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Consider a second-order ordinary differential equation y^('')+P(x)y^'+Q(x)y=0. If P(x) and Q(x) remain finite at x=x_0, then x_0 is called an ordinary point. If either P(x) ...

A polyhedron consisting of a n-gon, a parallel 2n-gon rotated a half-edge turn, and a band of paired triangles separated by pentagons. The only true member giving a ...

In discrete percolation theory, site percolation is a percolation model on a regular point lattice L=L^d in d-dimensional Euclidean space which considers the lattice vertices ...

Smale (1958) proved that it is mathematically possible to turn a sphere inside-out without introducing a sharp crease at any point. This means there is a regular homotopy ...

For a graph vertex x of a graph, let Gamma_x and Delta_x denote the subgraphs of Gamma-x induced by the graph vertices adjacent to and nonadjacent to x, respectively. The ...

A number of attractive 12-compounds of the regular tetrahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...

A number of attractive 18-compounds of the regular tetrahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

An attractive compound of three regular tetrahedra can be obtained by taking three tetrahedra with a C_2 axes aligned along the z-axis and rotating them a sixth of a turn ...

A number of attractive 50-compounds of the regular tetrahedron can be constructed. The compounds illustrated above will be implemented in a future version of the Wolfram ...

The equilateral triaugmented triangular prism is the Johnson solid J_(51) constructed by erecting a regular tetrahedron on each square face of an equilateral triangular ...