control, 4th Edition, by Montgomery Introduction to Thermal Systems Engineering: Thermodynamics, Fluid Mechanics, and Heat Transfer by Moran, Shapiro, Munson, DeWitt Introduction to Thermal Systems Engineering, by Moran, Shapiro Linear Algebra, by J. Hefferon Linear Algebra And Its Applications, 3rd Ed., by David C. Lay Linear Algebra with Applications, 2nd Edition - by Otto Bretscher Linear Algebra with Applications, 3rd Edition - by Otto Bretscher Linear Circuit Analysis: Time Domain, Phasor and Laplace.., 2nd Ed, Lin Machine Design: An Integrated Approach, 2nd Ed., by Robert L. Norton Machine Design: An Integrated Approach, 3rd Ed., by Robert L. Norton Managerial Accounting, 11th Ed., by Noreen, Brewer, Garrison Materials Science and Engineering: An Introduction, 6th Ed. by Callister Matrix Analysis and Applied Linear Algebra by Carl Meyer MC68HC11: An Introduction: Software/Hardware Interf, 2nd Ed, by Huang Mechanical Engineering Design, 7th Ed. by Mischke, Shigley Mechanical Vibrations, 3rd Edition, by S. S. Rao (99% same as 4th Edition, No Solutions Chapters 6, 9, and 12) Mechanics of Fluids, 8th Ed., by Bernard Massey Mechanics of Fluids, 4th Ed., Irving H. Shames Mechanics of Fluids, 8th Ed., by Bernard Massey Mechanics of Materials - 3rd Ed. by Beer, Johnston, Dewolf Mechanics of Materials - 6th Ed. by Hibbeler Mechanics of Materials, 6th Edition by James M. Gere (missing small portion, section 8.5) Mechanics of Materials, 6th Ed., by Sturges, Morris, Riley (part of Chapt 2 is missing but only #1 thru #60) Mechanics of Solids by C.T.F. Ross Microeconomic Analysis, 3rd Ed., by H. Varian (Ans. to Exercises: Ch. 1- Ch.25) Microeconomic Theory, by Mas-Colell, Whinston, Green Microelectronic Circuit Analysis and Design, 3rd Edition, by D. Neamen Microelctronic Circuits, 5th Ed. by Sedra and Smith Microelectronic Circuit Design, 2nd Edition by Jaeger, Blalock Microelectronic Circuit Design, 3rd Edition by Jaeger, Blalock Microelectronics: Digital and Analog Circuits and Systems by Millman Microwave and Rf Design of Wireless Systems, 1st Edition, by Pozar Microwave Engineering, 3rd Ed., by David M. Pozar Microwave Transistor Amplifiers: Analysis and Design, 2nd Ed., by Guillermo Gonzalez Miller & Freund's Probability and Statistics Engineers, 7th Edition, Johnson, Miller Modern Compressible Flow, 3rd Edition, by Anderson Modern Control Engineering, 3rd Edition, by Ogata Modern Control Engineering, 4th Edition, by Ogata Modern Digital and Analog Communication Systems, 3rd Ed., by Lathi Modern Control Systems, 9th Ed., by Richard C. Dorf, Robert H Bishop (98% same as the 10th Ed.) Modern Operating Systems,2nd Ed., by Andrew Tanenbaum Modern Physics 4th Edition by Tipler Monetary Theory and Policy, 2nd Edition, by Walsh Multivariable Calculus, 5th Edition, by James Stewart Operating Systems: Internals and Design Principles, 4th Edition, by Stallings Operating System Concepts, 7th Ed., Silberschatz, Galvin, Gagne Options, Futures and Other Derivatives, 4th Ed., by John Hull Options, Futures and Other Derivatives, 5th Ed., by John Hull (Chapters 1 thru 18 ONLY) Orbital Mechanics: Engineering Students by Howard Curtis (includes matlab scripts) Organic Chemistry, 4th Ed., by Carey, Atkins (Student Study Guide and Sol. Man.) Partial Differential Equations with Fourier Series and Boundary Value ) Physical Chemistry - 7th Edition - by Julio de Paula, Peter Atkins Physics, 6th Edition, by John Cutnell Physics, 5th Edition, Vol 2 by Halliday, Resnick, Krane (Chap 25-52) Physics Scientist and Engineers by Knight (No Chapt 36-42) Physics Scientist and Engineers, 6th Ed., by Serway Physics Scientists and Engineers-Vol 1, 5th Edition, Serway, Beichner (Chap. 1 - 22) Physics Scientists and Engineers-Vol 2, 5th Edition, Serway, Beichner (Chap. 23 - 46) Physics Scientists and Engineers, 3rd Ed., by Douglas C. Giancoli Physics Scientist and Engineers, 5th Edition, by Tipler, Mosca Physics: Principles with Applications, 6th Ed. by Giancoli Power System Analysis and Design, 3rd Ed., by Glover, Sarma Principles and Applications of Electrical Engineering 4th (Revised) Edition by Rizzoni Principles and Practices of Automatic Process Control, 3rd Edition by Smith, Corripio [ISBN: 0471431907] Principles of Communication: Systems, Modulation Noise, 5th Ed., Ziemer Principles of Physics, 3rd Edition, by Serway Principles of Physics, 4th Edition, by Serway Principles of Statics, 10th Ed., by Russell C. Hibbeler [ISBN: 0131866745] Probability and Statistics Engineers and Scientists, 3rd Edition, Hayter Probability and Statistics Engineering and the Sciences, 6th Ed., by Jay L. Devore Probability Random Variables, and Stochastic Processes, 4th Ed., by Papoulis, Pillai Quantum Mechanics: An Accessible Introduction, 1st Ed., by Robert Scherrer Recursive Macroeconomic Theory, 1st Ed., by Ljungqvist, Sargent Recursive Methods in Economic Dynamics, (2002) by Irigoyen, Rossi- Hansberg, Wright RF Circuit Design: Theory & Applications, by Bretchko, Ludwig Sears and Zemansky's University Physics 11th Edition by Young.. Semiconductor Device Fundamentals by Pierret Semiconductor Devices: Physics and Technology, 2nd Ed., S.M. Sze Semiconductor Physics And Devices -3rd Ed. by D. Neamen Separation Process Principles, 2nd Ed., Seader, Henley Signal Processing and Linear Systems by Lathi Signals and Systems, 2nd Edition, by Haykin, Van Veen Signals and Systems, 2nd Edition, Oppenheim, Willsky, Hamid, Nawab Signals and Systems: Analysis Using Transm Methods and MATLAB, 1st Ed., by M. J. Roberts Signals, Systems, and Transms, 3rd Ed., by Charles L. Phillips, Eve A. Riskin, John M. Parr Shigley's Mechanical Engineering Design, 8th Ed. by Budynas, Nisbett (No Sol. Chapt 18 & 19) Simply C#: An Application-Driven Tutorial Approach, by Deitel, Hoey (Chapters 1-32) Soil Mechanics: Concepts and Applications, 2nd Ed., by Powrie Solid State Electronic Devices - 5th Ed by Streetman Solid State Electronic Devices - 6th Ed by Streetman Statics and Mechanics of Materials: An Integrated Approach, 2nd Ed., by Riley, Sturges, Morris Structural Analysis, 5th Edition, by Hibbeler University Physics 11th Edition by Young.. Vector Mechanics: Statics 7th Edition by Beer I have the solutions manual in electronic format for the following textbooks. If interested, email me at fwaterfish [at] gmail (daught) [kom] Vector Mechanics: Dynamics, 7th Ed., by Beer, Johnston, Staab, Clausen Vibrations and Stability: Advanced Theory, Analysis, and Tools, 7th Ed., by Thomsen Wireless Communications: Principles and Practice, 2nd Ed, by Rappaport Theory and Design Mechanical Measurements, 4th Ed., Beasley, Figliola Thermal Physics, 2nd Edition, by Charles Kittel Thermal Physics, by Ralph Baierlein Thermodynamics: An Engineering Approach, 5th Ed., by Cengel, Boles (Missing solutions #118-149 of Chapter 7) Thermodynamics: An Engineering Approach, 6th Ed., by Cengel, Boles The Science and Engineering of Materials, 4th Ed., by Donald R. Askeland, Pradeep P. Phule Thomas' Calculus, Early Trans., Part 1, 10th Ed. by Thomas, Weir, Hass, Giordano Thomas' Calculus: Part 2, 10th Ed. (Multivariable, chs. 8-13), by Thomas, Weir, Hass, Giordano Thomas' Calculus, Early Trans., Part 1, 11th Ed. by Thomas, Weir, Hass, Giordano Thomas' Calculus: Part 2, 11th Ed. (Multivariable, chs. 11-16), by Thomas, Weir, Hass, Giordano Transport Phenomena, 1st Edition, by R. Byron Bird Transport Phenomena, 2nd Ed., by Bird. === Subject: Re: How to count rational numbers > I already discredited myself by my miscarried attempt to count sums of > prime numbers. Nevertheless, I try it again. > In the rational matrix R, r(i,j) = j/i > 1) n(n - 1)/2 elements are lesser than 1 in the matrix T, > 2) n elements are equal to 1, and > 3) n(n - 1)/2 elements are greater than 1. > The value 1/2 repeats in every even row, thus this fraction repeats n/ > 2 times, supposing that n is even. We must subtract [(n/2) - 1] from > the value of T to eliminated these repeated values 1/2. We will call > these orrective elements as c(i). > The values 1/3 and 2/3 repeat in every third row, thus these 2 > rational numbers repeat 2n/3 times in the matrix T. We must subtract > [(2n/3) - 2] from the value of T to eliminated repeated values 1/3 and > 2/3, again supposing that n is divisible by 3. > 1/4, 2/4, 3/4 repeat in every 4. row, but 2/4 was already counted as > 1/2. This leaves 2 uncounted elements in every 4. row. We must > subtract [(n/2) - 2] from the value of T to eliminated repeated values > 1/4 and 3/4. > The prime 5 gives repeatings as 4n/5, and the term [(4n/5) - 4], > generally [({p - 1}n/p) - p + 1]. > respectively. This leaves fractions 1/6 and 5/6 to be counted. > Carefully continuing, and finding ways to eliminate possible rounding > errors, it were possible to find the counting function for any n. > It can be conjectured, that for none n > T - sum c(i) is not equal to n. > kunzmilan > I think you're trying to count the number of fractions a / b with 0 < a < n + 1, 0 < b < n + 1, and gcd(a, b) = 1. This is twice the sum of phi(m), m from 1 to n, where phi(m) is the number of positive integers relatively prime to m and not exceeding m. It is well-known that the sum is asymptotic to (3 / pi^2) n^2. -- Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) === Subject: solution manuals I have solution manuals in electronic format for the following textbooks. Email me at fwaterfish [at] gmail [daught] [kom] if you're interested. Paypal, Credit, and Debit cards are all acceptable payment methods Analysis and Design of Analog Integrated Circuits, 4th Ed., by Gray,Hurst, Lewis, Meyer Analytical Mechanics, 7th Edition, by Fowels, Cassiday An Interactive Introduction to Mathematical Analysis, by Jonathan Lewin An Introduction to the Mathematics of Financial Derivatives, 2nd Ed.,by Neftci [ISBN:0125153929] Antenna Theory, 2nd Ed., by Balanis Antennas all Applications, 3rd Edition, Kraus, Marhefka Applied Linear Statistical Models, 5th Ed., by Neter (Selected Sol.) Applied Numerical Analysis, 6th Edition, by Gerald, Wheatley Applied Numerical Methods with MATLAB Engineers and Scientists,1st Ed,. by Chapra Applied Statistics and Probability Engineers, 3rd Ed., by Montgomery, Runger (Selected Solutions) Applied Strength of Materials, 4th Edition, by Mott A Transition to Advanced Mathematics, 5th Edition, by Smith, Eggen,Andre Automatic Control Systems, 8th Edition, by Kuo, Golnaraghi A Course in Game Theory by Osborne, Rubinstein A Course in Algebraic Number Theory by Cohen Adaptive Filter Theory, 4th Edition, by Haykin Adaptive Control, 2nd. Ed., by Astrom, Wittenmark Advanced Engineering Mathematics, 8th Editoin, by Erwin Kreyszig (even solutions) Advanced Engineering Mathematics, 9th Edition, by Erwin Kreyszig (even solutions) Advanced Macroeconomics, 1st Ed., by David Romer Advanced Mathematical Concepts Precalculus With Applications by Holliday [ISBN: 0028341759] Advanced Modern Engineering Mathematics, 3rd Ed., by G. James A First Course In Differential Equations, 7th Edition, by Zill, Cullen Analog Integrated Circuit Design, 1st Ed., by Johns, Martin (text ebook and solution manual) Basic Business Statistics: Concepts and Applications, 10th Ed., by Berenson, Krehbiel, Levine (chap1-18) Basic Engineering Circuit Analysis, 7th Ed., by J. David Irwin Basic Engineering Circuit Analysis, 8th Ed., by J. David Irwin, Nelms (Missing a chapter or 2) Bioprocess Engineering Principles by Doran Calculus: Study and Solutions Guide, Vol. 1, 7th Ed., by Larson,Hostetler, Edwards Chemical and Engineering Thermodynamics, 3rd Ed., Stanley I. Sandler Chemical Engineering Volume 1, 6th Edition, by Richardson, Coulson,Backhurst, Harker Thornton College Physics, Volume 1: 7th Edition, by Serway, Faugh College Physics, Volume 2: 7th Edition, by Serway, Faughn Communications Systems, 4th Ed., by Haykin Communications Systems Engineering, 2nd Edition, by Proakis Computational Techniques Fluid Dynamics by Srinivas, Fletcher Computer Networks, 4th Ed., by Andrew S. Tanenbaum Computer Networks: A Systems Approach, 3rd Edition, by Davie Control Systems Engineering, 4th Ed., by Norman Nise Corporate Finance, 6th Edition, by Ross C++ How to Program: Intro Object-Oriented Design with the UML, 3rd Ed., by Deitel, Nieto Calculus Early Transcendental, 5th Ed., by James Stewart Calculus - Early Transcendentals, 7th Ed., by Anton, Bivens, Davis Calculus: Graphical, Numerical, Algebraic, 3rd Ed., Waits, Finney,Demana, Kennedy Calculus: Multivariable, 5th Edition, by James Stewart Calculus: Single Variable, Early Transcendental, 5th Edition, by James Stewart Calculus, Single and Multivariable, 3rd Ed., by Hughes- Hallett,McCallum Integrated Circuits 3rd Edition by Muller Differential Equations with Boundary Value Problems, 2nd Ed., by Polking, Arnold Digital And Analog Communication Systems 7th Ed., Leon W. Couch Digital Communications, 4th Edition, by Proakis Digital Communications: Fundamentals and Applications, 2nd Ed, Skylar Digital Design, 4th Edition, by Mano, Ciletti Digital Image Processing, 2nd Edition, by Gonzalez, Woods Digital Integrated Circuits, 2nd Ed., by Rabaey (Solutions ONLY Chapters 3, 5, 6, 10) Digital Signal Processing: A Computer Based Approach, 1st Ed., by Mitra Digital Signal Processing: A Computer Based Approach, 2nd Ed., by S.Mitra Digital Signal Processing: A Computer Based Approach, 3rd Ed., by S.Mitra Digital Signal Processing: Principles, Algorithms and Applications, 3rd Edition, by Proakis Discrete Time Signal Processing, 2nd Edition, Oppenheim Dynamics of Mechanical Systems by C.T.F. Ross Data and Computer Communications, 8th Edition by Stallings Database Management Systems, 3rd Ed., by Ramakrishnan, Gehrke (Sol. Chapters 2-21, odd only) Design of Analog CMOS Integrated Circuits, 1st Edition, by Razavi Design of Analysis of Experiments, 6th Edition, Montgomery (missing chapter 6-8) Design of Machinery, 3rd Ed by Robert L. Norton Design With Operational Amplifiers and Analog Integrated Circuits, 2nd Ed., by Sergio Franco Design With Operational Amplifiers and Analog Integrated Circuits, 3rd Ed., by Sergio Franco Elementary Principles of Chemical Processes, 3rd Ed., by Felder,Rousseau Elements of Chemical Reaction Engineering, 3rd Ed., by H. Scott Fogler Engineering and Chemical Thermodynamics, by Koretsky [ISBN: 0471385867] (No sol. chapt 6) Engineering Circuit Analysis, 6th Edition, Hyat Engineering Electromagnetics, 6th Ed W. Hayt, J. Buck Engineering Electromagnetics, 7th Ed., Hayt, Buck Engineering Fluids Mechanics 7th Edition by Crowe Engineering Fluids Mechanics 8th Edition by Crowe Engineering Mathematics, 4th Ed., by John Bird Engineer Mechanics: Dynamics, 4th Ed., by Bedd Engineering Mechanics: Dynamics, 10th Ed., by Russell C. Hibbeler Engineering Mechanics: Dynamics 11th Ed. by Hibbeler Engineering Mechanics: Dynamics 5th Ed. by Meriam, Kraige Engineering Mechanics: Statics, 4th Edition - A. Bedd, Wallace Fowler Engineering Mechanics: Statics, 5th Ed., Meriam, Kraige Engineering Mechanics: Statics, 6th Ed., Meriam, Kraige Engineering Mechanics: Statics, 10th Ed., by Russell C. Hibbeler Engineering Mechanics: Statics 11th Ed. by Hibbeler Experiments with Economic Principles by Bergstrom, Miller Econometric Analysis, 5th Edition, by Greene Wooldridge Econometrics of Financial Markets, by Adamek, Cambell, Lo, MacKinlay, Viceira Electrical Properties of Materials, 7th Ed., by D. Walsh, L. Solymar Electric Circuits 6th Ed. by Nilsson Electric Circuits 7th Ed. by Nilsson Electric Machinery, 6th Ed., Fitzgerald, Kingsley, Umans Electric Machinery Fundamentals, 4th Ed by Chapman Electromagnetic Fields and Waves by Iskander Electronic Circuit Analysis, 2nd Ed., by Donald Neamen Electronics, 2nd Ed., by Allan R. Hambley Elementary Differential Equations, 8th Edition, by Boyce, DiPrima(some odd/even) Fundamentals of Applied Electromagnetics, 5th Ed., 2008 Media Edition,by Ulaby Fundamentals of Digital Logic with Verilog Design, 1st Edition, by Brown, Vranesic Fundamentals of Electric Circuits, 2nd Edition, by Alexander Fundamentals of Electromagnetics with Engineering Appls by Wentworth Fundamentals of Fluid Mechanics, 5th Ed. by Munson, Young.. Fundamentals of Heat and Mass Transfer, 4th Ed by Incropera... Fundamentals of Heat and Mass Transfer, 5th Ed by Incropera... Fundamentals of Heat and Mass Transfer, 6th Ed by Incropera... Fundamentals of Logic Design, 5th Ed., by Roth Jr. Fundamentals of Machine Component Design, 3rd Ed., by Juvinall Fundamentals of Machine Component Design, 4th Ed., by Juvinall Fundamentals of Machine Elements, 2nd Ed., Hamrock, Jacobson, Schmid Fundamentals of Physics by Halliday, 7th Ed., Walker, Resnick Fundamentals of Semiconductor Devices, 1st Edition by Anderson Fundamentals of Structural Analysis, 2nd Ed., Chia-Ming Uang, Kenneth Leet Fundamentals of Thermal-Fluid Sciences, 2nd Ed. by Cengel Fundamentals of Thermal-fluid Sciences, Int'l 2nd Ed. by Cengel Fundamentals of Engineering Thermodynamics, 5th Ed. by Shapiro Fundamentals of Thermodynamics, 5th Ed., by Sonntag, Borgnakke... Fundamentals of Thermodynamics, 6th Ed., by Sonntag Facilities Planning, 3rd Edition, by Tompkins, White, Bozer, Tanchoco Feedback Control of Dynamic Systems, 4th Edition, by Powell, Emami- Naeini Financial Accounting, 4th Ed., by Libby, Short (Chap1-14) Financial Accounting: An International Introduction, 2nd Ed., by Alexander, Nobes Finite Element Techniques in Structural Mechanics by Ross Fluid Mechanics - 5th Edition by Frank M. White Fluid Mechanics and Thermodynamics of Turbomachinery, 5th Ed., by S. L. Dixon [ISBN: 0750678704] Essentials of Fluid Mechanics: Fundamentals and Applications, 1st Ed., by Cengel & Cimbala Fluid Mechanics with Engineering Applications, 10th Edition, by Finnemore Fundamentals of Aerodynamics, 3rd Edition, by J. D. Anderson, Jr. Fundamentals of Applied Electromagnetics, 1st Ed., 2001 Media Edition, by Ulaby Geometry, 04 Edition, by McGraw-Hill [ISBN: 0078296374] Guide to Energy Management, 5th Edition, by Pawlik Heat Transfer: A Practical Approach - 2nd Edition by Cengel Hydraulics in Civil and Environmental Engineering, 4th Ed., by Andrew Chadwick Introduction to Algorithms, 2nd Ed by Cormen, Leiserson (Selected Sol.) Introduction To Chemical Engineering Thermodynamics, 7th Ed., by Van Ness, Smith, Abbott Introduction to Electric Circuits, 6th Ed., by Dorf, Svoboda Introduction to Electric Circuits, 7th Ed., by Dorf, Svoboda Introduction to Electrodynamics, 3rd Ed. by David Griffiths Introduction to Fluid Mechanics - 5th Ed. by Fox.. Introduction to Fluid Mechanics - 6th Ed by Fox, McDonald... Introduction to Linear Algebra, 3rd Ed., by Gilbert Strang Introduction to Linear Algebra, 5th Ed., Arnold, Johnson, Riess Introduction to Probability by Grinstead, Snell (odd solutions only, not just answers but step by step solutions) Introduction to Quantum Mechanics, 2nd Ed. by Griffiths Introdution to Solid State Physics, 8th Edition by Kittel Introduction to Statistical Quality Control, 4th Edition, by Montgomery Introduction to Thermal Systems Engineering: Thermodynamics, Fluid Mechanics, and Heat Transfer by Moran, Shapiro, Munson, DeWitt Introduction to Thermal Systems Engineering, by Moran, Shapiro Linear Algebra, by J. Hefferon Linear Algebra And Its Applications, 3rd Ed., by David C. Lay Linear Algebra with Applications, 2nd Edition - by Otto Bretscher Linear Algebra with Applications, 3rd Edition - by Otto Bretscher Linear Circuit Analysis: Time Domain, Phasor and Laplace.., 2nd Ed, Lin Machine Design: An Integrated Approach, 2nd Ed., by Robert L. Norton Machine Design: An Integrated Approach, 3rd Ed., by Robert L. Norton Managerial Accounting, 11th Ed., by Noreen, Brewer, Garrison Materials Science and Engineering: An Introduction, 6th Ed. by Callister Matrix Analysis and Applied Linear Algebra by Carl Meyer MC68HC11: An Introduction: Software/Hardware Interf, 2nd Ed, by Huang Mechanical Engineering Design, 7th Ed. by Mischke, Shigley Mechanical Vibrations, 3rd Edition, by S. S. Rao (99% same as 4th Edition, No Solutions Chapters 6, 9, and 12) Mechanics of Fluids, 8th Ed., by Bernard Massey Mechanics of Fluids, 4th Ed., Irving H. Shames Mechanics of Fluids, 8th Ed., by Bernard Massey Mechanics of Materials - 3rd Ed. by Beer, Johnston, Dewolf Mechanics of Materials - 6th Ed. by Hibbeler Mechanics of Materials, 6th Edition by James M. Gere (missing small portion, section 8.5) Mechanics of Materials, 6th Ed., by Sturges, Morris, Riley (part of Chapt 2 is missing but only #1 thru #60) Mechanics of Solids by C.T.F. Ross Microeconomic Analysis, 3rd Ed., by