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A polyomino-like object made by attaching squares joined either at sides or corners. Because neighboring squares can be in relation to one another as kings may move on a ...

Polysticks, sometimes also known as polyedges, are polyforms obtained from the edges of a regular grid. Square polysticks are polyforms obtained from the edges of a regular ...

A presheaf C of categories consists of the following data: 1. For every local homeomorphism f:Y->X of topological spaces X, Y, a category C(f:Y->X); 2. For every diagram f ...

Almost all processes that are not obviously simple can be viewed as computations of equivalent sophistication (Wolfram 2002, pp. 5 and 716-717). More specifically, the ...

The Prosthaphaeresis formulas, also known as Simpson's formulas, are trigonometry formulas that convert a product of functions into a sum or difference. They are given by ...

A pseudotree is a connected pseudoforest, i.e., an undirected connected graph that contains at most one graph cycle. Connected acyclic graphs (i.e., trees), are therefore ...

Quantization is a nonlinear process which generates additional frequency components (Thompson et al. 1986). This means that the signal is no longer band-limited, so the ...

The Racah V-coefficients are written V(j_1j_2j;m_1m_2m) (1) and are sometimes expressed using the related Clebsch-Gordan coefficients C_(m_1m_2)^j=(j_1j_2m_1m_2|j_1j_2jm), ...

The Radon-Nikodym theorem asserts that any absolutely continuous complex measure lambda with respect to some positive measure mu (which could be Lebesgue measure or Haar ...

Let the two-dimensional cylinder function be defined by f(x,y)={1 for r<R; 0 for r>R. (1) Then the Radon transform is given by ...