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The voter model is a simple mathematical model of opinion formation in which voters are located at the nodes of a network, each voter has an opinion (in the simplest case, 0 ...

The matrix product of a square set of data d and a matrix of basis vectors consisting of Walsh functions. By taking advantage of the nested structure of the natural ordering ...

For a given point lattice, some number of points will be within distance d of the origin. A Waterman polyhedron is the convex hull of these points. A progression of Waterman ...

If y has period 2pi, y^' is L^2, and int_0^(2pi)ydx=0, (1) then int_0^(2pi)y^2dx<int_0^(2pi)y^('2)dx (2) unless y=Acosx+Bsinx (3) (Hardy et al. 1988). Another inequality ...

A field K is said to be an extension field (or field extension, or extension), denoted K/F, of a field F if F is a subfield of K. For example, the complex numbers are an ...

There are a number of mathematical curves that produced heart shapes, some of which are illustrated above. A "zeroth" curve is a rotated cardioid (whose name means ...

An unsolved problem in mathematics attributed to Lehmer (1933) that concerns the minimum Mahler measure M_1(P) for a univariate polynomial P(x) that is not a product of ...

A group or other algebraic object is said to be Abelian (sometimes written in lower case, i.e., "abelian") if the law of commutativity always holds. The term is named after ...

The nonconservation of adiabatic invariants which arises in systems with three or more degrees of freedom.

Three elements x, y and z of a set S are said to be associative under a binary operation * if they satisfy x*(y*z)=(x*y)*z. (1) Real numbers are associative under addition ...