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The functional derivative is a generalization of the usual derivative that arises in the calculus of variations. In a functional derivative, instead of differentiating a ...

The G-transform of a function f(x) is defined by the integral (Gf)(x)=(G_(pq)^(mn)|(a_p); (b_q)|f(t))(x) (1) =1/(2pii)int_sigmaGamma[(b_m)+s, 1-(a_n)-s; (a_p^(n+1))+s, ...

The general unitary group GU_n(q) is the subgroup of all elements of the general linear group GL(q^2) that fix a given nonsingular Hermitian form. This is equivalent, in the ...

A geometric sequence is a sequence {a_k}, k=0, 1, ..., such that each term is given by a multiple r of the previous one. Another equivalent definition is that a sequence is ...

int_a^b(del f)·ds=f(b)-f(a), where del is the gradient, and the integral is a line integral. It is this relationship which makes the definition of a scalar potential function ...

The symbol defined by c^(a/b) = c(c+b)(c+2b)...[c+(a-1)b] (1) = b^a(c/b)_a (2) = (b^aGamma(a+c/b))/(Gamma(c/b)), (3) where (a)_n is the Pochhammer symbol and Gamma(z) is the ...

A function f(x) is logarithmically concave on the interval [a,b] if f>0 and lnf(x) is concave on [a,b]. The definition can also be extended to R^k->(0,infty) functions ...

A function f(x) is logarithmically convex on the interval [a,b] if f>0 and lnf(x) is convex on [a,b]. If f(x) and g(x) are logarithmically convex on the interval [a,b], then ...

Let (A,<=) be a partially ordered set. Then an element m in A is said to be maximal if, for all a in A, m!<=a. Alternatively, an element m in A is maximal such that if m<=a ...

A module homomorphism is a map f:M->N between modules over a ring R which preserves both the addition and the multiplication by scalars. In symbols this means that ...