Search Results for ""

Let M be a finitely generated module over a commutative Noetherian ring R. Then there exists a finite set {N_i|1<=i<=l} of submodules of M such that 1. intersection ...

A geometry in which Archimedes' axiom does not hold.

An algebra which does not satisfy a(bc)=(ab)c is called a nonassociative algebra.

A positive value of n for which x-phi(x)=n has no solution, where phi(x) is the totient function. The first few are 10, 26, 34, 50, 52, ... (OEIS A005278).

The term "nonisomorphic" means "not having the same form" and is used in many branches of mathematics to identify mathematical objects which are structurally distinct. ...

A quantity which does not equal zero is said to be nonzero. A real nonzero number must be either positive or negative, and a complex nonzero number can have either real or ...

A function f(n) has the normal order F(n) if f(n) is approximately F(n) for almost all values of n. More precisely, if (1-epsilon)F(n)<f(n)<(1+epsilon)F(n) for every positive ...

A null function delta^0(x) satisfies int_a^bdelta^0(x)dx=0 (1) for all a,b, so int_(-infty)^infty|delta^0(x)|dx=0. (2) Like a delta function, they satisfy delta^0(x)={0 x!=0; ...

It is possible to construct simple functions which produce growing patterns. For example, the Baxter-Hickerson function f(n)=1/3(2·10^(5n)-10^(4n)+2·10^(3n)+10^(2n)+10^n+1) ...

There are a number of attractive polyhedron compounds consisting of 25 octahedra. These compounds will be implemented in a future version of the Wolfram Language as ...