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Apéry's numbers are defined by A_n = sum_(k=0)^(n)(n; k)^2(n+k; k)^2 (1) = sum_(k=0)^(n)([(n+k)!]^2)/((k!)^4[(n-k)!]^2) (2) = _4F_3(-n,-n,n+1,n+1;1,1,1;1), (3) where (n; k) ...

Connecting the centers of touching spheres in a three-dimensional Apollonian gasket by edges given a graph known as the Apollonian network. This process is illustrated above ...

A bipartite graph, also called a bigraph, is a set of graph vertices decomposed into two disjoint sets such that no two graph vertices within the same set are adjacent. A ...

In most modern literature, a Boolean model is a probabilistic model of continuum percolation theory characterized by the existence of a stationary point process X and a ...

A complete tripartite graph is the k=3 case of a complete k-partite graph. In other words, it is a tripartite graph (i.e., a set of graph vertices decomposed into three ...

The conjugate gradient method is an algorithm for finding the nearest local minimum of a function of n variables which presupposes that the gradient of the function can be ...

The average distance between two points chosen at random inside a unit cube (the n=3 case of hypercube line picking), sometimes known as the Robbins constant, is Delta(3) = ...

The dilogarithm Li_2(z) is a special case of the polylogarithm Li_n(z) for n=2. Note that the notation Li_2(x) is unfortunately similar to that for the logarithmic integral ...

An equilateral triangle is a triangle with all three sides of equal length a, corresponding to what could also be known as a "regular" triangle. An equilateral triangle is ...

The Greenfield graph is the name given in this work to the 12-vertex graph illustrated above due to Greenfield (2011). This graph provided the first known example which ...