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A function f(x) is said to be nonincreasing on an interval I if f(b)<=f(a) for all b>a, where a,b in I. Conversely, a function f(x) is said to be nondecreasing on an interval ...

The nullity of a linear transformation f:V->W of vector spaces is the dimension of its null space. The nullity and the map rank add up to the dimension of V, a result ...

An expression that is of a given type. For example, all primes p>3 are "of the form" 6n+/-1. The term "of shape" is sometimes also used.

The portion of a surface left when an open disk is removed from it.

Let (xi_1,xi_2) be a locally Euclidean coordinate system. Then ds^2=dxi_1^2+dxi_2^2. (1) Now plug in dxi_1=(partialxi_1)/(partialx_1)dx_1+(partialxi_1)/(partialx_2)dx_2 (2) ...

A polygrammic prism is a prism formed by two regular polygrams offset along their symmetry axis and with corresponding edges connected by lateral faces. The hexagrammic prism ...

The power polynomials x^n are an associated Sheffer sequence with f(t)=t, (1) giving generating function sum_(k=0)^inftyx^kt^k=1/(1-tx) (2) and exponential generating ...

A general prism is a polyhedron possessing two congruent polygonal faces and with all remaining faces parallelograms (Kern and Bland 1948, p. 28; left figure). A right prism ...

Let R be a commutative ring. A category C is called an R-category if the Hom-sets of C are R-modules.

Each row and each column in the group multiplication table lists each of the group elements once and only once. From this, it follows that no two elements may be in the ...