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A connection on a vector bundle pi:E->M is a way to "differentiate" bundle sections, in a way that is analogous to the exterior derivative df of a function f. In particular, ...

A doubly periodic function with periods 2omega_1 and 2omega_2 such that f(z+2omega_1)=f(z+2omega_2)=f(z), (1) which is analytic and has no singularities except for poles in ...

The number 10 (ten) is the basis for the decimal system of notation. In this system, each "decimal place" consists of a digit 0-9 arranged such that each digit is multiplied ...

In algebra, a period is a number that can be written an integral of an algebraic function over an algebraic domain. More specifically, a period is a real number ...

A band over a fixed topological space X is represented by a cover X= union U_alpha, U_alpha subset= X, and for each alpha, a sheaf of groups K_alpha on U_alpha along with ...

The squared norm of a four-vector a=(a_0,a_1,a_2,a_3)=a_0+a is given by the dot product a^2=a_mua^mu=(a^0)^2-a·a, (1) where a·a is the usual vector dot product in Euclidean ...

Given a curve C and O=(x_0,y_0) a fixed point called the pedal point, then for a point P on C, draw a line perpendicular to OP. The envelope of these lines as P describes the ...

One of the symbols ( or ) used to denote grouping. Parentheses have a great many specialized meanings in mathematics. A few of these are described below. 1. Parentheses are ...

"The" trifolium is the three-lobed folium with b=a, i.e., the 3-petalled rose curve. It is also known as the paquerette de mélibée (Apéry 1987, p. 85), with paquerette being ...

An antisymmetric matrix, also known as a skew-symmetric or antimetric matrix, is a square matrix that satisfies the identity A=-A^(T) (1) where A^(T) is the matrix transpose. ...