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The full width at half maximum (FWHM) is a parameter commonly used to describe the width of a "bump" on a curve or function. It is given by the distance between points on the ...

A functional is a real-valued function on a vector space V, usually of functions. For example, the energy functional on the unit disk D assigns a number to any differentiable ...

Functional analysis is a branch of mathematics concerned with infinite-dimensional vector spaces (mainly function spaces) and mappings between them. The spaces may be of ...

An equation of the form f(x,y,...)=0, where f contains a finite number of independent variables, known functions, and unknown functions which are to be solved for. Many ...

An integer d is a fundamental discriminant if it is not equal to 1, not divisible by any square of any odd prime, and satisfies d=1 (mod 4) or d=8,12 (mod 16). The function ...

Let G be a subgroup of the modular group Gamma. Then an open subset R_G of the upper half-plane H is called a fundamental region of G if 1. No two distinct points of R_G are ...

Every polynomial equation having complex coefficients and degree >=1 has at least one complex root. This theorem was first proven by Gauss. It is equivalent to the statement ...

Let F_0 and F_1 denote two directly similar figures in the plane, where P_1 in F_1 corresponds to P_0 in F_0 under the given similarity. Let r in (0,1), and define ...

For a Galois extension field K of a field F, the fundamental theorem of Galois theory states that the subgroups of the Galois group G=Gal(K/F) correspond with the subfields ...

Consider h_+(d) proper equivalence classes of forms with discriminant d equal to the field discriminant, then they can be subdivided equally into 2^(r-1) genera of ...