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A magic square that remains magic when its border is removed. A nested magic square remains magic after the border is successively removed one ring at a time. An example of a ...

The great success mathematicians had studying hypergeometric functions _pF_q(a_1,...,a_p;b_1,...,b_q;z) for the convergent cases (p<=q+1) prompted attempts to provide ...

Let S_n be the set of permutations of {1, 2, ..., n}, and let sigma_t be the continuous time random walk on S_n that results when randomly chosen transpositions are performed ...

A Borel set is an element of a Borel sigma-algebra. Roughly speaking, Borel sets are the sets that can be constructed from open or closed sets by repeatedly taking countable ...

In Robert Louis Stevenson's "bottle imp paradox," you are offered the opportunity to buy, for whatever price you wish, a bottle containing a genie who will fulfill your every ...

A set S in a metric space (S,d) is bounded if it has a finite generalized diameter, i.e., there is an R<infty such that d(x,y)<=R for all x,y in S. A set in R^n is bounded ...

The order-n bouquet graph B_n is a pseudograph consisting of a single vertex with n self-loops. The bouquet graph B_1 is a pseudograph that can be considered to correspond to ...

Bourque and Ligh (1992) conjectured that the least common multiple matrix on a GCD-closed set S is nonsingular. This conjecture was shown to be false by Haukkanen et al. ...

A transformation which transforms from a two-dimensional continuous uniform distribution to a two-dimensional bivariate normal distribution (or complex normal distribution). ...

The box fractal is a fractal also called the anticross-stitch curve which can be constructed using string rewriting beginning with a cell [1] and iterating the rules {0->[0 0 ...