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If p_1, ..., p_n are positive numbers which sum to 1 and f is a real continuous function that is convex, then f(sum_(i=1)^np_ix_i)<=sum_(i=1)^np_if(x_i). (1) If f is concave, ...

The group Gamma of all Möbius transformations of the form tau^'=(atau+b)/(ctau+d), (1) where a, b, c, and d are integers with ad-bc=1. The group can be represented by the 2×2 ...

The q-analog of integration is given by int_0^1f(x)d(q,x)=(1-q)sum_(i=0)^inftyf(q^i)q^i, (1) which reduces to int_0^1f(x)dx (2) in the case q->1^- (Andrews 1986 p. 10). ...

A barrel solid of revolution composed of parallel circular top and bottom with a common axis and a side formed by a smooth curve symmetrical about the midplane. The term also ...

A busy beaver is an n-state, 2-color Turing machine which writes a maximum number Sigma(n) of 1s before halting (Rado 1962; Lin and Rado 1965; Shallit 1998). Alternatively, ...

The Greenfield graph is the name given in this work to the 12-vertex graph illustrated above due to Greenfield (2011). This graph provided the first known example which ...

The Meringer graph is one of the four (5,5)-cage graphs, discovered by Meringer (1999) after it had long been thought that only three such cages existed. Like the other ...

The (n+1)×(n+1) tridiagonal matrix (also called the Clement matrix) defined by S_n=[0 n 0 0 ... 0; 1 0 n-1 0 ... 0; 0 2 0 n-2 ... 0; | | ... ... ... |; 0 0 0 n-1 0 1; 0 0 0 0 ...

There are at least two definitions of hypercomplex numbers. Clifford algebraists call their higher dimensional numbers hypercomplex, even though they do not share all the ...

In general, it is possible to link two n-dimensional hyperspheres in (n+2)-dimensional space in an infinite number of inequivalent ways. In dimensions greater than n+2 in the ...