12196 Subject: Re: Fraud in Computer Science Publishing >> A list of instructions that a computer can execute. > Ok, then how would a computer execute a Predicate Calculus wff? You > can take a specific example, such as PRIME(x)^BETW(1000,x,1005). > This is pretty simple (only 2 relation references.) Could you > describe how it is executed, step by step? No; your paper does not give implementation details. How can I know? >> 4. Do you know of a way to specify it that isn't programming? > >> Not that the computer can understand. If the computer can understand it, >> it's programming. > But didn't you just imply that PC wffs can be executed? Yes, so what? I maintain my statement that using PC is programming. >> 5. Do you know of a simpler way to specify it? > >> Depends on the task to be accomplished. > The above wff. Who cares? You're arguing that PC is the best way to solve a trivial problem. I'm looking at the big picture. You're looking at the 20 (or so) exercises you have given. >> 7. Did you know that the state-of-the-art in Program Synthesis is to >> specify the program requirement as a Predicate Calculus wff? > >> This is meaningless. It's not because some people, however talented they >> are, have decided to use a specific language, that all other languages >> should not be considered. > I am not saying that. Then how is the statement relevant to the conversation? It is not. >> 9. How about the fact that a Predicate Calculus wff has no assignment, >> conditional execution, loops or the possibility of not terminating? > >> Lisp programs can have the above characteristics. the difference is, it >> doesn't force you to stay within these bounds. > You can't be sure whether any given program terminates. I'm starting to think you have no clue about programming outside of your system. Of course you can, provided the program is written correctly. just look at the source code, and you can see if there are conditions that can make the program not terminate. > You can be > sure of PC wffs, because they are not executed in the 1st place. False. They are compiled (or interptreted) and executed. Otherwise your system cannot be used on a computer. Which I am willing to accept. As Robert said, in the last step it's translated to machine code, if it runs. > And in your system, you do have to use general programs because the > user has to enter in new programs to satisfy new requests for a > program to be generated. Which is also the case in your system. You are still failing to see that even the simple: PRIME(I) is programming. >> 10. Do you think that Predicate Calculus wffs and computer programs >> are at the same level of abstraction? > >> Depends on the language used. Check out the Shakespeare programming >> language. Highly abstract :-) > It would take a > long FORTRAN program to twiddle bits, and a long assembly language > program to add two numbers. Have you ever programmed in assembly? Adding 2 numbers is done in 1 instruction. I can see cases where adding 2 numbers can be longer (hint: bignums) but if that's what you were talking about, you should have been more specific. I assume you were not. >> with several algorithms. On the other hand, some specifications cannot be >> expressed with PC. > Then they do have a one-to-many relationship? Each wff can be > implemented by multiple different algorithm? Yes. Which is, from what I understand, the purpose of your system, since you made it a requirement that the system should be able to generate mutliple algorithms for the same problem. >> 15. Do you see value in being able to determine the wff that a >> particular program computes? > >> Yes, because PC is closer to mathematical formalism than other languages. > That's It! That's why I was asking what Mathematicians use. Now you > see it! What's your point? I never said your system was useless. I said it was no different fundamentally than the other systems you do not accept. >> I know no system that determines programs that compute a given wff. > I maintain that my system does and it is explained in detail in my two > papers below, as I have given excerpts from in these messages. there is no way to verify that assertion, since you explicitely refused to let people look at your implmentation, or just try it. Sam -- [...] but the delight and pride of Aule is in the deed of making, and in the thing made, and neither in possession nor in his own mastery; wherefore he gives and hoards not, and is free from care, passing ever on to some new work. - J.R.R. Tolkien, Ainulindale (Silmarillion) Subject: GCD question Let S(*) be a commutative regular monoid. If a,b are in S then d=GCD(a,b) iff 1) d|a and d|b 2) if c|a and c|b, then c|d. Consider N_p{1}={1,2,4,6,8,10,...,2k} with k in N. In N_p{1}(*) (where * denotes the usual product in N) GCD(36,60) does not exist. Why? I think, for example, that 6 in N_p{1} satisfies 1) and 2). Thank you. Subject: Re: GCD question > Let S(*) be a commutative regular monoid. If a,b are in S then d=GCD(a,b) > iff > 1) d|a and d|b > 2) if c|a and c|b, then c|d. > Consider N_p{1}={1,2,4,6,8,10,...,2k} with k in N. You certainly mean {2k | k in N} ? > In N_p{1}(*) (where * denotes the usual product in N) GCD(36,60) does not > exist. Why? > I think, for example, that 6 in N_p{1} satisfies 1) and 2). In general you can compute the GCD of two elements from N_p{i} by computing their GCD in N. Observe, that N has a partial order given by a <= b iff a|b. With respect to this order, the GCD is just the infimum. and it is a general result, that you can compute infimums in 2/N by computing them in N. In fact, this is just a special case of the corresponding result for slice categories, but that would probably a bit of an overkill right now. Marc Subject: Re: GCD question Marc Olschok ha scritto nel messaggio > Let S(*) be a commutative regular monoid. If a,b are in S then d=GCD(a,b) > iff > 1) d|a and d|b > 2) if c|a and c|b, then c|d. > Consider N_p{1}={1,2,4,6,8,10,...,2k} with k in N. > You certainly mean {2k | k in N} ? I mean {2k | k in N} U {1} > In N_p{1}(*) (where * denotes the usual product in N) GCD(36,60) does not > exist. Why? > I think, for example, that 6 in N_p{1} satisfies 1) and 2). No, 12*3=36, 12*5=60 but this is true in Z, but 3 and 5 are not in {2k | k in N} U {1}. So 12 is not a divisor of 36,60. Subject: Re: GCD question Visiting Assistant Professor at the University of Montana. >> Let S(*) be a commutative regular monoid. If a,b are in S then d=GCD(a,b) >> iff >> 1) d|a and d|b >> 2) if c|a and c|b, then c|d. > > >> Consider N_p{1}={1,2,4,6,8,10,...,2k} with k in N. >You certainly mean {2k | k in N} ? union {1}? >> In N_p{1}(*) (where * denotes the usual product in N) GCD(36,60) does not >> exist. Why? >> I think, for example, that 6 in N_p{1} satisfies 1) and 2). >In general you can compute the GCD of two elements from N_p{i} by >computing their GCD in N. No, that does not work in general. For example, 2|6 in N, but 2 does not divide 6 in N_p{1}. What about 36 and 60? The common divisors are 1, 2, and 6. However, 6 does NOT satisfy condition (2), because 2 divides both 36 and 60 in N_p{1}, but does not divide 6. Likewise, neither does 2 nor 1. So 36 and 60 do not have a gcd in this monoid. Nothing wrong with that, there's no reason why gcds must exist, after all. ============================================================== ======== It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) ============================================================== ======== Arturo Magidin magidin@math.berkeley.edu Subject: Re: GCD question Arturo Magidin ha scritto nel messaggio > What about 36 and 60? The common divisors are 1, 2, and 6. However, 6 > does NOT satisfy condition (2), because 2 divides both 36 and 60 in > N_p{1}, but does not divide 6. Likewise, neither does 2 nor 1. So 36 > and 60 do not have a gcd in this monoid. Nothing wrong with that, > there's no reason why gcds must exist, after all. Ok. Subject: Re: GCD question Marc Olschok ha scritto nel messaggio >> Let S(*) be a commutative regular monoid. If a,b are in S then > d=GCD(a,b) >> iff >> 1) d|a and d|b >> 2) if c|a and c|b, then c|d. >> >> >> Consider N_p{1}={1,2,4,6,8,10,...,2k} with k in N. >> You certainly mean {2k | k in N} ? > I mean {2k | k in N} U {1} Ah, yes, sorry. >> In N_p{1}(*) (where * denotes the usual product in N) GCD(36,60) does > not >> exist. Why? >> I think, for example, that 6 in N_p{1} satisfies 1) and 2). > No, 12*3=36, 12*5=60 but this is true in Z, but 3 and 5 are not in {2k | k > in N} U {1}. So 12 is not a divisor of 36,60. You are right; I lie utterly corrected. I wonder, where I had my head. Marc Subject: Generalization of Analysis problem I saw a problem that goes something like this: If f is in L^2([a,b]) and the integral (over [a,b]) of f* x^n = 0 for all n >= 0, then f = 0 almost everywhere. It can be done using Cauchy-Schwartz and the fact that the set of polynomials is dense in L^2. I am curious about two generalizations of the problem. Firstly, if f is merely in L^1([a,b]), is the same implication true (if not, what is a counterexample?) Secondly, what if we change [a,b] to the reals? Here it would seem like the L^2 requirement would matter less since there is no hope of using the above argument. Thanks, Hugh Subject: Re: Generalization of Analysis problem > I saw a problem that goes something like this: > If f is in L^2([a,b]) and the integral (over [a,b]) > of f* x^n = 0 for all n >= 0, then f = 0 almost everywhere. > It can be done using Cauchy-Schwartz and the fact that the > set of polynomials is dense in L^2. > I am curious about two generalizations of the problem. > Firstly, if f is merely in L^1([a,b]), is the same > implication true (if not, what is a counterexample?) Sure. You can find a sequence of polynomials p_n such that |p_n| < 1 on [a,b] and f*p_n -> |f| a.e. on [a,b]. So if int_[a,b] f*p_n = 0 for all n, then int_[a,b] |f| = 0 by the dominated convergence theorem. Therefore f = 0 a.e. > Secondly, what if we change [a,b] to the reals? Here > it would seem like the L^2 requirement would matter > less since there is no hope of using the above argument. Well you have a problem: If f is in L^2(R) and p is a polynomial, then the integral of f*p over R need not be defined. But never mind that, because there's no hope here anyway. Suppose g is a C^oo function on R with compact support away from 0, g not identically 0. Then g and all of its derivatives vanish at 0. That implies int_R f(t)t^k dt = 0, k = 0, 1, 2, ..., where f is the inverse Fourier transform of g. But g is not identically 0, so neither is f. (f is in the Schwarz space, so f(t)t^k is in L^1(R) for every k.) Subject: growth rates of entire transcendental functions If f: C -> C is entire, but cannot be expressed as a polynomial function, then how slowly can sup_{z s.t. |z|<=R} ( |f(z)|) grow as a function of R? David Bernier Subject: Re: growth rates of entire transcendental functions >If f: C -> C is entire, but cannot be expressed as a polynomial function, >then how slowly can >sup_{z s.t. |z|<=R} ( |f(z)|) grow as a function of R? Use Cauchy's estimates. If your sup is M_f(R), then |f^(n)(0)| <= n!/R^n M_f(R) If f is not a polynomial, infinitely many of these are nonzero. This implies M_f(R) = Omega(R^n) as R -> infinity for every positive integer n, i.e. its growth is more than polynomial. On the other hand, suppose h(R) is any positive function on [1,infinity) that is Omega(R^n) as R -> infinity for all n. I claim there is a non-polynomial entire function f such that M_f(R) < h(R) for all R >= 1. So you can't say anything more about the growth of M_f(R). Namely, let f(z) = sum_{n=0}^infinity c_n z^n where c_n < 2^(-n) min_{h(R)/R^n: R >= 1}. Then for any R >= 1, M_f(R) <= sum_{n=0}^infinity c_n R^n < sum_{n=0}^infinity 2^{-n} h(R) = h(R) (and this estimate also shows the series converges uniformly on compact sets, so f is entire). Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 Subject: Re: Help! Algebraic Topology X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Punge: Micro$oft X-Sanguinate: themvsguy@email.com X-Terminate: SPA(GIS) X-Tinguish: Mark Griffith Given two maps f,g: X -> Y show that f~g (homotopic) if Y is >contractive. Calm down and compose yourself; you've already been given enough hints. -- Shmuel (Seymour J.) Metz, SysProg and JOAT Any unsolicited bulk E-mail will be subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail. Reply to domain Patriot dot net user shmuel+news to contact me. Do not reply to spamtrap@library.lspace.org Subject: HELP! Weighted combination of sample groups to match a Please forgive my lack of terms, I'm just a want-to-be mathematician. Where appropriate please tell me what term would be better. The problem: there are 20 dormitories on a campus. Three of them will be selected for a study related to weight. Which three and what ratio should be applied to each, to best match the nation. Using national college dormitory statistics database, I have a national histogram using the product of height*weight separated into 20 bins , (the x-axis? Is there another name for the horizontal line of a histogram?) vs. the accumulated number of people in each bin as a percentage of the total number of people in dormitories nation wide. I need to select the best 3 of 20 dormitories and combine them with three different weighting coefficients. To correlate how well a single dormitory matches the national, I'm using the coefficient of fit (R-squared) of the 20 bins- national vs. single dormitory- and forcing the intercept to zero. That is 20 different R-squared values. Easy enough for one dormitory but, three dormitories combined with weighting coefficients as variables (total of the three weighting factors is 1.00). If my reverse polish notation HP calculator is correct, that is 20 combined 3 or 1,140 R-squared calculations for an equal weighting factor of 1/3 on each group. Now start changing the weighting ratios!!! There has got to be a better way PLEASE, SOMEONE HELP ME! Subject: How do i find the group of automorphisms of the alternating group on four symbols? My higher algebra book has a lot of this type of problems, and I've no idea of how to get started except simply trying all possible mappings of the elements of the group onto itself. For the problem in the question the only thing I've come up with is that the permutations with two seperate transpositions (e.g. (13)(24)) are their own inverse and in any automorphism every such permutation must be mapped onto another of those permutations. I've also computed a table of every element of the group times all others, but I can't of a way to use this table to get the automorphisms. All help appreciated! The table: i = (1)(2)(3)(4) a = (12)(34) b = (13)(24) c = (14)(23) d = (123) d^2 = (132) e = (124) e^2 = (142) f = (134) f^2 = (143) g = (234) g^2 = (243) i a b c d d^2 e e^2 f f^2 g g^2 a a i c b f g f^2 g^2 d e d^2 e^2 b b c i a g^2 e d^2 f e^2 g f^2 d c c b a i e^2 f^2 g d g^2 d^2 e f d d g^2 e^2 f d^2 i c g e a b f^2 d^2 d^2 f^2 g e i d f b c g^2 e^2 a e e g f^2 d^2 b g^2 e^2 i a d f c e^2 e^2 f d g^2 f^2 c i e g b a d^2 f f e^2 g^2 d g a b d^2 f^2 i c e f^2 f^2 d^2 e g c e^2 g^2 a i f d b g g e d^2 f^2 a f d c b e^2 g^2 i g^2 g^2 d f e^2 e b a f^2 d^2 c i g Subject: Re: How do i find the group of automorphisms of the alternating group on four symbols? Visiting Assistant Professor at the University of Montana. >My higher algebra book has a lot of this type of problems, and I've no >idea of how to get started except simply trying all possible mappings of >the elements of the group onto itself. >For the problem in the question the only thing I've come up with is that >the permutations with two seperate transpositions (e.g. (13)(24)) are >their own inverse and in any automorphism every such permutation must be >mapped onto another of those permutations. Yes; much simpler would be to note that this is true because an automorphism must send an element of order 2 to an element of order 2. You also know that it must send an element of order 3 to an element of order 3. So it must send (123) to either (123), (132), (124), ... etc. And if know where it sends (12)(34) and where it sends (123), then you know where it sends every element, yes? Are you truly free to make every possible choice for (123) and for (12)(34) independently? If you could, you would have 8 choices for (123), and 3 for (12)(34), which would give you 24 possibilities; so there are at most 24 automorphisms of A_4. Now, here's something else to think about: A_4 is a normal subgroup of S_4; that means that every element of S_4 induces an automorphism on A_4 by conjugation. It is not hard to verify that an element induces the trivial automorphism if and only if it centralizes A_4, and that the centralizer of A_4 is the trivial subgroup. So that means that each element of S_4 gives you a ->different<- automorphism of A_4. That means that there must be at least |S_4| = 4! = 24 automorphisms of A_4. Ah, so how many are there, and what is a nice description of Aut(A_4)? ============================================================== ======== It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) ============================================================== ======== Arturo Magidin magidin@math.berkeley.edu Subject: Re: How do you discuss mathematics with a person who thinks mathematics is a part of physics? > The following is a repost of a post that I made > previously. Unfortunately, I did not have a correct > subject line. I hope that I have rectified this > situation with the new 'subject heading' with this > posting. > I was wondering if anybody had any idea on how to talk > about mathematics with a person whose attitude is that > a mathematical theory is worthless until validated by > physical experiments in the physical world (this was > the reason for my choice of the word realist - as > no alternative words occurred to me). The person in > question is a person who goes under the name of > Ken S. Tucker, and he has stated, as examples of the > attitude which I am discussing, that, for him, calculus > was validated by ballistics (presumably, for him, > calculus without a mechanical model may have no > validation). He also regards constants of integration > as physical quantities to which he can apply the > Principle of Relativity from physics (he never gives > an explicit explanation of exactly how he applies > the Principle). He calls the mathematics that is > done without any connection to the physical world imaginary. So just how is one supposed to convince > such an individual of the error of his way of looking > at things? Thanks. > Tom The problem is that he is right, *on his own terms of discussion*, and that he does not admit other terms of discussion. Thus it is not possible to convince him that he is wrong. You could try to bafflegab him, starting out with the premiss that mathematics is a tool to investigate the unknown and always has been. David Ames Subject: Re: How do you discuss mathematics with a person who thinks mathematics is a part of physics? > The following is a repost of a post that I made > previously. Unfortunately, I did not have a correct > subject line. I hope that I have rectified this > situation with the new 'subject heading' with this > posting. > I was wondering if anybody had any idea on how to talk > about mathematics with a person whose attitude is that > a mathematical theory is worthless until validated by > physical experiments in the physical world (this was > the reason for my choice of the word realist - as > no alternative words occurred to me). The person in > question is a person who goes under the name of > Ken S. Tucker, and he has stated, as examples of the > attitude which I am discussing, that, for him, calculus > was validated by ballistics (presumably, for him, > calculus without a mechanical model may have no > validation). He also regards constants of integration > as physical quantities to which he can apply the > Principle of Relativity from physics (he never gives > an explicit explanation of exactly how he applies > the Principle). He calls the mathematics that is > done without any connection to the physical world imaginary. So just how is one supposed to convince > such an individual of the error of his way of looking > at things? Thanks. > Tom > The problem is that he is right, *on his own terms of discussion*, and > that he does not admit other terms of discussion. Thus it is not > possible to convince him that he is wrong. > You could try to bafflegab him, starting out with the premiss that > mathematics is a tool to investigate the unknown and always has been. Always has been? Mathematics developed out of a need to determine when to plant crops. Early merchants needed to know how to keep business records. Mathematics has historically been driven by and intimately connected with real world affairs. Even today, just look at the periodic writings on this newsgroup of John Baez. The most abstract mathematical structures such as n-categories are developed for the purpose of understanding gravity. If you were to argue one extreme or the other: math is only about the physical world, or math is totaly unconcerned with the physical world, then you would be closer to the historical and contemporary truth by arguing that math is intimately related to the physical world. Subject: Re: How do you discuss mathematics with a person who thinks mathematics is a part of physics? > ... He calls the mathematics that is > done without any connection to the physical world imaginary. That's ok isn't it? Unless one is a physicalist (http://plato.stanford.edu/entries/physicalism/). -- G.C. Subject: Re: How do you discuss mathematics with a person who thinks mathematics is a part of physics? Salermo and Ames had great replies. the historical development of calculus, as opposed to the put-on of Newton and the Royal Society, was initiated by the work on the brachistochrone (tautochrone) by Bernoulli and Leibniz, a beautiful problem that also can be used ballisticaly. > attitude which I am discussing, that, for him, calculus > was validated by ballistics (presumably, for him, > calculus without a mechanical model may have no > validation). He also regards constants of integration > as physical quantities to which he can apply the > Principle of Relativity from physics (he never gives > an explicit explanation of exactly how he applies > the Principle). He calls the mathematics that is http://buckminster.info/Ideas/03-TetGeomTheorem4-ColorProof.htm --UN HYDROGEN (sic; Methanex (TM) reformanteurs) ECONOMIE?... La Troi Phases d'Exploitation de la Protocols des Grises de Kyoto: (FOSSILISATION [McCainanites?] (TM/sic))/ BORE/GUSH/NADIR @ http://www.tarpley.net/aobook.htm. Http://www.tarpley.net/bushb.htm (content partiale, below): 17 -- L'ATTEMPTER de COUP D'ETAT, 3/30/81 Subject: Re: How do you discuss mathematics with a person who thinks mathematics is a part of physics? > The following is a repost of a post that I made > previously. Unfortunately, I did not have a correct > subject line. I hope that I have rectified this > situation with the new 'subject heading' with this > posting. > I was wondering if anybody had any idea on how to talk > about mathematics with a person whose attitude is that > a mathematical theory is worthless until validated by > physical experiments in the physical world (this was > the reason for my choice of the word realist - as > no alternative words occurred to me). How about empiricist as a description? Note that in any physical world, such things as the Pythagorean theorem cannot be prove to be EXACTLY true, only approximately true. It follows that in this empiricist's world 2.0 + 2.0 = 4.0, as an addition of reals rather than integers, is also only known to be approximately true. > The person in > question is a person who goes under the name of > Ken S. Tucker, and he has stated, as examples of the > attitude which I am discussing, that, for him, calculus > was validated by ballistics (presumably, for him, > calculus without a mechanical model may have no > validation). He also regards constants of integration > as physical quantities to which he can apply the > Principle of Relativity from physics (he never gives > an explicit explanation of exactly how he applies > the Principle). He calls the mathematics that is > done without any connection to the physical world imaginary. So just how is one supposed to convince > such an individual of the error of his way of looking > at things? Thanks. > Tom Very likely, one isn't going to convince him. Consider the problems of explaining the charms of music to the tone deaf or the beauty of rainbows to the colorblind. Subject: Re: How do you discuss mathematics with a person who thinks mathematics is a part of physics? > The following is a repost of a post that I made > previously. Unfortunately, I did not have a correct > subject line. I hope that I have rectified this > situation with the new 'subject heading' with this > posting. > I was wondering if anybody had any idea on how to talk > about mathematics with a person whose attitude is that > a mathematical theory is worthless until validated by > physical experiments in the physical world (this was > the reason for my choice of the word realist - as > no alternative words occurred to me). The person in > question is a person who goes under the name of > Ken S. Tucker, and he has stated, as examples of the > attitude which I am discussing, that, for him, calculus > was validated by ballistics (presumably, for him, > calculus without a mechanical model may have no > validation). He also regards constants of integration > as physical quantities to which he can apply the > Principle of Relativity from physics (he never gives > an explicit explanation of exactly how he applies > the Principle). He calls the mathematics that is > done without any connection to the physical world imaginary. So just how is one supposed to convince > such an individual of the error of his way of looking > at things? Thanks. > Tom You may want to tell him what Nicomachus of Gerasa said circa 100 C.E. in Introduction to Arithmetic Book I, Chapter IV, verses 1 & 2 then verse 4 & 5, as well as Chapter 5 of the same book.. Verses 1 & 2, [1] Which then of these four methods must we first learn? Evidently, the one which naturally exists before them all, is superior and takes the place of origin and root and, as it were, of mother to the others. [2] And this is arithmetic (Plato, The Republic, 522), not solely because we said that it existed before all others in the mind of the creating God like some universal and exemplary plan, relying upon which as a design and archetypal example the creator of the universe sets in order his material creations and makes them attain to their proper ends; but also because it is naturally prior in birth, inasmuch as it abolishes other sciences with itself, but it is not abolished together with them. For example, 'animal' is naturally antecedent to 'man,' for abolish 'animal' and 'man' is abolished; but if 'man' be abolished, it no longer follows that 'animal' be abolished at the same time. ... Verse 4, 5, Chapter 5 verse 1, 2 and 3, then go on to explain how with the abolishment of arithmetic, treatment of the sciences is abolished, but not vice-versa. Subject: Re: How do you discuss mathematics with a person who thinks mathematics is a part of physics? X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Punge: Micro$oft X-Sanguinate: themvsguy@email.com X-Terminate: SPA(GIS) X-Tinguish: Mark Griffith I was wondering if anybody had any idea on how to talk >about mathematics with a person whose attitude is that >a mathematical theory is worthless until validated by >physical experiments in the physical world (this was >the reason for my choice of the word realist - as >no alternative words occurred to me). Sorry, but such a person is a philistine and is *not* a realist. Ask him to read Wigner's essay and to think about it. Also ask him how he validates Art and Music by physical experiments. Of course, if you did not accurately report what he said, then all bets are off. What were his exact words? -- Shmuel (Seymour J.) Metz, SysProg and JOAT Any unsolicited bulk E-mail will be subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail. Reply to domain Patriot dot net user shmuel+news to contact me. Do not reply to spamtrap@library.lspace.org Subject: Re: How do you discuss mathematics with a person who thinks mathematics is a part of physics? > The following is a repost of a post that I made > previously. Unfortunately, I did not have a correct > subject line. I hope that I have rectified this > situation with the new 'subject heading' with this > posting. > I was wondering if anybody had any idea on how to talk > about mathematics with a person whose attitude is that > a mathematical theory is worthless until validated by > physical experiments in the physical world (this was > the reason for my choice of the word realist - as > no alternative words occurred to me). The person in > question is a person who goes under the name of > Ken S. Tucker, and he has stated, as examples of the > attitude which I am discussing, that, for him, calculus > was validated by ballistics (presumably, for him, > calculus without a mechanical model may have no > validation). He also regards constants of integration > as physical quantities to which he can apply the > Principle of Relativity from physics (he never gives > an explicit explanation of exactly how he applies > the Principle). He calls the mathematics that is > done without any connection to the physical world imaginary. So just how is one supposed to convince > such an individual of the error of his way of looking > at things? Thanks. Well most of alt.sci.physics will tell you this every day. Penrose said that the universe functions to only a tiny fraction of all known mathematics, hence the physical world is a part of mathematics. Find a couple examples, like the proof there is no largest prime, that has no part in physics. Calculus was invented by 2 seperate people at the same time, which shows calculus has an existence by itself and does not depend on the inventor or his reasons for it. Herc Subject: Re: How do you discuss mathematics with a person who thinks mathematics is a part of physics? > The following is a repost of a post that I made > previously. Unfortunately, I did not have a correct > subject line. I hope that I have rectified this > situation with the new 'subject heading' with this > posting. > I was wondering if anybody had any idea on how to talk > about mathematics with a person whose attitude is that > a mathematical theory is worthless until validated by > physical experiments in the physical world (this was > the reason for my choice of the word realist - as > no alternative words occurred to me). The person in > question is a person who goes under the name of > Ken S. Tucker, and he has stated, as examples of the > attitude which I am discussing, that, for him, calculus > was validated by ballistics (presumably, for him, > calculus without a mechanical model may have no > validation). He also regards constants of integration > as physical quantities to which he can apply the > Principle of Relativity from physics (he never gives > an explicit explanation of exactly how he applies > the Principle). He calls the mathematics that is > done without any connection to the physical world imaginary. So just how is one supposed to convince > such an individual of the error of his way of looking > at things? Thanks. > Tom Tell him that mathematics was often, and perhaps more often than not, developed in its own right, and that uses were then found for it later. On the other hand, many times in order to solve a physics problem, it encourages them to develop new and more advanced mathematical tools. But, still, the physics problems were mainly theoretical physics rather than what would be considered 'practical' physics. Newton developed, or helped develop Calculus to help him solve certain formulas for gravitation. That is one point. In fact, I think there was another example of people developing mathematical tools to solve a problem. I think it was string theory or some other TOE class theory, but I'm not exactly sure. But I know I heard it somewhere. I also think it may have something to do with black holes. Does anybody know what I'm talking about? Anyways, the more 'imaginary' stuff was generally developed long before practical uses were found for them. While this probably won't convince him of anything, it may just give him something to think about. (...Starblade Riven Darksquall...) Subject: Re: How do you discuss mathematics with a person who thinks mathematics is a part of physics? > The following is a repost of a post that I made > previously. Unfortunately, I did not have a correct > subject line. I hope that I have rectified this > situation with the new 'subject heading' with this > posting. > I was wondering if anybody had any idea on how to talk > about mathematics with a person whose attitude is that > a mathematical theory is worthless until validated by > physical experiments in the physical world (this was > the reason for my choice of the word realist - as > no alternative words occurred to me). The person in > question is a person who goes under the name of > Ken S. Tucker, and he has stated, as examples of the > attitude which I am discussing, that, for him, calculus > was validated by ballistics (presumably, for him, > calculus without a mechanical model may have no > validation). He also regards constants of integration > as physical quantities to which he can apply the > Principle of Relativity from physics (he never gives > an explicit explanation of exactly how he applies > the Principle). He calls the mathematics that is > done without any connection to the physical world imaginary. So just how is one supposed to convince > such an individual of the error of his way of looking > at things? Thanks. One of the predominant features that distinguishes Mathematics from the rest of the sciences, is that new branches of Mathematics are developed for their own sake and later (usually _much_ later) solve a plethora of applied problems. Many examples here: Crystallography, X-Ray spectroscopy, semi-intelligent topological computer networks, molecular biology and the most notable example of all: Computers, which use Boolean logic. > Tom -- Ioannis http://users.forthnet.gr/ath/jgal/ ___________________________________________ Eventually, _everything_ is understandable. Subject: Re: How do you discuss mathematics with a person who thinks mathematics is a part of physics? > The following is a repost of a post that I made > previously. Unfortunately, I did not have a correct > subject line. I hope that I have rectified this > situation with the new 'subject heading' with this > posting. > I was wondering if anybody had any idea on how to talk > about mathematics with a person whose attitude is that > a mathematical theory is worthless until validated by > physical experiments in the physical world (this was > the reason for my choice of the word realist - as > no alternative words occurred to me). The person in > question is a person who goes under the name of > Ken S. Tucker, and he has stated, as examples of the > attitude which I am discussing, that, for him, calculus > was validated by ballistics (presumably, for him, > calculus without a mechanical model may have no > validation). He also regards constants of integration > as physical quantities to which he can apply the > Principle of Relativity from physics (he never gives > an explicit explanation of exactly how he applies > the Principle). He calls the mathematics that is > done without any connection to the physical world imaginary. So just how is one supposed to convince > such an individual of the error of his way of looking > at things? Thanks. Show him that while strictly speaking he might be correct, his way of thinking is very counterproductive in mathematics, and