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There are a few plane curves known as "bean curves." The bean curve identified by Cundy and Rowllet (1989, p. 72) is the quartic curve given by the implicit equation ...

A braid with M strands and R components with P positive crossings and N negative crossings satisfies |P-N|<=2U+M-R<=P+N, where U is the unknotting number. While the second ...

The polynomials defined by B_(i,n)(t)=(n; i)t^i(1-t)^(n-i), (1) where (n; k) is a binomial coefficient. The Bernstein polynomials of degree n form a basis for the power ...

A C-matrix is a symmetric (C^(T)=C) or antisymmetric (C^(T)=-C) C_n (-1,0,1)-matrix with diagonal elements 0 and others +/-1 that satisfies CC^(T)=(n-1)I, (1) where I is the ...

The Cauchy distribution, also called the Lorentzian distribution or Lorentz distribution, is a continuous distribution describing resonance behavior. It also describes the ...

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 ...

A doubly nonnegative matrix is a real positive semidefinite n×n square matrix with nonnegative entries. Any doubly nonnegative matrix A of order n can be expressed as a Gram ...

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) ...

The Gini coefficient (or Gini ratio) G is a summary statistic of the Lorenz curve and a measure of inequality in a population. The Gini coefficient is most easily calculated ...

Let there be m doctors and n<=m patients, and let all mn possible combinations of examinations of patients by doctors take place. Then what is the minimum number of surgical ...