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Let B={b_1,b_2,...} be an infinite Abelian semigroup with linear order b_1<b_2<... such that b_1 is the unit element and a<b implies ac<bc for a,b,c in B. Define a Möbius ...

Let g:R->R be a function and let h>0, and define the cardinal series of g with respect to the interval h as the formal series sum_(k=-infty)^inftyg(kh)sinc((x-kh)/h), where ...

Using a Chebyshev polynomial of the first kind T(x), define c_j = 2/Nsum_(k=1)^(N)f(x_k)T_j(x_k) (1) = 2/Nsum_(k=1)^(N)f[cos{(pi(k-1/2))/N}]cos{(pij(k-1/2))/N}. (2) Then f(x) ...

Conditional logit regression assumes a model of the form p_j=(e^(beta^'x_j))/(sum_(j)e^(beta^'x_j)) for j=1, ..., k+1. In this model, a subject is presented with choice ...

Defined for a vector field A by (A·del ), where del is the gradient operator. Applied in arbitrary orthogonal three-dimensional coordinates to a vector field B, the ...

The continuous Fourier transform is defined as f(nu) = F_t[f(t)](nu) (1) = int_(-infty)^inftyf(t)e^(-2piinut)dt. (2) Now consider generalization to the case of a discrete ...

Let d_G(k) be the number of dominating sets of size k in a graph G, then the domination polynomial D_G(x) of G in the variable x is defined as ...

The Droussent cubic is the triangle cubic with trilinear equation sum_(cyclic)(b^4+c^4-a^4-b^2c^2)aalpha(b^2beta^2-c^2gamma^2)=0. It passes through Kimberling centers X_n for ...

In physics, the word entropy has important physical implications as the amount of "disorder" of a system. In mathematics, a more abstract definition is used. The (Shannon) ...

A set function mu is said to possess finite subadditivity if, given any finite disjoint collection of sets {E_k}_(k=1)^n on which mu is defined, mu( union ...