would have hindered development in areas that are now commonly used in physics and other areas in which applications of mathematics are used. For example, complex numbers are now used everywhere in physics. Yet prima facie they seem to be very far removed from ordinary experience (no one experiences a complex quantity). Abstract algebra, vectors, quaternions, matrixes, even number theory and such like are routinely used in physics these days, but were once esoteric branches of mathematics with no immediate connection to physical practice. Also, mathematical theories study abstract structures, not specific ones, so it is very often possible to embed simple structures, such as the natural numbers, into richer structures, such as the real number system, in which the study of the properties of the simple system is much easier in an essential way. You could also cite a theorem of G.9adel which concerns lengths of proofs. This theorem essentially says that for any theory T there exists for any recursive function f an infinite number of statements provable in T which are provable in some theory T' extending T in m number of steps, but the shortest proofs of which in T all exceed f(m) in length. T' can be taken to be a 'conservative extension' of T in the sense that if T is believed to be true (sound), then T' is also true (sound). As an application, one can show that there are theorems of first order arithmetic with prohibitively strong proofs, but which have very elegant and simple proofs in second order arithmetic. G.9adel's speed-up theorem shows that one should not be overtly nominalistic when doing deduction, even if one really believes only in a very sparse ontology. It simply is not possible to prove some things even of the natural numbers without recourse to notions which are naturally developed within a more general and abstract conceptual field. -- Aatu Koskensilta (aatu.koskensilta@xortec.fi) Wovon man nicht sprechen kann, daruber muss man schweigen - Ludwig Wittgenstein, Tractatus Logico-Philosophicus Subject: Re: How do you discuss mathematics with a person who thinks mathematics is a part of physics? > >> >>>The following is a repost of a post that I made >>>previously. Unfortunately, I did not have a correct >>>subject line. I hope that I have rectified this >>>situation with the new 'subject heading' with this >>>posting. >>>I was wondering if anybody had any idea on how to talk >>>about mathematics with a person whose attitude is that >>>a mathematical theory is worthless until validated by >>>physical experiments in the physical world (this was >>>the reason for my choice of the word realist - as >>>no alternative words occurred to me). The person in >>>question is a person who goes under the name of >>>Ken S. Tucker, and he has stated, as examples of the >>>attitude which I am discussing, that, for him, calculus >>>was validated by ballistics (presumably, for him, >>>calculus without a mechanical model may have no >>>validation). He also regards constants of integration >>>as physical quantities to which he can apply the >>>Principle of Relativity from physics (he never gives >>>an explicit explanation of exactly how he applies >>>the Principle). He calls the mathematics that is >>>done without any connection to the physical world >>>imaginary. So just how is one supposed to convince >>>such an individual of the error of his way of looking >>>at things? Thanks. >>>Tom >>> >>The problem is that he is right, *on his own terms of discussion*, and >>that he does not admit other terms of discussion. Thus it is not >>possible to convince him that he is wrong. >>You could try to bafflegab him, starting out with the premiss that >>mathematics is a tool to investigate the unknown and always has been. >> >Always has been? Mathematics developed out of a need to determine when >to plant crops. Not according to Van der Waerden. According to him (_Algebra and Geometry in Ancient Civilizations_) the earliest mathematics was geometric constructions used in altar construction. He even quotes one algorithm for altar construction (I forget if it was Babylonian or Vedic) that ends with this way, you will not displease the god. > Early merchants needed to know how to keep business records. Mathematics has historically been driven by and intimately connected with real world affairs. Even today, just look at the periodic writings on this newsgroup of John Baez. The most abstract mathematical structures such as n-categories are developed for the >purpose of understanding gravity. That's certainly not clear to me. But you are not alone in this belief -- one poster asked whether linear algebra was developed as an explanation of quantum physics or if they developed together. >If you were to argue one extreme or the other: math is only about the >physical world, Oh, yeah, economics is real physical. > or math is totaly unconcerned with the physical world, then you would be closer to the historical and contemporary truth by arguing that math is intimately related to the physical world. > I think Eugene Wigner has a more realistic question. Noting that so much of math is developed without consideration of the physical world, how do you explain its unreasonable effectiveness in describing it? Jon Miller Subject: Re: How do you discuss mathematics with a person who thinks mathematics is a part of physics? > Geometry in Ancient Civilizations_) the earliest mathematics was > geometric constructions used in altar construction. He even quotes one > algorithm for altar construction (I forget if it was Babylonian or > Vedic) that ends with this way, you will not displease the god. just as I'm reading this post I am wondering what use I have for sci.math. Herc Subject: Re: How do you discuss mathematics with a person who thinks mathematics is a part of physics? > ... He calls the mathematics that is done without any connection to the > physical world imaginary. Like it or not, every major development in mathematics ( or in any science for that matter} is either inspired/provoked by reference, directly or indirectly, to a real physical situation. This applies perhaps as well to already realized or systemematized work. The form of equations in electomagnetic theory for example,( that once made Boltzmann to remark if it was not God's work afterall ) when physically/geometrically arranged on paper - are visualizations of beautiful relationships and concepts with symmetry. If information is ordered into a set, it is also a real world exercise. Subject: Re: How do you discuss mathematics with a person who thinks mathematics is a part of physics? >> ... He calls the mathematics that is done without any connection to the >> physical world imaginary. > Like it or not, every major development in mathematics ( or in any > science for that matter} Mathematics is not a science. I have no idea how to solve this, please help. > 2^x = a*x It can't be solved in terms of functions with which you're probably familiar, but it can be solved in terms of the Lambert W function. Briefly, it's the multivalued inverse of the function x*e^x; for more information on the Lambert W function, see . I'm guessing that you're interested in real solutions for x (and that a is also real). If that is the case, then it's easy to see (by graphing both 2^x and a*x) that there can be, depending on the value of a, either no solution, one solution, or two solutions. When there are real solutions, they are given by x = - LambertW(ln(2)/a) / ln(2) using one of, or both of, the real branches of the Lambert W function. David Cantrell Subject: how to calculate a paralell line hi everybody. i know this is pretty basic. i know i had this at school. i know there should be an answer allready formulated to this question somewhere in the web, but i can't find it. so i come to you folks. i have following question. i need a formula which allways calculates in a cart. coordinate system a second line in a certin given distance to a given first line. i know where the first line begins, where it ends, so what it gradient is. i know the distance between those two lines. i know that a line between those two lines, beeing in a right angle two both, will be as long as the distance. i know i only need one point of the second line, because it will have the same gradient as the first. i know it has to do something with the further going formulas of pythagoras, but i just can't get them reconfigured. so if anybody can set me on the right path, i would be very thankfull. thanks n ps: by the way this is for a visual programming task i am sitting on. Subject: Re: how to calculate a paralell line > i need a formula which allways calculates in a cart. > coordinate system a second line in a certin given distance to a given > first line. i know where the first line begins, where it ends, so what > it gradient is. i know the distance between those two lines. Lines, being infinite in extent, don't have a beginning nor an end. Let m = slope of lines, d = distance between lines First line y = mx + a Second line y = mx + a + d sin t where m = tan t; 1 + 1/m^2 = csc^2 t; sin t = m/sqr(1+m^2) > ps: by the way this is for a visual programming task i am sitting on. For visual sake, use capital letters when appropiate. ----== Posted via Newsfeed.Com - Unlimited-Uncensored-Secure Usenet News==---- http://www.newsfeed.com The #1 Newsgroup Service in the World! >100,000 Newsgroups ---= 19 East/West-Coast Specialized Servers - Total Privacy via Encryption =--- Subject: Re: how to calculate a paralell line Lines, being infinite in extent, don't have a beginning nor an end. > Let m = slope of lines, d = distance between lines > First line y = mx + a > Second line y = mx + a + d sin t > where > m = tan t; 1 + 1/m^2 = csc^2 t; sin t = m/sqr(1+m^2) I was wondering if anybody had any idea on how to talk >about mathematics with a person whose attitude is that >a mathematical theory is worthless until validated by >physical experiments in the physical world (this was >the reason for my choice of the word realist - as >no alternative words occurred to me). The person in >question is a person who goes under the name of >Ken S. Tucker, and he has stated, as examples of the >attitude which I am discussing, that, for him, calculus >was validated by ballistics (presumably, for him, >calculus without a mechanical model may have no >validation). He also regards constants of integration >as physical quantities to which he can apply the >Principle of Relativity from physics (he never gives >an explicit explanation of exactly how he applies >the Principle). He calls the mathematics that is >done without any connection to the physical world >imaginary. So just how is one supposed to convince >such an individual of the error of his way of looking >at things? Thanks. >Tom Subject: Re: How to discuss with a person with a realist attitude to mathematics > I was wondering if anybody had any idea on how to talk > about mathematics with a person whose attitude is that > a mathematical theory is worthless until validated by > physical experiments in the physical world (this was > the reason for my choice of the word realist - as > no alternative words occurred to me). The person in > question is a person who goes under the name of > Ken S. Tucker, and he has stated, as examples of the > attitude which I am discussing, that, for him, calculus > was validated by ballistics (presumably, for him, > calculus without a mechanical model may have no > validation). He also regards constants of integration > as physical quantities to which he can apply the > Principle of Relativity from physics (he never gives > an explicit explanation of exactly how he applies > the Principle). He calls the mathematics that is > done without any connection to the physical world imaginary. So just how is one supposed to convince > such an individual of the error of his way of looking > at things? Thanks. > Tom What you say does not sound erroneous to me. It may just amount to keeping track of the difference between pure mathematics and the application of mathematics to the physical world. Some individuals value one of these more than the other (and you can find those on each side). When someone thinks the other side is worthless, then there is grounds for objection. But, unfortunately, you can find obnoxious instances of both of these as well. from _Spontaneous Phenomena_, by F. Topsoe, Academic Press 1990: THESIS 22: Those who seek a phenomenon which exactly follows a mathematical model, seek in vain. -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ Subject: Re: How to discuss with a person with a realist attitude to mathematics > I was wondering if anybody had any idea on how to talk > about mathematics with a person whose attitude is that > a mathematical theory is worthless until validated by > physical experiments in the physical world (this was > the reason for my choice of the word realist - as > no alternative words occurred to me). The person in > question is a person who goes under the name of > Ken S. Tucker, and he has stated, as examples of the > attitude which I am discussing, that, for him, calculus > was validated by ballistics (presumably, for him, > calculus without a mechanical model may have no > validation). He also regards constants of integration > as physical quantities to which he can apply the > Principle of Relativity from physics (he never gives > an explicit explanation of exactly how he applies > the Principle). He calls the mathematics that is > done without any connection to the physical world imaginary. So just how is one supposed to convince > such an individual of the error of his way of looking > at things? Thanks. > Tom Tom, People hold to these beliefs often religiously and sometimes quite irrationally. You could reply to such a person with a hundred perfect arguments why pure math is valuable, and it will never get through. So don't even try is my advice. For more on this topic, read Mathematics, the Loss of Certainly, by Morris Kline to get a deeper appreciation of the different camps there are on this subject: Set theoretical, logical, formal, intuitional. My own view is that intuition is good as a heuristic for new ideas and for convincing oneself of some axiom (like the axiom of choice) that requires some justification. Logical is good for correct deduction, but not all axioms are purely logical, such as the axiom of infinity. Formal is good as a reminder that intuitions and visual representations only go so far as proofs. And, set theoretical is the main choice by mathematicians these days. An alternative to set theory is category theory, of which I don't know enough to further comment on. Patrick http://ajnpx.com/html/AJNP_math.html Subject: Re: How to discuss with a person with a realist attitude to mathematics >> I was wondering if anybody had any idea on how to talk >> about mathematics with a person whose attitude is that >> a mathematical theory is worthless until validated by >> physical experiments in the physical world (this was >> the reason for my choice of the word realist - as >> no alternative words occurred to me). In philosophy a realist attitude is one that asserts that the objects of scrutiny are real (often opposed to nominalist). A mathematical realist is then one who holds that mathematical objects are real. In reply to your question, though, conversing with such people about mathematics is a pointless exercise. -- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html His mind has been corrupted by colours, sounds and shapes. The League of Gentlemen Subject: Re: How to discuss with a person with a realist attitude to mathematics >> I was wondering if anybody had any idea on how to talk >> about mathematics with a person whose attitude is that >> a mathematical theory is worthless until validated by >> physical experiments in the physical world (this was >> the reason for my choice of the word realist - as >> no alternative words occurred to me). > In philosophy a realist attitude is one that asserts that the > objects of scrutiny are real (often opposed to nominalist). > A mathematical realist is then one who holds that mathematical > objects are real. > In reply to your question, though, conversing with such people > about mathematics is a pointless exercise. Pun unintended? A pointless exercise to converse about whether points are real? Subject: Re: How to discuss with a person with a realist attitude to mathematics > ... > side). When someone thinks the other side is worthless, then there is > grounds for objection. But, unfortunately, you can find obnoxious Was it Halmos who said that applied mathematics is bad mathematics? My apologies to him if I'm mistaken. -- G.C. Subject: Re: How to discuss with a person with a realist attitude to mathematics > ... > side). When someone thinks the other side is worthless, then there is > grounds for objection. But, unfortunately, you can find obnoxious > Was it Halmos who said that applied mathematics is bad mathematics? My > apologies to him if I'm mistaken. G. H. Hardy had a low opinion of applied mathematics also. He was inordinately fond of number theory because he thought that there could never be any practical applications of it. I wonder what he would think of its use in modern cryptography. Subject: how to estimate the value and position of the highest frequency coefficient for an image? Dear all, I am facing with the following problem: In a 8x8 image block, I can do DCT to get 64 frequency coefficients... But I want just the highest frequency coefficient value, and its position in terms of row and column index (i, j)... Do I also need to compute DCT to get all 64 frequency coefficients? Or is there any faster algorithm? The problem is that I don't know the position of this highest frequency coefficient... so I cannot just compute, say, the coefficient at (8, 8)... maybe (6, 4) is the highest... Can anybody give me any hint on this? Thanks a lot, -Walala Subject: how to measure the orthogonality of a matrix? Dear all, I am facing with the following question: If a matrix T is orthogonal/orthonormal, we can have T*T'=T'*T=I... Now I have matrix A which is known to be non-orthonogonal/orthonormal... but it is nearly orthogonal/orthonormal, that's to say, A*A' and A'*A are nearly identity matrix I(all ones on diagonal line and very few non-zeros off the diagonal line...) Is there any mathematical method/term that I can used to measure the degree of such kind of non-orthogonality? How much orthogonality does a matrix have? Can anybody give me some hints? Thanks a lot, -Walala Subject: Re: how to measure the orthogonality of a matrix? Reduce all rows to unit vectors by dividing by the norm. Compute the volume. Compare that to the volume of the cube (i.e. 1) Subject: Re: how to measure the orthogonality of a matrix? I am glad to see your answer post. Thanks a lot for your reply... Is there any mathematical background underlying the method you've pointed out? I am hoping to learn more mathematical material about the method... Also, computing the volume means computing the derterminant, right? Thanks, -Walala > Reduce all rows to unit vectors by dividing > by the norm. Compute the volume. > Compare that to the volume of the cube > (i.e. 1) Subject: Re: how to measure the orthogonality of a matrix? > Dear all, > I am facing with the following question: > If a matrix T is orthogonal/orthonormal, we can have T*T'=T'*T=I... > Now I have matrix A which is known to be non-orthonogonal/orthonormal... > but it is nearly orthogonal/orthonormal, that's to say, A*A' and A'*A are > nearly identity matrix I(all ones on diagonal line and very few non-zeros > off the diagonal line...) > Is there any mathematical method/term that I can used to measure the degree > of such kind of non-orthogonality? How much orthogonality does a matrix > have? > Can anybody give me some hints? A lot is possible I think. The most straightforward one I can come up with is sum_over_i_and_j (Xij)^2, with X = A*A'-I Subject: How to solve this kind of DE? A normal DiffEq of second degree looks like: y'' + p y' + q y = r and those are nice (well, nice) to solve. Note that every function (and it's derivate) have 1 as exponent. How do one go about to solve the DiffEq when some of the parts are squared? In power of three? Is there a general way to solve such task? -- Kindly Yet Curiously Kerstin K.8all (The Giraffe) -------------------------- Subject: Re: How to solve this kind of DE? Cool Giraffe > A normal DiffEq of second degree looks like: > y'' + p y' + q y = r > and those are nice (well, nice) to solve. Note > that every function (and it's derivate) have 1 > as exponent. Such a DE is said to be linear. These are relatively easy because the solutions of the homogeneous equation ( y'' + p y' + q y = 0) can be added or multiplied by scalars. > How do one go about to solve the > DiffEq when some of the parts are squared? > In power of three? Is there a general way to > solve such task? There is no general way, but some cases are manageable, e.g. if you can solve the equation for y in terms of x and y' (without y''), or if you can solve it for y' in terms of x and y. Larry Subject: Re: How to solve this kind of DE? >How do one go about to solve the >DiffEq when some of the parts are squared? >In power of three? Is there a general way to >solve such task? If one is missing, and one other a higher power, this is done by reduction to a lower order equation, by a number of methods, that can be learned, as calculus is learned. Say, the integration by parts in calculus. And then, the first technique in my diffie queue text, separation of variables. Which I think is a different technique in calculus with the same name. But a differential operator is, well, different. When you square it, y' becomes y''. And that make linear differential operator equations solvable, I think. Yours, Doug Goncz, Replikon Research, Seven Corners, VA Unequal distribution of apoptotic factors regulates embryonic neuronal stem cell proliferation Hey, it's a news group! So that's the news! Subject: Re: How to solve this kind of DE? >A normal DiffEq of second degree looks like: >y'' + p y' + q y = r >and those are nice (well, nice) to solve. Note >that every function (and it's derivate) have 1 >as exponent. How do one go about to solve the >DiffEq when some of the parts are squared? y'' + p y' + q y^2 = r (with p, q and r constant): reduces to a first order DE by writing y' = v(y): dv/dy = y''/y' so v dv/dy + p v + q y^2 = r. Unfortunately that first-order DE, which is an Abel equation of the second kind, class A, probably doesn't have closed-form solutions (at least Maple can't find any). y'' + p (y')^2 + q y = r (with p, q and r constant): an implicit solution can be found by writing x = x(y), x' = 1/y', x'' = - y''/(y')^3 so -x'' + p x' = (r - q y^2) (x')^3. Then with x' = v we have v' = p v - (r - q y^2) v^3 which is a Bernoulli equation and can be made linear with the substitution v = w^(-1/2). Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 Subject: Re: If you reject the unprovable, you have to accept the absurd! > In your last series of nonsensical diatribes where you indiscriminately > mixed continuous and discrete operations into a mish-mash of conflicting > concepts and false conclusions you proclaimed that certain calculations > were impossible (garbage-in-garbage-out). You also promised to leave this > newsgroup and never come back. Please honor your commitment. His probably out of his medication again. Goran Subject: Re: If you reject the unprovable, you have to accept the absurd! YY YY OOOO UU UU YY YY OO OO UU UU YY YY OO OO UU UU YYY OO OO UU UU YY OO OO UU UU YY OO OO UU UU YY OO OO UU UU YY OOO UUUUU are not very convincing. V.Gopal a .8ecrit dans le message de > When YOU see the same thing in the numerator as well as in the > denominator, YOU cancel both of them. YOU accept: (1) X*1/X=1 and > T*1/T=1. (2) XY=1 (same as X*1/X=1) (3) a^x/ * 1/a^x = 1 (4) TanA * > CotA=1 etc. > In X*1/X=1, if X continuously decreases then Y (or 1/x) has to > increase continuously. IF YOU WANT THIS TO HAPPEN YOU HAVE TO SATISFY > ALL THE FOLLOWING CONDITIONS: > (A) YOU have to maintain one to one relation between X and Y because > number of times YOU assign value to X = number of times YOU calculate > the value of Y. > (B) YOU have to accept that X and Y also indicate quantity, distance > or time FROM 0 because (X - 0) = X, (Y - 0) = 0. > (C) YOUR Y=F(X) has to maintain the same kind of continuity and order > in one direction in space or time, which a smooth curve is expected to > have. > (D) Therefore the first question YOU have to answer is: FROM WHAT > VALUE OF Y/X can increase or decrease in the value of Y/X in one > direction, begin? This value of Y/X gives the STARTING point of the > corresponding curve in geometry. > YOU CANNOT SHAOW a curve without showing its starting and ending > points. > (E) YOU have three options: Y=0 and X=infinity, Y=1, X=1 or Y=infinity > and X=0. > These starting points correspond to Y/X or Tan A= Tan0, Tan45 and > Tan90. > But YOU are compelled to chose Y=1, X=1 because YOU cannot even begin > to count from 0. If YOU chose X or Y, any one of them to be 0, then > the other automatically becomes infinity and problem of starting point > arises. Therefore YOUR starting point is always 1 (mother of all > numbers). BUT: > (1) If you begin from 1, to maintain continuity and order you have to > move in one direction in space or time and reach the end. It is > symmetrical about 1. > (2) YOU show a NUMBER LINE starting from 0, then show X<1 or fractions > then 1 and then finally X>1 or vulgar fractions, in an ascending > order, up to infinity. > 0----X---1-----2-----1/X or Y-----10^10--.88infinity (Figure 1) > (3) YOU have kept finite space towards 0, therefore space available > towards 0 goes on decreasing as number of values of X (in the > descending order) increases because, but space available towards > infinity never decreases due to increase in number of values of 1/X or > Y (in the ascending order) because 1/X or Y has no upper limit. Can > YOU accommodate the same number terms between 0 and 1 as YOU CAN > between 1 and infinity, to prove that X*1/X=1 is true? > (4) YOU show XY=1 by a hyperbola but show X*1/X=1 by a straight line, > why? > (5) a^x*a^(-x)=1. Even here YOU begin from 1. Here x gives number of > terms in both, numerator and denominator. Therefore when a^x (a<1) > becomes 0 by decreasing, a^(-x) also reaches infinity by increasing. > Here when x=0, Y=1; a^x and a^(-x) look like two halves of a > hyperbola, with top half rotated by 180 degrees. But YOU have to > explain how within the short duration between 0 and 1 the constant or > the base a vanishes. Between x= 0 and x=1 there are infinite terms or > number of numbers. Since the dispute about X*1/X=1 cannot be settled > YOU always assume X to be integer without reciprocal like number of > half-lives. > (6) TanA*CotA=1 is represented by two identical but independent > curves, which intersect at only one point - at Tan45. > Number of times YOU put value of X=number of times YOU get value of Y > Therefore CAN YOU superimpose all assigned values of X above the > calculated values of Y as shown below? (If No, please explain why.) > X=1;X=1;Tan45 Values assigned to X X=0; X=0; a^x all 0; Tan0 > a^0 -l---l---l---l---l---l----l---i-----> zero and infinity > 1/X=1;Y=1;Cot45 Calculated values of Y 1/X;Y,a^(-x)all infinity;Cot0 > Figure 2 > Do YOU want to prove the unprovable or do YOU want to accept the > absurd? > I am giving the list below, PLEASE GIVE YOUR CHOICE IN EACH CASE. > (1) The conventional number line as shown in Fig 1 is logically > correct. > (2) X*1/X=1 is correct; there IS one to one relation between X and 1/X > or Y. > (3) Therefore the number of numbers between 1 and 0 is same as the > number of numbers between 1 and infinity. (Number of numbers is like > length or time.) > (4) That means number of numbers between 1 and 0 is more than number > of numbers between 1 and 2, 2 and 3 etc. > (5) Even when X*1/X=1, one to one relation between X and 1/X does not > exist. (6) For each value of X less than 1, 1/X has more than one > value. > (7) X*1/X=1 is an incorrect statement > Before I proceed further YOU decide whether the statement: > Y=F(X) is smooth if and only if Y/X is a continuous variable. True or > False? > Then, please refer to fig. 2 and make your choice: [Y=F(X)-no > restriction.] > (8) There is one to one relation between X and Y in Y=F(X) even when > Y/X is not a constant and Y=F(X) is not a straight line (Yes? No?) > (9) Can YOU superimpose assigned values of X and calculated values of > Y as shown in figure 2? (length scales on both the axes are same.) > (10) Does the values of Y and X at every point on the line in figure 2 > correspond to value of Y/X at that point? (Yes? No?). Y is number of > numbers between 1 and Y, and, X is number of numbers between 1 and X. > We can use different scales. > (11) Does the value of Y/X (slope) change where YOU have assigned the > value of X and calculated the value of Y? (If Yes, it becomes temporal > change!) > (12) Does the value of Y/X change at points where YOU have not > assigned the value of X and calculated the value of Y? (If Yes, it > becomes temporal change.) > Note: Assigned values of X and calculated values of Y give a series of > triangles, in which shapes are unrelated. Curves in geometry are > porous; you can construct a series of triangle of any shape at you > will. If value of Y/X has to change continuously then value of Y must > slip relative to the value of X as both move, meaning YOU have to plot > Y/X= variable against Y/X constant. (This is INTERNAL CHANGE.) > Otherwise as variables, X and Y are independent > (13) Under these conditions can YOU suggest any Y=F(X) that does not > give porous line in geometry? > IS CALCULUS POSSIBLE WITH SET OF NUMBERS AND WITHOUT SMOOTH FUNCTIONS > OR CONTINUOUS AND SMOOTH CURVES? > In X*1/X=1 you can never prove that X and 1/X both are continuous; it > presents unprovable situation. Therefore, DO YOU THINK THERE IN ONE - > MANY RELATION BETWEEN X AND 1/X? Subject: Re: Integral posed in problem set: Elementary or not? > Steven escribi.97 en el > mensaje|nTCW_a.5$Op.2@news02.roc.ny: >> >>> I found the following problem listed on an old problem page. >>> Question: Is the following integral elementary? >> >>> INT[ sqrt(1 + ln(x)/x) dx ]? >>> Ray Steiner > >> If you mean INT[ sqrt(1+ln(x))/x dx], use u=ln(x) for your >> substitution. > >> -- >> Will Twentyman >> email: wtwentyman at copper dot net > > If you mean INT[ sqrt(1+ln(x))/x dx], you can let u= ln(x) but it > would be a little easier to try u = 1 = ln(x). > Steven > You meant u = 1 + ln(x), I suppose Sorry, all! I copied the question correctly: Is INT[ sqrt( 1 + (ln x/x) ) dx ] elementary? I suspect not, because MAPLE couldn't do this one either! Also, how does the substitution x = exp(2t^2 -1) reduce this to a well known non-elementary problem? Thanks for all your replies! Ray Steiner Subject: Intermediate Value Theorem Tested In Court I was teaching my younger brother to drive a manual car a few month back. At some point he came to a stop sign at the top of a hill. Of course prior to getting to the stop sign he was going forward, then he stop (not for too long) rolled backward, stop (not for very long!) and then took off. He was given a summons for not coming to a complete stop. The officer refused to agree that in fact he stopped twice. I went to court with my brother the other day. I asked the judge if I proved that my brother stopped twice if she would dismiss the charges. She replied once would be sufficient. I then asked the officer if he felt that my brother upon reaching the stopped sign rolled backward and then took off and he said yes as if this was not considered stopping. As he said yes the judge responded with case dismissed!!! The officer was shocked. Subject: Re: Intermediate Value Theorem Tested In Court >I was teaching my younger brother to drive a manual car a few month back. At >some point he came to a stop sign at the top of a hill. Of course prior to >getting to the stop sign he was going forward, then he stop (not for too >long) rolled backward, stop (not for very long!) and then took off. He was >given a summons for not coming to a complete stop. The officer refused to >agree that in fact he stopped twice. I went to court with my brother the >other day. I asked the judge if I proved that my brother stopped twice if >she would dismiss the charges. She replied once would be sufficient. I then >asked the officer if he felt that my brother upon reaching the stopped sign >rolled backward and then took off and he said yes as if this was not >considered stopping. As he said yes the judge responded with case >dismissed!!! The officer was shocked. Clever, but the intermediate value theorem fails in two dimensions. Your brother might drive a car along a road and make a U-turn at the end of a cul-de-sac, heading back the other direction while never stopping. Even if we approximate the problem as one-dimensional (no turns, no lane changes), your bother is supposed to stop at the STOP sign. If he goes past the STOP sign, then goes backwards, and reaches the STOP sign again in a forward direction, then there should be three STOPs. Two is not enough. -- Wanted: Experts at choosing the best of 100+ applicants for a position. Register as a California voter by September 22, and vote on October 7. Peter-Lawrence.Montgomery@cwi.nl Home: San Rafael, California Microsoft Research and CWI Subject: Re: Intermediate Value Theorem Tested In Court Content-transfer-encoding: 8bit > I was teaching my younger brother to drive a manual car a few month back. At > some point he came to a stop sign at the top of a hill. Of course prior to > getting to the stop sign he was going forward, then he stop (not for too > long) rolled backward, stop (not for very long!) and then took off. He was > given a summons for not coming to a complete stop. The officer refused to > agree that in fact he stopped twice. I went to court with my brother the > other day. I asked the judge if I proved that my brother stopped twice if > she would dismiss the charges. She replied once would be sufficient. I then > asked the officer if he felt that my brother upon reaching the stopped sign > rolled backward and then took off and he said yes as if this was not > considered stopping. As he said yes the judge responded with case > dismissed!!! The officer was shocked. Had your brother pulled this on a US Air Force base, he'd have been in for a surprise. The rule (forty years ago, at least, the last time I drove on one) was that you had to come to a full stop for FIVE SECONDS. That's an eternity. --Ron Bruck Subject: Invariants of polynomes How can I construct all the invariants of a polynome in several variables f(x1,x2,...,xn)=0? E.g. ax^2+bx+c has only one invariant: whether the zeroes are distinct or not. -- Hauke Reddmann <:-EX8 Private email:fc3a501@math.uni-hamburg.de For our chemistry workgroup,remove math from the address For spamming, remove anything else Subject: Re: Irredicibles of Z_p[x] > A finite field F_p^n, is a simple extension of its prime subfield F_p. > Indeed, F_p^n = F_p(g), where g is a generator of F_p^n. > For each positive integer n there exists an > irreducible polynomial of degree n over F_p. > How is this so? Can they be constructed? For a proof that this is so see, for example, Introduction to Finite Fields and their Applications -- by Rudolf Lidl Harald Niederreiter or most any book on abstract algebra. Or if you search around using Google you will probably find some notes where a proof of this can be found. For a proof with a minimum of machinery see Algebraic Coding Theory, -- by Elwyn R. Berlekamp The easiest way to get an irreducible polynomial of degree n over F_p is to just generate random polynomials until you find one that's irreducible. Here's a Maple procedure that will generate up to 1000 random polynomials searching for one that's irreducible. If the degree