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There are several versions of the Kaplan-Yorke conjecture, with many of the higher dimensional ones remaining unsettled. The original Kaplan-Yorke conjecture (Kaplan and ...

C. Kimberling has extensively tabulated and enumerated the properties of triangle centers (Kimberling 1994, 1998, and online), denoting the nth center in his numbering scheme ...

Let (P,B) denote a configuration with v points P={p_1,...,p_v} and b lines ("blocks") B=(B_1,...,B_b). Then the Levi graph L(P,B), also called the incidence graph, of a ...

An operation on rings and modules. Given a commutative unit ring R, and a subset S of R, closed under multiplication, such that 1 in S, and 0 not in S, the localization of R ...

The Lorenz curve is used in economics and ecology to describe inequality in wealth or size. The Lorenz curve is a function of the cumulative proportion of ordered individuals ...

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 ...

A k-matching in a graph G is a set of k edges, no two of which have a vertex in common (i.e., an independent edge set of size k). Let Phi_k be the number of k-matchings of ...

The (upper) matching number nu(G) of graph G, sometimes known as the edge independence number, is the size of a maximum independent edge set. Equivalently, it is the degree ...

Draw three circles in the plane, none of which lies completely inside another, and the common external tangent lines for each pair. Then points of intersection of the three ...

A direct search method of optimization that works moderately well for stochastic problems. It is based on evaluating a function at the vertices of a simplex, then iteratively ...