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For d>=1, Omega an open subset of R^d, p in [1;+infty] and s in N, the Sobolev space W^(s,p)(R^d) is defined by W^(s,p)(Omega)={f in L^p(Omega): forall ...

Sorting is the rearrangement of numbers (or other orderable objects) in a list into their correct lexographic order. Alphabetization is therefore a form of sorting. Because ...

Gardner showed how to dissect a square into eight and nine acute scalene triangles. W. Gosper discovered a dissection of a unit square into 10 acute isosceles triangles, ...

Given a set of n men and n women, marry them off in pairs after each man has ranked the women in order of preference from 1 to n, {w_1,...,w_n} and each women has done ...

A local Banach algebra A is stably unital if the collection M_infty(A) of square infinite-dimensional matrices with entries in A has an approximate identity consisting of ...

Stadium billiards refers to the investigation of the path of a billiard ball on a stadium-shaped billiard table, as first investigated by Bunimovich (1974).

A determinant used to determine in which coordinate systems the Helmholtz differential equation is separable (Morse and Feshbach 1953). A determinant S=|Phi_(mn)|=|Phi_(11) ...

The term "range" has two completely different meanings in statistics. Given order statistics Y_1=min_(j)X_j, Y_2, ..., Y_(N-1), Y_N=max_(j)X_j, the range of the random sample ...

A string of length n on an alphabet l of m characters is an arrangement of n not necessarily distinct symbols from l. There are m^n such distinct strings. For example, the ...

Subresultants can be viewed as a generalization of resultants, which are the product of the pairwise differences of the roots of polynomials. Subresultants are the most ...