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Given a commutative unit ring R, and an R-module M, a sequence {x_1,...,x_n} of elements of R is called a regular sequence for M (or an M-sequence for short), if, for all ...

According to most authors (e.g., Kelley 1955, p. 113; McCarty 1967, p. 144; Willard 1970, p. 92) a regular space is a topological space in which every neighborhood of a point ...

A two-regular graph is a regular graph for which all local degrees are 2. A two-regular graph consists of one or more (disconnected) cycles. The numbers a_n of two-regular ...

A polyhedral graph is completely regular if the dual graph is also regular. There are only five types. Let rho be the number of graph edges at each node, rho^* the number of ...

A topological space X such that for every closed subset C of X and every point x in X\C, there is a continuous function f:X->[0,1] such that f(x)=0 and f(C)={1}. This is the ...

A connected graph G is distance-regular if for any vertices x and y of G and any integers i,j=0, 1, ...d (where d is the graph diameter), the number of vertices at distance i ...

There are a number of attractive compounds of two regular tetrahedra. The most symmetrical is the arrangement whose outer hull is the stella octangula (left figure), while ...

Consider a second-order ordinary differential equation y^('')+P(x)y^'+Q(x)y=0. If P(x) and Q(x) remain finite at x=x_0, then x_0 is called an ordinary point. If either P(x) ...

A regular continued fraction is a simple continued fraction x = b_0+1/(b_1+1/(b_2+1/(b_3+...))) (1) = K_(k=1)^(infty)1/(b_k) (2) = [b_0;b_1,b_2,...], (3) where b_0 is an ...

A directed strongly regular graph is a simple directed graph with adjacency matrix A such that the span of A, the identity matrix I, and the unit matrix J is closed under ...