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The 20 Cayley lines generated by a hexagon inscribed in a conic section pass four at a time though 15 points known as Salmon points (Wells 1991). There is a dual relationship ...

A point process N is called self-correcting if cov(N(s,t),N(t,u))<0 for s<t<u where here, cov denotes the covariance of the two quantities. Intuitively, a process is ...

A separating family is a set of subsets in which each pair of adjacent elements are found separated, each in one of two disjoint subsets. The 26 letters of the alphabet can ...

Take the Helmholtz differential equation del ^2F+k^2F=0 (1) in spherical coordinates. This is just Laplace's equation in spherical coordinates with an additional term, (2) ...

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) ...

A graph is strongly perfect if every induced subgraph H has an independent vertex set meeting all maximal cliques of H (Berge and Duchet 1984, Ravindra 1999). Every strongly ...

A subset of an algebraic variety which is itself a variety. Every variety is a subvariety of itself; other subvarieties are called proper subvarieties. A sphere of the ...

The contraction of a tensor is obtained by setting unlike indices equal and summing according to the Einstein summation convention. Contraction reduces the tensor rank by 2. ...

There exist points A^', B^', and C^' on segments BC, CA, and AB of a triangle, respectively, such that A^'C+CB^'=B^'A+AC^'=C^'B+BA^' (1) and the lines AA^', BB^', CC^' ...

Consider the differential equation satisfied by w=z^(-1/2)W_(k,-1/4)(1/2z^2), (1) where W is a Whittaker function, which is given by ...