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A set of class representatives is a subset of X which contains exactly one element from each equivalence class.

A complex fraction is a fraction in which numerator, denominator, or both are themselves fractions, for example (2/3)/(4/5).

A constant, sometimes also called a "mathematical constant," is any well-defined real number which is significantly interesting in some way. In this work, the term "constant" ...

R_m(x,y) = (J_m^'(x)Y_m^'(y)-J_m^'(y)Y_m^'(x))/(J_m(x)Y_m^'(y)-J_m^'(y)Y_m(x)) (1) S_m(x,y) = (J_m^'(x)Y_m(y)-J_m(y)Y_m^'(x))/(J_m(x)Y_m(y)-J_m(y)Y_m(x)). (2)

A dynamical system in which the phase space volume contracts along a trajectory. This means that the generalized divergence is less than zero, (partialf_i)/(partialx_i)<0, ...

Given a differential operator D on the space of differential forms, an eigenform is a form alpha such that Dalpha=lambdaalpha (1) for some constant lambda. For example, on ...

An array of "trees" of unit height located at integer-coordinate points in a point lattice. When viewed from a corner along the line y=x in normal perspective, a quadrant of ...

Due to Euler's prolific output, there are a great number of theorems that are know by the name "Euler's theorem." A sampling of these are Euler's displacement theorem for ...

The ring of fractions of an integral domain. The field of fractions of the ring of integers Z is the rational field Q, and the field of fractions of the polynomial ring ...

An algebraic equation is algebraically solvable iff its group is solvable. In order that an irreducible equation of prime degree be solvable by radicals, it is necessary and ...