Search Results for ""

There are at least two statements which go by the name of Artin's conjecture. If r is any complex finite-dimensional representation of the absolute Galois group of a number ...

The definition of a set by enumerating its members. An extensional definition can always be reduced to an intentional one. An extension field is sometimes also called simply ...

Kontsevich's integral is a far-reaching generalization of the Gauss integral for the linking number, and provides a tool to construct the universal Vassiliev invariant of a ...

The notion of parallel transport on a manifold M makes precise the idea of translating a vector field V along a differentiable curve to attain a new vector field V^' which is ...

Let x be a real number, and let R be the set of positive real numbers mu for which 0<|x-p/q|<1/(q^mu) (1) has (at most) finitely many solutions p/q for p and q integers. Then ...

A nonzero ring S whose only (two-sided) ideals are S itself and zero. Every commutative simple ring is a field. Every simple ring is a prime ring.

The quantity twelve (12) is sometimes known as a dozen. It is in turn one twelfth of a gross. Base-12 is known as duodecimal. The Schoolhouse Rock segment "Little Twelvetoes" ...

The Bernoulli inequality states (1+x)^n>1+nx, (1) where x>-1!=0 is a real number and n>1 an integer. This inequality can be proven by taking a Maclaurin series of (1+x)^n, ...

If del xF=0 (i.e., F(x) is an irrotational field) in a simply connected neighborhood U(x) of a point x, then in this neighborhood, F is the gradient of a scalar field phi(x), ...

The group of all nonsingular n×n stochastic matrices over a field F. It is denoted S(n,F). If p is prime and F is the finite field of order q=p^m, S(n,q) is written instead ...