Math

Riemann Zeta function zeta(n) is transcendental for integers n > 1
Infact they are all Liouville numbers... Here's my paper http://www.2shared.com/file/9549992/5628e3e7/Irrationality_Of_Zeta_n.html Check it out, and do let me know if I am wrong... (Especially if I am intuitively wrong at the end)... Thanks Roupam ... 30 Nov 2009 09:09

Other solutions for 80abc(a^2+b^2+c^2) = d^5+e^5?
Hello all, There is a basic identity by Lander, (a+b+c)^5 = (-a+b+c)^5 + (a-b+c)^5 + (a+b-c)^5 + 80abc(a^2+b^2+c^2) Problem: Find {a,b,c} such that, 80abc(a^2+b^2+c^2) = d^5+e^5 (eq.1) I found this has an infinite number of non-trivial solns given by, {a,b,c} = {u^5, 25v^5, 50v^5}, and {d,e} = {10u^... 3 Dec 2009 22:44

Dr. Arthur Becker Weidman - Homework "Problems" SOLVED!
Dr. Arthur Becker-Weidman, founder of the Center for Family Development, addresses homework issues: �Mom, I need help with math!!� �OK, honey, I'll be right there.� Five minutes later the child is near tears and screaming, �You're not helping me!!�You fume, �I'm not going to just give you the answers.� Does this sou... 29 Nov 2009 12:23

ISO old-fashioned math exercises for kids
My nephew (age 10) is exceptionally good doing some mental math (specially additions and subtractions), but, despite this, he says he "hates math", considers himself no good at it, etc. In particular, he hates math class (the only class in which he did not have an A or a B+ in his last report card). I want ... 16 Dec 2009 15:44

New Primitive Programming Language - Is it Turing Complete?
Consider the following particularly simple programming language called LOOP+EQ: 1. Loop through the numbers 0, 1, 2, . . . with loop variable X or Y or Z . . . 2. Assign variables A, B, C . . . to a variable, constant 0 or 1, or a programmable function on variables. 3. Execute a (sub)program iff two given var... 20 Jan 2010 20:50

Why G. Chaitin mesure of complexity is wrong.
ON CHAITIN MEASURE OF COMPLEXITY By Ludovicus 20/10/2009 G. CHAITIN's article: 'Randomness and Mathematical Proof' in Scientific American (May 1975) asserts that:; 'The complexity of a series of digits is the number of bits tha... 16 Dec 2009 09:02

SuperKISS for 32- and 64-bit RNGs in both C and Fortran.
On Nov 3 I posted RNGs: A Super KISS sci.math, comp.lang.c, sci.crypt a KISS (Keep-It-Simple-Stupid) RNG combining, by addition mod 2^32, three simple RNGs: CMWC(Complementary-Multiply-With-Carry)+CNG(Congruential) +XS(Xorshift) with resulting period greater than 10^402575. The extreme period com... 1 Dec 2009 19:34

Positive definite and positive definite submatrices
Here is my problem: 1. A is a symmetric positive definite (PD) matrix if and only if the determinant of all its principal submatrices (Ak) are positive. Right? 2. det |Ak| = Product of eigenvalues of Ak. Thus, if Ak is PD, then det|Ak| > 0. Can then I say that: If all Ak are PD => A is PD? But all I c... 16 Dec 2009 15:44

Relative entropy / KL divergence (please help)
Hello, I need to compute the relative entropy (as defined in http://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence) between two discrete distributions with different number of samples. In addition, I need to compute the KL divergence between a two-dimensional multivariate normal distribution and two ... 16 Dec 2009 15:44

Prove/Disprove that nCr for (n-r) > r > 3 can never be a perfect square
Prove/Disprove that nCr for (n-r) > r > 3 can never be a perfect square. {Note: For r=2 we have http://www.research.att.com/~njas/sequences/A055997 which will always give perfect square nCr. For r=3 we have n={3,4,50} to give perfect square (these are the only three tetrahedral numbers which are also perfect sq... 4 Dec 2009 08:27