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In two-dimensional polar coordinates, the Helmholtz differential equation is 1/rpartial/(partialr)(r(partialF)/(partialr))+1/(r^2)(partial^2F)/(partialtheta^2)+k^2F=0. (1) ...

The interior product is a dual notion of the wedge product in an exterior algebra LambdaV, where V is a vector space. Given an orthonormal basis {e_i} of V, the forms ...

For a polynomial P(x_1,x_2,...,x_k), the Mahler measure of P is defined by (1) Using Jensen's formula, it can be shown that for P(x)=aproduct_(i=1)^(n)(x-alpha_i), ...

The term Nasik cube can refer to a number of different sorts of magic cubes. In particular, a Nasik cube is a magic cube in which additionally 1. The broken space diagonals ...

In a normal n×n Latin square, the entries in each row and column are chosen from a "global" set of n objects. Like a Latin square, a partial Latin square has no two rows or ...

The pentagonal wegde is one of the seven topologically distinct convex hexahedra. Like the cube, it contains 8 vertices, 12 edges, and 6 faces, but its faces consist of 2 ...

Quantile-quantile plots (also called q-q plots) are used to determine if two data sets come from populations with a common distribution. In such a plot, points are formed ...

A polynomial given in terms of the Neumann polynomials O_n(x) by S_n(x)=(2xO_n(x)-2cos^2(1/2npi))/n.

The p×p square matrix formed by setting s_(ij)=xi^(ij), where xi is a pth root of unity. The Schur matrix has a particularly simple determinant given by ...

The negative derivative S(v)=-D_(v)N (1) of the unit normal N vector field of a surface is called the shape operator (or Weingarten map or second fundamental tensor). The ...