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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 ...

A complete set of mutually conjugate group elements. Each element in a group belongs to exactly one class, and the identity element (I=1) is always in its own class. The ...

A covariant tensor, denoted with a lowered index (e.g., a_mu) is a tensor having specific transformation properties. In general, these transformation properties differ from ...

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^', ...

In cylindrical coordinates, the scale factors are h_r=1, h_theta=r, h_z=1, so the Laplacian is given by del ...

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 ...