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A completely positive matrix is a real n×n square matrix A=(a_(ij)) that can be factorized as A=BB^(T), where B^(T) stands for the transpose of B and B is any (not ...

There are a number of attractive polyhedron compounds involving four cubes, several of which are illustrated above. The first (left figures), also known as Bakos' compound, ...

Milnor (1956) found more than one smooth structure on the seven-dimensional hypersphere. Generalizations have subsequently been found in other dimensions. Using surgery ...

A number of strongly regular graphs of several types derived from combinatorial design were identified by Goethals and Seidel (1970). Theorem 2.4 of Goethals and Seidel ...

A heart-shaped surface given by the sextic equation (x^2+9/4y^2+z^2-1)^3-x^2z^3-9/(80)y^2z^3=0 (Taubin 1993, 1994). The figures above show a ray-traced rendering (left) and ...

An isohedron is a convex polyhedron with symmetries acting transitively on its faces with respect to the center of gravity. Every isohedron has an even number of faces ...

The perspective image of an infinite checkerboard. It can be constructed starting from any triangle DeltaOXY, where OX and OY form the near corner of the floor, and XY is the ...

The notion of parallel transport on a manifold M makes precise the idea of translating a vector field V along a differentiable curve to attain a new vector field V^' which is ...

A pair of elements (p_i,p_j) is called an inversion in a permutation p if i>j and p_i<p_j (Skiena 1990, p. 27; Pemmaraju and Skiena 2003, p. 69). For example, in the ...

A singular point of an algebraic curve is a point where the curve has "nasty" behavior such as a cusp or a point of self-intersection (when the underlying field K is taken as ...