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A set of positive integers S is called sum-free if the equation x+y=z has no solutions x, y, z in S. The probability that a random sum-free set S consists entirely of odd ...

An AB percolation is a discrete percolation model in which the underlying point lattice graph L has the properties that each of its graph vertices is occupied by an atom ...

Let two players each have a finite number of pennies (say, n_1 for player one and n_2 for player two). Now, flip one of the pennies (from either player), with each player ...

A tree having four branches at each node. Quadtrees are used in the construction of some multidimensional databases (e.g., cartography, computer graphics, and image ...

Given order statistics Y_1=min_(j)X_j, Y_2, ..., Y_(N-1), Y_N=max_(j)X_j with sample size N, the midrange of the random sample is defined by MR=1/2(Y_1+Y_N) (Hogg and Craig ...

A point process is a probabilistic model for random scatterings of points on some space X often assumed to be a subset of R^d for some d. Oftentimes, point processes describe ...

The hundred-dollar, hundred-digits challenge problems are a set of ten problems in numerical analysis published in the January/February 2002 issue of SIAM News ...

The mean line segment length l^_ is the average length of a line segment in line segment picking within some given shape. As summarized in the following table (where Delta(3) ...

Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), the Hilbert function of M is the map ...

An nth-rank tensor in m-dimensional space is a mathematical object that has n indices and m^n components and obeys certain transformation rules. Each index of a tensor ranges ...