H. Varian (Ans. to Exercises: Ch. 1- Ch.25) Microeconomic Theory, by Mas-Colell, Whinston, Green Microelectronic Circuit Analysis and Design, 3rd Edition, by D. Neamen Microelctronic Circuits, 5th Ed. by Sedra and Smith Microelectronic Circuit Design, 2nd Edition by Jaeger, Blalock Microelectronic Circuit Design, 3rd Edition by Jaeger, Blalock Microelectronics: Digital and Analog Circuits and Systems by Millman Microwave and Rf Design of Wireless Systems, 1st Edition, by Pozar Microwave Engineering, 3rd Ed., by David M. Pozar Microwave Transistor Amplifiers: Analysis and Design, 2nd Ed., by Guillermo Gonzalez Miller & Freund's Probability and Statistics Engineers, 7th Edition, Johnson, Miller Modern Compressible Flow, 3rd Edition, by Anderson Modern Control Engineering, 3rd Edition, by Ogata Modern Control Engineering, 4th Edition, by Ogata Modern Digital and Analog Communication Systems, 3rd Ed., by Lathi Modern Control Systems, 9th Ed., by Richard C. Dorf, Robert H Bishop (98% same as the 10th Ed.) Modern Operating Systems,2nd Ed., by Andrew Tanenbaum Modern Physics 4th Edition by Tipler Monetary Theory and Policy, 2nd Edition, by Walsh Multivariable Calculus, 5th Edition, by James Stewart Operating Systems: Internals and Design Principles, 4th Edition, by Stallings Operating System Concepts, 7th Ed., Silberschatz, Galvin, Gagne Options, Futures and Other Derivatives, 4th Ed., by John Hull Options, Futures and Other Derivatives, 5th Ed., by John Hull (Chapters 1 thru 18 ONLY) Orbital Mechanics: Engineering Students by Howard Curtis (includes matlab scripts) Organic Chemistry, 4th Ed., by Carey, Atkins (Student Study Guide and Sol. Man.) Partial Differential Equations with Fourier Series and Boundary Value ) Physical Chemistry - 7th Edition - by Julio de Paula, Peter Atkins Physics, 6th Edition, by John Cutnell Physics, 5th Edition, Vol 2 by Halliday, Resnick, Krane (Chap 25-52) Physics Scientist and Engineers by Knight (No Chapt 36-42) Physics Scientist and Engineers, 6th Ed., by Serway Physics Scientists and Engineers-Vol 1, 5th Edition, Serway, Beichner (Chap. 1 - 22) Physics Scientists and Engineers-Vol 2, 5th Edition, Serway, Beichner (Chap. 23 - 46) Physics Scientists and Engineers, 3rd Ed., by Douglas C. Giancoli Physics Scientist and Engineers, 5th Edition, by Tipler, Mosca Physics: Principles with Applications, 6th Ed. by Giancoli Power System Analysis and Design, 3rd Ed., by Glover, Sarma Principles and Applications of Electrical Engineering 4th (Revised) Edition by Rizzoni Principles and Practices of Automatic Process Control, 3rd Edition by Smith, Corripio [ISBN: 0471431907] Principles of Communication: Systems, Modulation Noise, 5th Ed., Ziemer Principles of Physics, 3rd Edition, by Serway Principles of Physics, 4th Edition, by Serway Principles of Statics, 10th Ed., by Russell C. Hibbeler [ISBN: 0131866745] Probability and Statistics Engineers and Scientists, 3rd Edition, Hayter Probability and Statistics Engineering and the Sciences, 6th Ed., by Jay L. Devore Probability Random Variables, and Stochastic Processes, 4th Ed., by Papoulis, Pillai Quantum Mechanics: An Accessible Introduction, 1st Ed., by Robert Scherrer Recursive Macroeconomic Theory, 1st Ed., by Ljungqvist, Sargent Recursive Methods in Economic Dynamics, (2002) by Irigoyen, Rossi- Hansberg, Wright RF Circuit Design: Theory & Applications, by Bretchko, Ludwig Sears and Zemansky's University Physics 11th Edition by Young.. Semiconductor Device Fundamentals by Pierret Semiconductor Devices: Physics and Technology, 2nd Ed., S.M. Sze Semiconductor Physics And Devices -3rd Ed. by D. Neamen Separation Process Principles, 2nd Ed., Seader, Henley Signal Processing and Linear Systems by Lathi Signals and Systems, 2nd Edition, by Haykin, Van Veen Signals and Systems, 2nd Edition, Oppenheim, Willsky, Hamid, Nawab Signals and Systems: Analysis Using Transm Methods and MATLAB, 1st Ed., by M. J. Roberts Signals, Systems, and Transms, 3rd Ed., by Charles L. Phillips, Eve A. Riskin, John M. Parr Shigley's Mechanical Engineering Design, 8th Ed. by Budynas, Nisbett (No Sol. Chapt 18 & 19) Simply C#: An Application-Driven Tutorial Approach, by Deitel, Hoey (Chapters 1-32) Soil Mechanics: Concepts and Applications, 2nd Ed., by Powrie Solid State Electronic Devices - 5th Ed by Streetman Solid State Electronic Devices - 6th Ed by Streetman Statics and Mechanics of Materials: An Integrated Approach, 2nd Ed., by Riley, Sturges, Morris Structural Analysis, 5th Edition, by Hibbeler University Physics 11th Edition by Young.. Vector Mechanics: Statics 7th Edition by Beer Vector Mechanics: Dynamics, 7th Ed., by Beer, Johnston, Staab, Clausen Vibrations and Stability: Advanced Theory, Analysis, and Tools, 7th Ed., by Thomsen Wireless Communications: Principles and Practice, 2nd Ed, by Rappaport Theory and Design Mechanical Measurements, 4th Ed., Beasley, Figliola Thermal Physics, 2nd Edition, by Charles Kittel Thermal Physics, by Ralph Baierlein Thermodynamics: An Engineering Approach, 5th Ed., by Cengel, Boles (Missing solutions #118-149 of Chapter 7) Thermodynamics: An Engineering Approach, 6th Ed., by Cengel, Boles The Science and Engineering of Materials, 4th Ed., by Donald R. Askeland, Pradeep P. Phule Thomas' Calculus, Early Trans., Part 1, 10th Ed. by Thomas, Weir, Hass, Giordano Thomas' Calculus: Part 2, 10th Ed. (Multivariable, chs. 8-13), by Thomas, Weir, Hass, Giordano Thomas' Calculus, Early Trans., Part 1, 11th Ed. by Thomas, Weir, Hass, Giordano Thomas' Calculus: Part 2, 11th Ed. (Multivariable, chs. 11-16), by Thomas, Weir, Hass, Giordano Transport Phenomena, 1st Edition, by R. Byron Bird Transport Phenomena, 2nd Ed., by Bird. === Subject: solution manuals I have solution manuals in electronic format for the following textbooks. Email me at fwaterfish [at] gmail [daught] [kom] if you're interested. Paypal, Credit, and Debit cards are all acceptable payment methods Analysis and Design of Analog Integrated Circuits, 4th Ed., by Gray,Hurst, Lewis, Meyer Analytical Mechanics, 7th Edition, by Fowels, Cassiday An Interactive Introduction to Mathematical Analysis, by Jonathan Lewin An Introduction to the Mathematics of Financial Derivatives, 2nd Ed.,by Neftci [ISBN:0125153929] Antenna Theory, 2nd Ed., by Balanis Antennas all Applications, 3rd Edition, Kraus, Marhefka Applied Linear Statistical Models, 5th Ed., by Neter (Selected Sol.) Applied Numerical Analysis, 6th Edition, by Gerald, Wheatley Applied Numerical Methods with MATLAB Engineers and Scientists,1st Ed,. by Chapra Applied Statistics and Probability Engineers, 3rd Ed., by Montgomery, Runger (Selected Solutions) Applied Strength of Materials, 4th Edition, by Mott A Transition to Advanced Mathematics, 5th Edition, by Smith, Eggen,Andre Automatic Control Systems, 8th Edition, by Kuo, Golnaraghi A Course in Game Theory by Osborne, Rubinstein A Course in Algebraic Number Theory by Cohen Adaptive Filter Theory, 4th Edition, by Haykin Adaptive Control, 2nd. Ed., by Astrom, Wittenmark Advanced Engineering Mathematics, 8th Editoin, by Erwin Kreyszig (even solutions) Advanced Engineering Mathematics, 9th Edition, by Erwin Kreyszig (even solutions) Advanced Macroeconomics, 1st Ed., by David Romer Advanced Mathematical Concepts Precalculus With Applications by Holliday [ISBN: 0028341759] Advanced Modern Engineering Mathematics, 3rd Ed., by G. James A First Course In Differential Equations, 7th Edition, by Zill, Cullen Analog Integrated Circuit Design, 1st Ed., by Johns, Martin (text ebook and solution manual) Basic Business Statistics: Concepts and Applications, 10th Ed., by Berenson, Krehbiel, Levine (chap1-18) Basic Engineering Circuit Analysis, 7th Ed., by J. David Irwin Basic Engineering Circuit Analysis, 8th Ed., by J. David Irwin, Nelms (Missing a chapter or 2) Bioprocess Engineering Principles by Doran Calculus: Study and Solutions Guide, Vol. 1, 7th Ed., by Larson,Hostetler, Edwards Chemical and Engineering Thermodynamics, 3rd Ed., Stanley I. Sandler Chemical Engineering Volume 1, 6th Edition, by Richardson, Coulson,Backhurst, Harker Thornton College Physics, Volume 1: 7th Edition, by Serway, Faugh College Physics, Volume 2: 7th Edition, by Serway, Faughn Communications Systems, 4th Ed., by Haykin Communications Systems Engineering, 2nd Edition, by Proakis Computational Techniques Fluid Dynamics by Srinivas, Fletcher Computer Networks, 4th Ed., by Andrew S. Tanenbaum Computer Networks: A Systems Approach, 3rd Edition, by Davie Control Systems Engineering, 4th Ed., by Norman Nise Corporate Finance, 6th Edition, by Ross C++ How to Program: Intro Object-Oriented Design with the UML, 3rd Ed., by Deitel, Nieto Calculus Early Transcendental, 5th Ed., by James Stewart Calculus - Early Transcendentals, 7th Ed., by Anton, Bivens, Davis Calculus: Graphical, Numerical, Algebraic, 3rd Ed., Waits, Finney,Demana, Kennedy Calculus: Multivariable, 5th Edition, by James Stewart Calculus: Single Variable, Early Transcendental, 5th Edition, by James Stewart Calculus, Single and Multivariable, 3rd Ed., by Hughes- Hallett,McCallum Integrated Circuits 3rd Edition by Muller Differential Equations with Boundary Value Problems, 2nd Ed., by Polking, Arnold Digital And Analog Communication Systems 7th Ed., Leon W. 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Giancoli Physics Scientist and Engineers, 5th Edition, by Tipler, Mosca Physics: Principles with Applications, 6th Ed. by Giancoli Power System Analysis and Design, 3rd Ed., by Glover, Sarma Principles and Applications of Electrical Engineering 4th (Revised) Edition by Rizzoni Principles and Practices of Automatic Process Control, 3rd Edition by Smith, Corripio [ISBN: 0471431907] Principles of Communication: Systems, Modulation Noise, 5th Ed., Ziemer Principles of Physics, 3rd Edition, by Serway Principles of Physics, 4th Edition, by Serway Principles of Statics, 10th Ed., by Russell C. Hibbeler [ISBN: 0131866745] Probability and Statistics Engineers and Scientists, 3rd Edition, Hayter Probability and Statistics Engineering and the Sciences, 6th Ed., by Jay L. 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Vector Mechanics: Statics 7th Edition by Beer Vector Mechanics: Dynamics, 7th Ed., by Beer, Johnston, Staab, Clausen Vibrations and Stability: Advanced Theory, Analysis, and Tools, 7th Ed., by Thomsen Wireless Communications: Principles and Practice, 2nd Ed, by Rappaport Theory and Design Mechanical Measurements, 4th Ed., Beasley, Figliola Thermal Physics, 2nd Edition, by Charles Kittel Thermal Physics, by Ralph Baierlein Thermodynamics: An Engineering Approach, 5th Ed., by Cengel, Boles (Missing solutions #118-149 of Chapter 7) Thermodynamics: An Engineering Approach, 6th Ed., by Cengel, Boles The Science and Engineering of Materials, 4th Ed., by Donald R. Askeland, Pradeep P. Phule Thomas' Calculus, Early Trans., Part 1, 10th Ed. by Thomas, Weir, Hass, Giordano Thomas' Calculus: Part 2, 10th Ed. (Multivariable, chs. 8-13), by Thomas, Weir, Hass, Giordano Thomas' Calculus, Early Trans., Part 1, 11th Ed. by Thomas, Weir, Hass, Giordano Thomas' Calculus: Part 2, 11th Ed. (Multivariable, chs. 11-16), by Thomas, Weir, Hass, Giordano Transport Phenomena, 1st Edition, by R. Byron Bird Transport Phenomena, 2nd Ed., by Bird. === Subject: Angle between two vectors as dimension->infinity If we look at the cosine of the angle between two random vectors with components sampled uniformly from [0,1], it seems to approach 3/4 as the dimension grows to infinity, is there a simple way to derive this analytically? http://www.yaroslavvb.com/research/reports/randvecs/randVecs.html === Subject: Re: Angle between two vectors as dimension->infinity > If we look at the cosine of the angle between two random vectors with > components sampled uniformly from [0,1], it seems to approach 3/4 as > the dimension grows to infinity, is there a simple way to derive this > analytically? http://www.yaroslavvb.com/research/reports/randvecs/randVecs.html If the vectors are (x_1, x_2, ... x_n) and (y_1, y_2, ... y_n) then the cosine of the angle is given by cos(theta) = sum_i=1^n x_i*y_i / (sqrt(sum_i=1^n x_i^2) * sqrt(sum_i=1^n y_i^2)) If x and y are independent and uniformly random on [0,1] then E(x*y) = E(x)*E(y) = 1/4, so E(sum_i=1^n x_i*y_i) = n/4 Also, E(x^2) = E(y^2) = 1/3, so E(sum_i=1^n x_i^2) = E(sum_i=1^n y_i^2) = n/3 As n -> oo we can invoke some law or other (TM) to say that the actual values will converge to the expected values in such a way that cos(theta) -> (n/4)/(sqrt(n/3)*sqrt(n/3)) = 3/4 === Subject: Re: #227 circle or sphere fail to have a Commutative; new textbook: Mathematical-Physics You may state where they lie. This is irrelevant. I ask > about arithmetic, especially myltiplication. What is > (pi) * (pi)? > (pi) x (pi) = 180 x 180 = 32,400 degrees = 90 (2pi) = 2pi > since they are all modulo. Isn't 90 half of 180 (degrees)? Shouldn't that be: (pi) * (pi) = 180 x 180 = 32,400 = 90 (mod 2 pi) = 90 = (pi)/2 (pi) * (pi) = (pi)/2 So then (pi)*(pi) = (pi)^2 = (pi)/2. Which also means that: pi^2 + pi^2 = pi/2 + pi/2 = pi(1/2 + 1/2) = pi Furthermore: pi^4 = (pi^2)^2 = (pi/2)^2 = (pi^2)/4 = (pi^2)(pi^2) = (pi/2)(pi/2) = (pi^2)/4 pi^6 = (pi^2)^3 = (pi/2)^3 = (pi^3)/8 pi^8 = (pi^2)^4 = (pi/2)^4 = (pi^4)/16 etc. And: pi^5 = (pi^2)^2.5 = (pi^2)^2 * (pi^2)^0.5 = (pi^2)^2 * pi = (pi^2)/4 * pi = (pi^3)/4 pi^7 = (pi^2)^3.5 = (pi^2)^3 * (pi^2)^0.5 = (pi^2)^3 * pi = (pi^3)/8 * pi = (pi^4)/8 etc. === Subject: #231 circle or sphere fail to have a Commutative; new textbook: Mathematical-Physics You may state where they lie. This is irrelevant. I ask > about arithmetic, especially myltiplication. What is > (pi) * (pi)? > (pi) x (pi) = 180 x 180 = 32,400 degrees = 90 (2pi) = 2pi > since they are all modulo. Isn't 90 half of 180 (degrees)? > Shouldn't that be: > (pi) * (pi) = 180 x 180 = 32,400 = 90 (mod 2 pi) = 90 = (pi)/2 > (pi) * (pi) = (pi)/2 So then (pi)*(pi) = (pi)^2 = (pi)/2. Which also means that: > pi^2 + pi^2 = pi/2 + pi/2 = pi(1/2 + 1/2) = pi Furthermore: > pi^4 = (pi^2)^2 = (pi/2)^2 = (pi^2)/4 > = (pi^2)(pi^2) = (pi/2)(pi/2) = (pi^2)/4 > pi^6 = (pi^2)^3 = (pi/2)^3 = (pi^3)/8 > pi^8 = (pi^2)^4 = (pi/2)^4 = (pi^4)/16 > etc. And: > pi^5 = (pi^2)^2.5 = (pi^2)^2 * (pi^2)^0.5 > = (pi^2)^2 * pi = (pi^2)/4 * pi = (pi^3)/4 > pi^7 = (pi^2)^3.5 = (pi^2)^3 * (pi^2)^0.5 > = (pi^2)^3 * pi = (pi^3)/8 * pi = (pi^4)/8 > etc. I have no complaint with any of the above. Trouble was me, for I still do not have many matters settled. Under modulo 360 then I agree with the above. My trouble is finding what multiplication means on a sphere surface. In Euclidean geometry we fall automatically into the correct operation of multiplication and give it no second thought. We fall into the notion and habit that 2 X 3 is a 2 by 3 rectangle with final answer of 6 square units. With a sphere, alot of thinking has to go into finding out what multiplication is. I think it is triangles with a rotation or spin. But have alot more thinking before home safe. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: Re: solutions manual <1895899.1188464091378.JavaMail.jakarta@nitrogen.mathforum.org have the following solution manuals.... > and i have thousands of textbooks as well > email me at diosbendit...@gmail.com if you want any of them > email at diosbenditome (at) gmail (dot) com > paypal paymets accepted only please email me rather than leaving a message here.. Chemical and Engineering Thermodynamics- 3rd Edition- Solutions > Manual.rar 11 MB > Prentice Hall - Solutions Manual; Communication Systems Engineering > (McGraw-Hill) (Instructors Manual) Electric Machinery Fundamentals 4th > Edition (Stephen J Chapman).pdf 5 MB > [eBook.med] Prentice.Hall- Digital image processing - Gonzalez 2Ed- > Solutions Manual (2002).pdf > 2 MB > [Ejercicios propuestos y sus soluciones] Algebra Lineal - Juan de > Burgos -.pdf > 7 MB > [Instructor's Solutions Manual] Introduction to Electrodynamics - 3rd > ed. David J. Griffiths.rar > 4 MB > [Manual Solution] Mechanics of Materials Hibbeler 4th-Chapter 12.pdf > 19 MB > [Problemas Selectos y Soluciones] Mecanismos de Reacci?n en Qu?mica > Org?nica - (W. C. Groutas) by polyto.pdf > 69 MB > [Problemas y Soluciones] 854 Problemas Seleccionados de F?sica > Elemental. (B.B.B?jotsev - V. D. Kr?vehemkov - G. Ya. Mi?kishev - > I. M. Sar?eva)(1979).pdf > 11 MB > [Soluciones a los problemas] FISICA 1 -2a ed. 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Devore.rar > 4 MB > Probability Random Variables and Stochastic Processes Solutions > Manual.Papoulis.McGraw Hill.2002.pdf > 16 MB > Problemas resueltos de Estad?stica I.rar > 143 KB > Rubik - Solucao Do Cubo Magico.pdf > 224 KB > Schaums Mathematical Handbook of Formulas and Tables.pdf > 26 MB > Signal Processing and Linear Systems - B P Lathi - Solutions > Manual.pdf > 11 MB > Solution Manual to engineering fluid mechanics 7e.pdf > 4 MB > Solution To Two-Dimensional Incompressible Navier-Stokes Equations- > Maciej Matyka.pdf > 373 KB > Thomas' Calculus, Early Trascendentals 10th ed Instructors Solutions > Manual.pdf > 19 MB > Wankat & Oreovicz - Teaching Engineering.rar > 911 KB > Wiley - Pozar - Microwave Engineering 3ed - Solutions Manual.rar > 11 MB > Wiley Chemical And Engineering Thermodynamics 3Ed Solutions Manual.pdf > 11 MB > Zwillinger D. et al - CRC Standard Probability and Statistic Tables > and Formulae (1999).pdf 9 Mb > analytical mechanics.rar > askeland science and engineering of materials solutions.rar > classical dynamics 5e thornton.rar > crowe 7e engineering fluid mechanics.rar > eng mech dyn bedford and fowler.rar > eng mech statics bedford 4e.rar > feedback control of dynamic systems.rar > fox 6th fluid mech solutions.rar > 13 Mb fund of ther open chs.rar > 32 Mb fundamentals of heat and mass transfer solutions.rar > 27 Mb fundamentals of machine component design 3e solutions.rar > 13 Mb Fundamentals of Thermal-Fluid Sciences.rar > 9 Mb heat transfer 2e solutions.rar > 41 Mb hibbler 10th statics.rar > 30 Mb hibbler dynamics 10E.rar > 93 Mb Introduction Fluid Mechanics, 6th Edition Fox,McDonald, & > Pritchard.rar > 7 Mb materials science and engineering an intro 6E callister.rar > 3 Mb mech eng design solutions.rar > 77 Mb merian eng mech ... I have the solutions manual in electronic format for the following textbooks. If interested email me at fwaterfish [at] gmail [daught] kom === Subject: Re: solutions manual <27234105.1193679954149.JavaMail.jakarta@nitrogen.mathforum.org i have the following solution manuals.... > and i have thousands of textbooks as well > email me at diosbendit...@gmail.com if you want any of them > email at diosbenditome (at) gmail (dot) com > paypal paymets accepted only please email me rather than leaving a message here.. Chemical and Engineering Thermodynamics- 3rd Edition- Solutions > Manual.rar 11 MB > Prentice Hall - Solutions Manual; Communication Systems Engineering > (McGraw-Hill) (Instructors Manual) Electric Machinery Fundamentals 4th > Edition (Stephen J Chapman).pdf 5 MB > [eBook.med] Prentice.Hall- Digital image processing - Gonzalez 2Ed- > Solutions Manual (2002).pdf > 2 MB > [Ejercicios propuestos y sus soluciones] Algebra Lineal - Juan de > Burgos -.pdf > 7 MB > [Instructor's Solutions Manual] Introduction to Electrodynamics - 3rd > ed. David J. Griffiths.rar > 4 MB > [Manual Solution] Mechanics of Materials Hibbeler 4th-Chapter 12.pdf > 19 MB > [Problemas Selectos y Soluciones] Mecanismos de Reacci.97n en Qu.93mica > Org.87nica - (W. C. Groutas) by polyto.pdf > 69 MB > [Problemas y Soluciones] 854 Problemas Seleccionados de F.93sica > Elemental. (B.B.B.9cjotsev - V. D. Kr.93vehemkov - G. Ya. Mi.87kishev - > I. M. Sar.87eva)(1979).pdf > 11 MB > [Soluciones a los problemas] FISICA 1 -2a ed. Luis Rodrigus > Valencia.pdf > 2 MB > [Soluciones a los problemas] Suplemento Calculo Infinitesimal > Calculus- Michael Spivak.pdf > 8 MB > [Solution Manual] CD Physics - Halliday, Resnick and Walker's - > Fundamentals of Physics 1, 2, 3 and 4 (4th ed.)(over 2000pages).rar > 43 MB > [Solutions Manual] Classical Electrodynamics - 2nd Ed. John David > Jackson byKasper van Wijk.pdf > 1 MB > [Solutions Manual] Communication Systems Engineering Proakis J > (2002).pdf > 2 MB > [Solutions Manual] [Instructors] Advanced Engineering Mathematics 8Ed > - Erwin Kreyszig.pdf > 19 MB > [Solutions Manual] [Instructors] Calculus 5Th Ed James Stewart .pdf > 75 MB > [Solutions Manual] [Instructors] Introduction to Linear Algebra--3rd > Edition - Gilbert Strang.pdf > 500 KB > [Solutions Manual] [Instructors] Physics by Resnick Halliday Krane, > 5th Ed. Vol 2.pdf > 1 MB > [Solutions Manual] Anton Bivens Davis CALCULUS early transcendentals > 7th edition.rar > 11 MB > [Solutions Manual] Applied Statistics and Probability for Engineers > 3rd Ed. Douglas C Montgomery, George C. Runger.rar > 58 MB > [Solutions Manual] > Applied.Statistics.and.Probability.for.Engineers.