Search Results for ""

A function f is Fréchet differentiable at a if lim_(x->a)(f(x)-f(a))/(x-a) exists. This is equivalent to the statement that phi has a removable discontinuity at a, where ...

A group action G×X->X is called free if, for all x in X, gx=x implies g=I (i.e., only the identity element fixes any x). In other words, G×X->X is free if the map G×X->X×X ...

Also known as the Serret-Frenet formulas, these vector differential equations relate inherent properties of a parametrized curve. In matrix form, they can be written [T^.; ...

Let a^p+b^p=c^p be a solution to Fermat's last theorem. Then the corresponding Frey curve is y^2=x(x-a^p)(x+b^p). (1) Ribet (1990a) showed that such curves cannot be modular, ...

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 ...

Goldberg polyhedra are convex polyhedra first described by Goldberg (1937) and classified in more detail by Hart (2013) for which each face is a regular pentagon or regular ...

If A is a graded module and there exists a degree-preserving linear map phi:A tensor A->A, then (A,phi) is called a graded algebra. Cohomology is a graded algebra. In ...

In Season 4 episode "Black Swan" of the television crime drama NUMB3RS, the character Amita Ramanujan refers to graph entropies when studying a map of the Los Angeles while ...

The inhomogeneous Helmholtz differential equation is del ^2psi(r)+k^2psi(r)=rho(r), (1) where the Helmholtz operator is defined as L^~=del ^2+k^2. The Green's function is ...

Gregory's formula is a formula that allows a definite integral of a function to be expressed by its sum and differences, or its sum by its integral and difference (Jordan ...