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The Laplace-Carson transform F of a real-valued function f is an integral transform defined by the formula F(p)=pint_0^inftye^(-pt)f(t)dt. (1) In most cases, the function F ...

The Lotka-Volterra equations describe an ecological predator-prey (or parasite-host) model which assumes that, for a set of fixed positive constants A (the growth rate of ...

Every totally ordered set (A,<=) is associated with a so-called order type. Two sets A and B are said to have the same order type iff they are order isomorphic (Ciesielski ...

A set of ascending sequences in a permutation is called a run (Graham et al. 1994) or sometimes a rise (Comtet 1974, p. 241). A sorted permutation consists of a single run, ...

A rooted graph is a graph in which one node is labeled in a special way so as to distinguish it from other nodes. The special node is called the root of the graph. The rooted ...

Let V be a real symmetric matrix of large order N having random elements v_(ij) that for i<=j are independently distributed with equal densities, equal second moments m^2, ...

A function is said to be piecewise constant if it is locally constant in connected regions separated by a possibly infinite number of lower-dimensional boundaries. The ...

Let a simple graph G have n vertices, chromatic polynomial P(x), and chromatic number chi. Then P(G) can be written as P(G)=sum_(i=0)^ha_i·(x)_(p-i), where h=n-chi and (x)_k ...

The number of ways to arrange n distinct objects along a fixed (i.e., cannot be picked up out of the plane and turned over) circle is P_n=(n-1)!. The number is (n-1)! instead ...

The Lucas polynomials are the w-polynomials obtained by setting p(x)=x and q(x)=1 in the Lucas polynomial sequence. It is given explicitly by ...