-.Student.,.3rd.Ed. > 2 MB > [Solutions manual] Calculus George Thomas 10th ed Vol 1.rar > 18 MB > [Solutions manual] Calculus George Thomas 10th ed Vol 2.rar > 15 MB > [Solutions Manual] Communication Systems 4Th Edition Simon Haykin.pdf > 32 MB > [Solutions Manual] Control Systems Engineering, Nise.rar > 5 MB > [Solutions Manual] Design of Analog CMOS Integrated Circuits [McGraw > Hill].pdf > 74 MB > [Solutions Manual] Signal Digital Processing - Proakis & Manolakis.pdf > 7 MB > [Solutions Manual] Digital Signal Processing; A Computer-Based > Approach 1st ed.pdf > 40 MB > [Solutions Manual] Econometric Analysis - Greene , Williame H. - 5th > Ed .pdf > 3 MB > [Solutions Manual] Electric Machinery 6Ed Fitzgerald, Kingsley, Uman > - .pdf > 3 MB > [Solutions Manual] Elementary Mechanics & Thermodynamics [2000] by > Professor Jhon W. Norbury.pdf > 577 KB > [Solutions manual] Engineering - Materials Science, Milton Ohring .pdf > 2 Mb > [Solutions Manual] Engineering Electromagnetics - 6th Edition - > William H. Hayt, John A. Buck.rar > 10 MB > [Solutions Manual] Engineering Fluid Mechanics, 7th ed. Clayton T. > Crowe, Donald F. Elger and John A. Roberson .pdf > 4 MB > [Solutions Manual] > Mechanic STATICS 10th Ed. R.C. Hibbeler.rar > 20 MB > Edition, (2002) - J. L. Meriam and L. G. Kraige.rar > 102 MB > Hibbeler.R.C.rar > 29 MB > [Solutions Manual] Fourier and Laplace Transform - Antwoorden.pdf > 2 MB > [Solutions Manual] Fundamental os Heat and Mass Transfer [Frank P. > Incropera - David P.DeWitt] ANOTHER EDITION.pdf > 33 MB > [Solutions Manual] Fundamental os Heat and Mass Transfer [Frank P. > Incropera - David P.DeWitt].pdf > 65 MB > [Solutions Manual] Fundamentals of Engineering Thermodynamics Moran, > M.J. & Shapiro H.N..pdf > 70 MB > [Solutions Manual] Fundamentals of Engineering Thermodynamics, M. J. > Moran and H. N. Shapiro, 5th edition.rar > 65 MB > [Solutions Manual] Fundamentals Of Fluid Mechanics 3Rd And 4Th > Edition.pdf > 53 MB [Solutions Manual] Fundamentals of Machine Component Design 3rd > Edition by Robert C. Juvinall and Kurt M. Marshek.rar > 31 MB > [Solutions Manual] Fundamentals of Thermodynamics 6th Ed Sonntag- > Borgnakke-Van Wylen.rar > 33 MB > [Solutions Manual] Fundamentals of Thermodynamics [Sonntag-Borgnakke- > Van Wylen].pdf > 2 MB > [Solutions Manual] Fundamentals.of.Thermodynamics.[Sonntag-Borgnakke- > Van.Wylen].pdf > 2 MB > [Solutions Manual] Hibbeler 4ed - Resist.90ncia dos Materiais.rar > 182 MB > [Solutions Manual] Introduction to Fluid Mechanics (Fox, 5th ed).pdf > 70 MB > [Solutions Manual] Introduction to Linear Algebra 3Ed - Gilbert > Strang.pdf > 551 KB > [Solutions Manual] Introduction to VLSI Circuits and Systems (2001 > draft) - John P Uyemura.pdf > 2 MB > [Solutions Manual] Mechanical Engineering Design 7th Ed. Shigley.rar > 11 MB > [Solutions Manual] Mechanics Of Materials - (3Rd Ed , By Beer, > Johnston, & Dewolf).pdf > 35 MB > [Solutions Manual] Mechanics of Materials, 6th Ed. by R. C. > Hibbeler.rar > 369 MB > [Solutions manual] Oppenheim's Discrete Time Signal Processing > text.pdf > 7 MB > [Solutions Manual] Probability And Statistics For Engineers And > Scientists .pdf > 5 MB > [Solutions manual] Probability and Statistics for Engineers and > Scientists Manual HAYLER.pdf > 5 MB > [Solutions Manual] Signals And Systems - 2nd Ed.- Oppenheim & > Wilsky.pdf > 174 MB > [Solutions Manual] Signals and Systems 2nd Ed. - Haykin.pdf > 4 MB > [Solutions Manual] Thermodynamics - An Engineering Approach, 5Th > Cengal Boles.rar > 26 MB > [Solutions Manual] University Physics - Sears and Zemansky's 11th > Ed.rar > 85 MB > [Solu.8d.8bo dos problemas] Redes de Computadores - 4a ed. - ANDREW S. > TANENBAUM.pdf > 247 KB > Part 1 - Mechanics, Relativity, and Electrodynamics.rar > 7 MB > Part 2 - Thermodynamics, Statistical Physics, and Quantum > Mechanics.rar > 6 MB > A Guide to Physics Problems, Part 1 - Mechanics, Relativity, and > Electrodynamics and Part 2 - Thermodynamics, Statistical Physics, and > Quantum Mechanics.rar > 211 B > Manual.pdf > 1 MB > Classical Mechanics - Goldstein Solved problems.pdf > 555 KB > Daniel Shanks - Solved And Unsolved Problems In Number Theory (2Nd > Ed), 1978.pdf > 12 MB > Electric Machinery Fundamentals (Solutions Manual).doc > 3 MB > Elementary Differential Equations And Boundary Value Problems, 7Th Ed > - Boyce And Diprima Student Solutions Manual, Charles W Haines Ode > Architect Companion.pdf > 11 MB > Fundamentals of Logic Design 5Ed - Charles Roth - Solutions Manual.pdf > 7 MB > Fundamentals of Thermodynamics 6th Ed (Solutions Manual) - Sonntag- > Borgnakke-Van Wylen.pdf > 21 MB > Griffiths, David - Introduction To Electrodynamics Solutions Manual - > With Update.pdf > 85 MB > Halliday, Resnick - Fundamentals Of Physics - 7Th Edition Instructors > Solutions Manual.rar > 21 MB > Instructor's Solutions Manual - Marion, Thornton - Classical Dynamics > 9 Mb > Instructors Solution Manual, Static- Meriam and L. G. Kraige.pdf > 85 MB > Introduction To Algorithms 2Nd Edition > Solutions(Instructor's.Manual).pdf > 2 MB > Introduction to Probability - Solutions Manual.pdf > 615 KB > Juvinall, Marshek - Fundamentals of Machine Component Design, 3rd ed - > Student Solutions Manual.pdf > 8 MB > McgrawHill - William H. Hayt, John A. Buck - Engineering > Electromagnetics, 6th Edition Solutions Manual !!!!!!!!!!!!!!.pdf > 14 MB > Microwave Engineering 3E - David M Pozar - Solutions Manual.pdf > 11 MB > Microwave Engineering 3e - David M Pozar - Solutions Manual.rar > 11 MB > Munson - Young - Okiishi.rar > 354 MB > Operating Systems Concepts 6th + SOLUTIONS MANUAL !!!.rar > 15 MB > Physical Chemistry 7ed - Peter Atkins - Julio de Paula - instructors > solution manual.rar > 8 MB > Physics For Scientists And Engineers 6E By Serway And Jewett - > Solutions Manual Vol 2.pdf > 6 MB > Proakis J. (2002) Communication Systems Engineering - Solutions Manual > (299s).pdf > 2 MB > Probability and Statistics for Engineering and the Sciences (with CD- > ROM and InfoTrac ) (Hardcover) by Jay L. Devore.rar > 4 MB > Probability Random Variables and Stochastic Processes Solutions > Manual.Papoulis.McGraw Hill.2002.pdf > 16 MB > Problemas resueltos de Estad.93stica I.rar > 143 KB > Rubik - Solucao Do Cubo Magico.pdf > 224 KB > Schaums Mathematical Handbook of Formulas and Tables.pdf > 26 MB > Signal Processing and Linear Systems - B P Lathi - Solutions > Manual.pdf > 11 MB > Solution Manual to engineering fluid mechanics 7e.pdf > 4 MB > Solution To Two-Dimensional Incompressible Navier-Stokes Equations- > Maciej Matyka.pdf > 373 KB > Thomas' Calculus, Early Trascendentals 10th ed Instructors Solutions > Manual.pdf > 19 MB > Wankat & Oreovicz - Teaching Engineering.rar > 911 KB > Wiley - Pozar - Microwave Engineering 3ed - Solutions Manual.rar > 11 MB > Wiley Chemical And Engineering Thermodynamics 3Ed Solutions Manual.pdf > 11 MB > Zwillinger D. et al - CRC Standard Probability and Statistic Tables > and Formulae (1999).pdf 9 Mb > analytical mechanics.rar > askeland science and engineering of materials solutions.rar > classical dynamics 5e thornton.rar > crowe 7e engineering fluid mechanics.rar > eng mech dyn bedford and fowler.rar > eng mech statics bedford 4e.rar > feedback control of dynamic systems.rar > fox 6th fluid mech solutions.rar > 13 Mb fund of ther open chs.rar > 32 Mb fundamentals of heat and mass transfer solutions.rar > 27 Mb fundamentals of machine component design 3e solutions.rar > 13 Mb Fundamentals of Thermal-Fluid Sciences.rar > 9 Mb heat transfer 2e solutions.rar > 41 Mb hibbler 10th statics.rar > 30 Mb hibbler dynamics 10E.rar > 93 Mb Introduction Fluid Mechanics, 6th Edition Fox,McDonald, & > Pritchard.rar > 7 Mb materials science and engineering an intro 6E callister.rar > 3 Mb mech eng design solutions.rar > 77 Mb merian eng mech ...... read more é === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad Due to the mapping of M, K and C, the probabilities of M, K and C are > complicatedly interactional. For the above example, the probability > of > plaintext changes when the ciphertext is fixed, even though the > ciphertext is unknown. > When only considering the fixed ciphertext and the equiprobability of > key, ... If the cyphertext is fixed then the key probablility is not uniform. > It is unknown (it depends both on the fixed value of the cyphertext, > and the probability distribution on the plaintext, neither > of which is known). The conclusion is not that the plaintext > probability > is uniform, but that the plaintext probability is unknown. - William > Hughes are addlepated for you do not know there is a one-to-one > correspondence between all the plaintexts and keys, so the > probabilities of the corresponding plaintext and key are the same. As > all the keys are equally likely ... No. True: For a fixed plaintext the keys are equally likely. False: For a fixed cyphertext the keys are equally likely. For a fixed cyphertext the probability of the keys depends > on the probability of the plaintext, which is unknown. So for > a fixed cyphertext the probability distribution on the keys > is unknown. -William Hughes- - - - True: For a fixed plaintext the keys are equally likely. False: For a fixed cyphertext the keys are equally likely. > -----------------see my precondition Your precondition is There is no information about the probability distribution > on the plaintext. Only information about the OTP is used. Under this precondition: for a fixed cyphertext the > probability distriution on the keys in unknown. For a fixed cyphertext the probability of the keys depends > on the probability of the plaintext, which is unknown. So for > a fixed cyphertext the probability distribution on the keys > is unknown. -------------------you repeat question regardless of my replies. can you tell me > If so, for a fixed cyphertext , the postior probability of plaintext > =the prior???? Yes. If you make an observation that tells you nothing about > the probability of the plaintext (e.g. the value of the cyphertext) > the posterior probability is equal to the prior probability. - William Hughes- - - - Your precondition is There is no information about the probability distribution > on the plaintext. Only information about the OTP is used. -----------------my precondition is only consider cipertext fixed, key > simiarly likey. You do not have one precondition you have two: cyphertext fixed > and key distribution uniform. These two conditions contradict > each other. If the cyphertext is fixed then the key > distribution is not uniform. The key distribution is uniform only when the cyphertext is > not fixed. - William Hughes- - - - You do not have one precondition you have two: cyphertext fixed and key distribution uniform. These two conditions contradict each other. If the cyphertext is fixed then the key distribution is not uniform. ----------------the precondition I get plaintext uniform is not what the two of you. regardluss of the prior, two conditions do not contradict each other. but you regard of the prior The key distribution is uniform only when the cyphertext is not fixed. -----you are wrong for wrong understanding. - William Hughes === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad > The key distribution is uniform only when the cyphertext is > not fixed. > -----you are wrong for wrong understanding. > No. It is very easy to see that for a fixed cyphertext the key distribution depends on the plaintext distribution. Since the plaintext distribution is unknown, the key distribution is unknown. - William Hughes === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad The key distribution is uniform only when the cyphertext is > not fixed. > -----you are wrong for wrong understanding. No. It is very easy to see that for a fixed cyphertext > the key distribution depends on the plaintext distribution. > Since the plaintext distribution is unknown, the key > distribution is unknown. - William Hughes The key distribution is uniform only when the cyphertext is > not fixed. > -----you are wrong for wrong understanding. No. It is very easy to see that for a fixed cyphertext the key distribution depends on the plaintext distribution. Since the plaintext distribution is unknown, the key distribution is unknown. ---my precondtions regardless the prior probabilityo of M. Then compromise the probabilities of incomplete condition. your unknown is too weak to slove problems. === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad > The key distribution is uniform only when the cyphertext is > not fixed. > -----you are wrong for wrong understanding. No. It is very easy to see that for a fixed cyphertext > the key distribution depends on the plaintext distribution. > Since the plaintext distribution is unknown, the key > distribution is unknown. - William Hughes The key distribution is uniform only when the cyphertext is not fixed. > -----you are wrong for wrong understanding. No. It is very easy to see that for a fixed cyphertext > the key distribution depends on the plaintext distribution. > Since the plaintext distribution is unknown, the key > distribution is unknown. > ---my precondtions regardless the prior probabilityo of M. > Then compromise the probabilities of incomplete condition. your unknown is too weak to slove problems. Here is a proof that the assumptions that the cyphertext is fixed and the key distribution is uniform are contradictory. Please indicate the first step you think is wrong. Assume the cyphertext is fixed. 1. If the cyphertext is fixed then there is a one to one correpondence between the plaintext and the key 2. The distribution of the key is determined by the distribution of the plaintext. 3. The distribution of the plaintext is unknown. 4. The distribution of the key is unknown. 5. It is a contradiction to say that the cyphertext is fixed and the key distribution is uniform. - William Hughes === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad The key distribution is uniform only when the cyphertext is > not fixed. > -----you are wrong for wrong understanding. No. It is very easy to see that for a fixed cyphertext > the key distribution depends on the plaintext distribution. > Since the plaintext distribution is unknown, the key > distribution is unknown. - William Hughes The key distribution is uniform only when the cyphertext is not fixed. > -----you are wrong for wrong understanding. No. It is very easy to see that for a fixed cyphertext > the key distribution depends on the plaintext distribution. > Since the plaintext distribution is unknown, the key > distribution is unknown. > ---my precondtions regardless the prior probabilityo of M. > Then compromise the probabilities of incomplete condition. your unknown is too weak to slove problems. Here is a proof that the assumptions > that the cyphertext is fixed and the > key distribution is uniform are contradictory. > Please indicate the first > step you think is wrong. Assume the cyphertext is fixed. 1. If the cyphertext is fixed then there > is a one to one correpondence between the > plaintext and the key 2. The distribution of the key is > determined by the distribution of the plaintext. 3. The distribution of the plaintext is unknown. 4. The distribution of the key is unknown. 5. It is a contradiction to say that the cyphertext > is fixed and the key distribution is uniform. - William Hughes- - - - my precondition is that key is uniform and c is fixed. under that condition M is uniform. === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad > The key distribution is uniform only when the cyphertext is > not fixed. > -----you are wrong for wrong understanding. No. It is very easy to see that for a fixed cyphertext > the key distribution depends on the plaintext distribution. > Since the plaintext distribution is unknown, the key > distribution is unknown. - William Hughes The key distribution is uniform only when the cyphertext is not fixed. > -----you are wrong for wrong understanding. No. It is very easy to see that for a fixed cyphertext > the key distribution depends on the plaintext distribution. > Since the plaintext distribution is unknown, the key > distribution is unknown. > ---my precondtions regardless the prior probabilityo of M. > Then compromise the probabilities of incomplete condition. your unknown is too weak to slove problems. Here is a proof that the assumptions > that the cyphertext is fixed and the > key distribution is uniform are contradictory. > Please indicate the first > step you think is wrong. Assume the cyphertext is fixed. 1. If the cyphertext is fixed then there > is a one to one correpondence between the > plaintext and the key 2. The distribution of the key is > determined by the distribution of the plaintext. 3. The distribution of the plaintext is unknown. 4. The distribution of the key is unknown. 5. It is a contradiction to say that the cyphertext > is fixed and the key distribution is uniform. - William Hughes- - - - my precondition is that key is uniform and c is fixed. > under that condition M is uniform. Stating contradictory conditions in the opposite order does not help. If c is fixed then the key is not uniform. If the key is uniform, then c is not fixed. Please indicate the first step you think is wrong Assume the cyphertext is fixed. 1. If the cyphertext is fixed then there is a one to one correpondence between the plaintext and the key 2. The distribution of the key is determined by the distribution of the plaintext. 3. The distribution of the plaintext is unknown. 4. The distribution of the key is unknown. 