is very large you may need to increase the 1000. > with(RandomTools): > Gen:=proc(n,p) > local i,f; > for i from 1 to 1000 do > f:=Generate(polynom(integer(range=0..p-1), x, degree=n)); > if Irreduc(f) mod p = true then return i,sort(f); fi; > od; > FAIL; > end proc: Using this to get an irreducible polynomial of degree 100 over F_17 in less than 4 seconds: Note that 54 is the number of polynomials tried before finding an irreducible. > start_time:=time(): > lprint(Gen(100,17)); > time_required:=(time()-start_time)*sec; 54, 5*x^100+9*x^99+14*x^98+12*x^96+11*x^95+9*x^93+8*x^92+5*x^91+7* x^90+11* x^89+9*x^88+6*x^87+4*x^85+x^84+12*x^83+5*x^82+x^81+6*x^80+7*x^ 79+12*x^ 78+12*x^77+8*x^76+9*x^75+10*x^74+2*x^73+6*x^72+7*x^71+15*x^70+ 16*x^69+ 10*x^68+15*x^67+16*x^66+12*x^65+9*x^64+14*x^63+15*x^62+7*x^61+ 6*x^60+4 *x^59+7*x^58+7*x^57+3*x^56+16*x^55+3*x^54+12*x^53+4*x^52+3*x^ 51+5*x^50 +4*x^49+5*x^48+14*x^47+9*x^46+12*x^45+14*x^44+15*x^43+6*x^42+ 11*x^41+2 *x^40+8*x^39+10*x^38+16*x^37+16*x^36+2*x^35+3*x^34+6*x^33+5*x^ 32+14*x^ 31+6*x^30+9*x^29+8*x^28+11*x^27+9*x^25+3*x^24+16*x^23+9*x^22+ 16*x^21+1 4*x^20+4*x^19+13*x^18+3*x^17+11*x^15+2*x^14+7*x^13+3*x^12+x^11 +3*x^10+ 6*x^9+x^8+7*x^7+6*x^6+13*x^5+6*x^3+9*x^2+16*x+6 time_required := 3.926 sec Subject: Re: Irredicibles of Z_p[x] Subject: Re: Irredicibles of Z_p[x] >> A finite field F_p^n, is a simple extension of its >> prime subfield F_p. >> Indeed, F_p^n = F_p(g), where g is a generator of F_p^n. >> For each positive integer n there exists an >> irreducible polynomial of degree n over F_p. >> Is there a direct way using the theorem above to show this? >Well, if you've already shown there's a field F_{p^n}, there >must be an irreducible polynomial f(x) of degree n such that >F_{p^n} = F_p[x]/(f(x)). Your comment is based upon F_p^n being a simple extension of F_p. As F_p^n = F_p(g), for some generator g of F_p^n, let k be the degree of g over F_p. Then F_p^n is a k-dimensional vector space over F_p which would have p^k elements. Thus k = n and the minimal polynomial for g is an irreducible polynomial in F_p[x] of degree n. ---- ----== Posted via Newsfeed.Com - Unlimited-Uncensored-Secure Usenet News==---- http://www.newsfeed.com The #1 Newsgroup Service in the World! >100,000 Newsgroups ---= 19 East/West-Coast Specialized Servers - Total Privacy via Encryption =--- Subject: Re: Irredicibles of Z_p[x] > Using this to get an irreducible polynomial of degree 100 over F_17 in > less than 4 seconds: > Note that 54 is the number of polynomials tried before finding an > irreducible. Lucky! As less than 1 in 100 is irreducible :-) -- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html Subject: Re: Irredicibles of Z_p[x] > Using this to get an irreducible polynomial of degree 100 over F_17 in > less than 4 seconds: > Note that 54 is the number of polynomials tried before finding an > irreducible. > Lucky! As less than 1 in 100 is irreducible :-) Not so lucky. The probability of getting an irreducible of degree 100 in 54 or less trials is more than 4/10. --Edwin Subject: Is there a simple way to see if a matrix can be factorized Is there a simple way to see if a matrix can be factorized? Example, A is a matrix A = |23, 34 | |77, 46 | Is there a simple way to know if A can be factorized as product of two matrix A= B*C, where each element of B and C is positive integer ? Thanks. Subject: Re: Is there a simple way to see if a matrix can be factorized If all vectors of A are orthogonal to each other, then we know A is the product of two other (and infinitely more) orthogonal matrices B and C. If each vector of A is linearly independent, likewise there exists an orthogonal matrix B, and a transformation matrix C such that C*B = A. In otherwords, if A is linearly independent, there exists the B, C you want. Oh yeah, if you want components of B, C to be positive, we have to enforce orthogonal matrix with positive components. > Is there a simple way to see if a matrix can be factorized? > Example, A is a matrix > A = |23, 34 | > |77, 46 | > Is there a simple way to know if A can be factorized as product > of two matrix A= B*C, where each element of B and C is positive integer ? > Thanks. Subject: Re: Is there a simple way to see if a matrix can be factorized ieee std > Is there a simple way to see if a matrix can be factorized? > Example, A is a matrix > A = |23, 34 | > |77, 46 | > Is there a simple way to know if A can be factorized as product > of two matrix A= B*C, where each element of B and C is positive integer ? If we're talking only of square matrices, det(A) will have to be equal to det(B)det(C). Better, the characteristic polynomial of A will be the product of the c.p.'s of B and C. But you might want to clarify just what is meant by factorization. E.g. if B is invertible (e.g. a 0-1 matrix representing a permutation) then we can always factor A as A=BDB^{-1} simply by setting D=B^{-1}AB. LH Subject: Re: Is there a simple way to see if a matrix can be factorized (For which 2x2 matrices A can we find 2x2 matrices B, C with positive integer entries such that A = BC?) If we simply require the elements of B and C to be positive, not necessarily positive integers, the problem is simple. Let A = [ a1 a2 ] for ease of notation [ a3 a4 ] If any element of A is nonpositive then it is clearly imposssible for all entries of B and C to be positive. On the other hand, if all of the elements a1, a2, a3, a4 of A *are* positive, we can let B be a positive perturbation of the identity matrix, guaranteeing that the matrix C is sufficiently close to A that it is itself positive. Explicitly, let B be the perturbed identity matrix [ 1 d ] [ d 1 ] where 0 < d < 1 is strictly less than min(a1/a3, a3/a1, a2/a4, a4/a2), and let C be the matrix 1/(1 - d^2) * [ a1 - d*a3 a2 - d*a4 ] [ a3 - d*a1 a4 - d*a2 ] Now, since 1/(1 - d^2) > 0, all the entries of C are positive from the definition of d (for instance, we can be certain that a1 - d*a3 > 0 since this is equivalent to d < a1/a3). The form of C can be found directly by inverting the matrix B and calculating B^(-1)A. It is simple to confirm that the product BC is equal to the original matrix A. Moreover, this result may be generalised to higher dimensions: for instance, given a 3x3 matrix A with positive entries, choose B to be the matrix [ 1 d d ] [ d 1 d ] [ d d 1 ] This matrix is certainly invertible for 0 < d < 0.5, and we can find a suitable d simply by computing C = B^(-1)A as a function of d, and decreasing d towards zero until C is sufficiently close to A that it is a positive matrix. HJ > If all vectors of A are orthogonal to each other, then we know A is > the product of two other (and infinitely more) orthogonal matrices B > and C. > If each vector of A is linearly independent, likewise there exists an > orthogonal matrix B, and a transformation matrix C such that C*B = A. > In otherwords, if A is linearly independent, there exists the B, C you > want. > Oh yeah, if you want components of B, C to be positive, we have to > enforce orthogonal matrix with positive components. > Is there a simple way to see if a matrix can be factorized? > Example, A is a matrix > A = |23, 34 | > |77, 46 | > Is there a simple way to know if A can be factorized as product > of two matrix A= B*C, where each element of B and C is positive integer ? > Thanks. Subject: Re: Is there a simple way to see if a matrix can be factorized Thanks for all reply. The original post is to seek A= BC where each element of A, B, C is positive integer. Is it a simple way to do this ? > (For which 2x2 matrices A can we find 2x2 matrices B, C with positive > integer entries such that A = BC?) > If we simply require the elements of B and C to be positive, not > necessarily positive integers, the problem is simple. > Let A = [ a1 a2 ] for ease of notation > [ a3 a4 ] > If any element of A is nonpositive then it is clearly imposssible for > all entries of B and C to be positive. > On the other hand, if all of the elements a1, a2, a3, a4 of A *are* > positive, we can let B be a positive perturbation of the identity > matrix, guaranteeing that the matrix C is sufficiently close to A that > it is itself positive. > > Explicitly, let B be the perturbed identity matrix > [ 1 d ] > [ d 1 ] > where 0 < d < 1 is strictly less than min(a1/a3, a3/a1, a2/a4, a4/a2), > and let C be the matrix > 1/(1 - d^2) * [ a1 - d*a3 a2 - d*a4 ] > [ a3 - d*a1 a4 - d*a2 ] > Now, since 1/(1 - d^2) > 0, all the entries of C are positive from the > definition of d (for instance, we can be certain that a1 - d*a3 > 0 > since this is equivalent to d < a1/a3). The form of C can be found > directly by inverting the matrix B and calculating B^(-1)A. > It is simple to confirm that the product BC is equal to the original > matrix A. Moreover, this result may be generalised to higher > dimensions: for instance, given a 3x3 matrix A with positive entries, > choose B to be the matrix > [ 1 d d ] > [ d 1 d ] > [ d d 1 ] > This matrix is certainly invertible for 0 < d < 0.5, and we can find a > suitable d simply by computing C = B^(-1)A as a function of d, and > decreasing d towards zero until C is sufficiently close to A that it > is a positive matrix. > HJ > If all vectors of A are orthogonal to each other, then we know A is > the product of two other (and infinitely more) orthogonal matrices B > and C. > If each vector of A is linearly independent, likewise there exists an > orthogonal matrix B, and a transformation matrix C such that C*B = A. > In otherwords, if A is linearly independent, there exists the B, C you > want. > Oh yeah, if you want components of B, C to be positive, we have to > enforce orthogonal matrix with positive components. > > Is there a simple way to see if a matrix can be factorized? > > Example, A is a matrix > > A = |23, 34 | > |77, 46 | > > Is there a simple way to know if A can be factorized as product > of two matrix A= B*C, where each element of B and C is positive integer ? > > Thanks. Subject: Re: Is there a simple way to see if a matrix can be factorized >Is it a simple way to do this ? If A has no coprime elements? Maybe. If the elements of A are pairwise coprime? I don't think so. Can anyone confirm? Yours, Doug Goncz, Replikon Research, Seven Corners, VA Unequal distribution of apoptotic factors regulates embryonic neuronal stem cell proliferation Hey, it's a news group! So that's the news! Subject: Re: Is there a simple way to see if a matrix can be factorized >>Is it a simple way to do this ? >If A has no coprime elements? Maybe. >If the elements of A are pairwise coprime? I don't think so. What, you mean like [ 5 9 ] [ 1 2 ] [ 1 1 ] [ 7 11 ] = [ 3 2 ] [ 2 4 ] ? Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 Subject: Re: Is there a simple way to see if a matrix can be factorized Larry Hammick ... > Better, the characteristic polynomial of A will be the product > of the c.p.'s of B and C. Oops, sorry, that needs a bit of work. But you get the idea :) The traces add, at least. LH Subject: Re: Is there a simple way to see if a matrix can be factorized >The original post is to seek A= BC where each element of A, B, C >is positive integer. >Is it a simple way to do this ? Maybe not really simple, but it's a finite search. Let's say [ a b ] [ s t ] [ w x ] A = [ c d ], B = [ u v ], C = [ y z ] Note that a + c = sw + ty + uw + vy = (s+u)w + (t+v)y >= 2 (w+y) and similarly b + d >= 2 (x + z). So search through all 2 x 2 matrices C of positive integers whose column sums are at most half the corresponding column sums of A, checking whether A C^(-1) is a matrix of positive integers, i.e. whether each of az-by, bw-ax, cz-dy, dw-cx is a positive multiple of det(C). The search might be cut down significantly. First note that we may assume det(C) > 0, since if B and C are a solution then so are BJ and JC where [ 0 1 ] J = [ 1 0 ] Moreover, det(C) must divide det(A). We want az - by > 0 and c z - d y > 0 so z > max(b/a, d/c) y, and similarly x < min(b/a, d/c) w. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 Subject: Re: Is there a simple way to see if a matrix can be factorized >Larry Hammick >... >> Better, the characteristic polynomial of A will be the product >> of the c.p.'s of B and C. >Oops, sorry, that needs a bit of work. But you get the idea :) The traces >add, at least. ??? Tr(B)+Tr(C)=Tr(B+C), but you're multiplying the matrices. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 Subject: Re: Is there a simple way to see if a matrix can be factorized A counterexample to my: >If A has no coprime elements? Maybe. >>If the elements of A are pairwise coprime? I don't think so. >What, you mean like >[ 5 9 ] [ 1 2 ] [ 1 1 ] >[ 7 11 ] = [ 3 2 ] [ 2 4 ] ? I bow before you, sir. That is to say, I have inspected your counterexample and found it surprising and correct. Let's see: Perhaps it will be true that: If A is a matrix of unique primes or is pairwise coprime, and B and C contain no factors of any number in A, and with special consideration for 1, which is not a prime, but can be a factor, and cannot be coprime to anything; Then A # B*C, and we have a new cryptographic method with public key one of A, B, or C, and private key one of the others? What is the strength of this method, and how does it increase with rank? Copy to sci.crypt? I can't do that with aol. Yours, Doug Goncz, Replikon Research, Seven Corners, VA The hormones work at different speeds. In a fight-or-flight scenario, glucocorticoids are the ones drawing up blueprints for new aircraft carriers; epinephrine is the one handing out guns. Subject: JSH: Frustration, venting, weird group Well I like being a writer, as one of the things I can do when I get frustrated is vent in ways that befuddle. I find it fascinating that my previous post gained the interest that it did. Your group is odd. In any event, various indicators have shown me that I don't have the kind of target penetration that I've thought I did. After all, these posts are for a purpose, but it doesn't look like I'm getting much bang for my buck, though there are a lot of useless tagalongs. Though at least I did find out about the field Z[1/2], or Z[1/7] or whatever you want to call it, though it's simpler to call it reals, so it wasn't a wash, still there's just something not satisfying about arguing here. I'll finish my current assessment, and see if there isn't any way to actually use this newsgroup to promote my work, rather than waste time arguing with people who have just shown me not only how little mathematics they know, but how dedicated they can be to replying to just about everything I put out. It's freaking bizarre. I almost wonder if I posted just a . how many people would reply. I mean I dragged this out a good ways to see what people would keep replying and you can just look at the threads. There were some people who were very dedicated. Are they serious? James Harris Subject: Re: JSH: Frustration, venting, weird group >Well I like being a writer, as one of the things I can do when I get >frustrated is vent in ways that befuddle. I find it fascinating that >my previous post gained the interest that it did. Your group is odd. >In any event, various indicators have shown me that I don't have the >kind of target penetration that I've thought I did. After all, these >posts are for a purpose, but it doesn't look like I'm getting much >bang for my buck, though there are a lot of useless tagalongs. >Though at least I did find out about the field Z[1/2], or Z[1/7] or >whatever you want to call it, though it's simpler to call it reals, >so it wasn't a wash, still there's just something not satisfying about >arguing here. >I'll finish my current assessment, and see if there isn't any way to >actually use this newsgroup to promote my work, rather than waste time >arguing with people who have just shown me not only how little >mathematics they know, but how dedicated they can be to replying to >just about everything I put out. >It's freaking bizarre. I almost wonder if I posted just a . how >many people would reply. I mean I dragged this out a good ways to see >what people would keep replying and you can just look at the threads. >There were some people who were very dedicated. Are they serious? Hint: Your traditional this was all a test thing works better if you don't include idiotic statements like saying Z[1/2] is a field. It _is_ fascinating how little mathematics the people here know. Even more fascinating is the fact that _everyone_ on the planet seems to be just as ignorant: the leading mathematicians you bother with email, the editors and referees for the journals you send papers to. Why, it turns out that even the authors of web sites that you cite to prove you're right about things don't know any math! mathworld doesn't seem to realize that the word means the same as convergent. Very strange - you seem to be the only person on Earth who's not ignorant of basic mathematics. Makes a person wonder why things work - given that they're designed by such ignoramuses you'd expect that computers would be crashing all the time, power grids would go down every few years, etc. Hmm. >James Harris ************************ Subject: Re: JSH: Frustration, venting, weird group > Well I like being a writer, as one of the things I can do when I get > frustrated is vent in ways that befuddle. I find it fascinating that > my previous post gained the interest that it did. Your group is odd. When you post something that sounds as if you think you're on some sort of mission from God to evaluate the human race, we think you mean it. That's because we're convinced that you're insane enough to believe it yourself. In fact, I'm willing to bet you *did* believe it. You either were drunk or hallucinating at the time, and the only reason you're backpedalling now is because you've sobered up or your delusions have eased up a bit, and you've realized how big a loon you were being. I'm confident that you're going to lose italtogether one of these days, and we'll get a *really* good show before they lock you away. -- Wayne Brown | When your tail's in a crack, you improvise fwbrown@bellsouth.net | if you're good enough. Otherwise you give | your pelt to the trapper. e^(i*pi) = -1 -- Euler | -- John Myers Myers, Silverlock Subject: Re: JSH: Frustration, venting, weird group > ... When I saw weird group in the Subject header I thought that you were about to prove that every abelian group is anti-commutative or something like that. -- G.C. Subject: Re: JSH: Frustration, venting, weird group X-ID: ZNu4WQZBZeV7cDWwZ4Ig4uM6pH4C4a5R+jyTUH9vQoGyuONntpjbkB > Well I like being a writer, as one of the things I can do when I get > frustrated is vent in ways that befuddle. I find it fascinating that > my previous post gained the interest that it did. Your group is odd. Oh, ... I thought it was even. > In any event, various indicators have shown me that I don't have the > kind of target penetration that I've thought I did. Probably you should try with a pussy instead? F. Subject: Re: JSH: Frustration, venting, weird group > Well I like being a writer, as one of the things I can do when I get > frustrated is vent in ways that befuddle. I find it fascinating that > my previous post gained the interest that it did. Your group is odd. Does this mean you've decided to change from crank to troll? > In any event, various indicators have shown me that I don't have the > kind of target penetration that I've thought I did. After all, these > posts are for a purpose, but it doesn't look like I'm getting much > bang for my buck, though there are a lot of useless tagalongs. Going for troll... > Though at least I did find out about the field Z[1/2], or Z[1/7] or > whatever you want to call it, though it's simpler to call it reals, > so it wasn't a wash, still there's just something not satisfying about > arguing here. Wrong. Look back at the proof in the thread you abandoned. If you don't like arguing, stop posting. Or start listening and asking *why* we claim what we claim. > I'll finish my current assessment, and see if there isn't any way to > actually use this newsgroup to promote my work, rather than waste time > arguing with people who have just shown me not only how little > mathematics they know, but how dedicated they can be to replying to > just about everything I put out. Sounds like a move to semi-troll, semi-crank. A new hybrid? > It's freaking bizarre. I almost wonder if I posted just a . how > many people would reply. I mean I dragged this out a good ways to see > what people would keep replying and you can just look at the threads. Of course! We're addicted to replying to you. I look forward to my daily fix and become depressed when I can't trash your latest claims. > There were some people who were very dedicated. Are they serious? To math, yes. > James Harris -- Will Twentyman email: wtwentyman at copper dot net Subject: JSH: Testing failure, once again Yet another round of testing is complete and once again the math community has failed ALL tests. I wish to point out that evaluating a species using mathematics is not only sensible, but fair. Mathematicians were tasked with representing homo sapiens sapiens, and they have failed all testing so far. It is my hope that the testing is complete, as I fail to see the point of continued rounds, but will do as tasked. So far the math community has shown a lack of basic mathematical understanding, an inability to be taught basic mathematics, and a refusal to engage in rational discourse at anything but a very basic level. It has been determined that mathematical understanding is at only a rudimentary level, with no evidence of ability beyond that level. Determination is that past assessments remain correct and that humanity lack basic abilities to advance beyond their present state, as they lack the necessary mathematical aptitude. It is my STRONG recommendation that testing cease as pointless. Mathematicians were tested for humanity; mathematicians failed. There seems to be no positive ending to this story, and no writer, not even I, can fix it. I recommend that the story be finished so that I can move on to the next group on this planet, as many indications are that they are stellar. James Harris Subject: Re: JSH: Testing failure, once again > Yet another round of testing is complete and once again the math > community has failed ALL tests. > I wish to point out that evaluating a species using mathematics is not > only sensible, but fair. Mathematicians were tasked with representing > homo sapiens sapiens, and they have failed all testing so far. > It is my hope that the testing is complete, as I fail to see the point > of continued rounds, but will do as tasked. > So far the math community has shown a lack of basic mathematical > understanding, an inability to be taught basic mathematics, and a > refusal to engage in rational discourse at anything but a very basic > level. > It has been determined that mathematical understanding is at only a > rudimentary level, with no evidence of ability beyond that level. > Determination is that past assessments remain correct and that > humanity lack basic abilities to advance beyond their present state, > as they lack the necessary mathematical aptitude. > It is my STRONG recommendation that testing cease as pointless. > Mathematicians were tested for humanity; mathematicians failed. > There seems to be no positive ending to this story, and no writer, not > even I, can fix it. > I recommend that the story be finished so that I can move on to the > next group on this planet, as many indications are that they are > stellar. > James Harris I'd strongly recommend another planet entirely. However, and with all due contempt, don't let the door slam you in the rear. -- There are two things you must never attempt to prove: the unprovable -- and the obvious. -- -- http://www.crbond.com Subject: Re: JSH: Testing failure, once again > Yet another round of testing is complete and once again the math > community has failed ALL tests. > I wish to point out that evaluating a species using mathematics is not > only sensible, but fair. Mathematicians were tasked with representing > homo sapiens sapiens, and they have failed all testing so far. > It is my hope that the testing is complete, as I fail to see the point > of continued rounds, but will do as tasked. > So far the math community has shown a lack of basic mathematical > understanding, an inability to be taught basic mathematics, and a > refusal to engage in rational discourse at anything but a very basic > level. > It has been determined that mathematical understanding is at only a > rudimentary level, with no evidence of ability beyond that level. > Determination is that past assessments remain correct and that > humanity lack basic abilities to advance beyond their present state, > as they lack the necessary mathematical aptitude. > It is my STRONG recommendation that testing cease as pointless. > Mathematicians were tested for humanity; mathematicians failed. > There seems to be no positive ending to this story, and no writer, not > even I, can fix it. > I recommend that the story be finished so that I can move on to the > next group on this planet, as many indications are that they are > stellar. The mathematical community will appeal your decision, and your decision will be reversed. David Bernier P.S. Who tasked you? Subject: Re: JSH: Testing failure, once again > Yet another round of testing is complete and once again the math > community has failed ALL tests. > I wish to point out that evaluating a species using mathematics is not > only sensible, but fair. Mathematicians were tasked with representing > homo sapiens sapiens, and they have failed all testing so far. And what species are you in? > It is my hope that the testing is complete, as I fail to see the point > of continued rounds, but will do as tasked. > So far the math community has shown a lack of basic mathematical > understanding, an inability to be taught basic mathematics, and a > refusal to engage in rational discourse at anything but a very basic > level. > It has been determined that mathematical understanding is at only a > rudimentary level, with no evidence of ability beyond that level. > Determination is that past assessments remain correct and that > humanity lack basic abilities to advance beyond their present state, > as they lack the necessary mathematical aptitude. > It is my STRONG recommendation that testing cease as pointless. > Mathematicians were tested for humanity; mathematicians failed. Does that mean humanity failed? If so, what does that say for you? > There seems to be no positive ending to this story, and no writer, not > even I, can fix it. > I recommend that the story be finished so that I can move on to the > next group on this planet, as many indications are that they are > stellar. > James Harris I find myself wondering if James's account has been hacked. This seems a bit over the top, even for him. -- Will Twentyman email: wtwentyman at copper dot net Subject: Re: JSH: Testing failure, once again > Yet another round of testing is complete and once again [the math > community] has failed ALL tests. > I wish to point out that evaluating a species using mathematics is not > only sensible, but fair. [Mathematicians] were tasked with representing > homo sapiens sapiens, and they have failed all testing so far. > It is my hope that the testing is complete, as I fail to see the point > of continued rounds, but will do as tasked. > So far [the math community] has shown a lack of basic mathematical > understanding, an inability to be taught basic mathematics, and a > refusal to engage in rational discourse at anything but a very basic > level. > It has been determined that mathematical understanding is at only a > rudimentary level, with no evidence of ability beyond that level. > Determination is that past assessments remain correct and that > [humanity] lack basic abilities to advance beyond their present state, > as they lack the necessary mathematical aptitude. > It is my STRONG recommendation that testing cease as pointless. > [Mathematicians] were tested for humanity; [mathematicians] failed. > There seems to be no positive ending to this story, and no writer, not > even I, can fix it. > I recommend that the story be finished so that I can move on to the > next group on this planet, as many indications are that they are > stellar. You know, if you replace each bracketed expression with James Harris and do some minor editing to restore subject-verb agreement, this hysterical rant becomes a lovely response to the original (well, except for the second paragraph, which is pretty close to being content-free). As has been said before, you can't buy entertainment like this. Rick Subject: Re: JSH: Testing failure, once again > I find myself wondering if James's account has been hacked. This seems > a bit over the top, even for him. No, that's him all right. Just recently in the 'linchpin' thread he confessed that I've had times when I [...] desperately wanted to be rescued from the planet by friendly aliens Subject: Re: JSH: Testing failure, once again > Yet another round of testing is complete and once again the math > community has failed ALL tests. > I wish to point out that evaluating a species using mathematics is not > only sensible, but fair. Mathematicians were tasked with representing > homo sapiens sapiens, and they have failed all testing so far. Does this mean you're sticking by your assertion that a ring must contain all infinite sums (i.e. limits of sequences of partial sums) of ring elements? This, despite the lack of any definition of ring that supports you? You've cited the Mathworld definition twice. What on that page do you think supports your position? - Randy Subject: Re: JSH: Testing failure, once again >> Yet another round of testing is complete and once again the math >> community has failed ALL tests. > >> I wish to point out that evaluating a species using mathematics is not >> only sensible, but fair. Mathematicians were tasked with representing >> homo sapiens sapiens, and they have failed all testing so far. >And what species are you in? > >> It is my hope that the testing is complete, as I fail to see the point >> of continued rounds, but will do as tasked. > >> So far the math community has shown a lack of basic mathematical >> understanding, an inability to be taught basic mathematics, and a >> refusal to engage in rational discourse at anything but a very basic >> level. > >> It has been determined that mathematical understanding is at only a >> rudimentary level, with no evidence of ability beyond that level. > >> Determination is that past assessments remain correct and that >> humanity lack basic abilities to advance beyond their present state, >> as they lack the necessary mathematical aptitude. > >> It is my STRONG recommendation that testing cease as pointless. > >> Mathematicians were tested for humanity; mathematicians failed. >Does that mean humanity failed? If so, what does that say for you? > >> There seems to be no positive ending to this story, and no writer, not >> even I, can fix it. > >> I recommend that the story be finished so that I can move on to the >> next group on this planet, as many indications are that they are >> stellar. > > >> James Harris >I find myself wondering if James's account has been hacked. This seems >a bit over the top, even for him. That was my first thought. Otoh it's possible that he's actually realized that those links he posted so triumphantly actually _do_ show that he was wrong about what those words mean, so he's a little desperate. ************************ Subject: Re: JSH: Testing failure, once again >>>[...] >>I find myself wondering if James's account has been hacked. This seems >>a bit over the top, even for him. >That was my first thought. Otoh it's possible that he's actually >realized that those links he posted so triumphantly actually >_do_ show that he was wrong about what those words mean, >so he's a little desperate. Or come to think of it, I bet it's just that the fact that he's realized what a complete fool he's been making of himself has driven him to posting while drunk again. Yeah, I bet that's it. ************************ Subject: Re: JSH: Testing failure, once again > Yet another round of testing is complete and once again the math > community has failed ALL tests. > I wish to point out that evaluating a species using mathematics is not > only sensible, but fair. Mathematicians were tasked with representing > homo sapiens sapiens, and they have failed all testing so far. I like that paragraph. There seems to be no positive ending to this story, and no writer, not > even I, can fix it. That should have been a clue. > I recommend that the story be finished so that I can move on to the > next group on this planet, as many indications are that they are > stellar. And yes I became curious--just how dedicated ARE some of these people to replying to me? Well, just look at all the posts in this thread. Then look at all the posts in the previous threads. Something odd is going on here. James Harris Writer Subject: Re: JSH: Testing failure, once again >>I find myself wondering if James's account has been hacked. This seems >>a bit over the top, even for him. > No, that's him all right. > Just recently in the 'linchpin' thread he confessed that I've had times when I [...] desperately wanted to be rescued from the planet by friendly aliens That's interesting. I looked at the NNTP-Posting-Host. In the thread, it was: 67.192.37.140. In an earlier discussion on JSH forgeries, I had made a list of so it seemed). One of these was: 67.192.37.160 , which is close to the one above. It seems that my IP address is 67.68.134.54 right now. Let's see if it shows up in the NNTP-Posting-Host How often does JSH include the JSH tag in his subject lines? David Bernier Subject: Re: JSH: Testing failure, once again did you ever hear/see/feel Tommy, the rockmusical?... at least, Tommy had one skill,as far as I can determine. seriously, it sounds like a note of suicide, and we're not going to let you take us out in your last will & testament, with the blame for it. the Heaven's Gate folks have already split the scene, so What in Hell are you referring to? > There seems to be no positive ending to this story, and no writer, not > even I, can fix it. > I recommend that the story be finished so that I can move on to the > next group on this planet, as many indications are that they are > stellar. --les ducs d'Enron! http://larouchepub.com Subject: Re: JSH: Testing failure, once again don't do it, James! http://www.schillerinstitute.org/newspanish/InstitutoSchiller/ Ciencia/Enterr arMatematicas.html http://www.21stcenturysciencetech.com/ > It is my hope that the testing is complete, as I fail to see the point > of continued rounds, but will do as tasked. --Dec.2000 'WAND' Chairman Paul O'Neill, reelected to Board. Newsish? http://www.rand.org/publications/randreview/issues/rr.12.00/ http://members.tripod.com/~american_almanac Subject: Re: JSH: Testing failure, once again >>> I find myself wondering if James's account has been hacked. This seems >>> a bit over the top, even for him. >> No, that's him all right. >> Just recently in the 'linchpin' thread he confessed that >I've had times when I [...] desperately wanted to be rescued from the >> planet by friendly aliens > That's interesting. I looked at the NNTP-Posting-Host. In the > thread, it was: 67.192.37.140. > In an earlier discussion on JSH forgeries, I had made a list of > so it seemed). > One of these was: 67.192.37.160 , which is close to the one above. > It seems that my IP address > is 67.68.134.54 right now. > Let's see if it shows up > in the NNTP-Posting-Host > How often does JSH > include the JSH tag in > his subject lines? > David Bernier I think that only tells us he's posting from Google. -- Will Twentyman email: wtwentyman at copper dot net Subject: Re: JSH: Testing failure, once again Beam me up, Scotty. Gib Subject: Re: JSH: Testing failure, once again >>>I find myself wondering if James's account has been hacked. >I bet it's just