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An algorithm used to recursively construct a set of objects from the smallest possible constituent parts. Given a set of k integers (a_1, a_2, ..., a_k) with a_1<a_2<...<a_k, ...

A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of ...

A refinement X of a cover Y is a cover such that every element x in X is a subset of an element y in Y.

Define g(k) as the quantity appearing in Waring's problem, then Euler conjectured that g(k)=2^k+|_(3/2)^k_|-2, where |_x_| is the floor function.

Let a patch be given by the map x:U->R^n, where U is an open subset of R^2, or more generally by x:A->R^n, where A is any subset of R^2. Then x(U) (or more generally, x(A)) ...

Two sets A and B are said to be independent if their intersection A intersection B=emptyset, where emptyset is the empty set. For example, {A,B,C} and {D,E} are independent, ...

A relation is any subset of a Cartesian product. For instance, a subset of A×B, called a "binary relation from A to B," is a collection of ordered pairs (a,b) with first ...

If V and W are Banach spaces and T:V->W is a bounded linear operator, the T is said to be a compact operator if it maps the unit ball of V into a relatively compact subset of ...

Let S be the set of all possibilities that satisfy hypothesis H, and let S^' be the set of all possibilities that satisfy hypothesis H^'. Then H^' is a nested hypothesis ...

A subset S subset R^n is said to be pseudo-convex at a point x in S if the associated pseudo-tangent cone P_S(x) to S at x contains S-{x}, i.e., if S-{x} subset P_S(x). Any ...