5. It is a contradiction to say that the key distribution is uniform and the cyphertext is fixed. - William Hughes === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad > I use the following C code: > [snipped] > to generate a 1000 character plaintext with P(M=0) = 0.9: > and a onetime pad > Why are you using a pseudo-random sequence to generate the > OTP data? Such a sequence is entirely predictable once the > first few bytes have been deciphered, and defeats the whole > design of a OTP encryption scheme. I never using a pseudo-random sequence to generate the OTP data Your code uses rand(), which is a pseudo-random sequence generator. It does not generate truly random sequences. If you are using rand() to produce both the plaintext and the OTP, they may be mathematically related instead of being completely independent of each other. Furthermore, using rand() to generate a OTP sequence is not secure, because the sequence is predictable after the first few values are known, which defeats the whole purpose of a OTP. === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad > I use the following C code: > [snipped] > to generate a 1000 character plaintext with P(M=0) = 0.9: > and a onetime pad > Why are you using a pseudo-random sequence to generate the > OTP data? Such a sequence is entirely predictable once the > first few bytes have been deciphered, and defeats the whole > design of a OTP encryption scheme. I never using a pseudo-random sequence to generate the OTP data Your code uses rand(), which is a pseudo-random sequence > generator. It does not generate truly random sequences. If you are using rand() to produce both the plaintext and the OTP, > they may be mathematically related instead of being completely > independent of each other. Furthermore, using rand() to generate a OTP sequence is not > secure, because the sequence is predictable after the first few > values are known, which defeats the whole purpose of a OTP. > I use the following C code: > [snipped] > to generate a 1000 character plaintext with P(M=0) = 0.9: > and a onetime pad > Why are you using a pseudo-random sequence to generate the > OTP data? Such a sequence is entirely predictable once the > first few bytes have been deciphered, and defeats the whole > design of a OTP encryption scheme. > I never using a pseudo-random sequence to generate the OTP data Your code uses rand(), which is a pseudo-random sequence generator. It does not generate truly random sequences. If you are using rand() to produce both the plaintext and the OTP, they may be mathematically related instead of being completely independent of each other. ----------you have never thougt over the problem.the mathematically related owe to the condition C is fixed,but not using rand() to produce both the plaintext and the OTP. there is a one-to-one between plaintext and key for fixed C, how can they completely independent of each other. Furthermore, using rand() to generate a OTP sequence is not secure, because the sequence is predictable after the first few values are known, which defeats the whole purpose of a OTP. ---------------I never using a pseudo-random sequence to generate the OTP data ,it's your confusion. === Subject: Re: Confirmation of Shannon's Mistake about Perfect Secrecy of One-time-pad > I use the following C code: > [snipped] > to generate a 1000 character plaintext with P(M=0) = 0.9: > and a onetime pad > Why are you using a pseudo-random sequence to generate the > OTP data? Such a sequence is entirely predictable once the > first few bytes have been deciphered, and defeats the whole > design of a OTP encryption scheme. I never using a pseudo-random sequence to generate the OTP data Your code uses rand(), which is a pseudo-random sequence > generator. It does not generate truly random sequences. If you are using rand() to produce both the plaintext and the OTP, > they may be mathematically related instead of being completely > independent of each other. Furthermore, using rand() to generate a OTP sequence is not > secure, because the sequence is predictable after the first few > values are known, which defeats the whole purpose of a OTP. > I use the following C code: > [snipped] > to generate a 1000 character plaintext with P(M=0) = 0.9: > and a onetime pad > Why are you using a pseudo-random sequence to generate the > OTP data? Such a sequence is entirely predictable once the > first few bytes have been deciphered, and defeats the whole > design of a OTP encryption scheme. > I never using a pseudo-random sequence to generate the OTP data Your code uses rand(), which is a pseudo-random sequence generator. It does not generate truly random sequences. If you are using rand() to produce both the plaintext and the OTP, they may be mathematically related instead of being completely independent of each other. ----------you have never thougt over the problem.the mathematically related owe to the condition C is fixed,but not using rand() to produce both the plaintext and the OTP. there is a one-to-one between plaintext and key for fixed C, how can they completely independent of each other. Furthermore, using rand() to generate a OTP sequence is not secure, because the sequence is predictable after the first few values are known, which defeats the whole purpose of a OTP. ---------------I never using a pseudo-random sequence to generate the OTP data ,it's your confusion. === Subject: Re: problem with integral (pretty hairy) > .... > I am having problems with that transformation. I have this set: > > {(x,y) | -1 <= x <= 1, 0 <= y <= sqrt(1-x^2)} > > I know that x = r*cos(theta) and y = r*sin(theta). But how do I find r > and theta? I assume that r is the radius so based on the above I get r=1 > therefore I get: > > -1 <= cos(theta) <= 1 => theta = 0 OR theta=k*Pi (1) > where k is an integer.... But your conditions on x and y are inequalities, giving a whole region of the plane. Shade that region on your diagram. Think about what inequalities r and theta satisfy throughout the region. If you just produce single values such as r = 1 or theta = 0, then they can't be right, can they? Ken Pledger. === Subject: Re: Polar coordinates > I have a set D defined as: > > D = {(x,y)| 0 <= y <= sqrt(2), y <= x <= sqrt(4-y^2)} > > based on the bounds x=y and x^2 + y^2 = 4. > > The corresponding polar set id: > > Dpol = {(r,theta)| r in [0,2], 0 <= theta <= Pi/4} > > > Since radius for the circle is sqrt(4) = 2 I assume thats where r in > [0,2] comes from. But why is the upper limit for theta Pi/4? Draw the diagram. Ken Pledger. === Subject: Topology with base and ... <5or1eqFo7nohU1@mid.individual.net> Useful equation to prove and remember for f:X ->Y. ff-1(A) = A / f(X) Thus when f surjection, your equation. === Subject: Re: Topology with base and ... > Yes, V = f[f^{-1}(V)]. > Useful equation to prove and remember for f:X ->Y. ff-1(A) = A / f(X) > Thus when f surjection, your equation. I had a question about my original proof. Let f : (X, T) -> (Y, T') be open and onto, and let P be a base for T. Then P' = {f[B] | B in P} is a base for T'. --------------------------------------------------- 1) For each y in Y, there is at least one basis element f[B] containing y. Because, Since f is onto, there is x such that f(x) = y. so, there is B in P such that x in B. so, y = f(x) in f(B) in P' 2) If y belongs to the intersection of two basis elements f[B_1] and f[B_2], then there is a basis element f[B_3] containing y such that f[B_3] subset f[B_1] / f[B_2]. (/ : intersection) Because, Since y in f[B_1] / f[B_2], y in f[B_1] and y in f[B_2]. so, f^{-1}(y) subset B_1 and f^{-1](y) subset B_2. so, f^{-1}(y) subset (B_1) / (B_2). so, y = f[f^{-1}(y)] in f[(B_1) / (B_2)] subset f[B_1] / f[B_2]. Since (B_1) / (B_2) = B_3 in P for some B_3. (This is trivial by the definition of subbasis.) right ?? ----------------------------------------------------- so, P' = {f[B] | B in P} is a base for topology generated by P'. But I can't guarantee that P' is a base for (Y, T'). Because, T' is any topology for Y=f(X). Namely, T' is unaffected by (X, T). Namely, T' is unaffected by function f. so, I can find a counter-example as Jose Carlos santos. My thinking is right ?? === Subject: Re: Topology with base and ... > Yes, V = f[f^{-1}(V)]. > Useful equation to prove and remember for f:X ->Y. > ff-1(A) = A / f(X) > Thus when f surjection, your equation. > > > I had a question about my original proof. > > Let f : (X, T) -> (Y, T') be open and onto, > and let P be a base for T. > Then P' = {f[B] | B in P} is a base for T'. > > --------------------------------------------------- > 1) > For each y in Y, there is at least one basis element f[B] containing y. > > Because, > Since f is onto, there is x such that f(x) = y. > so, there is B in P such that x in B. > so, y = f(x) in f(B) in P' > > 2) > If y belongs to the intersection of two basis elements f[B_1] and f[B_2], > then there is a basis element f[B_3] containing y > such that f[B_3] subset f[B_1] / f[B_2]. (/ : intersection) > > Because, > Since y in f[B_1] / f[B_2], y in f[B_1] and y in f[B_2]. > so, f^{-1}(y) subset B_1 and f^{-1](y) subset B_2. > so, f^{-1}(y) subset (B_1) / (B_2). > so, y = f[f^{-1}(y)] in f[(B_1) / (B_2)] subset f[B_1] / f[B_2]. > > Since (B_1) / (B_2) = B_3 in P for some B_3. > (This is trivial by the definition of subbasis.) > right ?? If B_1 and B_2 are in a base for a topology, that does not mean that (B_1) / (B_2) is necessarily in the base. An example can be given with RxR with the euclidean metric, and the usual topology. If P = { U subset RxR, such that U is an open disk of positive radius in R^2}, then the sets in P form a base for the usual topology on R^2. Open Disk: < http://mathworld.wolfram.com/OpenDisk.html > . In many cases, the intersection of two disks can give a lens-shape, which is not in P. But the lens-shape is a union of (infinitely many) open disks. Also, P union { R^2} generates the usual topology, so it's a subbase: < http://en.wikipedia.org/wiki/Subbase > . David Bernier === Subject: Re: Topology with base and ... > Yes, V = f[f^{-1}(V)]. > Useful equation to prove and remember for f:X ->Y. ff-1(A) = A / f(X) > Thus when f surjection, your equation. > I had a question about my original proof. > Let f : (X, T) -> (Y, T') be open and onto, > and let P be a base for T. > Then P' = {f[B] | B in P} is a base for T'. > --------------------------------------------------- > 1) > For each y in Y, there is at least one basis element f[B] containing y. > Because, > Since f is onto, there is x such that f(x) = y. > so, there is B in P such that x in B. > so, y = f(x) in f(B) in P' > 2) > If y belongs to the intersection of two basis elements f[B_1] and f[B_2], > then there is a basis element f[B_3] containing y > such that f[B_3] subset f[B_1] / f[B_2]. (/ : intersection) > Because, > Since y in f[B_1] / f[B_2], y in f[B_1] and y in f[B_2]. > so, f^{-1}(y) subset B_1 and f^{-1](y) subset B_2. > so, f^{-1}(y) subset (B_1) / (B_2). > so, y = f[f^{-1}(y)] in f[(B_1) / (B_2)] subset f[B_1] / f[B_2]. > Since (B_1) / (B_2) = B_3 in P for some B_3. > (This is trivial by the definition of subbasis.) > right ?? If B_1 and B_2 are in a base for a topology, that does not mean that > (B_1) / (B_2) is necessarily in the base. An example can be given with RxR with the euclidean metric, and > the usual topology. If P = { U subset RxR, such that U is an open disk of positive radius in > R^2}, then the sets in P form a base for the usual topology on R^2. Open Disk: < http://mathworld.wolfram.com/OpenDisk.html > . In many cases, the intersection of two disks can give a lens-shape, which > is not in P. But the lens-shape is a union of (infinitely many) > open disks. Also, P union { R^2} generates the usual topology, so it's a > subbase: > < http://en.wikipedia.org/wiki/Subbase > . But this is a counter-example about subbase. Namely, If B_1 and B_2 are in a subbase for a topology, that does not mean that (B_1) / (B_2) is necessarily in the subbase. I want to know the counter-examplce about base. === Subject: Re: Topology with base and ... <5or1eqFo7nohU1@mid.individual.net> Yes, V = f[f^{-1}(V)]. > Useful equation to prove and remember for f:X ->Y. ff-1(A) = A / f(X) I had a question about my original proof. Let f : (X, T) -> (Y, T') be open and onto, > Then P' = {f[B] | B in P} is a base for T'. > What is P? A base for X? A subbase for X? This is false because the identity from a multipoint indiscrete space on the same set with topology with at least three open sets, is counter example. > 1) > For each y in Y, there is at least one basis element f[B] containing y. Because, > Since f is onto, there is x such that f(x) = y. > so, there is B in P such that x in B. > so, y = f(x) in f(B) in P' 2) > If y belongs to the intersection of two basis elements f[B_1] and f[B_2], > then there is a basis element f[B_3] containing y > such that f[B_3] subset f[B_1] / f[B_2]. (/ : intersection) Because, > Since y in f[B_1] / f[B_2], y in f[B_1] and y in f[B_2]. > so, f^{-1}(y) subset B_1 and f^{-1](y) subset B_2. No! Only f^-1(y) subset f^-1f(B_1) You've assumed equality while in general just A subset f^-1f(A) > so, f^{-1}(y) subset (B_1) / (B_2). > so, y = f[f^{-1}(y)] in f[(B_1) / (B_2)] subset f[B_1] / f[B_2]. Since (B_1) / (B_2) = B_3 in P for some B_3. > (This is trivial by the definition of subbasis.) right ?? Wrong. If P is a subbase, consider that { (-oo,a), (a,oo) | a in R } is a subbase for R. If P is a base, consider the intersection of two balls. > so, P' = {f[B] | B in P} is a base for topology generated by P'. P' is a subbase for a topology for Y simply because f is surjection. f:R -> { 0,1,2 }, For B to be a subbase for some topology for S, all that's needed is /B = S. For B to be base for some topology for S, what's needed is /B = S; for all U,V in B, x in U / V ==> some W in B with x in W subset U / V For B to be a base for the topology of S, what's needed is /B = S; for all U in B, U open for all open U nhood x, some V in B with x in V subset U Exercise: f:X -> Y, B subbase, base, topology for Y ==> { f^-1(U) | U in B } subbase, base, topology resp. of a topology for X. > But I can't guarantee that P' is a base for (Y, T'). > Because, T' is any topology for Y=f(X). > Namely, T' is unaffected by (X, T). > Namely, T' is unaffected by function f. > so, I can find a counter-example as Jose Carlos santos. My thinking is right ?? > open continuous surjection f:X -> Y, B base for X ==> { f(B) | U in B } base for Y If open V nhood y: some x with y = f(x) x in open f^-1(V); some U in B with x in U subset f^-1(V) y = f(x) in f(U) subset ff^-1(V) subset V Why does f need to be open? === Subject: Re: Topology with base and ... <5or1eqFo7nohU1@mid.individual.net> (Y, T') be open and onto, > Then P' = {f[B] | B in P} is a base for T'. What is P? A base for X? A subbase for X? let P be a base for T. > 1) > For each y in Y, there is at least one basis element f[B] containing y. Because, > Since f is onto, there is x such that f(x) = y. > so, there is B in P such that x in B. > so, y = f(x) in f(B) in P' 2) > If y belongs to the intersection of two basis elements f[B_1] and f[B_2], > then there is a basis element f[B_3] containing y > such that f[B_3] subset f[B_1] / f[B_2]. (/ : intersection) Because, > Since y in f[B_1] / f[B_2], y in f[B_1] and y in f[B_2]. > so, f^{-1}(y) subset B_1 and f^{-1](y) subset B_2. No! Only > f^-1(y) subset f^-1f(B_1) > You've assumed equality while in general just > A subset f^-1f(A) Oh, you're right. > Since (B_1) / (B_2) = B_3 in P for some B_3. > (This is trivial by the definition of subbasis.) right ?? Wrong. If P is a subbase, consider that > { (-oo,a), (a,oo) | a in R } is a subbase for R. > If P is a base, consider the intersection of two balls. Just a moment.. If P is a base of (X, T) and B_1 in P and B_2 in P, then (B_1) / (B_2) in P. ------------------------------ If (B_1) / (B_2) not in B, (B_1) / (B_2) not in T. so, T is not topology. so, (B_1) / (B_2) in P. right ? > so, P' = {f[B] | B in P} is a base for topology generated by P'. P' is a subbase for a topology for Y simply because f is surjection. f:R -> { 0,1,2 }, For B to be a subbase for some topology for S, > all that's needed is /B = S. > For B to be base for some topology for S, what's needed is > /B = S; for all U,V in B, > x in U / V ==> some W in B with x in W subset U / V For B to be a base for the topology of S, what's needed is > /B = S; for all U in B, U open > for all open U nhood x, some V in B with x in V subset U Exercise: f:X -> Y, B subbase, base, topology for Y > ==> { f^-1(U) | U in B } subbase, base, topology resp. > of a topology for X. Oh, exercise... Strange. is this true ? There doest not exist the assumption that f is quotient map. > open continuous surjection f:X -> Y, B base for X > ==> { f(B) | U in B } base for Y I already prove it. { f(U) | U in B}. > If open V nhood y: some x with y = f(x) > x in open f^-1(V); some U in B with x in U subset f^-1(V) > y = f(x) in f(U) subset ff^-1(V) subset V Why does f need to be open? For f(U) is base element... === Subject: Re: Topology with base and ... > If P is a base of (X, T) > and B_1 in P > and B_2 in P, then (B_1) / (B_2) in P. > ------------------------------ If (B_1) / (B_2) not in P, > (B_1) / (B_2) not in T. so, T is not topology. > so, (B_1) / (B_2) in P. Sorry. wrong... Even if (B_1) / (B_2) not in P, I can't guarantee that (B_1) / (B_2) not in T. What's counter-example ? === Subject: Re: Topology with base and ... > If P is a base of (X, T) > and B_1 in P > and B_2 in P, then (B_1) / (B_2) in P. > ------------------------------ If (B_1) / (B_2) not in P, > (B_1) / (B_2) not in T. so, T is not topology. > so, (B_1) / (B_2) in P. [mina_world: ] > Sorry. wrong... > Even if (B_1) / (B_2) not in P, > I can't guarantee that (B_1) / (B_2) not in T. > > What's counter-example ? If C and D are circles (disks) of radius 10, and centers 20 apart, then they are tangent. If they are only 15 apart, they intersect in a lens-shape as in eye-glasses. If a point x is in the lens, then it is a distance d>0 from the edge of the lens. So the disk of radius d/2 centered at x is completely contained in the lens. This is true for any x in the lens, so the lens is a union of infinitely many open disks in the base. But the lens is not a disk, so the lens is not in the base P. P = {U: U is an open disk in R^2} . David Bernier === Subject: Re: Topology with base and ... > If P is a base of (X, T) > and B_1 in P > and B_2 in P, > then (B_1) / (B_2) in P. > ------------------------------ > If (B_1) / (B_2) not in P, > (B_1) / (B_2) not in T. so, T is not topology. > so, (B_1) / (B_2) in P. [mina_world: ] > Sorry. wrong... > Even if (B_1) / (B_2) not in P, > I can't guarantee that (B_1) / (B_2) not in T. > What's counter-example ? If C and D are circles (disks) of radius 10, and centers > 20 apart, then they are tangent. If they are only > 15 apart, they intersect in a lens-shape as in > eye-glasses. If a point x is in the lens, then it is a distance > d>0 from the edge of the lens. So the disk > of radius d/2 centered at x is completely > contained in the lens. This is true for any x in the > lens, so the lens is a union of infinitely many open > disks in the base. But the lens is not a disk, > so the lens is not in the base P. P = {U: U is an open disk in R^2} . Yes, you're right. P is a base. === Subject: The negative dimension Give an example of a space which has -1 dimension. Are there any spaces which are more negatively dimensional? === Subject: Re: The negative dimension > Give an example of a space which has -1 dimension. The empty set? --- Christopher Heckman > Are there any spaces which are more negatively dimensional? === Subject: Re: The negative dimension > Give an example of a space which has -1 dimension. The empty set? > Yes. By the small inductive definition of dimension. Hm, IIRC the dimension of a space is the same by the various definitions for compact Hausdorff spaces. Thus does one conclude the empty set has dimension -1 by the other definitions including the Hausdorff dimension? Do you have a copy of or recall the author of Dimensional Dementia wherein all of this consider with multidimensional illustrations? ;-) === Subject: Re: The negative dimension > Give an example of a space which has -1 dimension. The set of all good things about Alabama, under the discrete topology. > Are there any spaces which are more negatively dimensional? The semigroup of useful things accomplished by Aggies. (It's closed under addition.) Bart (What do I win?) -- Cheerfully resisting change since 1959. === Subject: Re: The negative dimension Give an example of a space which has -1 dimension. The set of all good things about Alabama, under the > discrete topology. Are there any spaces which are more negatively dimensional? The semigroup of useful things accomplished by Aggies. (It's > closed under addition.) Bart (What do I win?) Your homeomorphism to the Bush space of all good acts with the indiscrete topology does definitely qualify as negatively dementiated. > -- Cheerfully resisting change since 1959. Yes, but back then not even the coast guard had to put up with him. === Subject: The Curve Space in Maths The Curve Space in Maths we all know, the force is multiplied by force is equal to work. It is abstracted to be maths problem, it becomes dot product of vector , namely the inner procudt of vector. namely : .a6磨.a6å=.a6 .98.a6ç.a6.98.a6.98.a6å.a6 .98cos<.a6ç,.a6å>. Also, the force is multiplied by moment of force, it also can be abstracted to be maths problem, it becomes the vector problem, it is the exterior product of vector. namely: .a6.98.a6çÁç.a6[Capi talAHat].a6.98=.a6.98.a6ç.a6.98.a6[OGr ave].a6å.a6.98sin<.a6ç,.a6[CapitalAHat ]>. Also, to the Coulomb's law: F=kq1q2/r^2.we also abstract it into a maths problem, and when we calculate it respective in a dot, a line, an area,or a sphere.we can conclude the same result with by using the Gauss's electric flux theorem.but from the maths principle,it is contradiction,because from the title meaning, it cann't get into the dot,the line (this can get the correct and the same result with by using the Gauss's electric flux theorem),an area or a sphere(we use the calculous -the double integral in maths to calculte it, we get the result that it can get into the area or the shpere,and this result is the same with using the Gauss's electric flux theorem).So all of it shows we must create a new maths field to resolve this problem, this is calculous in the curve space. At the Gauss's electric flux theorem: it is false all. So, the curve space in maths, we can defined it im maths as following: In right handed system in quadrature frame,namely in three dimensional coordinate space:in XÁ¢YÁ¢Z, r is the dot of function f(x) of vector, rÁæf(xÁ¢Y[DownExclamati on]¢Z).or is the vector that from the origin of coordinates O to r. If any function F(xÁ¢YÁ¢Z)£[CapitalAHat ]has the relation with the origin of coordinates, namely: F(xÁ¢YÁ¢Z)=f(x[DownExclamation ]¢YÁ¢Z)/or^2 £.9exÁ¢YÁ¢Z[Down Exclamation]æR£[YAcute]£Âcomes into existence,it says f(xÁ¢YÁ¢Z) is in right handed system coordinate, it means there is a only core in the origin coordinates and the three