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Let U(P,Q) and V(P,Q) be Lucas sequences generated by P and Q, and define D=P^2-4Q. (1) Let n be an odd composite number with (n,D)=1, and n-(D/n)=2^sd with d odd and s>=0, ...

A weighted adjacency matrix A_f of a simple graph is defined for a real positive symmetric function f(d_i,d_j) on the vertex degrees d_i of a graph as ...

The following conditions are equivalent for a conservative vector field on a particular domain D: 1. For any oriented simple closed curve C, the line integral ∮_CF·ds=0. 2. ...

A coordinate system composed of intersecting surfaces. If the intersections are all at right angles, then the curvilinear coordinates are said to form an orthogonal ...

The ding-dong surface is the cubic surface of revolution given by the equation x^2+y^2=(1-z)z^2 (1) (Hauser 2003) that is closely related to the kiss surface. The surface can ...

A matrix with 0 determinant whose determinant becomes nonzero when any element on or below the diagonal is changed from 0 to 1. An example is M=[1 -1 0 0; 0 0 -1 0; 1 1 1 -1; ...

A normalized form of the cumulative normal distribution function giving the probability that a variate assumes a value in the range [0,x], ...

Given two normal subgroups G_1 and G_2 of a group, and two normal subgroups H_1 and H_2 of G_1 and G_2 respectively, H_1(G_1 intersection H_2) is normal in H_1(G_1 ...

Let Delta denote an integral convex polytope of dimension n in a lattice M, and let l_Delta(k) denote the number of lattice points in Delta dilated by a factor of the integer ...

A set X whose elements can be numbered through from 1 to n, for some positive integer n. The number n is called the cardinal number of the set, and is often denoted |X| or ...