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Let A be a set. An operation on A is a function from a power of A into A. More precisely, given an ordinal number alpha, a function from A^alpha into A is an alpha-ary ...

A surface which is homeomorphic to a finite collection of spheres, each with a finite number of handles, cross-handles, cross-caps, and perforations. A preliminary version of ...

A number of fractal curves are associated with Peano. The Peano curve is the fractal curve illustrated above which can be written as a Lindenmayer system. The nth iteration ...

Let f(z) be an analytic function in an angular domain W:|argz|<alphapi/2. Suppose there is a constant M such that for each epsilon>0, each finite boundary point has a ...

A positive matrix is a real or integer matrix (a)_(ij) for which each matrix element is a positive number, i.e., a_(ij)>0 for all i, j. Positive matrices are therefore a ...

If f(x) is a nonconstant integer polynomial and c is an integer such that f(c) is divisible by the prime p, that p is called a prime divisor of the polynomial f(x) (Nagell ...

For a quadratic form Q in the canonical form Q=y_1^2+y_2^2+...+y_p^2-y_(p+1)^2-y_(p+2)^2-...-y_r^2, the rank is the total number r of square terms (both positive and ...

On a three-dimensional lattice, a random walk has less than unity probability of reaching any point (including the starting point) as the number of steps approaches infinity. ...

Rubik's graph is the Cayley graph of Rubik's group. The graph diameter of this graph is sometimes known as God's number, and was shown in Aug. 2010 to be equal to 20 (Rokicki ...

If the integral coefficients C_0, C_1, ..., C_(N-1) of the polynomial f(x)=C_0+C_1x+C_2x^2+...+C_(N-1)x^(N-1)+x^N are divisible by a prime number p, while the free term C_0 ...