dimensional coordinate in this space with the core in origin coordinate is a curve sapce in maths. The integral with the function to the origin coordinate , ÁñF=Áñf(x[D ownExclamation]¢YÁ¢Z)/or^2d£¬x[Dow nExclamation]¢YÁ¢Z£© is the true calculous in curve sapce. I have found this question 20 years ago, but up to now, no one yet find and support me. sad for the knowledge achievement all over the world. caoyan 2007-5-2 http://thre-firewh2.home.sunbo.net/ === Subject: The Curve Space in Maths The Curve Space in Maths we all know, the force is multiplied by force is equal to work. It is abstracted to be maths problem, it becomes dot product of vector , namely the inner procudt of vector. namely : .a6磨.a6å=.a6 .98.a6ç.a6.98.a6.98.a6å.a6 .98cos<.a6ç,.a6å>. Also, the force is multiplied by moment of force, it also can be abstracted to be maths problem, it becomes the vector problem, it is the exterior product of vector. namely: .a6.98.a6çÁç.a6[Capi talAHat].a6.98=.a6.98.a6ç.a6.98.a6[OGr ave].a6å.a6.98sin<.a6ç,.a6[CapitalAHat ]>. Also, to the Coulomb's law: F=kq1q2/r^2.we also abstract it into a maths problem, and when we calculate it respective in a dot, a line, an area,or a sphere.we can conclude the same result with by using the Gauss's electric flux theorem.but from the maths principle,it is contradiction,because from the title meaning, it cann't get into the dot,the line (this can get the correct and the same result with by using the Gauss's electric flux theorem),an area or a sphere(we use the calculous -the double integral in maths to calculte it, we get the result that it can get into the area or the shpere,and this result is the same with using the Gauss's electric flux theorem).So all of it shows we must create a new maths field to resolve this problem, this is calculous in the curve space. At the Gauss's electric flux theorem: it is false all. So, the curve space in maths, we can defined it im maths as following: In right handed system in quadrature frame,namely in three dimensional coordinate space:in XÁ¢YÁ¢Z, r is the dot of function f(x) of vector, rÁæf(xÁ¢Y[DownExclamati on]¢Z).or is the vector that from the origin of coordinates O to r. If any function F(xÁ¢YÁ¢Z)£[CapitalAHat ]has the relation with the origin of coordinates, namely: F(xÁ¢YÁ¢Z)=f(x[DownExclamation ]¢YÁ¢Z)/or^2 £.9exÁ¢YÁ¢Z[Down Exclamation]æR£[YAcute]£Âcomes into existence,it says f(xÁ¢YÁ¢Z) is in right handed system coordinate, it means there is a only core in the origin coordinates and the three dimensional coordinate in this space with the core in origin coordinate is a curve sapce in maths. The integral with the function to the origin coordinate , ÁñF=Áñf(x[D ownExclamation]¢YÁ¢Z)/or^2d£¬x[Dow nExclamation]¢YÁ¢Z£© is the true calculous in curve sapce. I have found this question 20 years ago, but up to now, no one yet find and support me. sad for the knowledge achievement all over the world. caoyan 2007-5-2 http://thre-firewh2.home.sunbo.net/ === Subject: Halloween math http://www.pennergame.de/ref.php?refid=4682373 === Subject: Re: Halloween math > http://www.pennergame.de/ref.php?refid=4682373 > 31 OCT = 25 DEC === Subject: Re: #229 circle or sphere fail to have a Commutative; new textbook: Mathematical-Physics Nntp-Posting-Host: hera.cwi.nl > And just above I quoted you saying: > (pi) x (pi) = 180 x 180 = 32,400 degrees = 90 (2pi) = 2pi > since they are all modulo. > > So what is it, is it pi or 2pi? Or do you not know? Or does it depend > on the phase of the moon? > > It is (pi), since it is modulo (pi). How much of a difference that makes > for the overall arithmetic is unclear. Oh, now it is mod pi. Let's see: pi^2 = pi pi^2 - pi = 0 pi.(pi - 1) = 0 is that right? If so there are zerodivisors in your arithmetic other than 0 and 1. And furthermore, we cannot divide by pi, nor by (pi - 1). But further on this, I find: (4.pi - 1)(4.pi - 3) = 16.pi^2 - 16.pi + 3 = 3 and so 3 is not prime in the AP-adics. > (pi-2) is ....999998 so what is ....999998(pi), well it is pi since it > is even and > modulo Combined with your statement here, I find (pi - 1) = ...9999999 so we have ...9999999 * pi = 0 is that right? And so, we can not divide by ...9999999. > On the other hand, you have also stated that (pi - 2) does not exist (see > below). So, what is it? > > (pi - 2) is a subtraction and not a number. There are no negative > numbers in the Elliptic AP-adics. That number is ....9999998 But you have stated (when I used (pi - 2)) that it did not exist. So what is it? > So that pi.pi-2 is ....99998pi which is pi pi + pi.(pi - 2) = pi + pi^2 - 2.pi = pi + pi - 2.pi = 0. Right? And so pi + pi = 0. And from that 2.pi = 0, and so also 2 is a zero-divisor in your system, and you should not divide by it. > I have subtraction of the Hemisphere of 1 to 999....999999 and it is > not closed to addition > or subtraction for many of those answers fall into the other > Hemisphere of the imaginaries from > (pi) to 2(pi). But 2.pi = 0. See above for a proof. > But apparently it is not closed to addition, so there is no arithmetic. > > Show me an example of it not closed, for all additions are points that > land on either the 1 to 999...9999 hemisphere or land in the imaginary > hemisphere. Because you have not completely specified arithmetic this is a problem. But on what hemisphere is 0? > So there is no (pi - 2). > > > There are no negative numbers, and only subtraction when you > see a minus sign. But why did you write that (pi - 2) does not exist? There is no relation at all with negative numbers, there is only subtraction involved. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: #233 points on sphere are defined not by algebra but by geometry; new textbook: Mathematical-Physics > And just above I quoted you saying: > (pi) x (pi) = 180 x 180 = 32,400 degrees = 90 (2pi) = 2pi > since they are all modulo. > > So what is it, is it pi or 2pi? Or do you not know? Or does it depend > on the phase of the moon? > > It is (pi), since it is modulo (pi). How much of a difference that makes > for the overall arithmetic is unclear. > > Oh, now it is mod pi. Let's see: > pi^2 = pi > pi^2 - pi = 0 > pi.(pi - 1) = 0 > is that right? If so there are zerodivisors in your arithmetic other than > 0 and 1. And furthermore, we cannot divide by pi, nor by (pi - 1). > Sorry, the mod 180 does not work. What I am doing is figuring out what the multiplication should be according to Riemannian geometry, not to what someone likes to see a system of numbers. By the way, Dik, I am puzzled by one of your statements. Perhaps it was a flippant statement, or perhaps there is some depth to it. You said words to the effect ...if not closed (to addition or multiplication) it is not an arithmetic Now I know, Dik that we are battling about Field and Ring properties of commutative or closed or identities etc. But I was never aware of another *test* as to being an arithmetic. So is there two tests, test of arithmetic and then test of algebra. So let me ask you a question. What is an arithmetic as compared to a Galois Group or Field or Ring? > But further on this, I find: > (4.pi - 1)(4.pi - 3) = 16.pi^2 - 16.pi + 3 = 3 > and so 3 is not prime in the AP-adics. > > (pi-2) is ....999998 so what is ....999998(pi), well it is pi since it > is even and > modulo > > Combined with your statement here, I find > (pi - 1) = ...9999999 > so we have > ...9999999 * pi = 0 > is that right? > > And so, we can not divide by ...9999999. > > On the other hand, you have also stated that (pi - 2) does not exist (see > below). So, what is it? > > (pi - 2) is a subtraction and not a number. There are no negative > numbers in the Elliptic AP-adics. That number is ....9999998 > > But you have stated (when I used (pi - 2)) that it did not exist. So > what is it? > > So that pi.pi-2 is ....99998pi which is pi > > pi + pi.(pi - 2) = pi + pi^2 - 2.pi = pi + pi - 2.pi = 0. > > Right? And so pi + pi = 0. And from that 2.pi = 0, and so also 2 is a > zero-divisor in your system, and you should not divide by it. > > I have subtraction of the Hemisphere of 1 to 999....999999 and it is > not closed to addition > or subtraction for many of those answers fall into the other > Hemisphere of the imaginaries from > (pi) to 2(pi). > > But 2.pi = 0. See above for a proof. > > But apparently it is not closed to addition, so there is no arithmetic. > > Show me an example of it not closed, for all additions are points that > land on either the 1 to 999...9999 hemisphere or land in the imaginary > hemisphere. > > Because you have not completely specified arithmetic this is a problem. > But on what hemisphere is 0? 0 is the same point as 2(pi) and this point is imaginary. The numbers 1 to 999...9999 are on one hemisphere and the other hemisphere is imaginaries from (pi) the South Pole to 2(pi) the North Pole. So there are more imaginaries than there are numbers (in fact two more points than the other hemisphere.) > > So there is no (pi - 2). > > > There are no negative numbers, and only subtraction when you > see a minus sign. > > But why did you write that (pi - 2) does not exist? There is no relation > at all with negative numbers, there is only subtraction involved. I appreciate your questions Dik, but the fact is that I am uncertain and unclear as to all the operations. I am not sure of the interpretation of multiplication, whether it is a triangle of spin or rotation. So that when we have (pi) X (pi) we have a triangle of rotation. Or when we multiply ....00002 X ....999999 what triangle. In Euclidean geometry we know multiplication in grade school as 2 X 9 is a rectangle with sides 2 by 9 and answer of 18 square units. But what is multiplication on a sphere. So I am not doing this math to contrive a contrite system that is neat and shiny. But I am digging into this to find out what Riemannian geometry fixes multiplication. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: Re: #233 points on sphere are defined not by algebra but by geometry; Nntp-Posting-Host: hera.cwi.nl ... > It is (pi), since it is modulo (pi). How much of a difference that makes > for the overall arithmetic is unclear. > > Oh, now it is mod pi. Let's see: > pi^2 = pi > pi^2 - pi = 0 > pi.(pi - 1) = 0 > is that right? If so there are zerodivisors in your arithmetic other than > 0 and 1. And furthermore, we cannot divide by pi, nor by (pi - 1). > > Sorry, the mod 180 does not work. What I am doing is figuring out what > the multiplication should be according to Riemannian geometry, not to > what someone likes to see a system of numbers. So when you asked me some time ago to look at it because you had completely defined the arithmetic you were lying? > By the way, Dik, I am puzzled by one of your statements. Perhaps it was > a flippant statement, or perhaps there is some depth to it. You said > words to the effect ...if not closed (to addition or multiplication) > it is not an arithmetic I would state that for some operations to be called an arithmetic you should have two operators such that the system is closed to those two operators. > Now I know, Dik that we are battling about Field and Ring properties > of commutative or closed or identities etc. But I was never aware of > another *test* as to being an arithmetic. So is there two tests, test > of arithmetic and then test of algebra. For a field and ring it is a requirement that the system is closed under addition and multiplication. So it is not another test, it is part of the requirement for being a ring or field. > So let me ask you a question. What is an arithmetic as compared to a > Galois Group or Field or Ring? A group is only a group if it is closed under the operation considered. A field is only a field if it is closed under the operations considered. A ring is only a field if it is closed under the operations considered. All extremely basic mathematics. > But further on this, I find: > (4.pi - 1)(4.pi - 3) = 16.pi^2 - 16.pi + 3 = 3 > and so 3 is not prime in the AP-adics. No comment on this? > Because you have not completely specified arithmetic this is a problem. > But on what hemisphere is 0? > > 0 is the same point as 2(pi) and this point is imaginary. The numbers 1 > to 999...9999 are on one hemisphere and the other hemisphere is > imaginaries from (pi) the South Pole to 2(pi) the North Pole. So there > are more imaginaries than there are numbers (in fact two more points > than the other hemisphere.) > But why did you write that (pi - 2) does not exist? There is no relation > at all with negative numbers, there is only subtraction involved. > > I appreciate your questions Dik, but the fact is that I am uncertain and > unclear as to all the operations. > In Euclidean geometry > we know multiplication in grade school as 2 X 9 is a rectangle with > sides 2 by 9 and answer of 18 square units. But what is multiplication > on a sphere. In geometry you do not multiply lines together, but you multiply lengths. Quite something different. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: #235 Multiplication on AP-adics is Conservation of Angular Momentum; new textbook: Mathematical Physics (AP-adics primer) for age 6 years onward <4729521A.8000401@hotmail.com> It is (pi), since it is modulo (pi). How much of a difference that makes > for the overall arithmetic is unclear. Oh, now it is mod pi. Let's see: > pi^2 = pi > pi^2 - pi = 0 > pi.(pi - 1) = 0 > is that right? If so there are zerodivisors in your arithmetic other than > 0 and 1. And furthermore, we cannot divide by pi, nor by (pi - 1). Sorry, the mod 180 does not work. What I am doing is figuring out what > the multiplication should be according to Riemannian geometry, not to > what someone likes to see a system of numbers. So when you asked me some time ago to look at it because you had completely > defined the arithmetic you were lying? By the way, Dik, I am puzzled by one of your statements. Perhaps it was > a flippant statement, or perhaps there is some depth to it. You said > words to the effect ...if not closed (to addition or multiplication) > it is not an arithmetic I would state that for some operations to be called an arithmetic you > should have two operators such that the system is closed to those two > operators. Now I know, Dik that we are battling about Field and Ring properties > of commutative or closed or identities etc. But I was never aware of > another *test* as to being an arithmetic. So is there two tests, test > of arithmetic and then test of algebra. For a field and ring it is a requirement that the system is closed under > addition and multiplication. So it is not another test, it is part of > the requirement for being a ring or field. So let me ask you a question. What is an arithmetic as compared to a > Galois Group or Field or Ring? A group is only a group if it is closed under the operation considered. > A field is only a field if it is closed under the operations considered. > A ring is only a field if it is closed under the operations considered. > All extremely basic mathematics. But further on this, I find: > (4.pi - 1)(4.pi - 3) = 16.pi^2 - 16.pi + 3 = 3 > and so 3 is not prime in the AP-adics. No comment on this? Because you have not completely specified arithmetic this is a problem. > But on what hemisphere is 0? 0 is the same point as 2(pi) and this point is imaginary. The numbers 1 > to 999...9999 are on one hemisphere and the other hemisphere is > imaginaries from (pi) the South Pole to 2(pi) the North Pole. So there > are more imaginaries than there are numbers (in fact two more points > than the other hemisphere.) But why did you write that (pi - 2) does not exist? There is no relation > at all with negative numbers, there is only subtraction involved. I appreciate your questions Dik, but the fact is that I am uncertain and > unclear as to all the operations. > In Euclidean geometry > we know multiplication in grade school as 2 X 9 is a rectangle with > sides 2 by 9 and answer of 18 square units. But what is multiplication > on a sphere. In geometry you do not multiply lines together, but you multiply lengths. > Quite something different. > -- > dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 > home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ If excitement is lying then I am guilty of that. I am closer to solving what is Multiplication on Elliptic Geometry and it is Conservation of Angular Momentum. Multiplication in Euclidean geometry multiplication is Conservation of Energy. Let me show by example for AP-adics: .....9999 x ...0001 = ....999999 .....9999 x ....0002 = 1999.....99998 .....99999 x 3 = 2999....999997 .....99999 x 4 = 3999....999996 .....99999 x 5 = 4999.....999995 .....99999 x 6 = 599999....99994 .....9999 x 7 = 69999.....99993 ....99999 x 8 = 799999.....99992 ....99999 x 9 = 89999.....999991 ....99999 x ....0000010 = .....999990 ....99999 x .....00000011 = 109......89 ....33333 x ....00003 = ....999999 500....00000 x 5000....0000 = 2500...0000 ....6666 x ....00003 = 1999....9999998 Those are enough of a sampling to see how the Conservation of Angular Momentum is contained within those multiplications. First it is obvious that multiplication is closed since the product is confined to within 1 to ....99999. Visualize the globe and using longitude and latitude. The number 1 is on the same longitude line so we cannot form a triangle, but from 2 onwards a triangle is formed. In the case of ....9999 x 2 we have the longitude line going from North Pole to one unit short of South Pole and for latitude of 2 we have two units arclength going west (eastern hemisphere is imaginaries (pi to 2pi)) This forms a triangle whose legs are .... 9999 and ...00002 Construct triangles of all the other multiplications above listed. What is remarkable is that the arc-area of these triangles becomes a constant approaching the value of ....333333 X 3 As we can see in the triangle 5000....0000 X 50000....0000 = 2500....00000 So that Euclidean Geometry is conservation of Energy since multiplication there forms rectangles but here on the sphere Model of both Elliptic and Hyperbolic Geometry, multiplication becomes triangles that is the Conservation of Angular Momentum. Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: Re: #230 in fact a circle does not even obey associativity or commutative; ... > The distributive, associative and commutative laws do *not* depend > on the objects you are using, but do depend on the arithmetic you > define. > > The literature is quite huge on the NonCommutativity of the sphere > points where a Google search of noncommutative sphere has more than > 290,000 hits such as these: > > Yes, and they all are non-commutative due to the arithmetic defined on > them. > > When I type in Riemannian Geometry Commutatitive sphere there are > 214,000 hits Yes, and they are all commutative due to the arithmetic defined on them. But here you see that the sphere can be commutative or non-commutative, negating what you said. You can define on the circle and the sphere arithmetics that *are* commutative, associative and distributive. I gave you one for the circle, but you fail to understand it. