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A one-person game played on a rectangular lattice of lamps which can be turned on and off. A move consists of flipping a "switch" inside one of the squares, thereby toggling ...

The Riemann-Lebesgue Lemma, sometimes also called Mercer's theorem, states that lim_(n->infty)int_a^bK(lambda,z)Csin(nz)dz=0 (1) for arbitrarily large C and "nice" ...

The numbers of eigenvalues that are positive, negative, or 0 do not change under a congruence transformation. Gradshteyn and Ryzhik (2000) state it as follows: when a ...

The simplest class of one-dimensional cellular automata. Elementary cellular automata have two possible values for each cell (0 or 1), and rules that depend only on nearest ...

Machin-like formulas have the form mcot^(-1)u+ncot^(-1)v=1/4kpi, (1) where u, v, and k are positive integers and m and n are nonnegative integers. Some such formulas can be ...

A totalistic cellular automaton is a cellular automata in which the rules depend only on the total (or equivalently, the average) of the values of the cells in a ...

The Einstein field equations are the 16 coupled hyperbolic-elliptic nonlinear partial differential equations that describe the gravitational effects produced by a given mass ...

A shuffle of a deck of cards obtained by successively exchanging the cards in position 1, 2, ..., n with cards in randomly chosen positions. For 4<=n<=17, the most frequent ...

By choosing appropriate rules, it is possible to achieve many forms of synchronization within cellular automata. One version, known as the firing squad synchronization ...

Little's law states that, under steady state conditions, the average number of items in a queuing system equals the average rate at which the items arrive multiplied by the ...