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In discrete percolation theory, bond percolation is a percolation model on a regular point lattice L=L^d in d-dimensional Euclidean space which considers the lattice graph ...

A two-dimensional binary (k=2) totalistic cellular automaton with a von Neumann neighborhood of range r=1. It has a birth rule that at least 2 of its 4 neighbors are alive, ...

A Cartan matrix is a square integer matrix who elements (A_(ij)) satisfy the following conditions. 1. A_(ij) is an integer, one of {-3,-2,-1,0,2}. 2. A_(ii)=2 the diagonal ...

Differential evolution is a stochastic parallel direct search evolution strategy optimization method that is fairly fast and reasonably robust. Differential evolution is ...

In 1757, V. Riccati first recorded the generalizations of the hyperbolic functions defined by F_(n,r)^alpha(x)=sum_(k=0)^infty(alpha^k)/((nk+r)!)x^(nk+r), (1) for r=0, ..., ...

The Gergonne line is Oldknow's (1996) term for the perspectrix of a contact triangle DeltaDEF and its reference triangle DeltaABC. It is determined by the Nobbs points D^', ...

A mathematical statement that one quantity is greater than or less than another. "a is less than b" is denoted a<b, and "a is greater than b" is denoted a>b. "a is less than ...

A graph G=(V,E) is an interval graph if it captures the intersection relation for some set of intervals on the real line. Formally, P is an interval graph provided that one ...

The Johnson triangle DeltaJ_AJ_BJ_C, a term coined here for the first time, is the triangle formed by the centers of the Johnson circles. It has trilinear vertex matrix ...

The Lemoine axis is the perspectrix of a reference triangle and its tangential triangle, and also the trilinear polar of the symmedian point K of the reference triangle. It ...