that the fact that he's >realized what a complete fool he's been making of himself >has driven him to posting while drunk again. Yeah, I bet >that's it. Wally the Writer is a genuine, lovable, action figure your child will love. He comes with a certificate of adoption, a pair of faded blue jeans, a tan sweater, and a tiny bottle of good whiskey. He can answer the phone, argue with editors, and crumple paper..... When you squeeze his belly, he says No, really, it's coming along fine. It's in flux right now. Sort of an exploration of my... well.... it'll be ready soon. Wally comes with a diploma from the New York Art Institute and is incapable of rigor, which protects your precious child, who, as we've said, will just LOVE him! Yours, Doug Goncz, Replikon Research, Seven Corners, VA The hormones work at different speeds. In a fight-or-flight scenario, glucocorticoids are the ones drawing up blueprints for new aircraft carriers; epinephrine is the one handing out guns. Subject: limit problem?? hello. sir~ f(x,y) = [sin{(x^2)+(y^2)}] / {(x^2)+(y^2)} show lim f(x,y) =1 [(x,y) -> (0,0)] ---------------------------------- I can't take concrete delta with epsilon. help me in my problem. sir~ thank doctor in advance~ Subject: Re: limit problem?? > f(x,y) = [sin{(x^2)+(y^2)}] / {(x^2)+(y^2)} > show lim f(x,y) =1 [(x,y) -> (0,0)] As (x,y) -> (0,0) x^2 + y^2 -> 0 But you already know lim(u->0) (sin u)/u = 1 or actually in this case lim(u->0+) (sin u)/u = 1 ----== Posted via Newsfeed.Com - Unlimited-Uncensored-Secure Usenet News==---- http://www.newsfeed.com The #1 Newsgroup Service in the World! >100,000 Newsgroups ---= 19 East/West-Coast Specialized Servers - Total Privacy via Encryption =--- Subject: Re: limit problem?? [...] > f(x,y) = [sin{(x^2)+(y^2)}] / {(x^2)+(y^2)} > show lim f(x,y) =1 [(x,y) -> (0,0)] I'd suggest you try transforming to planar polar coordinates. This is usually done by: r^2 = x^2 + y^2 and an angle theta which depends on the direction of the vector (0,0) to (x,y). So, f(x,y) = [sin{(x^2)+(y^2)}] / {(x^2)+(y^2)} = [sin{r^2}]/{r^2} . Also, (x,y) -> (0,0) is synonymous with r -> 0 [ Question: Why? ] Subject: Re: limit problem?? In sci.math, hot-girl : > hello. sir~ > f(x,y) = [sin{(x^2)+(y^2)}] / {(x^2)+(y^2)} > show lim f(x,y) =1 [(x,y) -> (0,0)] > ---------------------------------- > I can't take concrete delta with epsilon. > help me in my problem. sir~ > thank doctor in advance~ First, you might notice that f(x,y) = g(z), where z = x^2 + y^2. The problem reduces, in a sense, to showing lim (z->0+) sin z/z = 1. We'll get back to that a little later. ( This one's a classic. :-) ) The limit requires that, for any epsilon > 0, one find a delta1 > 0 such that one can prove |g(x) - L| < epsilon for every z such that 0 < z < delta1. If one uses an infinite series for sin and restricts delta1 to be less than 1, this isn't too difficult, especially since 1 radian is about 57 degrees. As a formality, you may be required to show that, given a delta1 > 0, there's a delta2 > 0 such that x^2 + y^2 < delta1 for every point (x,y) such that |x| < delta2, |y| < delta2. That should be simple. Put both of them together and you have your proof. -- #191, ewill3@earthlink.net It's still legal to go .sigless. Subject: Re: limit problem?? > hello. sir~ > f(x,y) = [sin{(x^2)+(y^2)}] / {(x^2)+(y^2)} > show lim f(x,y) =1 [(x,y) -> (0,0)] > ---------------------------------- > I can't take concrete delta with epsilon. > help me in my problem. sir~ > thank doctor in advance~ You can take advantage of the circumstances: the inequality 1 - z^2/6 <= sin(z)/z <= 1 for all real z other than 0 can be obtained on the left side: by integrating, for z>=0, the inequality cos(z) <= 1 three times, respecting the initial conditions, then dividing by z, and extending by symmetry; on the right side: even easier. Then 1 - (x^2 + y^2)^2/6 <= f(x,y) <= 1 and it cannot get any better when it comes to playing with epsilons and deltas. Cheers, ZVK(Slavek). Subject: Re: limit problem?? > hello. sir~ Someone named Hot Girl is studying mathematics? Subject: Re: limit problem?? Yup. Waiting for someone to discover a short proof of FLT. > hello. sir~ > Someone named Hot Girl is studying mathematics? Subject: Re: limit problem?? > hello. sir~ > Someone named Hot Girl is studying mathematics? ... and very politely calling everyone sir. Dunno what the ladies here think of it. -- G.C. Subject: Re: limit problem?? > In sci.math, hot-girl > : > hello. sir~ > f(x,y) = [sin{(x^2)+(y^2)}] / {(x^2)+(y^2)} > show lim f(x,y) =1 [(x,y) -> (0,0)] > ---------------------------------- > I can't take concrete delta with epsilon. > help me in my problem. sir~ > thank doctor in advance~ > First, you might notice that f(x,y) = g(z), where > z = x^2 + y^2. The problem reduces, in a sense, > to showing lim (z->0+) sin z/z = 1. We'll get back > to that a little later. > ( This one's a classic. :-) ) > The limit requires that, for any epsilon > 0, > one find a delta1 > 0 such that one can prove > |g(x) - L| < epsilon for every z such that 0 < z < delta1. > If one uses an infinite series for sin and restricts The worry here may be (depending on how sine is defined) that one only knows the sine series after proving that (sin theta)/theta -> 1. > delta1 to be less than 1, this isn't too difficult, > especially since 1 radian is about 57 degrees. > As a formality, you may be required to show that, given > a delta1 > 0, there's a delta2 > 0 such that > x^2 + y^2 < delta1 for every point (x,y) such that > |x| < delta2, |y| < delta2. > That should be simple. Put both of them together > and you have your proof. > #191, ewill3@earthlink.net > It's still legal to go .sigless. -- G.C. Subject: linear congruential generators No doubt you are all familiar with the 'pseudo-random' number generators of linear congruential type (LC-PRNGs): x(n+1) = (a * x(n) + c) mod m where a, c, m, x are all integer. Prime values of the modulus m are useful, because they always generate maximum length sequences with no duplication of values - ie, the output sequence is always a permutation of M = [0,1,2,...m-1]. I became interested in LC-PRNGs because of their applications to simulation, cryptography etc. Below are 3 questions which seem obvious ones to ask. I do not have access to suitable reference books, so I'd be grateful for any answers. Q1. There are m! permutations of this set M. Can *all* of these be generated by a linear congruential generator with suitable choice of parameters? If so, how do you prove it? Q2. How do you find specific values of a, c, m, x(0) that would generate any given permutation of M? Q3. For any finite m, the number of distinct output sequences is finite. However, the number of choices of a,c,m,x(0) is infinite (even if the parameters are restricted to those that are coprime to each other). It follows that for any specific output sequence, there must be many distinct combinations of a,c,m,x(0) which produce the same sequence. How do you work out which combinations of a,c,m,x(0) will result in the same output sequence? Thanks Ross Subject: Re: linear congruential generators X-ID: XuzF6rZZ8eSxkdhggQdU9OEzXGKf-j+TB1aBUhe1VW3LxXsA4PSg8p > No doubt you are all familiar with the 'pseudo-random' number generators of > linear congruential type (LC-PRNGs): > x(n+1) = (a * x(n) + c) mod m > where a, c, m, x are all integer. Prime values of the modulus m are useful, > because they always generate maximum length sequences with no duplication of > values - ie, the output sequence is always a permutation of M = [0,1,2,...m-1]. > I became interested in LC-PRNGs because of their applications to simulation, > cryptography etc. Below are 3 questions which seem obvious ones to ask. I do > not have access to suitable reference books, so I'd be grateful for any answers. > Q1. There are m! permutations of this set M. Can *all* of these be generated > by a linear congruential generator with suitable choice of parameters? If so, > how do you prove it? > Q2. How do you find specific values of a, c, m, x(0) that would generate any > given permutation of M? > Q3. For any finite m, the number of distinct output sequences is finite. > However, the number of choices of a,c,m,x(0) is infinite (even if the > parameters are restricted to those that are coprime to each other). It follows > that for any specific output sequence, there must be many distinct combinations > of a,c,m,x(0) which produce the same sequence. How do you work out which > combinations of a,c,m,x(0) will result in the same output sequence? Any three successive values, say x0, x1 and x2, give rise to a set of two linear equations and hence correspond to a unique pair of a and c (mod m), which means that the sees that in general it is impossible to obtain all m! permuatations through varying the values of a and c. M. K. Shen Subject: Re: linear congruential generators > No doubt you are all familiar with the 'pseudo-random' number generators of > linear congruential type (LC-PRNGs): > x(n+1) = (a * x(n) + c) mod m > where a, c, m, x are all integer. Prime values of the modulus m are useful, > because they always generate maximum length sequences with no duplication of > values - ie, the output sequence is always a permutation of M = [0,1,2,...m-1]. > I became interested in LC-PRNGs because of their applications to simulation, > cryptography etc. Below are 3 questions which seem obvious ones to ask. I do > not have access to suitable reference books, so I'd be grateful for any answers. > Q1. There are m! permutations of this set M. Can *all* of these be generated > by a linear congruential generator with suitable choice of parameters? If so, > how do you prove it? No, the proof is a counting issue. [hint hint :-)] > Q2. How do you find specific values of a, c, m, x(0) that would generate any > given permutation of M? Do a polynomial fit. If the equation is linear [or affine] then that polynomial is an LCG that generates the permutation you want. > Q3. For any finite m, the number of distinct output sequences is finite. > However, the number of choices of a,c,m,x(0) is infinite (even if the > parameters are restricted to those that are coprime to each other). It follows > that for any specific output sequence, there must be many distinct combinations > of a,c,m,x(0) which produce the same sequence. How do you work out which > combinations of a,c,m,x(0) will result in the same output sequence? I don't see that that follows. I'm speculating but I can imagine a sub-optimal LCG may generate a permutation that contains another smaller ideal LCG [I can't offer a proof of that] but two ideal LCGs should not generate the same permutation [that much I'm rather certain of]. Tom Subject: Re: Lines Affecting Themselves (Within Polygons) > This is more a fun project than heavy math. But there are some good > questions to ask about this, but others will have to ask them ... > Start with any arbitrary convex polygon. > Draw a path consisting of connected straight line-segments such that: > The path starts in any location within the polygon, and heads in any > direction. > The path does not change direction, except... > When the path hits the edge of the polygon, it reflects as if the > polygon has a mirrored inner-surface, or by some other rule, remaining > inside the polygon. > And when the path crosses itself, as it has already been drawn to that > point, the path changes direction by some rule. For example, it > crosses a previously-drawn segment, but acts as if it was reflected by > a mirror which crosses the previously-drawn segment perpendicularly. > Or, another example, it crosses unimpeded every 3rd time it encounters > a previously-drawn portion of the path, and is reflected the other > times. > (But beware of ambiguous cases, such as when the path hits a > previously-drawn intersection of 2 or more segments, or when the path > hits a vertex of the polygon. Such cases can be dealt with as you > wish.) > End the path after drawing a finite number of segments, or for some > other reason (such as the path approaching a limit-point or loop or > being reflected exactly back along itself). > So, I have drawn a few of these paths by-hand, and I have noticed that > they can look interesting, even beautiful. And they seem to act often > in chaotic ways: such as settling into a partially-repeating cycle > (strange attractor?), or simply spiraling into a point, etc. > I wonder if these paths are as really as interesting-looking as I > assume, since I am currently unable to plot these with a computer. > But the question occurs to me, given such a path, is there a > closed-form (ie non-recursive) way to determine where the path is > drawn? > I highly doubt this. I came up with an idea for a game (best played on computer, perhaps) based on the above. The polygon and starting segment are 1st generated randomly by the computer. Then, each segment is plotted by the computer until an intersection with a previously drawn segment is encountered. At this point, the player has a choice: Should the path pass through the intersecting-segment, changing direction as if (as with original post) a mirror placed perpendicular to the intersecting-segment (at the point of the segments' intersection) has reflected the path? Or should the path pass through the intersecting-segment without changing its direction? The goal of this game could be to get the path to, say, end up in a certain location within the polygon (such as at a vertex), or to get the path to take on certain behavior, such as to spiral inwards or to settle into any specific (or unspecific) pattern. And, watch out for such ambiguous situations such as the path hitting a vertex of the polygon or intersecting at the previously-existing intersection of 2 or more segments. An alternative game would be to not give a choice at each intersection, but to simply allow the player to choose the starting segment's location and direction, and to then let the game (or aesthetics experiment) run itself from then on. Thanks, Leroy Quet Subject: Maple, MatLab, MathCad, and Mathematica -- Decisions, Decisions My second son is a freshman in college this semester and is a science major taking Calculus. His prof is using Maple, a software package about which I know very little. I am familiar with MathCad but not Mathematica or Matlab. I understand with a TI connectivity kit you can exchange information in MathCad, but can you do that with Maple, MatLab, or Mathematica? (He has a TI-89.) I understand you can use Maple in conjuntion with the other software packages. I'm trying to decide what is the best software package to get him. My funds are limited (typically, I know). Thanks for any helpful suggestions and comments. -- Cindy Smith Unless the LORD build the house, cms@dragon.com they labor in vain who build. cms@5sc.net Unless the LORD guard the city, cms@romancatholic.org in vain does the guard keep watch. Me transmitte sursum, -- Psalm 127:1 Caledoni! All your base are belong to us. A Real Live Catholic You are on the way to destruction. in Georgia! What you say. >->> <<-< Go against the flow! You have no chance to survive make your time. Subject: Re: Maple, MatLab, MathCad, and Mathematica -- Decisions, Decisions > My second son is a freshman in college this semester and is a science > major taking Calculus. His prof is using Maple, a software package > about which I know very little. I am familiar with MathCad but not > Mathematica or Matlab. I understand with a TI connectivity kit you > can exchange information in MathCad, but can you do that with Maple, > MatLab, or Mathematica? (He has a TI-89.) I understand you can use > Maple in conjuntion with the other software packages. I'm trying to > decide what is the best software package to get him. My funds are > limited (typically, I know). > Thanks for any helpful suggestions and comments. Maple is for symbolic manipulation. I understand it is also part of MatLab, but I normally use MatLab for numerical algorithms. Here's an example of a Maple command to illustrate symbolic processing: solve( a*x + b = c, x ) This command will produce output like: (c - b)/a I typically run MatLab on Wintel and Linux boxes, and I have Maple installed on a Macintosh OS 9.?. I'll be interested to see what other responses you get. -- Try http://csf.colorado.edu/pkt/pktauthors/Vienneau.Robert/ Bukharin.html To solve Linear Programs: .../LPSolver.html r c A game: .../Keynes.html v s a Whether strength of body or of mind, or wisdom, or i m p virtue, are found in proportion to the power or wealth e a e of a man is a question fit perhaps to be discussed by n e . slaves in the hearing of their masters, but highly @ r c m unbecoming to reasonable and free men in search of d o the truth. -- Rousseau Subject: Re: Maple, MatLab, MathCad, and Mathematica -- Decisions, Decisions > My second son is a freshman in college this semester and is a science > major taking Calculus. His prof is using Maple, a software package > about which I know very little. I am familiar with MathCad but not > Mathematica or Matlab. I understand with a TI connectivity kit you > can exchange information in MathCad, but can you do that with Maple, > MatLab, or Mathematica? (He has a TI-89.) I understand you can use > Maple in conjuntion with the other software packages. I'm trying to > decide what is the best software package to get him. My funds are > limited (typically, I know). > Thanks for any helpful suggestions and comments. My personal experience (from having taught calculus using software packages like Mathematica and Maple) is that the best way to learn is to use pen and paper. If the prof is not telling the students they need a software package, the best thing is not to get one. If the prof is saying the students need one, then the best bet is to get whatever the prof says to get. It is possible that later in his studies that ownership of such a package will prove useful, but I recommend waiting until that day comes before buying it. -- Stephen Montgomery-Smith stephen@math.missouri.edu http://www.math.missouri.edu/~stephen Subject: Re: Maple, MatLab, MathCad, and Mathematica -- Decisions, Decisions Subject: Maple, MatLab, MathCad, and Mathematica -- Decisions, Decisions Message-id: ->> <<-< Go against the flow! You have no chance to survive make your time. With that strong faith of yours you do not need any science. You accept things by faith, not by scientific proof. Get on your knees and ask your carpenter which of the programs is the best. Carpenters are good at math, they know that 2x4s are really 1.5x3.5s. And God bless! Subject: Re: Maple, MatLab, MathCad, and Mathematica -- Decisions, Decisions >> My second son is a freshman in college this semester and is a science >> major taking Calculus. His prof is using Maple, a software package >> about which I know very little. I am familiar with MathCad but not >> Mathematica or Matlab. I understand with a TI connectivity kit you >> can exchange information in MathCad, but can you do that with Maple, >> MatLab, or Mathematica? (He has a TI-89.) I understand you can use >> Maple in conjuntion with the other software packages. I'm trying to >> decide what is the best software package to get him. My funds are >> limited (typically, I know). > >> Thanks for any helpful suggestions and comments. > >My personal experience (from having taught calculus using software packages like >Mathematica and Maple) is that the best way to learn is to use pen and paper. Good answer. (I was going to say that but I feared sounding like an old fuddy-duddie...) My impression is that the idea that a lot of people are convinced that we need computers to teach math these days, but they've got relatively little hard evidence to support the idea that it actually has a positive effect on how students learn things like calculus, it's more a matter of faith. >If the prof is not telling the students they need a software package, the best >thing is not to get one. If the prof is saying the students need one, then the >best bet is to get whatever the prof says to get. It is possible that later in >his studies that ownership of such a package will prove useful, but I recommend >waiting until that day comes before buying it. ************************ Subject: Re: Maple, MatLab, MathCad, and Mathematica -- Decisions, Decisions >If the prof is not telling the students they need a software package, the >best >thing is not to get one. If the prof is saying the students need one, then >the >best bet is to get whatever the prof says to get. Therefore if the prof is telling the students to choose their own software package, the best thing to do is for the students to choose their next prof? I write this with some irony. I have been working on an ultracapacitor electric bicycle with stall surge power of 800 W and system weight 16 pounds. I have been in contact with business people all over America on the telephone, via fax and email, and through web site technical and sales literature, and through orders for supplies. I contact academia through newsgroups like this one because most web based discussion fora are thread free. Many many recent internet participants access these web based fora exclusively and accept unthreaded, massive, chronological message hash as a fact of life, not knowing, for instance, that a news URL has no slashes. I use MathCad 6.0 Plus and it was donated to me while I paid for the 6.0 + / 6.0 Student manual and CD and used Student for years. I spoke with Mathcad regarding commision sales to consortia. A consortium is in this use a coalition of academics and business types who use a common software. The business types usually pay 10 x the academic price. Well, maybe 6x. It's fair and necessary. I do not seek to average these software prices to achieve a lower per user price. I seek only to facilitate the sharing of airline miles between business types, who have too many, can't get a miles seat because their schedules are too impromptu, and cannot have sex with coworkers and customers (usually), and academic types, who need to fly an average of 12,000 miles (more irony) to attend three day conferences with their peers at discount fares since they plan months if not years in advance. My smoochie and I are going to Hawaii for Valentine's day. On miles. Try it some time. 15 airports in HI, 3 here near DC, and four flight days each way. 45x4=180, x 2 = 360. Since smoochie has enough mles on United for one ticket and Delta for the other, that's 360 searches for each of two carefully selected United and Delta reps to achieve a coincidence of high order. Call early. Yours, Doug Goncz, Replikon Research, Seven Corners, VA The hormones work at different speeds. In a fight-or-flight scenario, glucocorticoids are the ones drawing up blueprints for new aircraft carriers; epinephrine is the one handing out guns. Subject: Re: Maple, MatLab, MathCad, and Mathematica -- Decisions, Decisions May I recommend for your enjoyment: http://wolfram.com and (sorry about line breaks) http://search.wolfram.com/index.cgi?config=forums&method=and& words=ti-89&m atchesperpage=10&format=wri-long and also My God, are you THE Cindy Smith? I am honored to make your acquaintance! Did you go to Hanau American High School? So you had kids, huh? That is soooo cool. Good luck! Yours, Doug Goncz, Replikon Research, Seven Corners, VA The hormones work at different speeds. In a fight-or-flight scenario, glucocorticoids are the ones drawing up blueprints for new aircraft carriers; epinephrine is the one handing out guns. Subject: Re: Mathematicians Living in the Past X-Cise: tanbanso@iinet.net.au X-CompuServe-Customer: Yes X-Coriate: admin@interspeed.co.nz X-Ecrate: tanandtanlawyers.com X-Punge: Micro$oft X-Sanguinate: themvsguy@email.com X-Terminate: SPA(GIS) X-Tinguish: Mark Griffith I have come to the conclusion that many of the regular posters here >at sci.math are dwelling in a nostalgic past where people could just >magically throw half-defined commentary around and have it pass for >mathematics. No doubt. Unfortunate, you have failed miserably in identifying who those are. >We live in a more refined world and these days >mathematics must be rigorous. Alas, you seem to not have grasped what the word means. >A good example of this sort of nonsense is the collective works of >Cantor. The man came up with a whimsical notion of mathematics >which would do fine in science fiction but not in any respected >textbook. Ah, you are living in the past and cannot cope with more modern concepts. It is true that Cantor failed to be rigorous. It is also true that Newton failed to be rigorous and that your beloved Euclid failed to be rigorous. In fact, there work had far more serious problems than Cantor's, and Bishop Berkeley's criticisms were correct, although short sighted. >Well, I will concede. Cantor is 100% true and rigorous, *if* you >live in the magical neverland where you can just twist and >manipulate axioms however you please. You are, of course, free to reject the real world as a magical neverland. That won't, however, make it go away. >Some posters to this newsgroup seem to live in such a world. If >they feel like it, they'll accept the Axiom of Choice. If not, then >not. And that is bad because? Your personal prejudices do not constitute a reasoned condemnation, only a fit of pique. >It is as simple as this: if Cantor's theorems are really the >absolute truths some people hold them to be, then you will provide a >proof of them using nothing but the postulates of Euclid. To every complex question there is an answer that is simple, obvious and wrong. That has been known for a long time. Thank you for demonstrating that there is also an answer that is simple, obvious, wrong and ludicrous. Of what possible relevance are the axioms of Euclid[1] to, e.g., Galois Theory? >But I defy you to do this. I defy you to derive Barber's Adagio for Strings from Euclid's axioms. That's just as relevant. Again, your insane appeal to Euclid demonstrates that it is *you* who is living in the past. Indeed, if you were not living in the past then you would be addressing, e.g, GB, ZF, rather than Cantor's work, just as you would address contemporary Real Analysis rather than fluxions. >Even speaking non rigorously, That's the only way you can speak; you have neither the education nor the intellect to speak rigorously. Worse, you lack the mother wit to recognize those deficiencies in yourself. >on a level that you liberal arts minors Listen you addlepated coprophage with delusions of adequacy, you haven't got a clue who minored in what. I'll go farther and say that you haven't got a clue, period. >Cantor's character Is relevant only to fools who are unable to analyze his work on its merits. >The people who still stubbornly hold onto >Cantor's lies, refusing to hear the disproofs which are so common >and irrefutable, Is that what the voices in your head told you? >I speak to you as a friend, Come to do business with us? Sorry, but your only friends here are AP and JSH. The rest of us have higher standards. [1] Who, BTW, got them wrong; his theorems do not follow from his axioms and postulates, and his definitions don't define. -- Shmuel (Seymour J.) Metz, SysProg and JOAT Any unsolicited bulk E-mail will be subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail. Reply to domain Patriot dot net user shmuel+news to contact me. Do not reply to spamtrap@library.lspace.org Subject: Re: Matrix exponential approximation > If exp(A) = I + S and exp(P) = I + T, you want > exp(ln(I+S) ln(I+T)). > If S and T are small, ln(I+S) = S - S^2/2 + S^3/3 - ... > ln(I+T) = T - T^2/2 + T^3/3 - ... > exp(A P) > = exp(S T - S^2 T/2 - S T^2/2 + S T^3/3 + S^2 T^2/4 + S^3 T/3 + ...) > = I + S T - S^2 T/2 - S T^2/2 + S T S T/2 + S T^3/3 + S^2 T^2/4 > + S^3 T/3 + ... > More terms are available if needed. Thanks for the reply. I am still not clear on the idea of S and T being 'small' though. As for the matrices I am looking at, A is diagonal with entries ranging from -1 to 1. P is a hermitian sparse matrix that is the result of FFT * a sparse matrix * complex conjugate transpose(FFT) I was trying to avoid taking the exponential of a non-diagonal sparse matrix by writing my own sparse exponential function using the Taylor series with about 20 terms. Thanks~~!!! Mheto > Robert Israel israel@math.ubc.ca > Department of Mathematics http://www.math.ubc.ca/~israel > University of British Columbia > Vancouver, BC, Canada V6T 1Z2 Subject: Re: Matrix exponential approximation X-ID: ZjNx9ZZO8e8UiMCwZKwrW8TwL-aV9XrO89srhBtSjWfWNE8zpnJBgV Besides the comment from Dr. Israel you might be interested in 19 doubious ways to compute the exponential of a matrix of Cleve Moler and Charles van Loan file accessible online via http://www.jstor.org/journals/siam.html I found it a very instructive essay. Gottfried Helms Subject: Re: Matrix exponential approximation Thanks!!!! currently on campus and I am from Canada, but now I know what to look for :-) Mheto Subject: maximum entropy methods: book recommendation? I wonder if anyone can recommend an introductory book (or chapter) on maximum entropy methods? I remember this book http://www.oup.co.uk/isbn/0-19-853963-0 being popular with at least one individual but wonder if the subject has made many advances since it was published, ten years ago? Tom Subject: Re: Meaning of curly d? >I have some review books for differential equations, and they don't explain >the difference between e.g. dM/dx and (curly)dM/dx. What's the >difference?? > The second one stands for a partial derivative, while the first one > stands for (ordinary) differentiation. I have a different question: is there any difference in pronounciation when you read these two expressions? I've heard them both pronounced as dee em dee eks, but I wonder if there is any convention which gives a different pronounciation to the partial derivative? --Mark Subject: Re: Meaning of curly d? >I have a different question: is there any difference in pronounciation when >you read these two expressions? I've heard them both pronounced as dee em >dee eks, but I wonder if there is any convention which gives a different >pronounciation to the partial derivative? I would pronounce it partial dee M dee x -- Alastair Rae, London, Europe. My opinions are not necessarily those of my employers. Subject: Re: Meaning of curly d? >I have some review books for differential equations, and they don't > explain >the difference between e.g. dM/dx and (curly)dM/dx. What's the >difference?? > The second one stands for a partial derivative, while the first one > stands for (ordinary) differentiation. > I have a different question: is there any difference in pronounciation when > you read these two expressions? I've heard them both pronounced as dee em > dee eks, but I wonder if there is any convention which gives a different > pronounciation to the partial derivative? Yes: Partial M with respect to x. Seriously, that's the only way I've ever heard it read. That or some slightly different phrase beginning with the word partial. - Randy Subject: Re: Meaning of curly 'd' NNTP-Posting_Host: student-concordia-dorm.student.concordia.net NNTP-P0STING-HOST: 210.117.60.5 >> I have a different question: is there any difference in pronounciation when >> you read these two expressions? I've heard them both pronounced as dee em >> dee eks, but I wonder if there is any convention which gives a different >> pronounciation to the partial derivative? >Yes: Partial M with respect to x. >Seriously, that's the only way I've ever heard it >read. That or some slightly different phrase beginning >with the word partial. > - Randy I've heard: Partial-partial eks on em. and Partial em, partial eks I don't think it really matters too much, but what does matter is this... Do NOT call a partial a curly dee, just call it a partial. I only say this because calling a partial a curly dee might make for some confusion if you ever get into the path integral where everyone calls the integration variable big curly dee adam Subject: Re: Meaning of curly d? > I have some review books for differential equations, and they don't explain > the difference between e.g. dM/dx and (curly)dM/dx. What's the > difference?? See http://ajnpx.com/html/SD.html Patrick Subject: Re: Meaning of curly d? >>I have some review books for differential equations, and they don't >explain >>the difference between e.g. dM/dx and (curly)dM/dx. What's the >>difference?? >> The second one stands for a partial derivative, while the first one >> stands for (ordinary) differentiation. >I have a different question: is there any difference in pronounciation when >you read these two expressions? I've heard them both pronounced as dee em >dee eks, but I wonder if there is any convention which gives a different >pronounciation to the partial derivative? >--Mark I saw a calculus course given on the Canadian learning television channel by a professor at the University of Waterloo, Ont., and she pronounced the partial derivative symbol die as in die M over die x. Subject: Re: Meaning of curly d? I have a different question: is there any difference in pronounciation when > you read these two expressions? I've heard them both pronounced as dee em > dee eks, but I wonder if there is any convention which gives a different > pronounciation to the partial derivative? > Yes: Partial M with respect to x. > Seriously, that's the only way I've ever heard it > read. That or some slightly different phrase beginning > with the word partial. I seem to recall a professor of mine pronouncing it dye M by dye x, possibly because he was trying to avoid having to say the word partial all the time. -Mike Subject: Re: Meaning of curly d? I saw a calculus course given on the Canadian learning television > channel by a professor at the University of Waterloo, Ont., and she > pronounced the partial derivative symbol die as in die M over die x. Hey, that was probably my professor! (see my other post on this subject) -Mike Subject: Re: Meaning of curly 'd' >Partial-partial eks on em. Add with two, divide by ten. Throw in pi and e and i Cube root, square root, four oh nine Cosine, Secant, Tangent, sine. One, Two, Three, Four, Six, Eight, Five. Math is what keeps me alive! Yours, Doug Goncz, Replikon Research, Seven Corners, VA The hormones work at different speeds. In a fight-or-flight scenario, glucocorticoids are the ones drawing up blueprints for new aircraft carriers; epinephrine is the one handing out guns. Subject: Mod Hey Guys, I'm reading through some lecture notes and have come across something I don't understand.... 0 mod m. What is the point of 0 mod m? Surely the answer is just 0 regardless of the value of m? The notes state things like: Using the relation: (a-3)^2 = 0 mod m at one point. And for the equation X(subscript:n+1) = aX(subscript:n) mod p; If X0 != 0 mod p and a is a primitive root mod p then the sequence has period p-1. In my mind 0 mod p = 0 everytime. It also uses 0 mod 1 later on, but surely that is 0 as well? Am most confused, and trawled through the web looking for an answer but didn't come across one. Actually not true, there is some stuff on congruence which looked interesting, but it always used brackets in its notation whereas these notes never do and don't even mention this congruence relation. Ahh nevermind, if any of you can help I'd be most appreciative. J Subject: Re: Mod Visiting Assistant Professor at the University of Montana. >Hey Guys, >I'm reading through some lecture notes and have come across something I >don't understand.... 