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: #232 in fact a circle does not even obey associativity or commutative; > ... > The distributive, associative and commutative laws do *not* depend > on the objects you are using, but do depend on the arithmetic you > define. > > The literature is quite huge on the NonCommutativity of the sphere > points where a Google search of noncommutative sphere has more than > 290,000 hits such as these: > > Yes, and they all are non-commutative due to the arithmetic defined on > them. > > When I type in Riemannian Geometry Commutatitive sphere there are > 214,000 hits > > Yes, and they are all commutative due to the arithmetic defined on them. > > But here you see that the sphere can be commutative or non-commutative, > negating what you said. You can define on the circle and the sphere > arithmetics that *are* commutative, associative and distributive. I > gave you one for the circle, but you fail to understand it. JSTOR: Random Walk on a Sphere and on a Riemannian Manifold I only shake my head, Dik, when in the very first hit from University Leeds about a spherical manifold that commutativity does **not hold in general**. Is it that you cannot accept the fact that you are wrong? Archimedes Plutonium www.iw.net/~a_plutonium whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies === Subject: Re: #232 in fact a circle does not even obey associativity or commutative; Nntp-Posting-Host: hera.cwi.nl > ... > The distributive, associative and commutative laws do *not* depend > on the objects you are using, but do depend on the arithmetic you > define. > > The literature is quite huge on the NonCommutativity of the sphere > points where a Google search of noncommutative sphere has more than > 290,000 hits such as these: > > Yes, and they all are non-commutative due to the arithmetic defined on > them. > > When I type in Riemannian Geometry Commutatitive sphere there are > 214,000 hits > > Yes, and they are all commutative due to the arithmetic defined on them. > > But here you see that the sphere can be commutative or non-commutative, > negating what you said. You can define on the circle and the sphere > arithmetics that *are* commutative, associative and distributive. I > gave you one for the circle, but you fail to understand it. > > JSTOR: Random Walk on a Sphere and on a Riemannian Manifold > > I only shake my head, Dik, when in the very first hit from University > Leeds about a spherical manifold that commutativity does **not hold in > general**. Is it that you cannot accept the fact that you are wrong? Yes, so what? In many cases when you define some arithmetic it is not commutative. For other cases when you define another arithmetic it *is* commutative. Can't you accept the fact that you are wrong? -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ === Subject: AIMS can't calculate kids' math prowess http://www.tucsoncitizen.com/daily/opinion/67337.php Published: 10.31.2007 Stanton: AIMS can't calculate kids' math prowess BILLIE STANTON, Tucson Citizen Kudos to students in 111 Arizona schools, including 15 in Pima County, who have improved their math scores on our state test. And a nod to the Rodel Charitable Foundation of Arizona, which has been providing these low-income schools with its MAC-Ro program to rev up math learning. But while higher achievement on AIMS (Arizona's Instrument to Measure Standards) is a terrific accomplishment, the true test will be how these children fare with math years from now. A child needs more than the ability to give correct answers on AIMS; she needs to understand the concept behind that math. Noted intellectual Sheila Tobias, Tucson author of Overcoming Math Anxiety and many other books, says today's students get a process that focuses on memorization, testing for short-term recall and extrinsic rewards. What we have to inculcate, Tobias says, is the intrinsic curiosity and satisfaction and learning of concepts that will motivate them to stick with math when math gets really hard. The rise in test scores may or may not be meaningful, says Alan H. Schoenfeld, education professor at the University of California at Berkeley. In many cases, scores on a state test went up, but scores on other tests, such as the National Assessment of Educational Progress, did not. The kids were able to do precisely what they were drilled on, Schoenfeld says, but there was no transfer and no greater understanding of core mathematical concepts than before. Student understanding of mathematics appears to be shallow, indeed, according to a survey of students graduating from New York high schools. There were three effects they were absolutely sure of, says Florence D. Fasanelli, mathematician in residence at the American Association for the Advancement of Science If you see a decimal point, move it. If you see a sign, change it. And if you see a fraction, invert it, Fasanelli laments. But such misconceptions begin long before high school. Kids should understand that the equal sign (=) means quantities flanking that sign are the same. Most U.S. kids are taught that it means 'the answer goes here,' says Phil Daro, a mathematics educator at the University of California, senior fellow in mathematics at America's Choice and site director of SERP in San Francisco. In kindergarten through third grade, few children are exposed to the number line - which shows numerical progression: -2 -1 0 1 2 3 4 5 and so on. Spending time to deepen conceptual understanding of numbers using the number line might not improve K-3 performance compared to practicing subtraction problems, Daro says, but it will pay off in improved fourth-grade performance. So how can schools infuse a deep understanding of mathematical concepts in their students? Train the teachers, Fasanelli says. A typical elementary school teacher will not have had more than two years of math in high school, she says. Then they get a course in how to teach it. And that's it. That's all they know. Veteran teachers must be given an opportunity to gain a deeper knowledge of content. Mathematics is not just a series of steps; there's some underlying logic to it. A teacher with a strong grasp of mathematical concepts can impart that information more easily to the child. The future depends on these children, Fasanelli says, particularly children from underrepresented groups because there are so many of them. We have to do it right. Tobias says, Somewhere between here and college, they're going to have to develop an intrinsic interest and satisfaction in learning mathematics. Whether MAC-Ro will have lasting effects is uncertain. It is important to follow the students in the program and see how they benefit in higher grades before proclaiming victory, Daro says. If they persist in standing above the crowd, terrific. Fred Stevenson, mathematics professor at the University of Arizona, echoes that sentiment. If Rodel and institutions like Rodel can fund these kinds of ventures for generations and even lifetimes, rather than for the short intervals of time that administrators and legislators serve, then our country can become what our leaders claim they want it to be - a truly mathematically literate country, Stevenson says. Billie Stanton may be reached at bstanton@tucsoncitizen.com and 573-4664. 8 Comments on this Story Noted intellectual Sheila Tobias... Oh, please. Her inane theories on math anxiety have stifled progress on teaching mathematics. Elementary teachers have only had two years of high school math. Add to that, they have only had one college math course; Math for Elementary Teachers. Most of them could not pass College Algebra and many are Math(s) flunkees. That is why they were elementary ed majors to begin with. My experience with people educated using modern techniques has been far from great. I have had employees with Masters degrees that had a difficult time in writing a comprehensive paragraph not to mention that they could not spell. I have had college graduate employees with business degrees that could not even balance their own check books. It wasn't that these people were stupid, far from it, they just had not gotten the idea of practical applications for what they learned. At least testing these students to a standard gives a flicker of an idea of what they have ahead. Rating: 3 Thumbs Up Perhaps an annual AIMS type test for teachers, with mandated remedial education courses for those not achieving acceptable grades would be a step in the right direction. Just a thought,as statistics seem to indicate the national public education system, but particularly in ARIZONA, is deplorable. 5. Comment by shane l. (maranaman) - October 31,2007 @ 12:34PM Rating: 3 Thumbs Up I am sick and tired of always blaming the teachers. My children's education is my responsibility and I appreciate the teachers ASSISTING me. The education system is fine; it is the parents that are deplorable. I know exactly what subjects my children are learning in school and I go over the subjects with them. I assist the mathematic lessons by showing them what a number line is. I make sure all their homework is finished. I make sure they understand the concepts of the lessons. If your children are not learning, look in the mirror. Place the blame where it belongs. 6. Comment by Hugh M. (shuggie) - October 31,2007 @ 1:01PM Rating: 1 Thumb Down If we're talking about numeracy, fine, but school mathematics has little to do with real mathematics, and lack of success with it at school proves very little. The subject bored me stiff at school, but I graduated in it at university and I now pursue it as a hobby. The penny drops eventually or it doesn't. I had a lecturer with a doctorate in math who asked us not to submit the arithmetical bits, since neither we nor would get any better at that particular branch of the subject. True. 7. Comment by Dabil G. (Red Star) - October 31,2007 @ 4:00PM Rating: 1 Thumb Up If the student hasn't learned, the teacher hasn't taught. 8. Comment by J Z. (#4898) - October 31,2007 @ 4:26PM Rating: 1 Thumb Up ... and the parent hasn't cared. === === Subject: Math skills lag for LCC freshmen Math skills lag for LCC freshmen By Carrie Pederson / The Daily News Oct 29, 2007 Most of the students who enroll at Lower Columbia College aren't ready for college's lowest-level math courses. Ninety-three percent of first-year LCC students are required to enroll in a pre-college-level math course, and 89 percent of them are straight out of high school. LCC and high school educators are now trying to figure out how to deal with the problem. LCC offers seven courses below College Algebra, the school's lowest- level college math class. First-year student Anna Owen, who graduated from Kelso High School last year, is taking a pre-college course from Tim Trinkle, an adjunct professor. I wish that I had placed in a higher class, that way it wouldn't take as long, she said. Some students have to take four classes to get to the college level, LCC math professor Rick Swee said. A lot of students place in Math 092 (Elementary Algebra), said Janelle Runyon, spokeswoman for LCC. That class is four levels below College Algebra. To complete many of the college's programs, students need to be at the college level, said Dawn Draus, faculty chair of the math department at LCC. For transfer programs, as well as programs in nursing, business technology, early childhood education and welding, College Algebra is not necessarily required, she said. There are more math-intensive programs-- engineering and some science and computer-related programs that require about six college-level math classes, Swee said. Some students think that the college's placement test doesn't accurately reflect their skills. The test is way harder than (Trinkle's) class, but I can't go further without placing higher, said Samantha Petrich, a first-year student who graduated from W.F. West in Chehalis last year. Students don't get to go around the test very often, Swee said. In some cases, they may convince a counselor they can work at the top of their ability in math, he said. Students used to be able to sign up with whatever they want, that created havoc, he said. They would fail the class, retake it and fail again. To tackle the problem of getting students to pass the test and advance in math more quickly at LCC, local math educators went to a conference in Leavenworth last summer called the Transitions Math Project. The project, about two years old, was started through the State Board of Community and Technical Colleges to address the fact that, statewide, 46 percent of first-year community college students just out of high school were below the college math level. Teachers from Kelso, Mark Morris, R.A. Long, Kalama and Castle Rock compared their math courses with the LCC's pre-college course work by looking at a map of the college's curriculum. We say these are our expectations, if you hope students are placed in college algebra, Swee said. I found out about some things kids are being tested on for placement, said Wayne Heuett, math teacher at Castle Rock. I thought we were covering everything, but it turns out we didn't match up on all the curriculum. Some of the stuff the we are teaching in pre-calculus we could teach in algebra two, and vice-versa, he said. Castle Rock's traditional math curriculum, which teaches algebra, geometry and calculus sequentially, more closely aligns with LCC, Swee said. Some local schools use the integrated system which hits equations in a different order, he explained. The group continues to expand its mapping project-- Woodland, Toutle Lake, Clatskanie, Wahkiakum and Rainier high schools have been invited to join. The idea is to get lots of schools to aim for a more universal seamless transfer, Swee said, but any time you get this many institutions and people trying to pull in one direction it's a logistic nightmare. With much to consider, plans are in the infancy stage, Heuett said, though he's learning through the process. I'm learning more now than in 10 years of teaching what's happening around me, he said. It's been a fun opportunity to re-access what I'm doing. In the meantime, students like Aurelia Bell appreciate the chance to strengthen math skills through Trinkle's class and LCC's pre-college program. Math is easier here, said the Castle Rock graduate. The environment is better, it's less rushed to learn. User Comments: Just Opt Out This is a problem in every single college and university in this state. It's called FUZZY math, supported and mandated by the Office of the Superintendent of Public Instruction (OSPI). This reform math does not prepare students for college. WASL rules our educational world, and this is a sad result of teaching our kids new math that meets the standards the state has set. Our state is in the process of revising the math standards, but they have hired The Dana Center in Texas to do this monumental task...the Dana Center is widely known for screwing up Texas math education and they loudly promote this new reform math...the same math that is getting us into trouble. There is not ONE person on the revision committee that is against this math, which is troubling. Contact your legislature and tell them you've had enough. If anyone reading this has had difficulties helping your elementary student with math homework, you know firsthand what I'm speaking of. The WASL must go. I encourage ALL parents to opt your children out of this test. Elementary and middle school students aren't required to pass this nutty test, so there is NOTHING to lose by opting out. It does not effect grades or placement in classes, or promotion to the next grade. There are many other measuring tools our schools use to judge your child's progress. If we, as parents, don't finally take a stand...things will get much worse. Write a letter to your child's principal politely requesting your child not participate in the WASL. If enough parents do this, the state will be forced to listen. Taking pre-college level math courses in college may be nice for those students we've failed in public school, but having our kids prepared in the first place would be a much better path. === Subject: Math GRE subject test practice questions v2 Last night I asked a couple of questions about the Math GRE and people for your help with any suggestions you may have. This is another set of questions of the type I've seen often and think are worthwhile covering. Any help is appreciated. I If A and B are events in a probability space such that 0 < P(A) = P(B) = P(A intersect B) < 1, which of the following cannot be true? ans a) A and B are independent b) A is a proper subset of B c) A != B d) A intersect B = A union B e) P(A)P(B) < P(A intersect B) I thought the answer would be C since P(A) = P(B) = P(A intersect B)... II This type of question is very very common If x, y and z are selected independently and at random from the interval [0,1], then probability that x >= yz is ans a) 3/4 b) 2/3 c) 1/2 d) 1/3 e) 1/4 Intuitively I know that yz is most likely smaller than x but I cannot go beyond saying that the answer is over 1/2. III Another very common type If x is a real number and P is a polynomial, then lim h->0 [P(x + 3h) + P(x - 3h) - 2P(x)]/h^2 = a) 0 b) 6P'(x) c) 3P''(x) ans d) 9P''(x) e) infinity I saw another problem where they asked the same except the limit was lim h->0 [P(x+h) - P(x-h)]/h and I intuitively answered correctly, that the answer was 2P'(x). What is the procedure for this type of question? IV Consider the sytem of equations ax^2 + by^3 = c dx^2 + ey^3 = f Where a, b, c, d, e and f are real constants and ae != bd. The maximum possible number of real solutions (x,y) of the system is a) none b) one ans c) two d) three e) five I thought a system of equations would have only 0, 1 or infinitely many solutions... === Subject: Re: Math GRE subject test practice questions v2 > Last night I asked a couple of questions about the Math GRE and people > for your help with any suggestions you may have. This is another set of questions of the type I've seen often and think > are worthwhile covering. Any help is appreciated. I > If A and B are events in a probability space such that 0 < P(A) = P(B) > = P(A intersect B) < 1, which of the following cannot be true? ans a) A and B are independent > b) A is a proper subset of B > c) A != B > d) A intersect B = A union B > e) P(A)P(B) < P(A intersect B) I thought the answer would be C since P(A) = P(B) = P(A intersect > B)... If A and B are independent then P(A)P(B) = P(A n B) (I think that this is the definition of independence), which cannot be true since P(B) is less than 1 so P(A)P(B) < P(A) = P(A n B). Examples may be used to show that the others are possible: if we take the probability space to be the unit interval with uniform probability then letting A = [0,1/2) and B = [0,1/2] (i.e. B includes the point 1/2 whereas A does not) then both b) and c) hold. Any example with A = B satisfies d). e) is necessarily true since P(A)P(B) < P(A) = P(A n B) for the reason given above. II This type of question is very very common > If x, y and z are selected independently and at random from the > interval [0,1], then probability that x >= yz is ans a) 3/4 > b) 2/3 > c) 1/2 > d) 1/3 > e) 1/4 Intuitively I know that yz is most likely smaller than x but I cannot > go beyond saying that the answer is over 1/2. There might be a better way of doing this but one way is to think in terms of volume: the probability is equal to the volume of the region in [0,1]^3 with x > yz. This can be calculated by a triple integral (with integrand 1) with appropriate limits: let y and z vary from 0 to 1 and x vary from yz to 1. Integrating wrt x gives 1-yz, integrating this wrt y gives 1-z/2, integrating this wrt z gives 1 - 1/4 = 3/4. III Another very common type > If x is a real number and P is a polynomial, then lim h->0 [P(x + 3h) > + P(x - 3h) - 2P(x)]/h^2 = a) 0 > b) 6P'(x) > c) 3P''(x) > ans d) 9P''(x) > e) infinity I saw another problem where they asked the same except the limit was > lim h->0 [P(x+h) - P(x-h)]/h and I intuitively answered correctly, > that the answer was 2P'(x). What is the procedure for this type of > question? Firstly I would define j = 3h so that the limit is now written lim j- >0 9[P(x + j) + P(x - j) - 2 P(x)]/j^2. Then note that the quantity in whose limit we are interested can be written 9{[(P(x + j) - P(x))/j - (P(x) - P(x-j)/j)]/j} so intuitively (P(x + j) - P(x))/j is close to the derivative of P at x for small j, and (P(x) - P(x-j)/j) is the same thing with values of x shifted by -j, so the whole expression behaves like the difference of two derivatives evaluated at x values differing by j, divided by j, i.e. the second derivative. This is far from being rigorous but hopefully is convincing enough to make one confident that d) is the right answer. IV > Consider the sytem of equations ax^2 + by^3 = c > dx^2 + ey^3 = f Where a, b, c, d, e and f are real constants and ae != bd. The > maximum possible number of real solutions (x,y) of the system is a) none > b) one > ans c) two > d) three > e) five I thought a system of equations would have only 0, 1 or infinitely > many solutions... It helps to think of this as a matrix problem - I shall attempt some ascii art: / a b / u / c | | | | = | | d e / v / f / The fact that ae != bd means that the determinant of the matrix is non- zero, so it is invertible. Therefore there is a unique pair of numbers u,v which satisfy the above equation. We want real x and y such that x^2 = u, y^3 = v. Any number has a unique real cube root, so y is uniquely determined. If u is negative then no x will work, if it is zero then x = 0, and if it is positive then it has two square roots. So the maximum number of solutions is two. === Subject: Re: Math GRE subject test practice questions v2 > If x is a real number and P is a polynomial, > then lim h->0 [P(x + 3h) + P(x - 3h) - 2P(x)]/h^2 = > a) 0 > b) 6P'(x) > c) 3P''(x) > ans d) 9P''(x) > e) infinity > Firstly I would define j = 3h so that the limit is now written lim j->0 > 9[P(x + j) + P(x - j) - 2 P(x)]/j^2. Then note that the quantity in > whose limit we are interested can be written 9{[(P(x + j) - P(x))/j - > (P(x) - P(x-j)/j)]/j} so intuitively (P(x + j) - P(x))/j is close to > the derivative of P at x for small j, and (P(x) - P(x-j)/j) is the > same thing with values of x shifted by -j, so the whole expression > behaves like the difference of two derivatives evaluated at x values > differing by j, divided by j, i.e. the second derivative. This is far > from being rigorous but hopefully is convincing enough to make one > confident that d) is the right answer. SIMPLER Suffices to consider P(x) = x^2 > Consider the sytem of equations > ax^2 + by^3 = c > dx^2 + ey^3 = f > Where a, b, c, d, e and f are real constants and ae != bd. The > maximum possible number of real solutions (x,y) of the system is > a) none > b) one > ans c) two > d) three > e) five > > It helps to think of this as a matrix problem - I shall attempt some > ascii art: > > / a b / u / c > | | | | = | | > d e / v / f / > > The fact that ae != bd means that the determinant of the matrix is non- > zero, so it is invertible. Therefore there is a unique pair of numbers > u,v which satisfy the above equation. We want real x and y such that > x^2 = u, y^3 = v. Any number has a unique real cube root, so y is > uniquely determined. If u is negative then no x will work, if it is > zero then x = 0, and if it is positive then it has two square roots. > So the maximum number of solutions is two. SIMPLER (x^2,y^3) is the intersection of 2 non-parallel lines in R^2. --Bill Dubuque === Subject: Re: Free Spatial Dynamic Geometry Software: Calques3D examples from your website so that they can be opened in Calcques? > The application Calques 3D, developed by Professor Nicolas van > Labeke, is a dynamic spatial geometry software for free (you can use > it and distribute it to your students without paying anything for it). Http://www.calques3d.org As their two-dimensional cousins (Cabri, Ruler and Compass and > GeoGebra), Calques3D allows the construction of points, segments, > straight lines, planes, polygons, spheres, cubes and cylinders in > space. Advanced features include loci in space, a window of algebra > (for coordinates of points, equations of lines and planes) and a > renderer in OpenGL. > === Subject: calculous in the curve space theorem 3 Cao's theorem 3 can conclude follow theorem 1, Á§sin dx=dx Á.88 Áñsin dx dx=Áñdxdx=1 2, Á§ edx-1=dx Á.88 Áñ(edx-1)dx=Á[CapitalOGrave ]dxdx=1 3, Á§ ln(1+dx)=dx Á.88 Áñln(1+dx)dx=Á[CapitalOGrav e]dxdx=1 4, Á§ (1+dx)^¤.84-1=¤.84dx Á.88 Áñ[(1+dx)^¤.84-1]dx=[D ownExclamation]ñ¤.84dxdx=¤[Cap italNTilde]Áñdxdx=¤.84 These all can show even if a very tiny digital such as dx in the integral formula, we cann't deal it with 0 and then calculate them again, that is incorrect. Because even if a very tiny digital such as dxÁ.9c0 , as after we calculate the integral formula , it is a number that cann't be ignored. The 4 can explain it throughly. caoyan 2007-10-31 http://thre-firewh2.home.sunbo.net/index.php?xname=AB6BP01 === Subject: Re: number sequence > , > > I am recreationally trying to figure out this sequence, but cannot. > Would someone please complete this for me and explain: > 1,9,25,__,81,100 > a) 36 > b) 45 > c) 56 > d) 64 > > 42 > > > You are welcome. > Why 42? It is not one of the answers? Does anyone have a serious answer? === Subject: Re: number sequence , > I am recreationally trying to figure out this sequence, but cannot. > Would someone please complete this for me and explain: > 1,9,25,__,81,100 > a) 36 > b) 45 > c) 56 > d) 64 42 > You are welcome. Why 42? It's the answer to the question of Life, the Universe and Everything. > It is not one of the answers? That's a joke, son. > Does anyone have a serious answer? 64 The first 3 are squares of consective odd integers (1**2, 3**2, 5**2), but the last two are just squares of consecutive integers (9**2, 10**2). But, by symmetry, there must be three consecutive integers squared. Thus, the number that precedes 9**2 must be 8**2 or 64. === Subject: Re: number sequence > , > I am recreationally trying to figure out this sequence, but cannot. > Would someone please complete this for me and explain: > 1,9,25,__,81,100 > a) 36 > b) 45 > c) 56 > d) 64 > 42 > You are welcome. > Why 42? > > It's the answer to the question of Life, > the Universe and Everything. > > It is not one of the answers? > > That's a joke, son. Not a joke fella, In order to describe an integer sequence it must be able to be written in formula notation: x + (x+2)^2 + ((x+2)^2)^2 .... or some such, i'm still working on this and i think it has to do with primes. Imploring help from the > > Does anyone have a serious answer? > > 64 > > The first 3 are squares of consective > odd integers (1**2, 3**2, 5**2), but > the last two are just squares of > consecutive integers (9**2, 10**2). > > But, by symmetry, there must be three > consecutive integers squared. Thus, the > number that precedes 9**2 must be 8**2 > or 64. > > === Subject: Re: number sequence , > I am recreationally trying to figure out this sequence, but cannot. > Would someone please complete this for me and explain: > 1,9,25,__,81,100 > a) 36 > b) 45 > c) 56 > d) 64 > 42 > You are welcome. > Why 42? It's the answer to the question of Life, > the Universe and Everything. > It is not one of the answers? That's a joke, son. Not a joke fella, In order to describe an integer sequence it must be > able to be written in formula notation: x + (x+2)^2 + ((x+2)^2)^2 .... or some such, i'm still working on this > and i think it has to do with primes. Imploring help from the > Does anyone have a serious answer? unfortunately the question is a joke question and if you have a professor asking this question they are not very good teachers it really is that simple these questions are usually trying to test some kind of pattern recognition but this is not how recognition works recognition must be verified which means unknown properties must be predicted or the pattern refined this requires the ability to query more numbers in the sequence static problems like this don't allow that so there are always possibilities that cannot be ruled out in particular for these problems _all_ possibilities are never ruled out if this is an IQ test or equivalent then understand that this is one of the many reasons such tests are often scorned particularly in mathematical circles IQ tests have featured these and other fuzzy metaphor and analog questions for many years despite that such questions _grow_ more answers the more one knows don't take the answers negatively against you but joke answers are pretty tame compared to the screeds one _could_ post as a response -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- galathaea: prankster, fablist, magician, liar === Subject: Re: number sequence > , > I am recreationally trying to figure out this sequence, but cannot. > Would someone please complete this for me and explain: > 1,9,25,__,81,100 > a) 36 > b) 45 > c) 56 > d) 64 > 42 > You are welcome. > Why 42? > > It's the answer to the question of Life, > the Universe and Everything. > > It is not one of the answers? > > That's a joke, son. Not a joke fella, In order to describe an integer sequence it must be >able to be written in formula notation: x + (x+2)^2 + ((x+2)^2)^2 .... or some such, i'm still working on this >and i think it has to do with primes. Imploring help from the The problem has no definite answer. In fact, every one of the choices qualifies as a possible answer. And so would any other number (for example 42). In that sense, the problem is not well posed. To see one method to which can be used to build formulas, look up Lagrange Interpolation. As an experiment, evaluate each of the following functions for x = 1, 2, 3, 4, 5, 6. a(x) = 120 ( -151 x^5 + 2525 x^4 - 15695 x^3 + 45115 x^2 - 57714 x + 26040 ) b(x) = 120 ( -61 x^5 + 995 x^4 - 6065 x^3 + 17485 x^2 - 22074 x + 9840 ) c(x) = 120 ( 49 x^5 - 875 x^4 + 5705 x^3 - 16285 x^2 + 21486 x - 9960 ) d(x) = 40 ( 43 x^5 - 745 x^4 + 4755 x^3 - 13615 x^2 + 17722 x - 8120 ) After you've performed the above evaluations, it should then be clear that for the given multiple choice problem, none of the choices can be eliminated. quasi === Subject: Re: number sequence , > I am recreationally trying to figure out this sequence, but cannot. > Would someone please complete this for me and explain: > 1,9,25,__,81,100 > a) 36 > b) 45 > c) 56 > d) 64 > 42 > You are welcome. > Why 42? It's the answer to the question of Life, > the Universe and Everything. > It is not one of the answers? That's a joke, son. Not a joke fella, I'm not saying _your_ problem is a joke, I'm saying that 42 is used by flippant mathematians as a joke answer to any question. It comes from Douglas Adams' novels The Hitchhikers's Guide to the Galaxy, et al. The answer was given at the beginning as 42 and the novels are a pursuit to find what the original question was. When finally revealed to be: what do you get when you multiply 6 x 9, the hero realizes that a cock-up has occured somewhere along the way. > In order to describe an integer sequence it must be > able to be written in formula notation: x + (x+2)^2 + ((x+2)^2)^2 .... or some such, i'm still working on this > and i think it has to do with primes. Imploring help from the > Does anyone have a serious answer? 64 The first 3 are squares of consective > odd integers (1**2, 3**2, 5**2), but > the last two are just squares of > consecutive integers (9**2, 10**2). But, by symmetry, there must be three > consecutive integers squared. Thus, the > number that precedes 9**2 must be 8**2 > or 64. === Subject: Probability of elements from Gaussian/normal PDF overlapping? If elements, Ea, and Eb, are picked, respectively, from iid random processes, Ra and Rb, where Ra and Rb have a Gaussian/normal PDF with STD Sa and Sb, and medians Ma and Mb, with Ma >= Mb, what is the probability that Ea >= Eb? John -- John Conover, conover@email.rahul.net, http://www.johncon.com/ === Subject: Re: Probability of elements from Gaussian/normal PDF overlapping? > If elements, Ea, and Eb, are picked, respectively, from iid random > processes, Ra and Rb, where Ra and Rb have a Gaussian/normal PDF > with STD Sa and Sb, and medians Ma and Mb, with Ma >= Mb, what is > the probability that Ea >= Eb? iid means independently and identically distributed. If the means or variances differ then the distributions are not identical, and you should say just independent, not iid. === Subject: Re: Probability of elements from Gaussian/normal PDF overlapping? If we write Ra = N(Ma, Sa^2), Rb = N(Mb, Sb^2), is it useful to know that Ra - Rb is distributed like N(Ma - Mb, Sa^2 + Sb^2)? If we want to test that Ea >= Eb, then we are considering Ea - Eb >= 0. The z- score of 0 is: z = (0 - mean)/std = (Mb - Ma)/sqrt(Sa^2 + Sb^2). and the probability is 1 - Phi(z) where Phi(z) is the cumulative probability distribution. === Subject: Re: JSH: Why self-encryption? <873avtz9mr.fsf@phiwumbda.org> Obviously if I have an idea that takes off in the entertainment > industry then I would have a lot of power to shape how the world > looks at mathematicians, and you know a lot about what I'd say. > Right. Like that guy who invented CSS. He's super-powerful these > days and he's using his new found power to punish English literature > departments worldwide. > So if he can do it... So you compare inventing CSS to allowing people to copy their DVD's > without hassle? And were people getting sued over anything with CSS? Reminder to people who didn't read my lead post, my idea is that your > DVD burner would encrypt a copy you made of, say, the movie > Transformers, so only it could read it without a key. that makes it platform dependent, how could anyone do a wide distribution ? > A DVD that works on only one DVD burner ? > No. You'd buy the DVD from the store like you do now. And when you took it home you could copy it, freely. Easily. And you'd have no problems, as long as only you used it, but if you gave it away, no one else could use it as the copy was encrypted--to your equipment. Get it yet? Your response indicates you don't understand the idea. Say you want Transformers. You buy it from the store, legally. You take it home. You make a backup copy on, say, your computer. That copy works fine, and you know no difference. But if your buddy says, hey, I want a copy of Transformers and you say, no prob, and hand that copy to your buddy, he takes it home, puts it in his player and it doesn't work, as his player can't read your encrypted copy. If instead you give him your bought copy then he can use it. But you have to hand him the copy you bought from the store, not a copy you made. To handle networks of friends handing off copies, the full DMESE standard that I've created, would ask for the bought DVD after 30 days to be re-introduced to the drive, so your friend will need the bought one again in 30 days if you really, really, really want to help people make copies illegally. Get it yet? It amazes me how often people who pretend to be so smart on math newsgroups can't get even the simplest ideas. It is depressing. It's like, maybe dumb people like to post on math newsgroups like arsonists dream of becoming firefighters. James Harris === Subject: Re: JSH: Why self-encryption? Originator: richard@cogsci.ed.ac.uk (Richard Tobin) >Say you want Transformers. You buy it from the store, legally. You take it home. You make a backup copy on, say, your computer. That copy works fine, and you know no difference. But if your buddy says, hey, I want a copy of Transformers and you >say, no prob, and hand that copy to your buddy, he takes it home, puts >it in his player and it doesn't work, as his player can't read your >encrypted copy. If instead you give him your bought copy then he can use it. But you have to hand him the copy you bought from the store, not a >copy you made. To handle networks of friends handing off copies, the full DMESE >standard that I've created, would ask for the bought DVD after 30 days >to be re-introduced to the drive, so your friend will need the bought >one again in 30 days if you really, really, really want to help people >make copies illegally. How is your friends copy different from your backup? What use is your backup if you need the original to use it? -- Richard -- Consideration shall be given to the need for as many as 32 characters in some alphabets - X3.4, 1963. === Subject: Re: JSH: Why self-encryption? <873avtz9mr.fsf@phiwumbda.org> Obviously if I have an idea that takes off in the entertainment > industry then I would have a lot of power to shape how the world > looks at mathematicians, and you know a lot about what I'd say. > Right. Like that guy who invented CSS. He's super-powerful these > days and he's using his new found power to punish English literature > departments worldwide. > So if he can do it... So you compare inventing CSS to allowing people to copy their DVD's > without hassle? And were people getting sued over anything with CSS? Reminder to people who didn't read my lead post, my idea is that your > DVD burner would encrypt a copy you made of, say, the movie > Transformers, so only it could read it without a key. that makes it platform dependent, how could anyone do a wide distribution ? > A DVD that works on only one DVD burner ? No. You'd buy the DVD from the store like you do now. And when you > took it home you could copy it, freely. Easily. And you'd have no problems, as long as only you used it, but if you > gave it away, no one else could use it as the copy was encrypted--to > your equipment. Get it yet? Your response indicates you don't understand the idea. Say you want Transformers. You buy it from the store, legally. You take it home. You make a backup copy on, say, your computer. That copy works fine, and you know no difference. But if your buddy says, hey, I want a copy of Transformers and you > say, no prob, and hand that copy to your buddy, he takes it home, puts > it in his player and it doesn't work, as his player can't read your > encrypted copy. If instead you give him your bought copy then he can use it. But you have to hand him the copy you bought from the store, not a > copy you made. To handle networks of friends handing off copies, the full DMESE > standard that I've created, would ask for the bought DVD after 30 days > to be re-introduced to the drive, so your friend will need the bought > one again in 30 days if you really, really, really want to help people > make copies illegally. Get it yet? It amazes me how often people who pretend to be so smart on math > newsgroups can't get even the simplest ideas. It is depressing. It's like, maybe dumb people like to post on math > newsgroups like arsonists dream of becoming firefighters. James Harris Man, you *really* want that Transformers DVD don't you? Will it shut you up if I just buy you your own copy? === Subject: Re: JSH: Why self-encryption? <873avtz9mr.fsf@phiwumbda.org> [...] > Reminder to people who didn't read my lead post, my idea is that your > DVD burner would encrypt a copy you made of, say, the movie > Transformers, so only it could read it without a key. that makes it platform dependent, how could anyone do a wide distribution ? > A DVD that works on only one DVD burner ? No. You'd buy the DVD from the store like you do now. And when you > took it home you could copy it, freely. Easily. And you'd have no problems, as long as only you used it, but if you > gave it away, no one else could use it as the copy was encrypted--to > your equipment. Get it yet? Your response indicates you don't understand the idea. Say you want Transformers. You buy it from the store, legally. You take it home. You make a backup copy on, say, your computer. That copy works fine, and you know no difference. But if your buddy says, hey, I want a copy of Transformers and you > say, no prob, and hand that copy to your buddy, he takes it home, puts > it in his player and it doesn't work, as his player can't read your > encrypted copy. If instead you give him your bought copy then he can use it. But you have to hand him the copy you bought from the store, not a > copy you made. To handle networks of friends handing off copies, the full DMESE > standard that I've created, would ask for the bought DVD after 30 days > to be re-introduced to the drive, so your friend will need the bought > one again in 30 days if you really, really, really want to help people > make copies illegally. So ... the DVD player will refuse to play the copy, unless you have the original? What keeps one person, in a dorm say, from buying one DVD, passing it around so that people can copy it, and then keeping the DVD in a common library, so that they can get it back if they need it again? Piracy. A better solution would be the following: Create special DVDs which are the only ones which can have copyrighted media burned onto them, and then put a corrosive acid inside a flat container which is embedded in the DVD. After 30 days, the container breaks itself, and the DVD is corrupted beyond playability. Of course, you would have to recall any recordable media which is already out in society, but JSH's scheme requires as large of a leap of faith to work. > Get it yet? It amazes me how often people who pretend to be so smart on math > newsgroups can't get even the simplest ideas. It is depressing. It's like, maybe dumb people like to post on math > newsgroups like arsonists dream of becoming firefighters. Does JSH realize the irony of stating the last sentence in a post IN A MATH NEWSGROUP??? --- Christopher Heckman === Subject: Re: JSH: Why self-encryption? <873avtz9mr.fsf@phiwumbda.org > Obviously if I have an idea that takes off in the entertainment > industry then I would have a lot of power to shape how the world > looks at mathematicians, and you know a lot about what I'd say. Right. Like that guy who invented CSS. He's super-powerful these > days and he's using his new found power to punish English literature > departments worldwide. So if he can do it... So you compare inventing CSS to allowing people to copy their DVD's > without hassle? And were people getting sued over anything with CSS? Reminder to people who didn't read my lead post, my idea is that your > DVD burner would encrypt a copy you made of, say, the movie > Transformers, so only it could read it without a key. So you can't give away that copy to your friends, without a key, so > the movie industry can