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The term "loop" has a number of meanings in mathematics. Most simply, a loop is a closed curve whose initial and final points coincide in a fixed point p known as the ...

Roughly speaking, a tangent vector is an infinitesimal displacement at a specific point on a manifold. The set of tangent vectors at a point P forms a vector space called the ...

The map-Airy distribution is a statistical distribution having probability density function and distribution function P(x) = 2e^(-2x^3/3)[xAi(x^2)-Ai^'(x^2)] (1) D(x) = (2) ...

A general formula giving the number of distinct ways of folding an m×n rectangular map is not known. A distinct folding is defined as a permutation of N=m×n numbered cells ...

A projection which maps a sphere (or spheroid) onto a plane. Map projections are generally classified into groups according to common properties (cylindrical vs. conical, ...

The winding number W(theta) of a map f(theta) with initial value theta is defined by W(theta)=lim_(n->infty)(f^n(theta)-theta)/n, which represents the average increase in the ...

The Mercator projection is a map projection that was widely used for navigation since loxodromes are straight lines (although great circles are curved). The following ...

A map projection given by the following transformation, x = lambda-lambda_0 (1) y = 5/4ln[tan(1/4pi+2/5phi)] (2) = 5/4sinh^(-1)[tan(4/5phi)]. (3) Here, x and y are the plane ...

The Mollweide projection is a map projection also called the elliptical projection or homolographic equal-area projection. The forward transformation is x = ...

For the rational curve of an unperturbed system with rotation number r/s under a map T (for which every point is a fixed point of T^s), only an even number of fixed points ...