0 mod m. >What is the point of 0 mod m? Surely the answer is just 0 regardless of the >value of m? The notes state things like: >Using the relation: >(a-3)^2 = 0 mod m >at one point. You posted this a few days ago, and it was answered then. Your confusion arises from thinking that mod m refers only to one side of the equation. What it really says is (a-3)^2 = 0 (mod m), meaning that (a-3)^2 and 0 are congruent modulo m; that is, (a-3)^2-0 is a multiple of m. Please try to review the responses you got to your previous query before reposting the same question again: http://groups.google.com/groups?selm=wcS%25a.40234% 24bo1.33902%40news-server .bigpond.net.au http://groups.google.com/groups?selm=bhorbp%24b26%241% 40agate.berkeley.edu If you still don't understand what is happening, or something someone said confuses you, then post a reply to that message. ============================================================== ======== It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) ============================================================== ======== Arturo Magidin magidin@math.berkeley.edu Subject: Re: Mod >>Hey Guys, >>I'm reading through some lecture notes and have come across something I >>don't understand.... 0 mod m. >>What is the point of 0 mod m? Surely the answer is just 0 regardless of >>the >>value of m? The notes state things like: >>Using the relation: >>(a-3)^2 = 0 mod m >>at one point. > You posted this a few days ago, and it was answered then. Your > confusion arises from thinking that mod m refers only to one side of > the equation. What it really says is > (a-3)^2 = 0 (mod m), > meaning that (a-3)^2 and 0 are congruent modulo m; that is, (a-3)^2-0 is > a multiple of m. In addition the equals sign = isn't used, rather the congruence sign with three horizontal lines is used (except here as ascii lacks the congruence sign). A congruence a = b (mod m) [where = is really a congruence sign] is a relation between the *three* numbers a, b and m not an assertion that a equals something called b (mod m). -- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html His mind has been corrupted by colours, sounds and shapes. The League of Gentlemen Subject: Re: Comparison of Mathematica on Various Computers > If you pay full list, it is, arguably, overpriced. Although you'll > find nothing cheaper with the same capabilities. (Sadly, Maple has > crept up to almost match Mathematica in price.) Maxima may eventually > catch up, and it's free, but I can't get it to work on any of my > operating systems except Windows, and I ain't willing to make that much > of a sacrifice (running Windows). Which operating systems are you using? Maxima works on Linux, Windows, Mac OS X and various commercial Unices. Please ask on the Maxima mailing list if you are having trouble getting it to work on a particular platform. --Jim Amundson Subject: Maple to Matlab conversion by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBJ5Srh20257; Hi everybody, I am a graduate student in the department of chemical engineering at Clarkson University, Potsdam, USA. My research interests are in the areas of modelling and simulation. Currently, I am working on some modelling issues related to fuel cells and of late, I have been using Maple (version 9) to setup the model equations, which are essentially PDEs. Right now, I am interested in doing the following: setup the model equations using Maple and convert them into C or MATLAB routines and solve them. Final aim is to be able to develop detailed models (a highly nonlinear system of PDEs) quickly using Maple, but solve them in MATLAB. Can somebody please let me know whether this is practical and if possible can you provide me some Maple code as an example to start with. madhu Subject: Re: Maple to Matlab conversion Three questions for you: 1. Can you explain what you can't do using Maple? 2. Have you seen this? 3. Have you looked at codegen/C/procedure ? RJF > Hi everybody, > I am a graduate student in the department of chemical > engineering at Clarkson University, Potsdam, USA. My research > interests are in the areas of modelling and simulation. Currently, I > am working on some modelling issues related to fuel cells and of late, > I have been using Maple (version 9) to setup the model equations, > which are essentially PDEs. > Right now, I am interested in doing the following: setup the > model equations using Maple and convert them into C or MATLAB routines > and solve them. Final aim is to be able to develop detailed models (a > highly nonlinear system of PDEs) quickly using Maple, but solve them > in MATLAB. Can somebody please let me know whether this is practical > and if possible can you provide me some Maple code as an example to > start with. > madhu Subject: Re: Problem solved via Inverse Function Theorem? > If we have a function f:R^n -> R^m, m < n, how can we prove that f is > one to one? The hint is that we define a function g:R^n -> R^n with > g(x) = (f_1(x),...,f_m(x),x_(m+1),...,x_n) > and apply the inverse function theorem to g. Here is my question: > In order to apply the inverse function theorem we need to know that > det ( g'(x) ) is not equal to zero at some point x in R^n. What if > det (g'(x))=0 for all x in R^n? Does that imply that f is one to one? > Can anyone explain why that would follow? Thanks! So far this is just nonsense. Subject: Re: Problem solved via Inverse Function Theorem? > If we have a function f:R^n -> R^m, m < n, how can we prove that f is > one to one? The hint is that we define a function g:R^n -> R^n with > g(x) = (f_1(x),...,f_m(x),x_(m+1),...,x_n) > and apply the inverse function theorem to g. Here is my question: > In order to apply the inverse function theorem we need to know that > det ( g'(x) ) is not equal to zero at some point x in R^n. What if > det (g'(x))=0 for all x in R^n? Does that imply that f is one to one? > Can anyone explain why that would follow? Thanks! > So far this is just nonsense. Let me clarify for you. The problem is from Spivak's Calculus on Manifolds. Its statement is: If f:R^n -> R^m, m < n, is continuously differentiable, prove that f is NOT one to one. My own addition was the hint that we could define a new function g:R^n -> R^n with g(x) = (f_1(x),...,f_m(x),x_(m+1),...,x_n) and apply the inverse function theorem to g. I was able to solve the problem - if any one requests it I will post the solution for critique. Thanks to all who replied. Subject: parent requesting help with daughters homework Well I have done and put my foot in mouth when I told my daughter I would check over her math. Apparently she is taking a some quality management course and silly me thought it would be just like a business management course. I have gotten stuck on some of her problems and am unsure of a few of the answers. i am hoping that i can bounce what I have off others to see if I am right. many thanks in advance for those that can help out. 1. A manufacturer estalishes X-bar and R charts for the time taken to complete a subprocess. A sample size of n=6 is used. Four weeks (24 days) of data proudced the following results: X-doublebar = 12 mins, s-bar= 1.5 mins, R-bar= 5 mins The controls limits for the X-bar chart are? UCLx= 14.415 ; LCLx= 9.585 2. Using the same data for the above question, the UCL and LCL are respectively 9.62 and 0.38 3. A process with an average value of 2.5 defects and a standard variation of 0.5 yields the following set of readings: 2.3, 2.6, 2.5, 3.4, 3.2, 2.6, 3.1, 3.4, 3.2, 2.6, 2.3, 2.1, 3.0, 1.7, 1.9, 2.0, 2.3, 2.7, 2.8, 3.2, 3.1, 2.7, 2.4, 3.0, 3.1 The rend exhibits an oscillating trend or would it be a run variation? Last one for now. 4. Given a process sample standard deviation of 3, the population standard deviation with a sample group size of 5 is 3.19. Once again, thanks to all who take this time to read and offer their help :) Subject: Last question on a Christmas Quiz I am doing....... It's dark. In a drawer you have 17 pair of red socks, 17 pairs of green socks and 17 pairs of blue socks. All are loose. How many socks would you need to take out of the drawer to make sure you get a pair of socks of each colour? I think the answer is 70. Is this correct? If not, please explain your answer. Much appreciated. Merry Christmas!! Simon T Subject: Re: Last question on a Christmas Quiz I am doing....... > It's dark. In a drawer you have 17 pair of red socks, 17 pairs of > green socks and 17 pairs of blue socks. All are loose. How many socks > would you need to take out of the drawer to make sure you get a pair > of socks of each colour? I think the answer is 70. > Is this correct? If not, please explain your answer. I get the same answer. Reasoning: The highest number of socks you can pick up without getting a pair of each is 69 (all the socks from two colors plus one sock from the third). Therefor we take one more sock. > Much appreciated. You're welcome. > Merry Christmas!! > Simon T /Tomas Subject: Algebra two - Exponential Equations - Please Help! - Word Problems I just had a quiz and I did not get any of the word problems correct now I have a test tomorrow! If someone would please walk me through getting the correct equation that would really help me. Thank you for your time. P = Psubsero * (R + 1)^t thats the standerd equation im using. ok, here are the problems: 1. The number of water hyacinth plants growing on a lake increases exponentially with time. On Tuesday the number of plants is 150. That Friday the number has risen to 240. If it takes 3400 plants to completely cover the lake, will the lake be covered by 20 days after Tuesday? 2. Assume that the concentration of aspirin in the blood system decreases exponentially with time after you take the tablets. At time t = 0 the concentration is 100 units, and at time t = 40 minutes the concentration is 73 unit. Find the particular equation and use it to predict the concentration at t = 95 minutes. 3. You decide to plant asparagus in you kitchen garden. You first harvest 10 stalks in 1986. By 1988 you produce thirty stalks. Assume that the number of stalks you harvest varies exponentially with the number of years since you started harvesting the plants. a. Find the particular equation of this function expressing number of stalks in terms of the time since you harvested. b. You will need 100 stalks to enter the gardening contest at the local fair. When can you enter the contest? c. According to your model, when did you harvest the first stalk? d. What will be your production in the year 2000? Subject: Re: Algebra two - Exponential Equations - Please Help! - Word Problems > I just had a quiz and I did not get any of the word problems correct now I > have a test tomorrow! If someone would please walk me through getting the > correct equation that would really help me. > Thank you for your time. > P = Psubsero * (R + 1)^t > thats the standerd equation im using. ok, here are the problems: > 1. The number of water hyacinth plants growing on a lake > increases exponentially with time. On Tuesday the number of plants is 150. > That Friday the number has risen to 240. If it takes 3400 plants to > completely cover the lake, will the lake be covered by 20 days after > Tuesday? I think you are a little late getting started. Also, it would be helpful if you had shown what work you had done so people could point out where you need help. Let me give some hints on the first one. If you let time 0 (t=0) be Tues. You get P = 150 on Tues and that is P subzero (why?). Day 3 would be Fri. So 240 = 150*(R+1)^3. How do you find R? Once you find R, how do you find out what happens on day 20? Bill Subject: Re: Algebra two - Exponential Equations - Please Help! - Word Problems > I just had a quiz and I did not get any of the word problems correct now I > have a test tomorrow! If someone would please walk me through getting the > correct equation that would really help me. > Thank you for your time. > P = Psubsero * (R + 1)^t > thats the standerd equation im using. ok, here are the problems: > 1. The number of water hyacinth plants growing on a lake > increases exponentially with time. On Tuesday the number of plants is 150. > That Friday the number has risen to 240. If it takes 3400 plants to > completely cover the lake, will the lake be covered by 20 days after > Tuesday? > I think you are a little late getting started. Also, it would be helpful if > you had shown what work you had done so people could point out where you need > help. Let me give some hints on the first one. If you let time 0 (t=0) be > Tues. You get P = 150 on Tues and that is P subzero (why?). Day 3 would be > Fri. So 240 = 150*(R+1)^3. How do you find R? Once you find R, how do you find > out what happens on day 20? > Bill 240 = 150*(R+1)^3 240/150 = (r+1)^3 cuberoot(240/150) = r+1 1 plus or minus cuberoot(240/150) = r -- was my error that i had t as two instead of three? Subject: Re: Algebra two - Exponential Equations - Please Help! - Word Problems > I just had a quiz and I did not get any of the word problems correct now > I > have a test tomorrow! If someone would please walk me through getting > the > correct equation that would really help me. > > Thank you for your time. > > P = Psubsero * (R + 1)^t > > thats the standerd equation im using. ok, here are the problems: > > 1. The number of water hyacinth plants growing on a > lake > increases exponentially with time. On Tuesday the number of plants is > 150. > That Friday the number has risen to 240. If it takes 3400 plants to > completely cover the lake, will the lake be covered by 20 days after > Tuesday? > > > I think you are a little late getting started. Also, it would be helpful > if > you had shown what work you had done so people could point out where you > need > help. Let me give some hints on the first one. If you let time 0 (t=0) be > Tues. You get P = 150 on Tues and that is P subzero (why?). Day 3 would be > Fri. So 240 = 150*(R+1)^3. How do you find R? Once you find R, how do you > find > out what happens on day 20? > Bill > 240 = 150*(R+1)^3 > 240/150 = (r+1)^3 > cuberoot(240/150) = r+1 > 1 plus or minus cuberoot(240/150) = r > was my error that i had t as two instead of three? Yes I think so. I think only one value of R will work - or else you will end happens at time 20. Bill Subject: Re: Algebra two - Exponential Equations - Please Help! - Word Problems > > > I just had a quiz and I did not get any of the word problems correct now > I > > have a test tomorrow! If someone would please walk me through getting > the > > correct equation that would really help me. > > > Thank you for your time. > > > P = Psubsero * (R + 1)^t > > > thats the standerd equation im using. ok, here are the problems: > > > 1. The number of water hyacinth plants growing on a > lake > > increases exponentially with time. On Tuesday the number of plants is > 150. > > That Friday the number has risen to 240. If it takes 3400 plants to > > completely cover the lake, will the lake be covered by 20 days after > > Tuesday? > > > I think you are a little late getting started. Also, it would be helpful > if > you had shown what work you had done so people could point out where you > need > help. Let me give some hints on the first one. If you let time 0 (t=0) be > Tues. You get P = 150 on Tues and that is P subzero (why?). Day 3 would be > Fri. So 240 = 150*(R+1)^3. How do you find R? Once you find R, how do you > find > out what happens on day 20? > > Bill > > > 240 = 150*(R+1)^3 > 240/150 = (r+1)^3 > cuberoot(240/150) = r+1 > 1 plus or minus cuberoot(240/150) = r > -- > was my error that i had t as two instead of three? > Yes I think so. I think only one value of R will work - or else you will end > happens at time 20. It seems there is another equation: B = a * b^t (t,B) and that worked for some of them... Is there just a general equation I can use for all exponential equations or do I have to memorize all of them? I'm up to 3 atm... > Bill Subject: Re: Algebra two - Exponential Equations - Please Help! - Word Problems > It seems there is another equation: > B = a * b^t > (t,B) > and that worked for some of them... > Is there just a general equation I can use for all exponential equations or > do I have to memorize all of them? I'm up to 3 atm... They all do pretty much the same thing in the end. So it is a matter of what makes things easier. I like the second one better. Good luck! Bill Subject: Re: Algebra two - Exponential Equations - Please Help! - Word Problems > I just had a quiz and I did not get any of the word problems correct now I > have a test tomorrow! If someone would please walk me through getting the > correct equation that would really help me. > Thank you for your time. > P = Psubsero * (R + 1)^t > thats the standerd equation im using. ok, here are the problems: > 1. The number of water hyacinth plants growing on a lake > increases exponentially with time. On Tuesday the number of plants is 150. > That Friday the number has risen to 240. If it takes 3400 plants to > completely cover the lake, will the lake be covered by 20 days after > Tuesday? > I think you are a little late getting started. Also, it would be helpful if > you had shown what work you had done so people could point out where you need > help. Let me give some hints on the first one. If you let time 0 (t=0) be > Tues. You get P = 150 on Tues and that is P subzero (why?). Day 3 would be > Fri. So 240 = 150*(R+1)^3. How do you find R? Once you find R, how do you find > out what happens on day 20? > Bill I did: 240=150(1+r)^2 and i got -.483 = r so my equation looked like: p = psubzero (.5163977795)^t Subject: Simple Q: Probability Density Functions... Hello all, I have a quick question, and I have done a bit of research on finding an answer, but as yet I haven't found anything. So I thought i would ask here: The Normal Probability Density Function has equation: f(x) = 1 / (sigma * sqrt(2 * pi)) * exp(-1 * (x - mu)^2 / 2*sigma^2). So I was wondering, do other distributions like: - The t-distribution, - Chi-Square distribution, - F-distribution, - etc. have formulae as well, or does one have to rely on tables to work out the area under the curve as required in hypothesis testing, etc...? Thanks in advance. m. Subject: Re: Simple Q: Probability Density Functions... > Hello all, > I have a quick question, and I have done a bit of research on finding an > answer, but as yet I haven't found anything. So I thought i would ask > here: > The Normal Probability Density Function has equation: > f(x) = 1 / (sigma * sqrt(2 * pi)) * exp(-1 * (x - mu)^2 / 2*sigma^2). > So I was wondering, do other distributions like: > - The t-distribution, > - Chi-Square distribution, > - F-distribution, > - etc. > have formulae as well, or does one have to rely on tables to work out > the area under the curve as required in hypothesis testing, etc...? > Thanks in advance. m. Sure. Look here and you will find a bunch of them. http://www.itl.nist.gov/div898/handbook/eda/section3/eda366.htm Bill Subject: Re: Simple Q: Probability Density Functions... > Sure. Look here and you will find a bunch of them. > http://www.itl.nist.gov/div898/handbook/eda/section3/eda366.htm Thanks, just what I was looking for! :-) And also: Youch! There's some pretty ugly looking formulae... m. Subject: Re: Simple Q: Probability Density Functions... Original Message: Subject: Simple Q: Probability Density Functions... Hello all, I have a quick question, and I have done a bit of research on finding an answer, but as yet I haven't found anything. So I thought i would ask here: The Normal Probability Density Function has equation: f(x) = 1 / (sigma * sqrt(2 * pi)) * exp(-1 * (x - mu)^2 / 2*sigma^2). So I was wondering, do other distributions like: - The t-distribution, - Chi-Square distribution, - F-distribution, - etc. have formulae as well, or does one have to rely on tables to work out the area under the curve as required in hypothesis testing, etc...? Thanks in advance. m. The distributions you mention do have their own pdfs. If interested, I suggest you consult one of the mathematical statistics textbooks aimed at math majors or grad students ( such as Hogg, and Craig, or Bain and Engelhart). -- Rob George Subject: A parametric integral Originator: israel@math.ubc.ca (Robert Israel) Can the functions f_n, defined for complex z not on the positive real line, f_n(z):= integral_{0 to inf} dx x^{-n}e^{-x}/(z-x), be expressed in terms of elementary or well-known special functions? At least for n=0? Arnold Neumaier Subject: Re: A parametric integral Originator: israel@math.ubc.ca (Robert Israel) >Can the functions f_n, defined for complex z not on the positive >real line, > f_n(z):= integral_{0 to inf} dx x^{-n}e^{-x}/(z-x), >be expressed in terms of elementary or well-known special functions? >At least for n=0? I believe that f_0(z) = -Ei(1,-z) exp(-z) f_(1/2)(z) = Pi exp(-z) (erfi(sqrt(z))/sqrt(z) - 1/sqrt(-z)) and for non-integer n < 1 f_n(z) = (-n WhittakerM(-n/2,(n+1)/2,z) - WhittakerM(1-n/2,(n+1)/2,z)) Gamma(-n) exp(-z/2) z^(-1-n/2)/(1+n) - Pi csc(Pi n) (-1/z)^n exp(-z) Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 Subject: Re: A parametric integral Originator: israel@math.ubc.ca (Robert Israel) > Can the functions f_n, defined for complex z not on the positive > real line, > f_n(z):= integral_{0 to inf} dx x^{-n}e^{-x}/(z-x), > be expressed in terms of elementary or well-known special functions? > At least for n=0? > Arnold Neumaier For n=0, rewrite it as: -e^{-z} f_0(-z) = integral_{z to inf} dx e^{-x}/x for |arg(z)| < Pi which is E_1(z) in the Handbook of Mathematical Functions. http://jove.prohosting.com/~skripty/page_228.htm For other n it should be possible to use partial fractions and the higher E_n(z) functions in the same chapter. Subject: Re: Distribution Originator: israel@math.ubc.ca (Robert Israel) The degree of freedom is for a(t) and b(t) different. The characteristic function of a(t) and b(t) are easy, I agree with you. But How can I make the back transformation A(f)*B(f). BRG, Fatih > >>Hello all, >> > >>I am searching for the distribution of the following random variable: >>f(t)=a(t)+b(t) >> > >>a(t) and b(t) are central Chi-Square distributions but with different >>parameters: >> > >>a(t): sigma_a^2;(Which corresponds to the sigma_a^2 of the normal >>distribution N(0,sigma_a^2), >> n_a, degree of freedom >> > >>b(t): sigma_b^2 >> n_b >> >The characteristic function is easy. In the case the >number of degrees of freedom are both 1, it involves >Bessel functions. One can use efficient numerical >integration techniques to evaluate it by complex >integration. > -- Fatih Çapar, Dipl.-Ing. wiss. Ang. Universit.8at Karlsruhe(TH), Institut f.9fr Nachrichtentechnik, Geb. 30.44, 6. Stock, Raum 627 D-76128 Karlsruhe, Tel: +49 721 608 4097, Fax: +49 721 608 6071 Subject: International Journal of Mathematics - TOC alert Originator: israel@math.ubc.ca (Robert Israel) International Journal of Mathematics View table-of-contents and abstracts at http://www.worldscinet.com/ijm.html Contents: A C*-Algebraic Framework For Quantum Groups T. Masuda, Y. Nakagami and S. L. Woronowicz The Kappa Function Masanobu Kaneko And Masaaki Yoshida For more information, go to http://www.worldscinet.com/ijm.html Subject: Re: orthogonal polynomials and creation/annihilation operators > I'm interested in generalizations of the usual annihilation > and creation operators ... > My question is whether something like this works for other > cases... for example the Laguerre case! ... As a follow-up to the suggestions and (partial) answers by I want to point to the two references [1] D. Basu and K.B. Wolf, The unitary irreducible representations of SL(2,R) in all subgroup reductions, J. Math. Phys. 23 (1982), 189-206. [2] B. Kostant, On Laguerre polynomials, Bessel functions, Hankel transform and a series in the unitary dual of the simply-connected covering group of SL(2,R), Represent. Theory 4 (2000), 181-224; http://www.ams.org/ert/home-2000.html. They realize the discrete series representations of SL(2,R) (or in [2] their analogues for the universal covering group of SL(2,R)) on the Hilbert space of L^2 functions on the interval (0,infinity). This realization is such that the nilpotent lower (or upper) diagonal subgroup N acts by multiplication by exponentials. The nontrivial Weyl group element acts as a Hankel transform. The (generalized) Laguerre polynomials L_n^a(x) multiplied by the square of their weight function then form a K-basis of C^infinity vectors for L^2((0,infinity)). The action of the complexified Lie algebra sl(2,C) on this basis essentially realizes the differential recurrence relations for Laguerre polynomials which were observed in the reactions to John Baez' question mentioned above: (1) (x d/dx - n) L_n^a(x) = -(n+a) L_{n-1}^a(x) (2) (x d/dx + n+a+1-x) L_n^a(x) = (n+1) L_{n+1}^a(x) (see Erdelyi, Higher Transcendental Functions, Vol. 2, formula 10.12(12)) In order to get the Lie algebra operators, replace on the left-hand side of (1) and (2) -n by x d^2/dx^2 + (a+1-x) d/dx In the case of [1] we realize nonnegative integer values of a. In the case of [2] we realize all real a>-1. Kostant [2] also relates the cases a=1/2 and a=-1/2 to the metaplectic representation. Then contact can be made with the usual creation and annihilation operator for Hermite polynomials. For this observe the quadratic transformation formulas connecting Hermite with Laguerre polynomials: (3) H_{2n}(x) = (-1)^n n! 2^{2n} L_n^{-1/2}(x^2) (4) H_{2n+1}(x) = (-1)^n n! 2^{2n+1} x L_n^{1/2}(x^2) (see section 1.13 in Koekoek and Swarttouw, http://aw.twi.tudelft.nl/~koekoek/askey/ ) Finally I want to remark that the pair of formulas (3) d/dx H_n(x) = 2n H_{n-1}(x) (4) (d/dx - 2x) H_n(x) = -H_{n+1}(x) can also be obtained from (1) and (2) by the limit formula lim_{a -> infinity} (2/a)^{n/2} L_n^a((2a)^{1/2} x + a) = (-1)^n H_n(x) / n! (see section 2.11 in Koekoek and Swarttouw, http://aw.twi.tudelft.nl/~koekoek/askey/ ) Tom Koornwinder Subject: Finite presentation of PSL(2,Q) Epigone-thread: plahflilgho Originator: israel@math.ubc.ca (Robert Israel) We know that PSL(2,Z), where Z is the set of integers, is finitely generated by (z)x=-(1/z), of order 2, and by (z)y=(z-1)/z, of order three. So that finite presentation becomes . Now what is the finite presentation of PSL(2,Q), where Q is the field of rational numbers. Huma Subject: Re: Finite presentation of PSL(2,Q) Originator: israel@math.ubc.ca (Robert Israel) >We know that PSL(2,Z), where Z is the set of integers, is finitely >generated by (z)x=-(1/z), of order 2, and by (z)y=(z-1)/z, of order >three. So that finite presentation becomes . Now what >is the finite presentation of PSL(2,Q), where Q is the field of >rational numbers. Is there a reason PSL(2,Q) should be finitely presented? Naively, it seems unlikely. Lee Rudolph Subject: The Petrov Types of a metric Epigone-thread: ghexkedang Originator: israel@math.ubc.ca (Robert Israel) What is the Patrov type of the schwarzschild interior spcetime (with constant density and pressure as a function of r) Subject: Global optimum Originator: israel@math.ubc.ca (Robert Israel) I want to maximize the following function: f(x_1,...,x_n) = 1 - product_i (1 - p_i) Where p_i = yL_i + (yR_i - yL_i)/(1 + exp (-x_i/b_i)) and sum_i x_i = Constant Further: b_i >0 yR_i > 0 > yL_i x_i > 0 I know that p_i is a logistic curve and that this curve is convex for x_i > 0, but I don't know how f(x_1,...,x_n) behaves. My question is: When I find a local maximum (x_1,...,x_n) for f(x_1,...,x_n), is this also a global maximum? Kind regards, Jantine Subject: Numbers represented by a linear form Epigone-thread: swoucaylim Originator: israel@math.ubc.ca (Robert Israel) What are the rational integers w,x,y and z that can be represented by w=as+cr y=aq+cp x=bs+dr z=aq+cp where s,p,q and r are rational integers such that sp-rq=1. a,b,c and d are fixed integers such that ad-bc=n. It is clear that if ad-bc=1 then every 4-tuple (w,x,y,z), an element of Z^4 (Z is the set of integers), of integers can be represented as above form. But what about general case ad-bc=n. Also for fixed n how many partitioning does (w,x,y,z) made of Z^4, where Z is the set of integers. Subject: request help for solve eigenvalue problem on large sparse matrix hi, I have to solve an eigenvalue problem of some large sparse matrix(symmetric real and about 60000*60000 , 500 non-zero elements). I haven't found a good computing package to solve it under linux .Now I get the arpack++ from the netlib , it works not so well ,does anyone have any good sugestion ? the second problem is how can i estimate the number of eigenvalues of that sparse matrix (not need to be the exact accurate),. I need this parameter to pass to the arpack++ function which can help me solve the problem. merry christmas! thanks! Subject: Re: request help for solve eigenvalue problem on large sparse matrix > hi, > I have to solve an eigenvalue problem of some large sparse matrix(symmetric > real and about 60000*60000 , 500 non-zero elements). > I haven't found a good computing package to solve it under linux .Now I get > the arpack++ from the netlib , it works not so well ,does anyone have any > good sugestion ? > the second problem is how can i estimate the number of eigenvalues of that > sparse matrix (not need to be the exact accurate),. I need this parameter to > pass to the arpack++ function which can help me solve the problem. > merry christmas! > thanks! another suggestion: http://www.math.ruu.nl/people/vorst/jd.html Hans Mittelmann Subject: Re: request help for solve eigenvalue problem on large sparse matrix > I have to solve an eigenvalue problem of some large sparse matrix(symmetric > real and about 60000*60000 , 500 non-zero elements). Any suggestions??? Try putting this query into google: eigenvalue sparse matrix symmetric library and look at the top search return: http://vlsicad.cs.ucla.edu/sparse.html I know China blocks Google's cache, but surely blocking this kind of search hurts not only your Institute and the Acadamy itself, but is bad for your entire country as well. James Subject: use of SVD (on a underdetermined system) to solve a minimization problem 1. I have a vector b (n). Now I need a solution vector x for A ( A * x = 0 ) ,who is of minimal distance to b: min x - b ^ 2; s.t. A x = 0; How do I get this vector? How do I use the SVD on A to get this vector? I know that the SVD of A gives me a pseudoinverse of A. But how is that suppose to help me? 2.Important: The matrix A has more columns then rows!!! m < n ! x must be a solution to A*x=0! Thanks in advance, Han Subject: source code for pid controller by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id hBNKncL30994; please send me any source code for pid controller Subject: Re: What do you do with num-analysis? Distribution: inet X-NewsReader: GRn 3.2n February 9, 1999 > However, the only penalty for the size is the > download time and by industry standards for this > field, it's still a lean, thin, and mean executable. > It's distributed as a 5MB self-extracting gzip'ed > executable that contains 1500+ files in addition to > the executable. > We put men on the moon with probably less code than > that in all the computers involved, ground and mobile. > I sure hope so, it's about half a million lines of densely > written C++ code. The simulator is far beyond 60's > technology. It does full chip, transistor level > simulation of IC's much larger than were available during > the moon shots. It's routinely used for IC's with 10,000 > transistors solved in a single matrix 100,000 elements on > a side. Technology moves on, even if it feels like all > the good engineering has already been done. I'm just trying to fathom how it takes so much code to simulate transistors. One line of code per electron? Subject: Re: Mathematical proof Mersenne Primes Hi Eddie, The exact wording is difficult in std text ... but here is my best go ... (The A is supposed to be inverted (up side down) meaning that For ALL) Is the proposition {A prime p: 2^p - 1 is prime} true or false? Prove your assertion. -- Regards Luke ------ Q: What does FAQ stand for? A: We are Frequently Asked this Question, and we have no idea. ------ > I know that p=11 is a counter example, but is simply stating that > adequate proof from an academic point of view? > Yes. > My experience to date > says they want a more professional/academic explanation. > Perhaps I'm barking up the wrong tree insofar as there isn't a way of > proving it mathematically? > You (and conceivably they) may be confusing different sorts of > propositions. Can you please reproduce EXACTLY what the question says? > The precise wording may be crucial. Subject: Re: Mathematical proof Mersenne Primes > Hi Eddie, > The exact wording is difficult in std text ... but here is my best go > ... > (The A is supposed to be inverted (up side down) meaning that For > ALL) > Is the proposition {A prime p: 2^p - 1 is prime} true or false? Prove OK. That's fine. Producing a single counterexample is immediately sufficient to prove the proposition is false. It is possibly a trick question, intended to see who will spend huge amounts of time trying to prove a proposition to be true which is actually false. Have a look at http://www.utm.edu/research/primes/mersenne/index.html#hist Enjoy your experiences with number theory, Luke. In my view, it's the most intrinsically fascinating branch of mathematics, because it's so basic but presents such difficult problems, many of them still unsolved. Eddie Subject: Re: Mathematical proof Mersenne Primes > (The A is supposed to be inverted (up side down) meaning that For > ALL) > Is the proposition {A prime p: 2^p - 1 is prime} true or false? Prove > OK. That's fine. Producing a single counterexample is immediately > sufficient to prove the proposition is false. The url you've provided lists many more that have proven the proposition to be false so there is a large body of evidence to prove it false ... the thing is, that I expected that we were required to prove it in a more mathematical way. For example,we were also asked to prove that the first n even numbers was equal to n(n+1) This one was reasonably simple insofar as it was was easy to figure out equations for n and n+1even numbers, subtract the respective LHS's and the respective RHS and the result was proven. But proving the prime number problem via contradiction or otherwise was significantly more frustrating. > It is possibly a trick question, intended to see who will spend huge > amounts of time trying to prove a proposition to be true which is > actually false. You could be right. I found the True proof on that utm.edu site and was almost ready to submit my answer when a bit more research showed I was way of the mark. I guess it shows just how careful you need to be sometimes. > Have a look at > http://www.utm.edu/research/primes/mersenne/index.html#hist Yes, I did have a look ... seems curious to me that mathematicians in the early days seemed to make fundamental errors, but I suppose it's a lot easier with calculators and computers these days. > Enjoy your experiences with number theory, Luke. In my view, it's the > most intrinsically fascinating branch of mathematics, because it's so > basic but presents such difficult problems, many of them still unsolved. Thanks for the encouragement Eddie, but I'm not sure that I am passionate enough about discrete maths to pursue the subject beyond this current course. I have to say, I see little value in getting excited about the discovery of the next Mersenne prime and probably more importantly, what value it possesses for humanity in the long term ... its not like it is another Pi or e or something 8>) Thanks for your help ... Luke. Subject: Re: Check it out!! > girl bent over taking it from both ends.. me an my friend took it > last summer when we were on vacation!! more comming > http://home.mchsi.com/~relentless/Young_Girls.scr file (screen saver) that takes you directly to the download page without any choice of seeing what's on the actual webpage has to be a fairly suspect download. -- Sandgroper 2002 CB250 ---------------------------------- Remove KNICKERS to Email steveray@KNICKERSiinet.net.au Subject: Re: Check it out!! heheheh My Mac LAUGHED at the executable script. >>girl bent over taking it from both ends.. me an my friend took it >>last summer when we were on vacation!! more comming >>http://home.mchsi.com/~relentless/Young_Girls.scr > file (screen saver) that takes you directly to the download page without any > choice of seeing what's on the actual webpage has to be a fairly suspect > download. > Sandgroper > 2002 CB250 > ---------------------------------- > Remove KNICKERS to Email > steveray@KNICKERSiinet.net.au -- Look beyond the window, don't just focus on your own reflection. abuse@spamcop.net for all spam. Subject: Re: Check it out!! > heheheh > My Mac LAUGHED at the executable script. Hehehe You are using a Mac? , now that is funny. :P -- Sandgroper 2002 CB250 ---------------------------------- Remove KNICKERS to Email steveray@KNICKERSiinet.net.au Subject: Re: Check it out!! osx I laugh as well for all the correct reeasons:P >>heheheh >>My Mac LAUGHED at the executable script. > Hehehe > You are using a Mac? , now that is funny. > :P > Sandgroper > 2002 CB250 > ---------------------------------- > Remove KNICKERS to Email > steveray@KNICKERSiinet.net.au -- Look beyond the window, don't just focus on your own reflection. abuse@spamcop.net for all spam. Subject: Re: Grad school part: > On the topic of math grad programs, the Princeton Review ranks > graduate programs. See also U.S. News and World Report's Web site (usnews.com, I think) for its rankings. msh210@math.wustl.edu Of a reply, then, if you have been cheated, http://math.wustl.edu/~msh210/ Likely your mail's by mistake been deleted. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: Grad school > part: >> On the topic of math grad programs, the Princeton Review ranks >> graduate programs. > See also U.S. News and World Report's Web site (usnews.com, I think) for > its rankings. Be very wary of both the Princeton Review and the US News and World Report rankings. They often bear little relationship to what people in a given field believe about the schools. Their facts are often wrong also (for example, for many years UC Santa Cruz was listed in US News and World Report as an urban campus, while UCLA was suburban). -- Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Professor of Computer Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Affiliations for identification only. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: Grad school I lot of things are pointing to UIUC so far.... except for the experience of figuring out the cost of food while attending there...it would take a PhD to figure out their credit system. Otherwise looks like a great school from what I've read so far. Just have to maintain my 3.0 or better and do well on the GRE. Thanks for your help! John > Matt's high school has a number of Ph.D.s on the faculty, of varying > degrees of excellence as teachers. One Ph.D. in biology was a > disaster as AP Biology teacher. > On the topic of math grad programs, the Princeton Review ranks > graduate programs. Among top-ranked in the Midwest are Chicago, > Michigan, UIUC, Madison. > mattsmom -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: graphing tools Does anyone know any good mathematical graphing tools for computers I can download? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: graphing tools > Does anyone know any good mathematical graphing tools for computers I > can download? The gnuplot program is free and will run on any unix or Linux machine. Probably also Mac OS X, but I've not tried it there yet. -- Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Professor of Computer Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Affiliations for identification only. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: graphing tools >> Does anyone know any good mathematical graphing tools for computers I >> can download? > The gnuplot program is free and will run on any unix or Linux > machine. Probably also Mac OS X, but I've not tried it there yet. Sorry to followup on my own post, but I just installed the latest (Panther) version of Mac OS X on my laptop, and it does include gnuplot. Seems to work fine (except that the help command is broken---possibly an installation problem.) -- Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Professor of Computer Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Affiliations for identification only. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: graphing tools >> Does anyone know any good mathematical graphing tools for computers I >> can download? ============================================================== ======= If validity of output is a concern, you might try GrafEq (www.peda.com/grafeq) which is a relation-plotter for Mac or Win : shareware - register if found appropriate. Gary Tupper Terrace -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: graphing tools Gnuplot will run under quite a lot of operating systems, including but not limited to Unix/Linux, VAX/VMS, Mac, PC-Windows, etc. See www.gnuplot.info/faq Gnuplot is a really useful tool - it will do quite a lot of computation as well as very useful graphing. The documentation is quite functional, also, so that it isn't too hard to figure out how to do something new. ************************************************************** ********** Ellen M. Wijsman COURIER DELIVERY ADDRESS ONLY: Research Professor Ellen M. Wijsman Div. of Medical Genetics and 1914 N 34th St., suite 209 Dept. Biostatistics Seattle, WA 98103 BOX 357720, University of Washington (Note: Use this address Seattle, WA 98195-7720 EXACTLY as given above, and phone: (206) 543-8987 use ONLY for courier delivery!!!) fax: (206) 616-1973 email: wijsman@u.washington.edu web page: http://faculty.washington.edu/wijsman ************************************************************** *********** > Does anyone know any good mathematical graphing tools for computers I > can download? > The gnuplot program is free and will run on any unix or Linux > machine. Probably also Mac OS X, but I've not tried it there yet. > Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus > life member (LAB, Adventure Cycling, American Youth Hostels) > Effective Cycling Instructor #218-ck (lapsed) > Professor of Computer Engineering, University of California, Santa Cruz > Undergraduate and Graduate Director, Bioinformatics > Affiliations for identification only. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: graphing tools If you only need it for a short time, the new version of Derive is available for a 30 day download. http://education.ti.com/us/product/software/derive/features/ features.html > Does anyone know any good mathematical graphing tools for computers I > can download? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: graphing tools X-No-Archive: yes >Does anyone know any good mathematical graphing tools for computers I >can download? Assuming your platform is either DOS, or any of the Windows family, Graphmatica is pretty good... http://www8.pair.com/ksoft/ -- charlie dick The right to be left alone -- the most comprehensive of rights, and the right most valued by a free people. - Justice Louis Brandeis, Olmstead v. U.S. (1928). -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: 1,572,864 ways to order hash browns? Could someone check my numbers and logic? Several evenings ago I slipped into a Waffle House restaurant as I returned home from being out of town. I ordered my usual: order over medium plate with one sausage and a Coke (Two eggs over medium, hash browns, two sausage patties, two pieces of toast and a Coke.) As I began reading over the menu (which I should be familiar with by now) I mulled over their claim that there are 1,572,864 ways of ordering hash browns. I don't think that's correct. Waffle House serves hash browns in three different sizes: regular, large and triple size. Each order can then be scattered and... 1. Smothered with onions... 2. Covered with cheese... 3. Chunked with ham... 4. Topped with chili... 5. Diced with tomatos 6. Scattered with Jalapenos or... 7. Capped with mushrooms. Now, I consider that 10 items, but because I'm trying to think of how Waffle House came up with such a large number, I'll give them the possibility that someone might actually order a large order of hash browns, scatter them and not add an additional item. To find the number of combinations you would use the formula: 2^11 = 2,048 2,048 is no where near 1,572,864! Even if you consider order (regular hash browns scattered and covered with cheese is different from scattered and covered with cheese with regular hash browns) which is a permutation, not a combination, that be expressed as a factorial: 11! = 39,916,800 So, I'm sitting there, slapping my dripping eggs over medium on top of a triangle of toast, scribbling numbers on a napkin and I figured out that somebody at the Waffle House main office doesn't know their high school math. I later contacted Waffle House, and the attached spreadsheet included additional items that the customer could request or put on the hashbrowns him or herself. Well, now I see how they come up with more than the 2,048 I can up with.. However, I'm not going to allow extra anything because that just muddys the waters, and I'm not going to allow scattered by itself because that's akin to saying I'd like pie a'la mode but without ice cream. So, to recap, we have 3 sizes: 1. Regular 2. Double and 3. Triple We have four preparations: 4. Plain (with oil) 5. Well (seared) 6. Steamed (with ice) 7. Dry (without anything) ...and we have 18 additional ingredients 8. Smothered with onions... 9. Covered with cheese... 10. Chunked with ham... 11. Topped with chili... 12. Diced with tomatos 13. Scattered with Jalapenos 14. Capped with mushrooms 15. Ketchup 16. Heinz 57 17. Picante sauce 18. Ranch dressing 19. Blue Cheese dressing 20. Thousand Island dressing 21. Tabasco sauce 22. Egg 23. Bacon 24. Sausage and/or... 25. Mayonnaise So, at 25 ingredients, preparations and sizes, the formula would be: 2^25 = 33,554,432 ...or, 31,981,568 more combinations than originally listed. And that's not counting extra chili or salt or pepper or sugar or any other weird ingredient. (Who in their right mind would put mayonnaise on hash browns?!?) Or, should the formula instead be: 3*(4*(2^18)) = 3,145,728 Anyone? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: 1,572,864 ways to order hash browns? > Could someone check my numbers and logic? > Several evenings ago I slipped into a Waffle House restaurant as I returned > home from being out of town. I ordered my usual: order over medium plate > with one sausage and a Coke (Two eggs over medium, hash browns, two sausage > patties, two pieces of toast and a Coke.) > As I began reading over the menu (which I should be familiar with by now) I > mulled over their claim that there are 1,572,864 ways of ordering hash > browns. I don't think that's correct. > Waffle House serves hash browns in three different sizes: regular, large and > triple size. Each order can then be scattered and... > 1. Smothered with onions... > 2. Covered with cheese... > 3. Chunked with ham... > 4. Topped with chili... > 5. Diced with tomatos > 6. Scattered with Jalapenos or... > 7. Capped with mushrooms. > Now, I consider that 10 items, but because I'm trying to think of how Waffle > House came up with such a large number, I'll give them the possibility that > someone might actually order a large order of hash browns, scatter them and > not add an additional item. > To find the number of combinations you would use the formula: 2^11 = 2,048 > 2,048 is no where near 1,572,864! Even if you consider order (regular hash > browns scattered and covered with cheese is different from scattered and > covered with cheese with regular hash browns) which is a permutation, not a > combination, that be expressed as a factorial: 11! = 39,916,800 > So, I'm sitting there, slapping my dripping eggs over medium on top of a > triangle of toast, scribbling numbers on a napkin and I figured out that > somebody at the Waffle House main office doesn't know their high school > math. > I later contacted Waffle House, and the attached spreadsheet included > additional items that the customer could request or put on the hashbrowns > him or herself. Well, now I see how they come up with more than the 2,048 I > can up with.. However, I'm not going to allow extra anything because that > just muddys the waters, and I'm not going to allow scattered by itself > because that's akin to saying I'd like pie a'la mode but without ice > cream. > So, to recap, we have 3 sizes: > 1. Regular > 2. Double and > 3. Triple > We have four preparations: > 4. Plain (with oil) > 5. Well (seared) > 6. Steamed (with ice) > 7. Dry (without anything) > ...and we have 18 additional ingredients > 8. Smothered with onions... > 9. Covered with cheese... > 10. Chunked with ham... > 11. Topped with chili... > 12. Diced with tomatos > 13. Scattered with Jalapenos > 14. Capped with mushrooms > 15. Ketchup > 16. Heinz 57 > 17. Picante sauce > 18. Ranch dressing > 19. Blue Cheese dressing > 20. Thousand Island dressing > 21. Tabasco sauce > 22. Egg > 23. Bacon > 24. Sausage and/or... > 25. Mayonnaise > So, at 25 ingredients, preparations and sizes, the formula would be: 2^25 = > 33,554,432 You can't answer yes/no to each of the 25 options. For instance, you can't have a regular hash brown and at the same time have a double hash brown. > ...or, 31,981,568 more combinations than originally listed. And that's not > counting extra chili or salt or pepper or sugar or any other weird > ingredient. (Who in their right mind would put mayonnaise on hash browns?!?) > Or, should the formula instead be: 3*(4*(2^18)) = 3,145,728 Yes. You have to choose one of the options from among 1-3, one from 4-7, and then answer yes/no to each of 8, 9, 10, ..., 25. This number is exactly twice what they claim, so maybe they added an ingredient since they did their calculations. -- Christopher Heckman -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: 1,572,864 ways to order hash browns? Believe it or not that was my first answer! So the correct answer would be 3 x 4 x 2^18 = 3145728 > This number is exactly twice what they claim, so maybe they added an ingredient > since they did their calculations. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: 1,572,864 ways to order hash browns? How about 3 x 4 x 2^17. > Could someone check my numbers and logic? > Several evenings ago I slipped into a Waffle House restaurant as I returned > home from being out of town. I ordered my usual: order over medium plate > with one sausage and a Coke (Two eggs over medium, hash browns, two sausage > patties, two pieces of toast and a Coke.) > As I began reading over the menu (which I should be familiar with by now) I > mulled over their claim that there are 1,572,864 ways of ordering hash > browns. I don't think that's correct. > Waffle House serves hash browns in three different sizes: regular, large and > triple size. Each order can then be scattered and... > 1. Smothered with onions... > 2. Covered with cheese... > 3. Chunked with ham... > 4. Topped with chili... > 5. Diced with tomatos > 6. Scattered with Jalapenos or... > 7. Capped with mushrooms. > Now, I consider that 10 items, but because I'm trying to think of how Waffle > House came up with such a large number, I'll give them the possibility that > someone might actually order a large order of hash browns, scatter them and > not add an additional item. > To find the number of combinations you would use the formula: 2^11 = 2,048 > 2,048 is no where near 1,572,864! Even if you consider order (regular hash > browns scattered and covered with cheese is different from scattered and > covered with cheese with regular hash browns) which is a permutation, not a > combination, that be expressed as a factorial: 11! = 39,916,800 > So, I'm sitting there, slapping my dripping eggs over medium on top of a > triangle of toast, scribbling numbers on a napkin and I figured out that > somebody at the Waffle House main office doesn't know their high school > math. > I later contacted Waffle House, and the attached spreadsheet included > additional items that the customer could request or put on the hashbrowns > him or herself. Well, now I see how they come up with more than the 2,048 I > can up with.. However, I'm not going to allow extra anything because that > just muddys the waters, and I'm not going to allow scattered by itself > because that's akin to saying I'd like pie a'la mode but without ice > cream. > So, to recap, we have 3 sizes: > 1. Regular > 2. Double and > 3. Triple > We have four preparations: > 4. Plain (with oil) > 5. Well (seared) > 6. Steamed (with ice) > 7. Dry (without anything) > ...and we have 18 additional ingredients > 8. Smothered with onions... > 9. Covered with cheese... > 10. Chunked with ham... > 11. Topped with chili... > 12. Diced with tomatos > 13. Scattered with Jalapenos > 14. Capped with mushrooms > 15. Ketchup > 16. Heinz 57 > 17. Picante sauce > 18. Ranch dressing > 19. Blue Cheese dressing > 20. Thousand Island dressing > 21. Tabasco sauce > 22. Egg > 23. Bacon > 24. Sausage and/or... > 25. Mayonnaise > So, at 25 ingredients, preparations and sizes, the formula would be: 2^25 = > 33,554,432 > ...or, 31,981,568 more combinations than originally listed. And that's not > counting extra chili or salt or pepper or sugar or any other weird > ingredient. (Who in their right mind would put mayonnaise on hash browns?!?) > Or, should the formula instead be: 3*(4*(2^18)) = 3,145,728 > Anyone? -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Data encryption 360 degrees rotation document 90 degrees and encryption Data encryption 360 degrees rotation document 90 degrees and encryption on every angel then change it two binary code and fold it over like a piece of paper then having the one's and zero cancel each other out. if you written a very long letter and then change it two binary code it would look like this 01010101010101010101010 10010101010101010101010 01010101001010101010010 00010101000101010101010 10010101010100101010101 would equal = 01 01010101010100001100101 01001010101010101010111 11110111001101010101010 01010101010101010101010 10101010101010101010101 if you took the piece of paper and folded it and folded it and folded it the 0 and 1 would cancel each out and if you keep folding the piece of paper too the smallest you would have 4 numbers left if 1+1 = nothing and 0 + 0 = nothing 1+0=1 and 0+1+0 01 now if the key new the folding times you could send 2 bytes over the internet and unzip a 100 zetabyte program you computer could store all the programs ever written but just need the key to unzip then you could us this for SETI for signals or can you imagine a computer processor that would be 1.8 Hz but run like 100 million zeta hz you could use the new 64 bit process second side to unzip while the front side processes. or use this for the matrix or quantum computing or supercomputer. 64 bit. 1+1 = nothing and 0 + 0 = nothing 1+0=1 and 0+1+0 dont forrget to use < and > signes 0>1+1<0 HTTP://WWW.SPEEDYPC.20M.COM -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: Data encryption 360 degrees rotation document 90 degrees and encryption > Data encryption 360 degrees rotation document 90 degrees and > encryption > on every angel then change it two binary code and fold it over like a > piece of paper then having the one's and zero cancel each other out. > if you written a very long letter and then change it two binary code > it would look like this > 01010101010101010101010 > 10010101010101010101010 > 01010101001010101010010 > 00010101000101010101010 > 10010101010100101010101 would equal = 01 > 01010101010100001100101 > 01001010101010101010111 > 11110111001101010101010 > 01010101010101010101010 > 10101010101010101010101 > if you took the piece of paper and folded it and folded it and folded > it the 0 and 1 would cancel each out and if you keep folding the piece > of paper too the smallest you would have 4 numbers left if 1+1 = > nothing and 0 + 0 = nothing 1+0=1 and 0+1+0 > 01 now if the key new the folding times you could send 2 bytes over > the internet and unzip a > 100 zetabyte program you computer could store all the programs ever > written but just need the key to unzip then you could us this for SETI > for signals or can you imagine a computer processor that would be 1.8 > Hz but run like 100 million zeta hz you could use the new 64 bit > process second side to unzip while the front side processes. or use > this for the matrix or quantum computing or supercomputer. 64 bit. 1+1 > = nothing and 0 + 0 = nothing 1+0=1 and 0+1+0 dont forrget to use < > and > signes 0>1+1<0 > HTTP://WWW.SPEEDYPC.20M.COM if you wrot the program in C++ a=0 b=1 c=10 d=11 e=100 f=101 g=111 h=1000 and so on when you the message was finished the program would turn it into this code. the numbers of folds could be added to the code from a spread sheet like program. folded on 25 and L the ptrogram would turn 25 and L into this example binary the message would still shrink becasue the 0 and 1 would cancell each other out so you would end up with a code of 01 and a key of (25L)50L and so on you would end up with 36 byes on how you folded it. send it to entu make allot of money. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: multiple choice test format on Microsoft Word Over the summer, I attended a math teacher conference in MD. At this conference, someone taught me the proper way to type a letter with a circle around it in hopes of creating my own multiple choice tests. I have since forgotten. I checked wingdings and I know how to place a number with a circle around it on a page, but I cannot find the letters. Can anyone help point me in the right direction? Thank you. -- Adam -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: multiple choice test format on Microsoft Word > Over the summer, I attended a math teacher conference in MD. At this > conference, someone taught me the proper way to type a letter with a circle > around it in hopes of creating my own multiple choice tests. I have since > forgotten. I checked wingdings and I know how to place a number with a > circle around it on a page, but I cannot find the letters. Can anyone help > point me in the right direction? Thank you. > -- > Adam I have MS Word 98, and after typing circled text (without quote marks) into the help box, I got references to shapes autoshapes ( or is it auto shapes?) As is typical with the on-line help, you have to play with the suggested technique to see if it works for you. What little playing I did seems to indicate that it might do what you want. I hope that someone has an easier, better way to do what you want. FWIW :) --- Joe -- Delete the second o to e-mail me. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Rieman Sums to Integrals Hey to all, quick question about Rieman Sums Wouldn't the following Summation: lim(n->infinity) (1/n)Sum(1/(k/n)) where Sum is k=1 to n equal the intergarl Intergral(1/x)dx from 0 to 1? Why not? I mean, decomposing the Summation we would get length of each interval = 1/n start of integral = k/n where k = 1, n=infinity = 0 end of integral = k/n where k=n, n=infinity =1 and there are n intervals in total Thanks Doug Subject: Re: Rieman Sums to Integrals > Wouldn't the following Summation: > lim(n->infinity) (1/n)Sum(1/(k/n)) where Sum is k=1 to n > equal the intergarl > Intergral(1/x)dx from 0 to 1? Yes, they are both equal to oo. Subject: Re: Rieman Sums to Integrals > Intergral(1/x)dx from 0 to 1? One other note: As an American I would pronounce integral differently if it were spelled intergral, since to us the r preceeding the g represents quite a different sound from what is heard in integral. Mike Hardy Subject: Re: Rieman Sums to Integrals Looks correct to me. I think the person who suggested 1/k rather than 1/(k/n) was quite mistaken. The integral diverges to infinity, and so should the sum. Please note that Riemann has two ns at the end. > Hey to all, quick question about Rieman Sums > Wouldn't the following Summation: > lim(n->infinity) (1/n)Sum(1/(k/n)) where Sum is k=1 to n > equal the intergarl > Intergral(1/x)dx from 0 to 1? > Why not? > I mean, decomposing the Summation we would get > length of each interval = 1/n > start of integral = k/n where k = 1, n=infinity = 0 > end of integral = k/n where k=n, n=infinity =1 > and there are n intervals in total > Thanks > Doug Subject: Re: Rieman Sums to Integrals Michael is right. I forgot that each x-value was k/n. That is, in lim(n --> inf) Sum( f(x_k) delta x_k ) = lim(n --> inf) Sum( (1/x_k) delta x_k ) = lim(n --> inf) Sum( 1/(k/n) * (1/n) ) each x_k = k/n. Sorry for the inconvenience, Brian > Looks correct to me. I think the person who suggested > 1/k rather than 1/(k/n) was quite mistaken. The integral > diverges to infinity, and so should the sum. > Please note that Riemann has two ns at the end. > Hey to all, quick question about Rieman Sums > Wouldn't the following Summation: > lim(n->infinity) (1/n)Sum(1/(k/n)) where Sum is k=1 to n > equal the intergarl > Intergral(1/x)dx from 0 to 1? > Why not? > I mean, decomposing the Summation we would get > length of each interval = 1/n > start of integral = k/n where k = 1, n=infinity = 0 > end of integral = k/n where k=n, n=infinity =1 > and there are n intervals in total > Thanks > Doug Subject: Re: Rieman Sums to Integrals > Hey to all, quick question about Rieman Sums > Wouldn't the following Summation: > lim(n->infinity) (1/n)Sum(1/(k/n)) where Sum is k=1 to n > equal the intergarl > Intergral(1/x)dx from 0 to 1? > Why not? > I mean, decomposing the Summation we would get > length of each interval = 1/n > start of integral = k/n where k = 1, n=infinity = 0 > end of integral = k/n where k=n, n=infinity =1 > and there are n intervals in total > Thanks > Doug Only in the sense that both are undefined. The limit does not exist (as a real number) and the integral does not exist (as a real number). Subject: Re: Rieman Sums to Integrals Content-transfer-encoding: 8bit > Hey to all, quick question about Rieman Sums > Wouldn't the following Summation: > lim(n->infinity) (1/n)Sum(1/(k/n)) where Sum is k=1 to n > equal the intergarl > Intergral(1/x)dx from 0 to 1? I guess so in a way. If I'm reading you correctly you have the limit of sum(1/k, k=1..n) as n -> oo. In other words, you have sum(1/k, k=1..oo) which diverges as does int(1/x, x=0..1). -- Paul Sperry Columbia, SC (USA) Subject: Re: Rieman Sums to Integrals Doug: I think you have one too many n's there. The sum should be lim(n->infinity) (1/n)Sum(1/k) where Sum is k=1 to n The reasoning is as follows: The base of each rectangle is 1/n (that accounts for the 1/n in the sum), and the height of each rectangle is 1/k ( if x = k, then 1/x = 1/k). Area of each rectangle = base * height = (1/n) * (1/k). There really isn't anything more to do but add up the areas of each of the rectangles (hence the summation). Hope this helps, Brian > Hey to all, quick question about Rieman Sums > Wouldn't the following Summation: > lim(n->infinity) (1/n)Sum(1/(k/n)) where Sum is k=1 to n > equal the intergarl > Intergral(1/x)dx from 0 to 1? > Why not? > I mean, decomposing the Summation we would get > length of each interval = 1/n > start of integral = k/n where k = 1, n=infinity = 0 > end of integral = k/n where k=n, n=infinity =1 > and there are n intervals in total > Thanks > Doug Subject: Re: Calculating new position of two wheeled robot google for: kalman filter robot tine Christophe > As part of my dissertation, I have to model a robot with > two wheels inside a two dimensional environment. Each wheel is spaced > equally from the centre of the body. > For each time frame, the new position of the robot must be calculated. > Things that are known: > current position of the robot, > current angle of the robot, > distance the left wheel has traveled since the last frame, > distance the right wheel has traveled since the last frame > It is relatively simple to work out the new position if the distance > traveled by the left and right wheels are greater or equal to 0 (for the > time frame). However, it seems more complex to work out the new position > if one wheel is going backwards and the other forwards. > Can anyone solve this complex problem? or at least point me in a useful > direction? Any help would be greatly appreciated. > Thanks > Colin > As an approximate solution, you could pose your problem as > one that you can already solve. Instead of iterating a frame > with both wheels moving opposite directions simultaneously, > break each frame into smaller frames where the wheels take > turns moving while the other remains stationary. Once you > have an approximate solution, it might help you recognize > the form of the exact solution. Sounds like a fun problem. > - Brian Subject: Re: Calculating new position of two wheeled robot > google for: kalman filter robot tine Some well educated college! Franz Subject: Crest of the Peacock I am reading this book. Can someone recommend another like it? thanks in advance, matt Subject: Re: Easy Probabity question charset=iso-8859-1 > Hi all, > I have a Prob. & Stat. book which seems to use circular reasoning: > P(A intersection B) = P(A|B) * P(B), but > the def. of P(A|B) = P(A intersection B) > _______________ > P(B) > Well, how do you find P(A intersection B); since, one is defined in terms > of > the other? Stupid reasoning! > No. If you have any two of these distributions you can calculate the third. > I am trying to use it to solve a basic problem: > If 25 people comprise a society of Mathematicians and Statisticians, and > 16 > are Mathematicians, and 19 are Statisticians, how many are both? > Given that, all you can say is that there are at least 10 and no more than > 16. > Duncan Except, there are none who are not mathematicians and not statisticians, so it has to be 10. Duncan Subject: Re: Easy Probabity question > If 25 people comprise a society of Mathematicians and Statisticians, > and 16 are Mathematicians, and 19 are Statisticians, how many are both? > I was hoping to use P(A U B) = P(A) + P(B) - P(A intersection B). That is correct. P(A U B) = 1, P(A) = 16/25, P(B) = 19/25. No conditional probabilities are involved. -- Mike Hardy Subject: Re: Calculating new position of two wheeled robot >As part of my dissertation, I have to model a robot with >two wheels inside a two dimensional environment. Each wheel is spaced >equally from the centre of the body. >For each time frame, the new position of the robot must be calculated. >Things that are known: > current position of the robot, > current angle of the robot, > distance the left wheel has traveled since the last frame, > distance the right wheel has traveled since the last frame >It is relatively simple to work out the new position if the distance >traveled by the left and right wheels are greater or equal to 0 (for the >time frame). However, it seems more complex to work out the new position >if one wheel is going backwards and the other forwards. >Can anyone solve this complex problem? or at least point me in a useful >direction? Any help would be greatly appreciated. If you know how to solve the problem when both distances are greater or equal to zero, then you're done. Indeed, it is easy to reduce the general problem to this one if you remark the following: if you rotate the environment, appropriately, you fall back in the positive case. You simply have to find the point around which the robot rotates. On the other hand, if you are carefull enough, doing the previous calculation, you will realize that you can solve the problem directly. Remember that you can use negative angles in geometry: you may even be able to use the formulas you already have. If you know a little of complex geometry, this is easy; but using cartesian coordinates is not much more difficult. It may be conceptually easier to consider a local coordinate system, whose origine is the center of the rotation. Tell me if you have a problem solving this, but we are not here to give you the complete solution, are we ? :) /er. Subject: Prices of Maths Book In US, the price of a book for example Elementary Linear Algebra by Howard Anton cost more that USD$100 dollars. In Singapore for instance the price of the same book is only Singapore$50 which is equivalent to approx USD$25. And even with the shipping rate of a staggering USD$35, it is still cheaper than the price in US. Anyone knows why is that? Subject: Re: Prices of Maths Book X-NFilter: 1.2.0 >In US, the price of a book for example Elementary Linear Algebra by Howard >Anton cost more that USD$100 dollars. >In Singapore for instance the price of the same book is only Singapore$50 >which is equivalent to approx USD$25. And even with the shipping rate of a >staggering USD$35, it is still cheaper than the price in US. >Anyone knows why is that? One reason is that Singapore has an extremely spotty record enforcing copyrights. < Subject: Re: Prices of Maths Book > In US, the price of a book for example Elementary Linear Algebra by Howard > Anton cost more that USD$100 dollars. > In Singapore for instance the price of the same book is only Singapore$50 > which is equivalent to approx USD$25. And even with the shipping rate of a > staggering USD$35, it is still cheaper than the price in US. > Anyone knows why is that? For the same reason that the same prescription drugs sold in Canada are significantly lower that the price for the same drugs sold in US. At the bequest and insistence of the prescription drug cartel, congress is passing a measure that will prevent Americans from having prescriptions drugs send to them from a pharmacy in Canada. In otherwords, the publishers have a monolpoly on texts and they are colluding to gouge US students as much as they can. BTW, does the text include an index? That's a recent damnable cheat they're doing to make more undeserved money for their mega-rich selves. Is the table of contents laid out with chapter and section titles? I've seen some high math books designed more like a novel and a text useful for reference. If you want to find something, recall from your reading and go leaving thru the trash text. The last insult to mention is finding in a text with an index, a listing for a reknown basketball team. What might you ask was that doing in a math text. I wondered too, taking time out from tutoring to find how important it was to have that teamed referenced in the index. They were mentioned in a problem. Bah, humbug! So if you can stand living in a ultra-corrupt hyper-commercialized society, have a happy new year, if you can or dare to have one. Subject: Re: Prices of Maths Book << In US, the price of a book for example Elementary Linear Algebra by Howard Anton cost more that USD$100 dollars. In Singapore for instance the price of the same book is only Singapore$50 which is equivalent to approx USD$25. And even with the shipping rate of a staggering USD$35, it is still cheaper than the price in US. Anyone knows why is that? > What is similarly interesting that earlier editions of Math books could be bought as used significantly cheaper. Recently I bought Lial: Finite Mathematics and Calculus w/ application for 99 cents (and 3.50 for S&H). The new price is about $100. I have a feeling that the faculties get some kickback money for using the books, and this is represented in the price. Subject: Re: Prices of Maths Book >I have a feeling that the faculties get >some kickback money for using the books, and this is represented in the >price. I don't think so: I know nobody has ever offered me any! We do often get free examination copies.(*) That might add something to the cost of the books, but I can't imagine it would be more than 10%. (*) whether we ask for them or not. I had to call a textbook publisher to replace a defective CD in a paid-for desk copy. They apparently put me on their statistics mailing list. In the next semester, at intervals, I seven different unrequested textbooks from that publisher. They were good sources of exam questions, at least! -- Stan Brown, Oak Road Systems, Cortland County, New York, USA http://OakRoadSystems.com Modern cyberspace is a deadly festering swamp, teeming with dangerous programs such as viruses, worms, Trojan horses, and licensed Microsoft software that can take over your computer and render it useless. --Dave Barry Subject: Re: Prices of Maths Book [...] > We do often get free examination copies.