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A theorem outlined by Kolmogorov (1954) which was subsequently proved in the 1960s by Arnol'd (1963) and Moser (1962; Tabor 1989, p. 105). It gives conditions under which ...

If all the diagonals--including those obtained by "wrapping around" the edges--of a magic square sum to the same magic constant, the square is said to be a panmagic square ...

An involution of a set S is a permutation of S which does not contain any permutation cycles of length >2 (i.e., it consists exclusively of fixed points and transpositions). ...

In 1913, Ramanujan asked if the Diophantine equation of second order 2^n-7=x^2, sometimes called the Ramanujan-Nagell equation, has any solutions other than n=3, 4, 5, 7, and ...

The rising factorial x^((n)), sometimes also denoted <x>_n (Comtet 1974, p. 6) or x^(n^_) (Graham et al. 1994, p. 48), is defined by x^((n))=x(x+1)...(x+n-1). (1) This ...

Abstractly, a spatial configuration F is said to possess rotational symmetry if F remains invariant under the group C=C(F). Here, C(F) denotes the group of rotations of F and ...

The score sequence of a tournament is a monotonic nondecreasing sequence of the outdegrees of the graph vertices of the corresponding tournament graph. Elements of a score ...

The Sobolev embedding theorem is a result in functional analysis which proves that certain Sobolev spaces W^(k,p)(Omega) can be embedded in various spaces including ...

A spectral sequence is a tool of homological algebra that has many applications in algebra, algebraic geometry, and algebraic topology. Roughly speaking, a spectral sequence ...

By analogy with the sinc function, define the tanc function by tanc(z)={(tanz)/z for z!=0; 1 for z=0. (1) Since tanz/z is not a cardinal function, the "analogy" with the sinc ...