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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 ...

A prime p is called a Wolstenholme prime if the central binomial coefficient (2p; p)=2 (mod p^4), (1) or equivalently if B_(p-3)=0 (mod p), (2) where B_n is the nth Bernoulli ...

Let f be a real-valued, continuous, and strictly increasing function on [0,c] with c>0. If f(0)=0, a in [0,c], and b in [0,f(c)], then int_0^af(x)dx+int_0^bf^(-1)(x)dx>=ab, ...

Trigonometry

de Rham cohomology is a formal set-up for the analytic problem: If you have a differential k-form omega on a manifold M, is it the exterior derivative of another differential ...

The first de Villiers point is the perspector of the reference triangle and its BCI triangle, which is Kimberling center X_(1127) and has triangle center function ...

A Hamiltonian cycle, also called a Hamiltonian circuit, Hamilton cycle, or Hamilton circuit, is a graph cycle (i.e., closed loop) through a graph that visits each node ...

A (0,1)-matrix is an integer matrix in which each element is a 0 or 1. It is also called a logical matrix, binary matrix, relation matrix, or Boolean matrix. The number of ...

There are four completely different definitions of the so-called Apollonius circles: 1. The set of all points whose distances from two fixed points are in a constant ratio ...

A Boolean algebra is a mathematical structure that is similar to a Boolean ring, but that is defined using the meet and join operators instead of the usual addition and ...