Search Results for ""

Every Lie algebra L is isomorphic to a subalgebra of some Lie algebra A^-, where the associative algebra A may be taken to be the linear operators over a vector space V.

Let G be a locally compact Abelian group. Let G^* be the group of all continuous homeomorphisms G->R/Z, in the compact open topology. Then G^* is also a locally compact ...

A result in control theory. Define H(psi,x,u)=(psi,f(x,u))=sum_(a=0)^npsi_af^a(x,u). Then in order for a control u(t) and a trajectory x(t) to be optimal, it is necessary ...

A positive definite function f on a group G is a function for which the matrix {f(x_ix_j^(-1))} is always positive semidefinite Hermitian.

Given f:X->Y, the image of x is f(x). The preimage of y is then f^(-1)(y)={x|f(x)=y}, or all x whose image is y. Images are elements of the range, while preimages are subsets ...

Find two numbers such that x^2=y^2 (mod n). If you know the greatest common divisor of n and x-y, there exists a high probability of determining a prime factor. Taking small ...

A primitive group action is transitive and it has no nontrivial group blocks. A transitive group action that is not primitive is called imprimitive. A group that has a ...

An extension A subset B of a group, ring, module, field, etc., such that A!=B.

Given a Pythagorean triple (a,b,c), the fractions a/b and b/a are called Pythagorean fractions. Diophantus showed that the Pythagorean fractions consist precisely of ...

The doublestruck capital letter Q, Q, denotes the field of rationals. It derives from the German word Quotient, which can be translated as "ratio." The symbol Q first ...