Math

GAP command
Hi, I need to verify some of my Galois group exercises using GAP. How do I find the Galois group of the polynomial x^4 + 2x^2 + x +3 over Q using GAP? Can I also find the splitting field of it using GAP? How do I also find the Galois group of the same polynomial over GF(7) rather than Q? I googled and trie... 10 May 2010 13:13

volume of the 4-dimensional unit sphere--
calvin wrote: Why do you call it volume? In two dimensions, it's area. In three dimensions, it's volume. In four dimensions, it would be something else. In four dimensions, volume would be to that something else as cross-sectional area is to volume in three dimensions. Then it is up to you to dev... 6 May 2010 20:57

volume of the 4-dimensional unit sphere-
hw wrote: How does one calculate the volume of the 4-dimensional unit sphere? Thanks. Still another method - in two steps: (A) Calculate the 3D hyper-area (3D volume) of S^3, the 3D hypersphere at the hyper-surface of the unit 4D ball {(u, x, y, z) | u^2 + x^2 + y^2 + z^2 <= 1}. An S^3 with radius R... 6 May 2010 18:44

superadditivity
Hello everyone, here is a little problem I have. Let u_n bet a superadditive sequence, that is u_(n+m) >= u_m + u_n for all n,m it is quite easy to show that : lim n-> infty u_n/n = sup_n u_n/n exists. Let denote L this limit. Now I want to show that : L = lim m-> infty lim_inf n-> infty (u_(m+n) - u... 6 May 2010 22:03

superadditivity
Hello everyone, here is a little problem I have. Let u_n bet a superadditive sequence, that is u_(n+m) >= u_m + u_n for all n,m it is quite easy to show that : lim n-> infty u_n/n = sup_n u_n/n exists. Let denote L this limit. Now I want to show that : L = lim m-> infty lim_inf n-> infty (u_(m+n) - u... 6 May 2010 16:31

Chapt 3, Fiberglass Experiment; using only luminosity for distance measure #62; ATOM TOTALITY
The Luminet team of researchers found a diameter of the Cosmos at 30 billion light years across with a Poincare Dodecahedral Space. I was wondering if that matches the 3rd layer Ring of Jarrett's mapping: http://spider.ipac.caltech.edu/staff/jarrett/papers/LSS/ The third layer (0.01 < z < 0.02) is dominat... 6 May 2010 16:31

invertible 4 × 4 matrices
How does one determine how many invertible 4 × 4 matrices are there with entries in Z(5) (the integers mod 5)? Thanks. ... 9 May 2010 09:58

Proton Radius Cannot Be Derived From Standard Model
On Apr 26, 6:24 pm, "Robert L. Oldershaw" <rlolders...(a)amherst.edu> wrote: On Apr 26, 2:22 pm, glird <gl...(a)aol.com> wrote: A new paradigm already exists. The trouble is that nobody, other than its sire, is willing or able to consider the merits of anything that disagrees with the old one embed... 17 Jun 2010 01:24

CRUCIAL THEOREM IN THERMODYNAMICS
Kelvin's version of the second law of thermodynamics: It is impossible to perform a cyclic process with no other result than that heat is absorbed from a reservoir, and work is performed. THEOREM: Kelvin's version of the second law is true if and only if, whenever two INTERACTING heat engines absorb heat from a r... 6 May 2010 05:17

string of integers puzzle
I'm working on a project that depends on solving this puzzle. Any help would be greatly appreciated, even perhaps help in rephrasing this problem in a less clumsy way: I'm looking to create a string of letters (or integers) with certain properties. The main property involves looking at consecutive groups of 4 ... 10 May 2010 16:34