(*) That might add > something to the cost of the books, but I can't imagine it would be > more than 10%. I'd be a bit surprised if it were even that high, though I have no figures. I suspect that the modern extras like CDs, examination banks, and interactive web sites for particular texts add at least as much. [...] Brian Subject: Re: Prices of Maths Book [...] > What is similarly interesting that earlier editions of Math books could > be bought as used significantly cheaper. Recently I bought Lial: Finite > Mathematics and Calculus w/ application for 99 cents (and 3.50 for S&H). > The new price is about $100. I have a feeling that the faculties get > some kickback money for using the books, and this is represented in the > price. They certainly do not. Many of us are quite as unhappy about textbook prices as our students are. Brian Subject: Re: Prices of Maths Book << They certainly do not. Many of us are quite as unhappy about textbook prices as our students are. Brian > I belive you. However, what is than the reason that homeworks are usually assigned by the latest edition page/exercise number, so no student can take the risk to use a previous edition for the fraction of the price? And also why is dropping the price of the previous editions so fast, significantly faster tha the computer books, which really get obsoleted? Subject: Re: Prices of Maths Book >> They certainly do not. Many of us are quite as >> unhappy about textbook prices as our students are. > I belive you. However, what is than the reason that homeworks > are usually assigned by the latest edition page/exercise > number, so no student can take the risk to use a previous > edition for the fraction of the price? Usually the current edition is the only one that is guaranteed to be available, so it's the one that gets chosen by the person or committee responsible for the decision. And once a particular textbook has been chosen, it's the most readily available source of exercises, so instructors are likely to use it. In many of my courses I recommend specific problems as homework but don't collect and mark them, so that it's often possible for a student to use an earlier edition of the text even if it has slightly different exercises; there's a real problem only when the author has significantly changed the content or presentation. > And also why is dropping the price of the previous editions so > fast, significantly faster tha the computer books, which > really get obsoleted? I don't know. Brian Subject: Homotopy I'd be most appreciative if someone could help with the following: If I=[0,1] and X is a path connected space, then the set of homotopy classes from I into X, [I,X], consists of one element. So can you conclude from this that the number of path homotopy classes from I into X is atmost one (since path homotopies are also homotopies)? If not, why? I ask because if this was correct (I imagine it isn't), wouldn't this make the fundamental group of X relative to some fixed base point trivial (i.e., X would be simply connected) ? Subject: measurement Could you please tell me how many feet equal one mile? Thank you! -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: measurement 5280 > Could you please tell me how many feet equal one mile? Thank you! -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: measurement 5280 feet = 1 mile Paul > Could you please tell me how many feet equal one mile? Thank you! -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: measurement 5280ft = 1 mile > Could you please tell me how many feet equal one mile? Thank you! -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: measurement > Could you please tell me how many feet equal one mile? Thank you! 5280ft=1mile -- David Moran Chief Meteorologist Oklahoma Storm Team -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: measurement X-No-Archive: yes >Could you please tell me how many feet equal one mile? Yes, I could. >Thank you! You are welcome. Oh, btw... http://www.factmonster.com/ipka/A0876863.html -- charlie dick The right to be left alone -- the most comprehensive of rights, and the right most valued by a free people. - Justice Louis Brandeis, Olmstead v. U.S. (1928). -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: measurement > Could you please tell me how many feet equal one mile? Thank you! I find the American units hard to remember also, even though I've used them all my life. Perhaps the easiest for me is to remember that the 440-yard dash is a 1/4 mile. So 1 mile = 4 * 1/4 mile = 4 * 440 yards = 4 * 440 yards * 3 feet/yard = 12 * 440 feet = 4400 + 880 feet = 5280 feet I can do that arithmetic in my head without a calculator, and for some reason remembering that 1/4 mile = 440 yards is easier and less error-prone for me than remembering that 1 mile = 5280 feet. I still prefer 1 km = 1000 m, though I have trouble sometimes thinking of local distances in km, since everything local (maps, bike computers, road signs, ...) is calibrated in miles. I wish the US would join the 21st century and adopt the metric system. It'll be hard on us old folks for a few years, but it would save our kids a load of grief. -- Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Professor of Computer Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Affiliations for identification only. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: measurement >I wish the US would join the 21st century and adopt >the metric system. It'll be hard on us old folks >for a few years, but it would save our kids a load >of grief. Look on the bright side. The US military and the US medical industries are very pro-metric. The car industry has gone metric. Most packed products in the US supermarket come with dual units (metric and non-metric) on the label. There is now a US federal proposal to permit metric only on the label. Here are presentations from a 2002 workshop discussing it: http://ts.nist.gov/ts/htdocs/200/202/forum/forumdir.htm -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: measurement kahlil0692@msn.com asks this: >Could you please tell me how many feet equal one mile? Thank you! Handbook, physics book, some basic math books; no need to ask on a newsgroup. This information is too easy to find. Maybe your encyclopedia or dictionary will have it. OR, look in a peechee folder. G C -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: Grad school At Syracuse University, the masters exam covers analysis and linear algebra. Students accepted to the MA/Ph. D. program were typically the best math students at their undergraduate school, and the failure rate is still very high at the Ph.D. level. Lynn > part: >> On the topic of math grad programs, the Princeton Review ranks >> graduate programs. > See also U.S. News and World Report's Web site (usnews.com, I think) for > its rankings. > Be very wary of both the Princeton Review and the US News and World > Report rankings. They often bear little relationship to what people > in a given field believe about the schools. Their facts are often > wrong also (for example, for many years UC Santa Cruz was listed in US > News and World Report as an urban campus, while UCLA was suburban). > -- > Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus > life member (LAB, Adventure Cycling, American Youth Hostels) > Effective Cycling Instructor #218-ck (lapsed) > Professor of Computer Engineering, University of California, Santa Cruz > Undergraduate and Graduate Director, Bioinformatics > Affiliations for identification only. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: integration question Not everyone agrees with this definition of area. I teach from Stewart's calculus books which uses the net area concept effectively. Lynn > posted and emailed (demunge address to reply) > The definite integral represents net area. The positive area above the > X-axis less the negative area below the S-axis. > No. Area is *never* negative by definition(*), therefore definite > integrals, since they *may* be negative, do not necessarily directly > correspond to an area. Certain conditions must exist in order to directly > interpret the value of a definite integral as an area in the plane, not the > least of which are continuity and nonnegativity on the interval in question. > This is even stated explicitly, usually, in any decent calculus text BTW. > Perhaps the areas you have been finding are very neat in the sense they > are rigged that this is always the case, which could explain your honest but > incorrect assumption the definite integrals always represent an area (or as > you say, a net area). > Suppose we were posed the following question: > For f(x)=sin(x), find the area bounded by f, y=0, x=0, and x=2pi. By your > reasoning, the positive area and negative area negate each other, > resulting in a net area of 0. And indeed: > int[0,2pi] sin(x) dx = 0 > However, 0 is not the answer to the question. > (*) Definition of the area of a plane region, courtesy any decent elementary > calculus text, so I suggest you find one and look it up, and I chalenge you > to find entries for negative area, and anything that defines net area as > the difference between positive and negative area: > Let f be continuous and nonnegative on [a,b]. The area of the region > bounded by the graph of f, the x-axis, and the vertical lines x=a and x=b > is: > Area = lim n-->oo sum(i=1,n) f(c_i) Delta(x), x_(i-1)= where delta(x) = (b-a)/n > The rhs of that equation happens to be the equivelent of the Reimann > *definition* of the definite integral: > int[a,b] f(x) dx > So, area = int[a,b]f(x)dx, provided f is continuous and *nonnegative* on > [a,b]. In the case of the sample question above, it could be tackled a > number of ways, but directly intpreting int[0,2pi]sin(x)dx as the answer is > NOT one of them. > -- > Darrell -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: integration question > Not everyone agrees with this definition of area. I teach from Stewart's > calculus books which uses the net area concept effectively. Hi Lynn. That's fine, but please specify the definition. I do not have access to Stewart at the moment. area,) I still see this as implying the net area of the region bounded by f(x)=sin(x), x=0, x=2pi, is 0. Positive area is 2, negative area is 2, and 2-2=0. Of course now I fully expect you to tell me that I misinterpreted, that negative area boils down to a negative real number, and not the (nonnegative) area that happens to be below the x-axis. I repeat the request: Please quote these definitions of net area and what positive area and, most importantly to my present concern, what negative area means. I'm not saying Stewart can't define them (apparently he does since you said so) but you have yet to tell me what these definitions are. Then, please quote me Stewart's definition of the area of a plane region. (not net area, negative area, or positive area, but area of a plane region) and see if anything I (rather Larson, et. al) is contradicted by that. In any event, for the *OP*'s problem, it is not a straightforward application of int[a,b]f(x)dx that directly yields the answer to the question which was really my only point. I maintain that area of a region in the plane is nonnegative. (eg just because a 2ftx2ft rug may lie below a room's dividing line, or some other coordinate axis in some coordinate system), does not mean it is comprised of -4ft^2 of material. I also maintain that Stewart, unless you can quote otherwise, says the area of such a region in the plane is not -4. I am guessing you can quote me some recipe such that net area is calculated as positive area-negative area, 0-(-4)=+4, but that would just reaffirm my claim that the actual *area* of the region in question is nonnegative. An analog would be the concept of distance. We often speak of directed distance, which may be negative, but actual *distance* is never negative. Perhaps Stewart is using a similar notion of negative area that is analogous to directed distance in this regard, but I suspect that actual area remains nonnegative according to Stewart. Perhaps he refers to area always as net area. -- Darrell -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: integration question > Not everyone agrees with this definition of area. I teach from Stewart's > calculus books which uses the net area concept effectively. Hi Lynn. That's fine, but please specify the definition. I do not have access to Stewart at the moment. area,) I still see this as implying the net area of the region bounded by f(x)=sin(x), x=0, x=2pi, is 0. Positive area is 2, negative area is 2, and 2-2=0. Of course now I fully expect you to tell me that I misinterpreted, that negative area boils down to a negative real number, and not the (nonnegative) area that happens to be below the x-axis. I repeat the request: Please quote these definitions of net area and what positive area and, most importantly to my present concern, what negative area means. I'm not saying Stewart can't define them (apparently he does since you said so) but you have yet to tell me what these definitions are. Then, pleae quote me Stewart's definition of the area of a plane region. (not net area, negative area, or positive area, but area of a plane region) and see if anything I (rather Larson, et. al) is contradicted by that. In any event, for the *OP*'s problem, it is not a straightforward application of int[a,b]f(x)dx that directly yields the answer to the question which was really my only point. I maintain that area of a region in the plane is nonnegative. (eg just because a 2ftx2ft rug may lie below a room's dividing line, or some other coordinate axis in some corrdinat system), does not mean it is comprised of -4ft^2 of material. I also maintain that Stewart, unless you can quote otherwise, says the area of such a region in the plane is not -4. I am guessing you can quote me some recipe such that net area is calculated as positive area-negative area, 0-(-4)=+4, but that would just reaffirm my claim that the actual *area* of the region in question is nonnegative. An analog would be the concept of distance. We often speak of directed distance, which may be negative, but actual *distance* is never negative. Perhaps Stewart is using a similar notion of negative area that is analogous to directed distance in this regard, but I suspect that actual area remains nonnegative according to Stewart. Perhaps he refers to area always as net area. -- Darrell > Lynn > posted and emailed (demunge address to reply) > The definite integral represents net area. The positive area above > the > X-axis less the negative area below the S-axis. > No. Area is *never* negative by definition(*), therefore definite > integrals, since they *may* be negative, do not necessarily directly > correspond to an area. Certain conditions must exist in order to directly > interpret the value of a definite integral as an area in the plane, not > the > least of which are continuity and nonnegativity on the interval in > question. > This is even stated explicitly, usually, in any decent calculus text BTW. > Perhaps the areas you have been finding are very neat in the sense they > are rigged that this is always the case, which could explain your honest > but > incorrect assumption the definite integrals always represent an area (or > as > you say, a net area). > Suppose we were posed the following question: > For f(x)=sin(x), find the area bounded by f, y=0, x=0, and x=2pi. By your > reasoning, the positive area and negative area negate each other, > resulting in a net area of 0. And indeed: > int[0,2pi] sin(x) dx = 0 > However, 0 is not the answer to the question. > (*) Definition of the area of a plane region, courtesy any decent > elementary > calculus text, so I suggest you find one and look it up, and I chalenge > you > to find entries for negative area, and anything that defines net area > as > the difference between positive and negative area: > Let f be continuous and nonnegative on [a,b]. The area of the region > bounded by the graph of f, the x-axis, and the vertical lines x=a and x=b > is: > Area = lim n-->oo sum(i=1,n) f(c_i) Delta(x), x_(i-1)= where delta(x) = (b-a)/n > The rhs of that equation happens to be the equivelent of the Reimann > *definition* of the definite integral: > int[a,b] f(x) dx > So, area = int[a,b]f(x)dx, provided f is continuous and *nonnegative* on > [a,b]. In the case of the sample question above, it could be tackled a > number of ways, but directly intpreting int[0,2pi]sin(x)dx as the answer > is > NOT one of them. > -- > Darrell -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: GRE Hi there... I have a few questions about the GRE. The school I've all but choose requires both the general and subject test. When during my undergrad should I take the general test? I have one full year of classes left plus one semester of student teaching after that. So I'm looking at entering grad school Fall 2005. I don't think there is anything else left in my undergrad that will help with the general test, I don't have any English classes left and I've taken all the math any non-math major would have. Can anyone recommend books to review for the math subject test? I think I'll be ok on the general test, but the math subject worries me a bit. However, I have the three highest level classes yet to go in my undergrad. Thanks -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: GRE > Hi there... > I have a few questions about the GRE. > The school I've all but choose requires both the general and subject test. > When during my undergrad should I take the general test? I have one full > year of classes left plus one semester of student teaching after that. So > I'm looking at entering grad school Fall 2005. I don't think there is > anything else left in my undergrad that will help with the general test, I > don't have any English classes left and I've taken all the math any non-math > major would have. > Can anyone recommend books to review for the math subject test? I think I'll > be ok on the general test, but the math subject worries me a bit. However, I > have the three highest level classes yet to go in my undergrad. As it happens, I just took the general test recently. I first took it during my senior year of college, and I wish I'd taken it earlier; there was really nothing I learned my last year that helped at all. For the subject test, sure, you want to wait as long as possible, but you might as well take the general test now. Plus, if you screw up (I did - wasn't feeling well that day and got under 700 on two sections) you have time to retake it :-) The math section is IMO quite easy; both times that I took the test I ended up with 800. (Computer science major here BTW) You basically need to be able to do basic algebra, geometry, and statistics, and be able to read a graph. (Of course, being able to multiply quickly and accurately by hand helps :-)) When you register for the test they'll send you a free CD with two sample tests on it, so you can get an idea of what you'll be seeing. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Re: GRE > Hi there... > I have a few questions about the GRE. > The school I've all but choose requires both the general and subject test. > When during my undergrad should I take the general test? I have one full > year of classes left plus one semester of student teaching after that. So > I'm looking at entering grad school Fall 2005. I don't think there is > anything else left in my undergrad that will help with the general test, I > don't have any English classes left and I've taken all the math any non-math > major would have. Take the general test whenever you feel like it---it's not much different from an SAT---that is it basically tests high-school-level skills. That's probably the reason that the mode on the GRE math test is 800 (the highest possible score). Some stats that were recently given to me: Verbal: fairly normal bell curve, with high-end fat tail and mean: 477 median: 480 mode: 460 (on best fit curve) Quant: rising end to curve, with mean: 579 median: 590 mode: 800 (yes, by far the most common score!) For all Engineering majors, Quant: curve looks like rising exponential mean: 716 median: 740 mode: 800 If you want to get into grad school as a math major, you should have GRE scores at least as good as most engineering students (740 or above). > Can anyone recommend books to review for the math subject test? I think I'll > be ok on the general test, but the math subject worries me a bit. However, I > have the three highest level classes yet to go in my undergrad. I have no idea what they put on the Math Subject test these days. Long, long ago, when I took it, I remember thinking that it didn't test any math that I had learned since my freshman year, just a little calculus and linear algebra. It may well be different now, though a little web browsing reveals that recent exams have been about 50% calculus, 25% algebra, linear algebra, and abstract algebra, and 25% additional topics studied areas. (http://www.gre.org/subdesc.html#math) The other seems to come in large part from simple probability and combinatorics---so if you've never had that, take it! Pure mathematicians often turn up their noses at probability and statistics, but they are far more useful for teachers than most of what is taught in graduate math programs. In fact, if I were hiring a math teacher, I'd much rather see a masters in statistics than in pure math. I'd also like to see more college and college-bound students taking an elementary probability and statistics course in place of the badly-misnamed precalculus course that so many take as their final exposure to math. -- Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karplus life member (LAB, Adventure Cycling, American Youth Hostels) Effective Cycling Instructor #218-ck (lapsed) Professor of Computer Engineering, University of California, Santa Cruz Undergraduate and Graduate Director, Bioinformatics Affiliations for identification only. -- submissions: post to k12.ed.math or e-mail to k12math@k12groups.org private e-mail to the k12.ed.math moderator: kem-moderator@k12groups.org newsgroup website: http://www.thinkspot.net/k12math/ newsgroup charter: http://www.thinkspot.net/k12math/charter.html Subject: Primes As a person of *extremely* limited mathematical education could someone please explain to me the significance and importance of prime numbers? How are they employed in real-world applications? Cheers, big H Subject: Re: Primes > As a person of *extremely* limited mathematical education could someone > please explain to me the significance and importance of prime numbers? > How are they employed in real-world applications? > Cheers, > big H I will treat these as two seperate questions. The significance of prime numbers is that many of the most beautiful and deepest thereoms in mathematics are based upon prime numbers. Prime numbers are part of number theory. Many believed that this was the most beautiful parts of mathematics, all the more so since most other branches of maths had practical application (for working out cannon trajectories etc). Then they discovered a means of creating secret computer codes through using primes, and prime numbers make the purchase of groceries over the internet possible. Prime numbers are also involved (though not directly) in the mathematics that makes error correcting codes possible, and hence the existence of the CD as well as cable modems. Really, if you are interested you should look on the net. The net incidentally just found the new largest prime, and you can use your CPU idle time (screensaver) to help discover the next biggest prime. Subject: math help Need help on math, visit www.helptosolve.com Just try. Want to help others with math, visit www.helptosolve.com and join the team. Subject: y^2=x^3 + 7 I can't prove that this equation : y^2=x^3 + 7 has no integer solutions. Can you help me? Subject: Re: question about matrices Perhaps it is indeed time to read some background, such as the excellent text by Howard Anton on matrices and linear algebra, or Richard Hill. However it might also be time for some of us to learn some manners. If you can't be bothered going into details for someone you think is not quite up to speed, then just don't answer. What does a matrix represent? What would you like it to represent? There are so many applications that it is difficult to know where to start. Linear transformations is indeed a great application. Fitting curves to measured data is another good one. However one of my favourites is dominance matrices for tipping sporting competitions. Label a (square) matrix P with the names of all the teams along the rows and columns. The labels are not a part of the matrx, they are just there for our convenience. Make every element of the matrix 0. Then, every time team i beats team j, increase the value of entry (i,j) by 1. You can then predict the winner of a match between teams k and l as follows. Find the dominance matrix D=P+0.5*P^2. (P itself gives one step dominance, where team i beat team j. P^2 gives second step dominances, such as team i beat team j who beat team k. These second step dominances are less important than direct victories, that is why P^2 has a coefficient of 0.5.) To tip the matches for the next round, sum every row of the matrix D. Teams with a higher row sum are tipped to triumph over teams with a lower row sum. There are some wrinkles you might want to think about. What happens if two teams have the same row sum, which one will you tip? Personally I would tip the home team. Should you include the home ground factor at all? Well, I have experimented with increasing the row sum of the home team by 5%. Most critically, how can you deal with a situation where the number of games is not always identical? (This happenes in the Australian National Basketball League, which I tipped with reasonable success using this method.) Before find the matrix D, divide every row of P by the row sum of that row, ie ennsure that every row sums to 1. Proceed as usual. Good luck in your study of matrices. They are a very rich topic to study. Garry Lockwood. Subject: bouncing ball Could you help me with the following question: A ball is dropped from a height of h feet and repeatedly bounces off the floor. After each bounce , the ball reaches a height that is 2/3 of the height from which it previously fell. Express the the above assignment in the form of a summation notation. Thanks, Dennis Subject: Re: bouncing ball > Could you help me with the following question: > A ball is dropped from a height of h feet and repeatedly bounces off the > floor. After each bounce , the ball reaches a height that is 2/3 of the > height from which it previously fell. Express the the above assignment in > the form of a summation notation. > Thanks, > Dennis I guess the question is: How far does the ball travel before stopping? Anyway, maybe my answer to this question will answer yours. Before hitting the ground the first time, the ball travels h feet. and so on. This gives a total of Total distance = h + 2*(2/3)h + 2*((2/3)^2)h +2*((2/3)^3)h +... = -h +2*((2/3)^0)h + 2*((2/3)^1)h + 2*((2/3)^2)h +2*((2/3)^3)h +... = -h + sum_{n=0}^inf 2*((2/3)^n)h = -h + 2*(sum_{n=0}^inf (2/3)^n )h = -h + 2*(1/(1-(2/3))h, using formula for geometric series! = -h + 2*3h = 5h Now I have written the total distance using summation notation. And I have calculated the sum. Mogens Subject: Re: bouncing ball > Could you help me with the following question: > A ball is dropped from a height of h feet and repeatedly bounces off the > floor. After each bounce , the ball reaches a height that is 2/3 of the > height from which it previously fell. Express the the above assignment in > the form of a summation notation. > Thanks, > Dennis I'm not sure what the above assignment is. But you have h and then 2/3*h. Right? What comes after that? Are you supposed to make a summantion notation for all these bounces? You should be able to do that after you write out a few. Bill Subject: Re: bouncing ball > Could you help me with the following question: > A ball is dropped from a height of h feet and repeatedly bounces off the > floor. After each bounce , the ball reaches a height that is 2/3 of the > height from which it previously fell. Express the the above assignment in > the form of a summation notation. What's the problem? Expressing yourself? Subject: To find a trig.polymomial Let phi = (1+sqrt(5))/2 and f(x)= 1+phi*cos(x)+A*cos(2x)+B*cos(3x) . with real parameters A and B. It is known that f(x) >= 0 for all x in [0,pi] . Try to find A and B. It seems that A= phi-1 (?) ====== Subject: Re: Homotopy > I'd be most appreciative if someone could help with the following: > If I=[0,1] and X is a path connected space, then the set of homotopy classes > from I into X, [I,X], consists of one element. So can you conclude from > this that the number of path homotopy classes from I into X is atmost one > (since path homotopies are also homotopies)? If not, why? I'm not sure that I'm using exactly the same definitions as you are (what's a path homotopy, f'rinstance ?), but here's the idea: The easiest way to prove Theorem: If C is contractible and X is path-connected, then any two maps f, g: C --> X are homotopic. is to let H: CxI --> C be a contraction (so H is the identity on Cx{0} and maps Cx{1} to some point c0 in C). Then f o H gives a homotopy from f to the constant map that sends all of C to f(c0) and g o H gives a homotopy from g to the constant map to g(c0). Pick a path p: I --> X from f(c0) to g(c0) and use it to construct a homotopy between the two constant maps in the previous sentence -- P: CxI --> X: (c,t) |--> p(t). Now, build a map CxI --> X by reproducing f o H on Cx[0,1/3], P on Cx[1/3.2/3] and running g o H in the opposite direction on Cx[2/3,1] -- this gives a homotopy from f to g. Notice, however, that this construction doesn't allow you to keep the image of some subspace of C fixed while you're moving things around ... and that's the problem with your argument -- to compute the fundamental group of X, you consider maps f: (I,bdry(I)) --> (X,x0) and require that all of your homotopies are through maps of that same sort. And that breaks if you try the trick outlined above -- in any contraction of the interval, at least one of the endpoints will have to move into the interior of the interval ... the argument then falls apart ... > I ask because if this was correct (I imagine it isn't), wouldn't this make > the fundamental group of X relative to some fixed base point trivial (i.e., > X would be simply connected) ? Yep -- that _would_ follow. But ... it's OK ... you're wrong :-) Seriously, have you encountered _no_ spaces that aren't simply connected ?? For instance, the fact that the circle, S^1, is _not_ simply connected is (usually) proved fairly early in discussions about homotopy and fundamental groups and such ... Subject: Re: Homotopy > I'd be most appreciative if someone could help with the following: > If I=[0,1] and X is a path connected space, then the set of homotopy classes What do you mean homotopy class? > from I into X, [I,X], consists of one element. So can you conclude from > this that the number of path homotopy classes from I into X is atmost one > (since path homotopies are also homotopies)? If not, why? What's a path homotopy? > I ask because if this was correct (I imagine it isn't), wouldn't this make > the fundamental group of X relative to some fixed base point trivial (i.e., > X would be simply connected) ? If X homotopic I, then X is contractible, as I is contractible and contractible spaces are simply connected. Subject: Re: calculate radius Just to add to this excellent idea. Again, just an idea. It would appear to me that if I was doing it, I know I would be introducing errors in my measurements. Using 10 ft increments, and distances of about 18 ft introduces a little error. Then not being perfectly perpendicular would also introduce small errors. Here is what I was thinking. Do the best you can at finding the Center of the arc. You are using a string to show a straight line from post to post, and this distance is 169.15' Fold a similar length string in half to find the center of this cord. Fold a little longer string in half, cut, and place at each end post. Join them, and you should have a way to see a line from the center of cord to a point perpendicular. You should measure 18.76 away from the chord as David has shown you. Again, do the best you can at nailing this center post. NOw, instead of measuring 10' either side, just repeat the process you just did. Run a string from your new center post to each end post. Make another string from the same two end points, fold in half, and cut. The length of the cut string should tell you the center of the new cord. Join two equally cut strings from each end (they should join outside the circle), and this should point you along the perpendicular. Measure a distance of about 4.746'. Just repeat by cutting the distances in half. The original half angle (B) is about 25.01 degrees, or .4366 Radians. B = ArcSin[169.15/(2*200)] 0.4366156110410458 The first 5 distances from the cord to the arc would be: Table[400*Sin[B/2^j]^2, {j, 1, 5}] 18.76239525142692, 4.746932226770613, 1.1902749427912451, 0.2977904335536014, 0.07446146966456187 Again, this is just an idea. It would appear to help me cut down on my measurement errors. -- Dana DeLouis = = = = = = = = = = = = = = = = = > David, > Wow, after looking at your solution, it seems so simple. > One stupid question, where did the 181.24 come from? > Thank you! >>Sorry about the wrong terminology. > That's OK. >>The survey shows an arc length of 174.65' and a cord length of 169.15' > Excellent. Then here's an answer for you. > You were wanting distances from the chord to the arc, to be measured > perpendicular to the chord at various places along it. Although I think > that you had intended those places to be at multiples of 10' from an end of > the chord, it will actually be slightly easier (and more symmetrical) if > you first locate the center of the chord. Letting x be the distance along > the chord from its center, the perpendicular distance to the arc there is, > in feet, > Sqrt( 200^2 - x^2 ) - 181.24 > where Sqrt means square root and x^2 means x squared. > As examples: to > the arc is, in feet, 200 - 181.24 = 18.76 . > perpendicular distance to the arc is, in feet, > Sqrt( 200^2 - 10^2 ) - 181.24 = 18.51 . > perpendicular distance to the arc is, in feet, > Sqrt( 200^2 - 80^2 ) - 181.24 = 2.06 . > I hope you get the idea. > David Subject: Automatic Theorem Proving A long long long long time ago I did a course on basic logic. As the course developed proofs were distilled into valid strings of logical symbols, in a sense further and further removed from the problem at hand. It struck me that these symbols really belonged in a computer program: I figured you could end up proving all sorts by a systematic search for valid symbol strings. Of course at the time I thought this was a great insight. I asked the lecturer about this and he said something like, 'Yeah automatic theorem proving: it's all the rage.' So what is the status of automatic theorem proving? Have any great breakthroughs been made using this approach? cheers dd Subject: Re: Automatic Theorem Proving > A long long long long time ago I did a course on basic logic. As the course > developed proofs were distilled into valid strings of logical symbols, in a > sense further and further removed from the problem at hand. It struck me > that these symbols really belonged in a computer program: I figured you > could end up proving all sorts by a systematic search for valid symbol > strings. Of course at the time I thought this was a great insight. I asked > the lecturer about this and he said something like, 'Yeah automatic theorem > proving: it's all the rage.' So what is the status of automatic theorem > proving? Have any great breakthroughs been made using this approach? Douglas Hofstadter's _Godel, Escher, and Bach_ gives the theory behind automatic theorem proving, as well as its limitations. _A = B_ is a wonderful book about looking for the closed form of a sum of hypergeometric terms; sometimes it can even be proved that there is no nice formula for a sum. This book is by Marko Petkovsek, Herbert Wilf, and Doron Zeilberger. -- Christopher Heckman Subject: Re: Automatic Theorem Proving ... So what is the status of automatic theorem > proving? Have any great breakthroughs been made using this approach? Here's a place at least to begin looking for the answers to your questions: http://gtps.math.cmu.edu/tps.html -- Wayne Brown (HPCC #1104) | When your tail's in a crack, you improvise fwbrown@bellsouth.net | if you're good enough. Otherwise you give | your pelt to the trapper. e^(i*pi) = -1 -- Euler | -- John Myers Myers, Silverlock Subject: Real Projective Plane? Can anyone help alleviate some difficulty of mine in understanding the details of the real projective plane and a few of its homeomorphic spaces? What is the significance of the addition of the infinite line to the projection? I would assume that a better understanding of the idea of the thing would assist me in understanding certain homeomorphisms. For instance, its being homeomorphic to a sphere with antipodal points identified. Or a disc with boundary points identified. Or, in what seems the most confusing analogy, the set of all lines in R^3. How can that be the case? I'm just at a total loss here. Any good references on this? The books I have either don't mention it or almost completely gloss over it. As usual, any and all help is very much appreciated. Thanks! Subject: Re: Code To Evaluate Mathematical Expressions > Does anyone know where I can obtain pseudo-code that can calculate arbitrary > mathematical calculations such as: > 5 * pi > ((5 - myvar) + c) / pi > The above is taken from the below : > Set myvar = 5 * pi > Set myvar = ((5 - myvar) + c ) / pi > Where c is speed of light. > Thank you, > Christopher Lusardi Yes. If you look on the page http://www.phys.virginia.edu/classes/551.jvn.fall01/ under the link Forth system and example programs you will find a Forth program for translating such expressions into Forth. You will also find a free Windoze Forth, Win32Forth, to run it on, or if you are using a Linux box, get (or compile--the source is in C) the appropriate version of GForth (GNU free Forth). Both are ANS Forths, so both areguaranteed to run my program, ftran201.f . Make sure to download the accompanying ftrandoc.txt file for instruc- tions on how to use ftran201.f to generate Forth from Fortran-like expressions. The DOC also includes a discussion of how the parser works (recursive descent applied to the Backus-Naur Format for expressions and fragments thereof). If you don;t know Forth, look at the link A Beginner's Guide to Forth (HTML) for a primer on how to use it. Since some people think of Forth (like C) as a universal assembler, you can then easily translate the Forth output into assembler-like pseudocode. That's the best I can do for you today. Good luck and best wishes. -- Julian V. Noble Professor Emeritus of Physics jvn@lessspamformother.virginia.edu ^^^^^^^^^^^^^^^^^^ http://galileo.phys.virginia.edu/~jvn/ Science knows only one commandment: contribute to science. -- Bertolt Brecht, Galileo. Subject: Re: Code To Evaluate Mathematical Expressions Hi Christopher, try CioinaEval from http://www.geocities.com/alexei_cioina/cioinaeval.html > Does anyone know where I can obtain pseudo-code that can calculate arbitrary > mathematical calculations such as: > 5 * pi > ((5 - myvar) + c) / pi > The above is taken from the below : > Set myvar = 5 * pi > Set myvar = ((5 - myvar) + c ) / pi > Where c is speed of light. > Thank you, > Christopher Lusardi Subject: Free proof writing software at my website Download a free beta version of my new proof writing software, PC Proof, at http://www.dcproof.com Having worked out a few bugs and added some what I hope are useful enhancements since my first release last month, I believe you will find it interesting from both a theoretical and a pedagogical perspective. It makes use of a simplified version of the standard set theory that nevertheless avoids the known contradictions of naive set theory. The user manual includes a tutorial with exercises (excerpts at my homepage) that demonstrate the main features of my program. Dan Christensen Toronto, Canada Subject: Re: Free proof writing software at my website >Download a free beta version of my new proof writing software, PC Proof, at >http://www.dcproof.com >Having worked out a few bugs and added some what I hope are useful >enhancements since my first release last month, I believe you will find it >interesting from both a theoretical and a pedagogical perspective. It makes >use of a simplified version of the standard set theory that nevertheless >avoids the known contradictions of naive set theory. The user manual >includes a tutorial with exercises (excerpts at my homepage) that >demonstrate the main features of my program. You might want to look at Qu-Prolog: http://www.svrc.it.uq.edu.au/pages/QuProlog_release.html Earlier versions http://svrc.it.uq.edu.au/Bibliography/svrc-tr.html?00-20 http://svrc.it.uq.edu.au/Bibliography/svrc-tr.html?00-21 This is a theorem prover (or proof verification system) that admits one to work on the meta-level, to introduce binders such as the quantifiers, etc. You might want to make your program a front end interface for such a program. The thing is that it is very difficult to make a program that in a strictly mathematical sense admits one to write correct proofs. I am myself writing on a proof verification system which builds on metamathematics (not available publicly yet). The difference relative Qu-Prolog is that I work directly with metamathematics, whereas Qu-Prolog works more like a meta-Prolog inference system. Within such a system, one then chooses ones favorite axiomatic set theory. This is the only approach that can be expected to work in serious math. Hans Aberg Subject: Re: Free proof writing software at my website >Download a free beta version of my new proof writing software, PC Proof, at >http://www.dcproof.com >Having worked out a few bugs and added some what I hope are useful >enhancements since my first release last month, I believe you will find it >interesting from both a theoretical and a pedagogical perspective. It makes >use of a simplified version of the standard set theory that nevertheless >avoids the known contradictions of naive set theory. The user manual >includes a tutorial with exercises (excerpts at my homepage) that >demonstrate the main features of my program. > You might want to look at Qu-Prolog: > http://www.svrc.it.uq.edu.au/pages/QuProlog_release.html This link doesn't work at this time. You might instead try http://www.itee.uq.edu.au/~pjr/HomePages/QuPrologHome.html > Earlier versions > http://svrc.it.uq.edu.au/Bibliography/svrc-tr.html?00-20 > http://svrc.it.uq.edu.au/Bibliography/svrc-tr.html?00-21 > This is a theorem prover (or proof verification system) that admits one to > work on the meta-level, to introduce binders such as the quantifiers, etc. > You might want to make your program a front end interface for such a > program. The thing is that it is very difficult to make a program that in > a strictly mathematical sense admits one to write correct proofs. > I am myself writing on a proof verification system which builds on > metamathematics (not available publicly yet). The difference relative > Qu-Prolog is that I work directly with metamathematics, whereas Qu-Prolog > works more like a meta-Prolog inference system. > Within such a system, one then chooses ones favorite axiomatic set theory. > This is the only approach that can be expected to work in serious math. While I believe my program to be capable of quite serious math, its primary purpose is educational -- to introduce the non-specialist to rigors of logic and proof. I have adopted a notation that is fairly close to that in introductory algebra and calculus textbooks, and that I hope can be quickly mastered by most 1st or 2nd year, non-specialist undergraduates. Dan Visit DC Proof Online at http://www.dcproof.com Subject: Re: Free proof writing software at my website >> You might want to look at Qu-Prolog: >> http://www.svrc.it.uq.edu.au/pages/QuProlog_release.html >This link doesn't work at this time. You might instead try >http://www.itee.uq.edu.au/~pjr/HomePages/QuPrologHome.html Thank you. My reference is old. I will change that. >> I am myself writing on a proof verification system which builds on >> metamathematics (not available publicly yet). The difference relative >> Qu-Prolog is that I work directly with metamathematics, whereas Qu-Prolog >> works more like a meta-Prolog inference system. >> Within such a system, one then chooses ones favorite axiomatic set theory. >> This is the only approach that can be expected to work in serious math. >While I believe my program to be capable of quite serious math, its >primary purpose is educational -- to introduce the non-specialist to rigors >of logic and proof. I have adopted a notation that is fairly close to that >in introductory algebra and calculus textbooks, and that I hope can be >quickly mastered by most 1st or 2nd year, non-specialist undergraduates. The problem is to ensure that the math is formally correct. How do you do that? -- The only secure approach I know of is by relying on metamathematics. This proves to be very tricky. One can still, on top of that choose a user friendly syntax. I build my implementation around the notion of semantic trees, i.e., ordered trees with labelled nodes, rather than syntactic constructs. For example, the semantic trees of (lambda x.f) and x |-> f are lambda |- / / x f x f So, these are the same except for the relabelling of lambda to |->, which makes it easy to create a common, internal object representing them both. This way, one can easily admit different common syntaxes to be mixed. Hans Aberg Subject: Re: Free proof writing software at my website >> You might want to look at Qu-Prolog: >> http://www.svrc.it.uq.edu.au/pages/QuProlog_release.html >This link doesn't work at this time. You might instead try >http://www.itee.uq.edu.au/~pjr/HomePages/QuPrologHome.html > Thank you. My reference is old. I will change that. >> I am myself writing on a proof verification system which builds on >> metamathematics (not available publicly yet). The difference relative >> Qu-Prolog is that I work directly with metamathematics, whereas Qu-Prolog >> works more like a meta-Prolog inference system. > >> Within such a system, one then chooses ones favorite axiomatic set theory. >> This is the only approach that can be expected to work in serious math. >While I believe my program to be capable of quite serious math, its >primary purpose is educational -- to introduce the non-specialist to rigors >of logic and proof. I have adopted a notation that is fairly close to that >in introductory algebra and calculus textbooks, and that I hope can be >quickly mastered by most 1st or 2nd year, non-specialist undergraduates. > The problem is to ensure that the math is formally correct. How do you do > that? -- The only secure approach I know of is by relying on > metamathematics. This proves to be very tricky. > One can still, on top of that choose a user friendly syntax. I build my > implementation around the notion of semantic trees, i.e., ordered trees > with labelled nodes, rather than syntactic constructs. For example, the > semantic trees of (lambda x.f) and x |-> f are > lambda |- > / / > x f x f > So, these are the same except for the relabelling of lambda to |->, > which makes it easy to create a common, internal object representing them > both. This way, one can easily admit different common syntaxes to be > mixed. be too flexible, and to have too many options. Isn't it better to simply put forth a single, user-friendly syntax and proceed from there? Dan Visit DC Proof Online at http://www.dcproof.com -- FREE download Subject: Re: Need help with a math problem > I've put a lot of time on this one and I can't come to the solution > yet. Here it is: > A gun shoot bullets at a given, regular interval. After it fire all of > it's bullets it need some time to reload until he can resume shooting. > Ammo : Number of bullets that the gun shoot before it need to reload. > RateOfFire : Time in seconds between each shot. Rate of Fire usually means the number of rounds fired per unit time, not the interval between rounds which is what you have here. Subject: Re: Listing all mupad commands: how? > Is there a similar way to obtain all the commands which are defined in > the kernel itself? all kernel functions are function environments (DOM_FUNC_ENV). All function environments consist of (at least) 3 entries, where the 1. is the evaluation function. If the evaluation function is an executable object (DOM_EXEC), you have a kernel function. select(anames(DOM_FUNC_ENV), x -> testtype(op(eval(x),1), DOM_EXEC) ) gives you a complete list of those functions. -- *---* MuPAD -- The Open Computer Algebra System *---*| |*--|* Ralf Hillebrand (tonner@mupad.de) *---* Subject: Re: Listing all mupad commands: how? >> Is there a similar way to obtain all the commands which are defined in >> the kernel itself? > all kernel functions are function environments (DOM_FUNC_ENV). > All function environments consist of (at least) 3 entries, > where the 1. is the evaluation function. If the evaluation > function is an executable object (DOM_EXEC), you have a kernel > function. > select(anames(DOM_FUNC_ENV), > x -> testtype(op(eval(x),1), DOM_EXEC) > ) > gives you a complete list of those functions. Well, I am a bit confused: in the list obtained this way I can't see any trigonometric function, nor abs and others. Where do they live? Fabio Subject: Re: Listing all mupad commands: how? > Well, I am a bit confused: in the list obtained this way I can't see > any trigonometric function, nor abs and others. Where do they live? the trigonometric functions are written in the MuPAD language and handle the symbolic cases. The float attributes of the trigonometric functions are kernel functions (written in C-Code). I misunderstood your previous question, I thought you were explicitly asking for kernel functions (things implented in C). The TAB-Completion uses a function Pref::allComplete. Maybe it is useful for you, too. Pref::allComplete() returns a set of strings with the names of all identifiers with assigned values, all option names, all environment variables and all keywords. When called in a fresh session, it should return what you search. Pref::noComplete() returns a set of things which are internal and should not show up in the TAB-completion. I think the command print(Unquoted, op(Pref::allComplete() minus Pref::noComplete())) is a good start for you. -- *---* MuPAD -- The Open Computer Algebra System *---*| |*--|* Ralf Hillebrand (tonner@mupad.de) *---* Subject: Re: Listing all mupad commands: how? by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i05LB7C16550; F> Well, I am a bit confused: in the list obtained this way I can't F> see any trigonometric function, nor abs and others. Where do F F> they live? What you are looking for are > anames(All); > anames(Protected); Best wishes, Vladimir Bondarenko http://www.cybertester.com/ http://maple.bug-list.org/ http://www.CAS-testing.org/ Subject: Re: Listing all mupad commands: how? > F> Well, I am a bit confused: in the list obtained this way I can't > F> see any trigonometric function, nor abs and others. Where do F > F> they live? > What you are looking for are >> anames(All); >> anames(Protected); I already considered these, but this way I can't separate the kernel functions from stdlib function. In any case, if there is not any other way out, I think its the only way to get something quite complete. The point of all this is that I am upgrading the vim syntax file for mupad and I would like to separate functions in the syntax file with regard to their environment... Bye Fabio Subject: Re: Listing all mupad commands: how? >> F> Well, I am a bit confused: in the list obtained this way I can't >> F> see any trigonometric function, nor abs and others. Where do F >> F> they live? > > >> What you are looking for are > >>> anames(All); >>> anames(Protected); > > I already considered these, but this way I can't separate the kernel > functions from stdlib function. In any case, if there is not any other > way out, I think its the only way to get something quite complete. > The point of all this is that I am upgrading the vim syntax file for > mupad and I would like to separate functions in the syntax file with > regard to their environment... Ralf's answer was correct: sin, cos, abs, ... are not kernel but library functions. Of course, their float-slots are kernel functions, but that is not what you asked for :-) Ok, if you want to distinguish function environments that have a kernel function among their slots from others, use hastype, e.g. hastype(sin, DOM_EXEC, {DOM_FUNC_ENV}) with hastype(besselJ, DOM_EXEC, {DOM_FUNC_ENV}) But why should this play a major role for a vim syntax file? -- Stefan Wehmeier stefanw@mupad.de Subject: Re: Listing all mupad commands: how? I will try all the hints in the next days. For the moment, thanks a lot > But why should this play a major role for a vim syntax file? You are right: it is not a major role, it is really a minor role. The reason is that what I am planning is the following: for the moment I don't have the time/intention to insert all possible mupad functions in the syntax file, so, for now, it could be enough just to pick up all identifiers which are protected; but I wish that little by little I can add all the functions. May be a library per week/month... In this direction, it could be useful to be able to distinguish functions depending on their originating library so that, maybe, one can choose different colors for different libraries or one can choose which library to highlight. It is like this, for example, in maple syntax file. Bye Fabio Subject: About my research by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i041SKV28838; Dear Readers The new list is as follows: Sincerely Dr.M.Basti 1-Basti.M. Solving polynomials with differential equations. Submitted 2-Basti.M. A class Polynomial. Submitted for publication to the Journal on computation 4-Basti.M. A class Polynomial III. Submitted for publication to the 5-Basti.M.Polyomials and Riccati differential equations. Submitted for 6-Basti.M. New Methods Of Solving Riccati Differential Equations. 7-Basti.M. New Methods Of Solving Riccati Differential Equations II. 8-Basti.M. On Bessel Differential Equations. Submitted for publication 9-Basti.M. New solutions of Bessel Differential Equations. Submitted 10-Basti.M. On New Trigonometric Bessel Functions. Submitted for 11-Basti.M.On Associated Legendre. Submitted for publication to the Subject: About my reseach by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i04I7kR00415; Dear readers: Very few differential equations in application admit polynomial solutions, even less so when adequate initial or boundary conditions are prescribed by applications In my paper on A class polynomial III, coefficients of polynomials are integrals of functions including its solution as an integral function of its coefficients. This has variety of applications in the future regarding hypergometric functions. So algebra will not be viewed as before. Even second order linear differential equations related to a class polynomial will find applications in its Riccati version in variety of forms. 21st century. The old ideas as above will be diminished and new versions with new numerical applications will manifest themselves. We need editors with more understanding of the future. This is all bout the new science. Sincerely Dr.M.Basti Subject: About my reseach by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i04I7kk00404; Dear readers: I would like to further elaborate on Prof.shus letter: Very few differential equations in application admit polynomial solutions, even less so when adequate initial or boundary conditions are prescribed by applications. Well this is the viewpoint of the old science, in the new science advancements of solving differential equations heavily dependent upon the advancements of class polynomials. What I wanted to say in broad sense was that the current algorithms cannot solve differential equations if it is written in general form not evaluated at some simple functions. We need to advance solving massive differential equations in the 21st century with the help of class polynomials. Current algorithms will not accomplish the objectives. This is an adventure of new science. Although the paper was over 90% in solving a class polynomial also its irreducible parts for all n. And I have briefly discussed the differential equation parts, which address the second order linear differential equations (Part of classical equations) as related to the class polynomial. You will tell me that this new second order differential equation in general form will not find applications in solving other classical functions?! Examples are concrete, the referee had to go trough the process of the paper to understand how it was done (I do not think this was the case). Incidentally this class polynomial has beautiful invariant properties, which will be discussed in the future papers and I believe it is one of the major class polynomials within others. The irreducible part beautifully generalized for all n the case for cubic irreducible case. Well, the journal missed the chance for this paper . Sincerely Dr.M.Basti Subject: About my reseach by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i04I7kx00387; Dear readers I would like to thank professor shu for answering the concerns. Although in the new science you will wait others to judge and possibly advance in the forms requested. This is a journal related to computing and all my polynomial examples were concrete computations on symbolic software. The Journal name was computing not differential equation, you may read the journals descriptions regarding computations on Algebra. Sincerely Dr.M.Basti His letter: Dear Dr. Basti, Your rebuttal has been read by the referee and associate editor. It is the opinion of the referee that your technique will help to find polynomial solutions of differential eqations, if such polynomial solutions exist. Very few differential equations in application admit polynomial solutions,even less so when adequate initial or boundary conditions are prescribed by applications. Thus, your paper is not suitable for this journal. You might want to try another more specialized journal on solving ordinary differential equations. Also, referees for this journal are anonymous. This is the case for most other journals as well. Sincerely, Chi-Wang Shu Subject: About my research by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i041SJ428828; Dear Readers Thank you for your recent notes. First of all I have received the following note from the editor of In this paper the author derives a class of polynomials which satisfy certain linear second order differential equations. The mathematics involves is elementary, and the results do not have significant impact on actual computations of complex differential equations in applications. The paper is not suitable for publication in this journal. This was my class polynomials including irreducible forms for all n: My answer to Dr.Shu: Dear Prof.Shu: The referee said and the results do not have significant Impact on actual computations of complex differential equations in applications How the referee can so quickly judge on the result that even took me 10 years to discover and it is not part of new advancements of research on mainstream papers but it is a new science. How he/she knows what does this new science is all about? Nothing. See my note about some of my equations solved by my methods and compare it with Maple, and see the difference. This differential equation is part of broad understanding that in order to solve a differential equation a class polynomial is behind it. The referee is missed whole the ideas. I hope that you can also release the name of the referee. This is a mediocre view that papers got to be complex; it is not in the rank of leaders, which I am in the new science. You put a negative record on your journal; it is better to correct it. Sincerely M.Basti And in My earlier note to him (within a week of acknowledgments: Dear Prof.Shu I have the feeling that the editor did not understand the concepts. This is solving polynomials with Differential equations not algebra and not Galois theory. The part concerning irreducible class was most beautiful. This paper took me 10 years to find, and has much advanced generalizations. Unfortunately your editor had short view sight on scientific issues. I have submitted the paper to other place. The view of some editors will not diminish the new science of the 21st century, only delay its dissemination. Here we are introducing polynomials as a class satisfying in a differential equation that is cornerstone of advancements; the editor missed a lot of issues. Sincerely Dr.Mehran Basti Subject: Your Research: Not So Revolutionary After All Well, Basti, reality is speaking: at least one journal finds your work not to be a revolutionary new science, indeed, not even worthy of publishing. Extraordinary claims demand extraordinary evidence. Once again, you have nothing but the delusions of a crank. I wonder if your new employers would have been so keen to hire you if they knew you were such a nutcase. Caesar Garcia > Dear Readers > First of all I have received the following note from the editor of > ....The paper is not suitable for publication in this journal. Subject: Re: Your Research: Not So Revolutionary After All by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id i066V1W23090; Dear Caesar Garcia, While I have not read these papers yet, and, thus, have none idea on account of if Dr Basti is right or wrong there, I must admit that I am feeling fairly unhappy with the way you were expressing your opinion this time. I'd say, I am hearing strong malevolence in your voice. AFAIK, torrent of emotion tends to break human reasoning. Publishing or not publishing a paper not necessarily means the paper is wrong; for example, it simply can be written in a difficult to read fashion etc. As you most probably know, the ultimate example of publishers' blunder is Galois' papers: nobody published them over decades. http://www.galois-group.net/ I was wondering have you read all Dr Basti's papers yourself? If not which seems to be the case, then - no comment. CG> I wonder if your new employers would have been so keen CG> to hire you if they knew you were such a nutcase. I am certain that if I would ever hire a person like you I would fall into a serious error as such a person is obviously not a team player and would make constant attempts to break communication within the company. Speaking so I do not mean that you are a bad or good person, IMHO, such statements are of no use; I also have none idea what talents you are endowed by. I just mean you looks like an individual player; there are and certainly there will be always individual players of superlative power, for example, a Nobel prize winner Frederick Soddy who once worked with Ernest Rutherford http://www.nobel.se/chemistry/laureates/1921/soddy-bio.html Could I kindly ask you to report us rather more facts about Dr Basti's papers? I am very interested in hearing from you on this and other points. Thank you. Best wishes, Vladimir Bondarenko Co-founder, CEO, Mathematical Director Cyber Tester, LLC http://www.cybertester.com/ ............................................................. Subject: Re: About my research It is best not to argue with journal editors about rejected papers. Instead, just submit to another journal. If it is a great paper, it is their loss. > My answer to Dr.Shu: > Dear Prof.Shu: > The referee said and the results do not have significant > Impact on actual computations of complex differential equations in > applications > [...] > I hope that you can also release the name of the referee. It is hard enough to get referees as it is. Releasing their names won't improve anything. -- G. A. Edgar http://www.math.ohio-state.edu/~edgar/ Subject: Re: About my research / reviewing Having been a recipient of good and bad referee reports, (sometimes regarding the same paper) and having been a referee, I must say I have mixed feelings about G. A. Edgar's advice. I have rejected at least 2 papers because the the authors' results were previously known (but apparently not to them.) My rejection letter was essentially: This paper should be rejected because its results are a subset of XXX published 15 years earlier. Subsequently I have seen the paper, unchanged, published elsewhere, apparently reviewed by a referee who was not aware of XXX. I count this kind of shopping around as authors' being dishonest. I think it is better to look at a reviewer's technical comments and try to understand how the paper can be improved so that the reviewer, as well as other readers, will be educated to understand the merits of the work. If the reviewer's objections can be overcome by an additional paragraph early in the paper, or even in the abstract, then it might make sense to re-submit, if that option is open. An improved paper might be sent to another journal. There are probably a few hundred other journals in lower readership. Sometimes editors are willing to pass correspondence back to reviewers. Releasing the names of the reviewers is inappropriate unless the reviewer identifies him/her self voluntarily. There are journals in which reviewers names are attached to papers, but I don't happen to know any offhand. Here's some discussion I found with Google, on peer review. http://www.ecs.soton.ac.uk/~harnad/Hypermail/Amsci/1099.html I think that some reviewers will dismiss a paper because it is not the way they have approached a problem, or seems to be amateurish -- for example, uses naive notation, or does not follow the conventional style or language. They conclude that the paper must be wrong. This is not a bad heuristic. You might look at this page.. http://www.amasci.com/freenrg/arrhenus.html > It is best not to argue with journal editors about rejected papers. > Instead, just submit to another journal. If it is a great paper, it is > their loss. >>My answer to Dr.Shu: >>Dear Prof.Shu: >>The referee said and the results do not have significant >>Impact on actual computations of complex differential equations in >>applications >>[...] >>I hope that you can also release the name of the referee. > It is hard enough to get referees as it is. Releasing their names > won't improve anything. Subject: MuPAD 2.5.3 and Scilab errors, etc. Hi all, I'm having trouble using MuPAD's (2.5.3) Scilab integration. The package seems to be loaded (*maybe*), but it's decidedly not working. Executing numeric::startHardwareFloats returns proc numeric::startHardwareFloats() ... end most of the time, once it returned False, but only once during my troubleshooting), and executing package(scilab) returns Warning: Package already defined. For redefinition use option Forced [package]. Executing scilab::start(), however, returns Error: Unknown slot scilab::start [slot], as does scilab::avail(). I looked through the .mu files in the Scilab directory in MuPAD and nothing looked odd. I set the MUP_SCI environment variable to Scilab's bin directory also, but it didn't result in any change. What am I doing wrong? I scoured the MuPAD documentation on numeric and scilab, as well as Google for a few hours, but didn't turn up anything relevant. On a completely different note, I have Scilab 2.7 installed on the same machine, and would love to be able to use it with MuPAD. Is there any way I can edit the included Scilab .mu files and/or UDX scripts to use it instead? Thanks in advance! -- Dan Moniz [http://www.pobox.com/~dnm/] Subject: Re: MuPAD 2.5.3 and Scilab errors, etc. >I'm having trouble using MuPAD's (2.5.3) Scilab integration. The package >seems to be loaded (*maybe*), but it's decidedly not working. There exist a problem with MuPAD and the Scilab link if there is no ld installed on the machine. Then Scilab cannot load it communication modules which are necessary for the link. We recognized this problem too late. So be sure that ld is installed on your system and it is accessable via your program search path. So try 'which ld' to see if it is there. BTW for the next version of the link it is not necessary to have the linker ld installed. >Executing scilab::start(), however, returns Error: Unknown slot >scilab::start [slot], as does scilab::avail(). That's really strange. Are you sure the Scilab package is installed? >On a completely different note, I have Scilab 2.7 installed on the same >machine, and would love to be able to use it with MuPAD. Is there any way >I can edit the included Scilab .mu files and/or UDX scripts to use it >instead? You can use Scilab 2.7 by setting the environment variable MUP_SCI to the path where Scilab is installed. This is the Scilab main directory where e.g. the Scilab bin directory can be found. MuPAD then uses this Scilab distribuiton and it works together with Scilab 2.7 If your problem is not solved by installing ld please contact me directly so that we can try to solve your problem. Greetings, ToM Subject: Re: Proving a function integrable > Let f:[0,1] X [0,1] - > R be defined by > f(x,y) = 0 if x is irrational > = 0 if x is rational, y is irrational > = 1/q if x is rational, y = p/q (in lowest terms) > Prove that the function f is Riemann integrable, and that > int [f,[0,1] X [0,1]] = 0 Let eps > 0. There are only finitely many rationals p/q in [0,1] with 1/q >= eps. Plot these rationals r1, ..., rn on the y-axis and then consider rectangles of length 1 and extremely small heights centered along the lines y = rm so that the areas of these rectangles sum to something less than eps. If you remove those rectangles, you are left with a bunch of others, and in these f is less than eps. All the rectangles together give a partition P of [0,1] X [0,1]. You'll then have U(P,f) - L(P,f) < 1*eps (summing over the first set of rectangles) + eps*1 (summing over the second set of rectangles) = 2eps. (I'm sure this is the idea in Mogens's post, but I just thought I would give a more intuitive description.) Subject: Re: Open University Greetings. Yes, the Open University (of the UK) isn't very open when it comes to Americans. They do have some courses available to Americans, but the assortment is unimpressive (IMHO). I once e-mailed OU UK about their policy, and I may have mentioned something about their showing little gratitude to the people who prevented their island from becoming a parking lot for Jerry tanks. Although their reply was wonderfully apologetic, they were firm. (I so like the English!) I believe that most of their courses were developed with a tincture of EU funds, and are therefore only available to EU citizens. An alternate choice for an adventurous, would-be math distance learner (and possibly others) is the University of South Africa (UNISA). See: http://www.unisa.ac.za/unisa.asp, http://www.unisa.ac.za/Default.asp?Cmd=ViewContent&ContentID=18 (search for mathematics), and http://www.unisa.ac.za/. If you are very patient, flexible, and understanding, UNISA distance learning expertise, non-dodgeyness, and extremely reasonable prices make them worth considering. It has also been nice practicing diversity, rather than just reading about it. Cordially, Richard Kanarek UNISA, nee TSA, non-math student >> the UK Open University has a distance-study programme in Mathematical >> Sciences. It's available for both UK and non-Uk residents, although >> non UK residents are charged a higher tuition fee. >> see for yourself at www.open.ac.uk >> cheers, >> Ian >Depends where you live. See >http://www3.open.ac.uk/courses/bin/p12.dll?C06M841 for a list of courses >available