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A face-centered cubic sphere packing obtained by placing layers of spheres one on top of another. Because there are two distinct ways to place each layer on top of the ...

The biaugmented pentagonal prism is Johnson solid J_(53), which is formed from double augmentation of two nonadjacent lateral faces of the equilateral pentagonal prism by an ...

A two-sided (doubly infinite) Laplace transform, L_t[f(t)](s)=int_(-infty)^inftyf(t)e^(-st)dt. While some authors use this as the primary definition of "the" Laplace ...

The smallest unit of binary information, equal to a single 0 or 1. Two bits are called a crumb, four bits are called a nibble, and eight bits are called 1 byte.

The only Wiedersehen surfaces are the standard round spheres. The conjecture was proven by combining the Berger-Kazdan comparison theorem with A. Weinstein's results for n ...

A bounded left approximate identity for a normed algebra A is a bounded net {e_alpha}_(alpha in I) with the property lim_(alpha)e_alphaa=a for a in A. Bounded right and ...

For every positive integer n, there exists a square in the plane with exactly n lattice points in its interior. This was extended by Schinzel and Kulikowski to all plane ...

For a fractal process with values y(t-Deltat) and y(t+Deltat), the correlation between these two values is given by the Brown function r=2^(2H-1)-1, also known as the ...

There are two identities known as Catalan's identity. The first is F_n^2-F_(n+r)F_(n-r)=(-1)^(n-r)F_r^2, where F_n is a Fibonacci number. Letting r=1 gives Cassini's ...

Chain equivalences give an equivalence relation on the space of chain homomorphisms. Two chain complexes are chain equivalent if there are chain maps phi:C_*->D_* and ...