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Rule 30 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

An ordinary differential equation of the form y^('')+P(x)y^'+Q(x)y=0. (1) Such an equation has singularities for finite x=x_0 under the following conditions: (a) If either ...

Let b(k) be the number of 1s in the binary expression of k, i.e., the binary digit count of 1, giving 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, ... (OEIS A000120) for k=1, 2, .... ...

Synthetic division is a shortcut method for dividing two polynomials which can be used in place of the standard long division algorithm. This method reduces the dividend and ...

The Taniyama-Shimura conjecture, since its proof now sometimes known as the modularity theorem, is very general and important conjecture (and now theorem) connecting topology ...

The torus grid graph T_(m,n) is the graph formed from the graph Cartesian product C_m square C_n of the cycle graphs C_m and C_n. C_m square C_n is isomorphic to C_n square ...

Consider the average length of a line segment determined by two points picked at random in the interior of an arbitrary triangle Delta(a,b,c) with side lengths a, b, and c. ...

A Turán graph, sometimes called a maximally saturated graph (Zykov 1952, Chao and Novacky 1982), with positive integer parameters n and k is a type of extremal graph on n ...

A Turing machine is a theoretical computing machine invented by Alan Turing (1937) to serve as an idealized model for mathematical calculation. A Turing machine consists of a ...

A uniquely k-colorable graph G is a chi-colorable graph such that every chi-coloring gives the same partition of G (Chao 2001). Examples of uniquely minimal colorable classes ...