Search Results for ""

A braid is an intertwining of some number of strings attached to top and bottom "bars" such that each string never "turns back up." In other words, the path of each string in ...

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 ...

The constant a_(-1) in the Laurent series f(z)=sum_(n=-infty)^inftya_n(z-z_0)^n (1) of f(z) about a point z_0 is called the residue of f(z). If f is analytic at z_0, its ...

A reduction system is called confluent (or globally confluent) if, for all x, u, and w such that x->_*u and x->_*w, there exists a z such that u->_*z and w->_*z. A reduction ...

Given an m×n matrix A, the fundamental theorem of linear algebra is a collection of results relating various properties of the four fundamental matrix subspaces of A. In ...

The Game of Logic, described by Lewis Carroll--author of Alice in Wonderland--in 1887 (Carroll 1972) consists of discussing the meaning of propositions like "Some fresh cakes ...

The first example discovered of a map from a higher-dimensional sphere to a lower-dimensional sphere which is not null-homotopic. Its discovery was a shock to the ...

The hyperbolic cosecant is defined as cschz=1/(sinhz)=2/(e^z-e^(-z)). (1) It is implemented in the Wolfram Language as Csch[z]. It is related to the hyperbolic cotangent ...

Two sets A and B are said to be independent if their intersection A intersection B=emptyset, where emptyset is the empty set. For example, {A,B,C} and {D,E} are independent, ...

Let P(z) and Q(z) be univariate polynomials in a complex variable z, and let the polynomial degrees of P and Q satisfy deg(Q)>=deg(P+2). Then int_gamma(P(z))/(Q(z))dz = ...