make more money. The idea works with CD's as well, so it could solve problems for the > music industry. That is problem solving at its finest--hated by the modern > mathematical community which fights to block ANY recognition of my > research because I know that it is hostile to knowledge while > pretending to be the opposite. So part of the point here is that the math community is not what most > people think it is, and it is hostile to new ideas and innovation. Mathematicians get away with it because, well, most people don't > really know or care what they are doing, so they escape serious and > critical scrutiny. But if I help the entertainment industry save millions of dollars then > people will listen when I say look closely. And I can explain to them how mathematicians lie, and how they clearly > know they are lying and do so with a sense of impunity because no one > has been there to focus attention on what they are doing. I will be that person, so that the world peers closely into the > details of what mathematicians around the world are actually doing > with me telling people they are lying, and how to see that they are > lying. And then those mathematicians won't teach students any more. James Harris I have a better idea, why not make a recorder that only copies the DVD 'Transformers' and nothing else? === Subject: Re: JSH: Why self-encryption? <873avtz9mr.fsf@phiwumbda.org But if I help the entertainment industry save millions of dollars then > people will listen when I say look closely. So why do you continue to try to pitch your idea here in sci.math? How come you aren't sharing your copy-protection plan with the folks in rec.video.dvd.tech or alt.video.dvd? Are you afraid that the reception you'd receive in those groups would be similar to the reception you received in, say, alt.fiction.original? You're scared that DMESE will be your next Mars Ascendant, aren't you? -- Before I'm done, the world will call you Magidin mathematicians, and your work will be Magidin work. The Magidin work of Magidin mathematicians must be questioned. The prizes that Magidin mathematicians give each other must be considered to possibly be specious. -- James Harris === Subject: Re: JSH: Why self-encryption? > Reminder to people who didn't read my lead post, my idea is that your > DVD burner would encrypt a copy you made of, say, the movie > Transformers, so only it could read it without a key. > > that makes it platform dependent, how could anyone do a wide distribution ? > A DVD that works on only one DVD burner ? I think he means a `DVD ripper', but the fact that he ignores any responses (except Jesse's) makes it difficult to tell. === Subject: Re: JSH: Why self-encryption? <873avtz9mr.fsf@phiwumbda.org> transformers that is 16 year old crap. Is that how young you are? More like 23. --- Christopher Heckman === Subject: Re: JSH: Why self-encryption? > Mathematicians get away with it because, well, most people don't > really know or care what they are doing, so they escape serious and > critical scrutiny. But if I help the entertainment industry save millions of dollars > then people will listen when I say look closely. > So who's stopping you? Quit your yapping like a little bitch and do > it. > > I dare you, no I *double-dare* ya. > > Bonus point question for those playing along at home: What excuse will > JSH use this time for not caring through with his genius idea? Blocked by the cynical mathematics cartel. -- Michael Press === Subject: JSH: Explaining DMESE, again I came up with a copy protection idea where if you buy a DVD, or a CD as it can work on that too, your copying equipment, like your CD burner would make an encrypted copy that only it could read. So you can't hand off the copy as it's encrypted--to your drive. That is why it is self-encryption. Enterprising people wanting to break the system and copy illegally could just hand off the CD or DVD they bought, to their friends so they could make their own encrypted copies, so I added that the system asks for the bought disk after 30 days. So you would need to give your friends the bought DVD or CD, again, after the system asks for it, later. Now then, some of you very poor people who can do nothing else, or you criminal types who will get something for free if you can no matter what, will laugh and say, no problem, you'll just have friends in line to get the DVD back again whenever, no matter how many hoops you have to jump through. But most people will just buy their own. That is DMESE--Digital Media Equipment Self-Encryption. It is about making it just annoying enough to make illegal copies that most people will not bother unless they are so poor they will go through the trouble, or unless they are so criminally minded they will jump through hoops to copy illegally. I have read replies to my posts that indicate that those of you willing to reply to me do NOT GET IT which amazes me because it means you are remarkably dumb. Because it is not that complicated!!! Now it is important on a math newsgroup because my issue with the math community is that it is full of fakes who know how to pretend to be smart when really that is ALL they know--pretending--and they do not really know mathematics, but get away with acting because society does not care to check. I know mathematicians act because I have the mathematical proofs that show it, as mathematicians continue to dodge them so I am going to the dramatic act of turning to industry to get leverage to embarrass mathematicians and bring serious scrutiny so that quite a few professors can be blocked from ever teaching students again. Now then, my idea I think is a good one, but the industry is actually supposed to be implementing some kind of standard for what they call managed copy at the end of the year. If by some remarkable miracle they implement something like my idea then I will use the attention generated to make mathematicians around the world very miserable. That is the story. You people need to show you have a modicum of intelligence and are not just totally dumb and understand the story. IF you cannot understand this story then you will make very dumb replies that show you have the intellect of a cow. Please try to sound at least quasi-intelligent in reply. James Harris === Subject: Re: JSH: Explaining DMESE, again > I came up with a copy protection idea where if you buy a DVD, or a CD > as it can work on that too, your copying equipment, like your CD > burner would make an encrypted copy that only it could read. So you can't hand off the copy as it's encrypted--to your drive. Which means that you can only use it in your computer, not in any other DVD player you might own. - William Hughes === Subject: Re: JSH: Explaining DMESE, again Now it is important on a math newsgroup because my issue with the math community is that it is full of fakes who know how to pretend to be smart when really that is ALL they know--pretending... You're not even good at _that_. Even when you pretend to be smart, you come off as the imbecil you really are. Stevie boy has a feeling of entitlement because someone once put him (obviously by mistake) in a high IQ program. He believe that that alone guarantess he is better than everyone. Get over it, loser. I know mathematicians act because I have the mathematical proofs that show it, as mathematicians continue to dodge them so I am going to the dramatic act of turning to industry to get leverage to embarrass mathematicians and bring serious scrutiny so that quite a few professors can be blocked from ever teaching students again. Good. Go for it. Like I told you, you would fit in in Fox news, with your standards. Why embarrass yourself only to the sci.math community, when you can make an idiot of yourself to the whole country!!!! === Subject: Re: JSH: Explaining DMESE, again > If by some remarkable miracle they implement something like my idea > then I will use the attention generated to make mathematicians > around the world very miserable. What if they use something like your idea, but don't mention your name? Then how will you get the needed attention? Will you sue the entertainment industry? On what grounds? -- Jesse F. Hughes I think the problem for some of you is that you think you are very comprehend and there is the problem. -- James S. Harris === Subject: Re: JSH: Explaining DMESE, again > IF you cannot understand this story then you will make very dumb > replies that show you have the intellect of a cow. > > Please try to sound at least quasi-intelligent in reply. Moo! Jose Carlos Santos === Subject: Re: JSH: Explaining DMESE, again > I came up with a copy protection idea where if you buy a DVD, or a CD > as it can work on that too, your copying equipment, like your CD > burner would make an encrypted copy that only it could read. So you can't hand off the copy as it's encrypted--to your drive. That is why it is self-encryption. Enterprising people wanting to break the system and copy illegally > could just hand off the CD or DVD they bought, to their friends so > they could make their own encrypted copies, so I added that the system > asks for the bought disk after 30 days. So you would need to give your friends the bought DVD or CD, again, > after the system asks for it, later. Now then, some of you very poor people who can do nothing else, or you > criminal types who will get something for free if you can no matter > what, will laugh and say, no problem, you'll just have friends in line > to get the DVD back again whenever, no matter how many hoops you have > to jump through. But most people will just buy their own. That is DMESE--Digital Media Equipment Self-Encryption. It is about making it just annoying enough to make illegal copies that > most people will not bother unless they are so poor they will go > through the trouble, or unless they are so criminally minded they will > jump through hoops to copy illegally. I have read replies to my posts that indicate that those of you > willing to reply to me do NOT GET IT which amazes me because it means > you are remarkably dumb. Because it is not that complicated!!! Now it is important on a math newsgroup because my issue with the math > community is that it is full of fakes who know how to pretend to be > smart when really that is ALL they know--pretending--and they do not > really know mathematics, but get away with acting because society does > not care to check. I know mathematicians act because I have the mathematical proofs that > show it, as mathematicians continue to dodge them so I am going to the > dramatic act of turning to industry to get leverage to embarrass > mathematicians and bring serious scrutiny so that quite a few > professors can be blocked from ever teaching students again. Now then, my idea I think is a good one, but the industry is actually > supposed to be implementing some kind of standard for what they call > managed copy at the end of the year. If by some remarkable miracle they implement something like my idea > then I will use the attention generated to make mathematicians around > the world very miserable. That is the story. You people need to show you have a modicum of intelligence and are not > just totally dumb and understand the story. IF you cannot understand this story then you will make very dumb > replies that show you have the intellect of a cow. Please try to sound at least quasi-intelligent in reply. James Harris *If* they implement anything remotely like 'your' idea, why would *you* get the attention for something 20 years old and utterly, trivially obvious. === Subject: Re: Explaining DMESE, again No one cares, you stupid ugly boring troll. >I came up with a festering pile o' nothin'. === Subject: Re: Explaining DMESE, again I came up with a copy protection idea where if you buy a DVD, or a CD > as it can work on that too, your copying equipment, like your CD > burner would make an encrypted copy that only it could read. So you can't hand off the copy as it's encrypted--to your drive. That is why it is self-encryption. Enterprising people wanting to break the system and copy illegally > could just hand off the CD or DVD they bought, to their friends so > they could make their own encrypted copies, so I added that the system > asks for the bought disk after 30 days. So you would need to give your friends the bought DVD or CD, again, > after the system asks for it, later. Now then, some of you very poor people who can do nothing else, or you > criminal types who will get something for free if you can no matter > what, will laugh and say, no problem, you'll just have friends in line > to get the DVD back again whenever, no matter how many hoops you have > to jump through. But most people will just buy their own. That is DMESE--Digital Media Equipment Self-Encryption. It is about making it just annoying enough to make illegal copies that > most people will not bother unless they are so poor they will go > through the trouble, or unless they are so criminally minded they will > jump through hoops to copy illegally. I have read replies to my posts that indicate that those of you > willing to reply to me do NOT GET IT which amazes me because it means > you are remarkably dumb. Because it is not that complicated!!! Now it is important on a math newsgroup because my issue with the math > community is that it is full of fakes who know how to pretend to be > smart when really that is ALL they know--pretending--and they do not > really know mathematics, but get away with acting because society does > not care to check. I know mathematicians act because I have the mathematical proofs that > show it, as mathematicians continue to dodge them so I am going to the > dramatic act of turning to industry to get leverage to embarrass > mathematicians and bring serious scrutiny so that quite a few > professors can be blocked from ever teaching students again. Now then, my idea I think is a good one, but the industry is actually > supposed to be implementing some kind of standard for what they call > managed copy at the end of the year. If by some remarkable miracle they implement something like my idea > then I will use the attention generated to make mathematicians around > the world very miserable. That is the story. You people need to show you have a modicum of intelligence and are not > just totally dumb and understand the story. IF you cannot understand this story then you will make very dumb > replies that show you have the intellect of a cow. Please try to sound at least quasi-intelligent in reply. James Harris The intent of making a copy of your purchased CD is to have a backup copy in case the origional gets damaged. If the copy is only good for 30 days, and your origional no longer works, you effectively no longer have backup capability. Enrico === Subject: Re: Math GRE subject test practice questions > > II Suppose that f(1 + x) = f(x) for all real x. If f is a > polynomial and f(5) = 11 then f(15/2) is > > a) -11 > b) 0 > ans c) 11 > d) 33/2 > e) not uniquely determined HINT A polynomial over a field must be constant if it assumes a value more times than its degree. > III Let x and y be positive integers such that 3x + 7y is > divisible by 11. Which of the following must also be divisible by 11? a) 4x + 6y > b) x + y + 5 > c) 9x + 4y > ans d) 4x - 9y > e) x + y - 1 HINT Which line is the same as 3x+7y = 0 over the field Z/11 ? > IV If a polynomial f(x) over the real numbers has the > complex numbers 2 + i and 1 - i as roots, then f(x) could be > > a) x^4 + 6X^3 + 10 > b) x^4 + 7x^2 +10 > c) x^3 - x^2 + 4x +1 > d) x^3 + 5x^2 + 4x +1 > ans e) x^4 - 6x^3 + 15x^2 - 18x +10 HINT Consider the sum of the roots. > VI Let x(sub 1) = 1 and x(sub n + 1) = sqrt(3 + 2*n(sub n)) for all > positive integers n. If it is assumed that {x(sub n)} converges, then > lim x -> infiniti x(sub n) = > > a) -1 > b) 0 > c) sqrt(5) > d) e > ans e) 3 HINT Consider the equation satisfied by a fixed point. --Bill Dubuque === Subject: Re: Math GRE subject test practice questions > IV This one seems common... > If a polynomial f(x) over the real numbers has the complex numbers 2 + > i and 1 - i as roots, then f(x) could be > > a) x^4 + 6X^3 + 10 > b) x^4 + 7x^2 +10 > c) x^3 - x^2 + 4x +1 > d) x^3 + 5x^2 + 4x +1 > ans e) x^4 - 6x^3 + 15x^2 - 18x +10 In a real polynomial the complex roots are present in pairs. Therefore the product of all the roots of the polynomial must be a multiple of (2 + i)(2 - i)(1 - i)(1 + i) = 10. In a degree four polynomial the constant term will be 10 and the degree 3 term will be -[(2 + i) + (2 - i) + (1 - i) + (1 + i)] = -6 -- Michael Press === Subject: Re: Math GRE subject test practice questions IV This one seems common... > If a polynomial f(x) over the real numbers has the complex numbers 2 + > i and 1 - i as roots, then f(x) could be a) x^4 + 6X^3 + 10 > b) x^4 + 7x^2 +10 > c) x^3 - x^2 + 4x +1 > d) x^3 + 5x^2 + 4x +1 > ans e) x^4 - 6x^3 + 15x^2 - 18x +10 In a real polynomial the complex roots are present in > pairs. Therefore the product of all the roots of the > polynomial must be a multiple of > (2 + i)(2 - i)(1 - i)(1 + i) = 10. In a degree four polynomial the constant term will be 10 > and the degree 3 term will be > -[(2 + i) + (2 - i) + (1 - i) + (1 + i)] = -6 -- > Michael Press the moment) four more questions if you don't mind. I will post them under the title Math GRE subject test practice questions v2 right after this message. === Subject: Re: Math GRE subject test practice questions > III Other than trying out the answers, is there a quicker way? > Let x and y be positive integers such that 3x + 7y is divisible by 11. > Which of the following must also be divisible by 11? > > a) 4x + 6y > b) x + y + 5 > c) 9x + 4y > ans d) 4x - 9y > e) x + y - 1 3x + 7y == 0 (mod 11) -> 12x + 28y == 0 (mod 11) -> x + 6y (mod 11) a) 4x + 6y - 4(x + 6y) == y (mod 11) b) x + y + 5 - (x + 6y) == -5y + 5 (mod 11) c) 9x + 4y - 9(x + 6y) == -50y (mod 11) d) 4x - 9y - 4(x + 6y) == -33y == 0 (mod 11) e) x + y - 1 -- Michael Press === Subject: Re: Math GRE subject test practice questions > > Let x and y be positive integers such that 3x + 7y is divisible by 11. > Which of the following must also be divisible by 11? > > a) 4x + 6y > b) x + y + 5 > c) 9x + 4y > d) 4x - 9y > e) x + y - 1 > > 3x + 7y == 0 (mod 11) -> 12x + 28y == 0 (mod 11) -> x + 6y (mod 11) > a) 4x + 6y - 4(x + 6y) == y (mod 11) > b) x + y + 5 -(x + 6y) == -5y + 5 (mod 11) > c) 9x + 4y - 9(x + 6y) == -50y (mod 11) > d) 4x - 9y - 4(x + 6y) == -33y == 0 (mod 11) > e) x + y - 1 SIMPLER It amounts to: which line equals 3x+7y = 0 over field Z/11. The line is uniquely determined by the 2 obvious points (0,0), (-7,3). But the first point isn't on b),e), and the second isn't on a),c). This solution requires less than 10 seconds of mental calculation. I discussed this problem at length in two posts in this prior thread --Bill Dubuque === Subject: Re: Math GRE subject test practice questions <02ehi3dub3en12v18pd9q5atv5f6k2q89j@4ax.com For this multiple choice test question, there's no > need to find the quadratics. The sum of the four > roots is +6 so the answer is (e). Choice (e) is the only quartic with -6 as the > coefficient of the x^3 term. Nice! Obviously, I didn't think about this when anymore). Dave L. Renfro === === Subject: Re: Power Method using Matlab I've made some modifications to my code because I realized I didn't do it as asked in the question. The goal is to compute the eigenvector x associated with the eigenvalue 1 of a matrix G. G is defined as G = alpha * H + (1/n)W[ alpha * a + (1-alpha)W]^T where W = (1,1,...,1)^T 0 < alpha < 1 is a constant H = AD^(+) where D = diag(d_1,d_2,...,d_n) and (d_1,d_2,...,d_n)^T = A^TW a = (a_1,a_2,...,a_n)^T where a_i = 1 if d_i = 0 and 0 otherwise I have to implement the power method to compute the eigenvector associated with the eigenvalue 1 of G. The function takes matrix A (not G) and alpha as inputs. Also, any full matrix of order O(n) is NOT to be constructed and stored explicitly in the function. Only the sparse matrix A may be used. Here is my modified code: function [x,absdiff] = powermethod(A,alpha) n = size(A,1); % Initialize the eigenvector by (1/n, 1/n ,..., 1/n)^T x = repmat(1/n,[n 1]); % Precompute some fixed quantities dn = A'*ones(n,1); a = zeros(n,1); for i=1:n if dn(i) > 0, a(i) = 0, elseif dn(i) == 0, a(i) = 1; end end for i=1:500 dn(i) = 1/dn(i); H = A*pinv(D); G = alpha*H + (1/n)*ones(n,1)*(alpha*a+(1-alpha)*ones(n,1))'; MAXITER = 1000; % Restrict the maximum no. of iterations iter = 0; absdiff = zeros(MAXITER,1); while iter