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The direct product is defined for a number of classes of algebraic objects, including sets, groups, rings, and modules. In each case, the direct product of an algebraic ...

Direct sums are defined for a number of different sorts of mathematical objects, including subspaces, matrices, modules, and groups. The matrix direct sum is defined by ...

A convex polyomino containing at least one edge of its minimal bounding rectangle. The perimeter and area generating function for directed polygons of width m, height n, and ...

Let c and d!=c be real numbers (usually taken as c=1 and d=0). The Dirichlet function is defined by D(x)={c for x rational; d for x irrational (1) and is discontinuous ...

There are several types of integrals which go under the name of a "Dirichlet integral." The integral D[u]=int_Omega|del u|^2dV (1) appears in Dirichlet's principle. The ...

The problem of finding the connection between a continuous function f on the boundary partialR of a region R with a harmonic function taking on the value f on partialR. In ...

Given an arithmetic progression of terms an+b, for n=1, 2, ..., the series contains an infinite number of primes if a and b are relatively prime, i.e., (a,b)=1. This result ...

If a is an arbitrary integer relatively prime to n and g is a primitive root of n, then there exists among the numbers 0, 1, 2, ..., phi(n)-1, where phi(n) is the totient ...

A series which is not convergent. Series may diverge by marching off to infinity or by oscillating. Divergent series have some curious properties. For example, rearranging ...

The divided difference f[x_0,x_1,x_2,...,x_n], sometimes also denoted [x_0,x_1,x_2,...,x_n] (Abramowitz and Stegun 1972), on n+1 points x_0, x_1, ..., x_n of a function f(x) ...