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Qubic is a generalization of tic-tac-toe in which players alternately place pieces to get four in a row (rows, columns, pillars, face diagonals, or space diagonals) on a ...

According to most authors (e.g., Kelley 1955, p. 113; McCarty 1967, p. 144; Willard 1970, p. 92) a regular space is a topological space in which every neighborhood of a point ...

The differential equation where alpha+alpha^'+beta+beta^'+gamma+gamma^'=1, first obtained in the form by Papperitz (1885; Barnes 1908). Solutions are Riemann P-series ...

A powerful numerical integration technique which uses k refinements of the extended trapezoidal rule to remove error terms less than order O(N^(-2k)). The routine advocated ...

A rook polynomial is a polynomial R_(m,n)(x)=sum_(k=0)^(min(m,n))r_kx^k (1) whose number of ways k nonattacking rooks can be arranged on an m×n chessboard. The rook ...

Two families of equations used to find roots of nonlinear functions of a single variable. The "B" family is more robust and can be used in the neighborhood of degenerate ...

Slovin's formula, somtimes also spelled "Sloven's forumula (e.g., Altares et al. 2003, p. 13), is an ad hoc formula lacking mathematical rigor (Ryan 2013) that gives an ...

A two-component complex column vector. Spinors can describe both bosons and fermions, while tensors can describe only bosons.

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) ...

Doob (1996) defines a stochastic process as a family of random variables {x(t,-),t in J} from some probability space (S,S,P) into a state space (S^',S^'). Here, J is the ...