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An antilinear operator A^~ satisfies the following two properties: A^~[f_1(x)+f_2(x)] = A^~f_1(x)+A^~f_2(x) (1) A^~cf(x) = c^_A^~f(x), (2) where c^_ is the complex conjugate ...

A formal mathematical theory which introduces "components at infinity" by defining a new type of divisor class group of integers of a number field. The divisor class group is ...

The area element for a surface with first fundamental form ds^2=Edu^2+2Fdudv+Gdv^2 is dA=sqrt(EG-F^2)du ^ dv, where du ^ dv is the wedge product.

Given a group action G×F->F and a principal bundle pi:A->M, the associated fiber bundle on M is pi^~:A×F/G->M. (1) In particular, it is the quotient space A×F/G where ...

Let P be the set of primes, and let Q_p and Z_p(t) be the fields of p-adic numbers and formal power series over Z_p=(0,1,...,p-1). Further, suppose that D is a "nonprincipal ...

Let the characteristic polynomial of an n×n complex matrix A be written in the form P(lambda) = |lambdaI-A| (1) = ...

There are several different definitions of the barbell graph. Most commonly and in this work, the n-barbell graph is the simple graph obtained by connecting two copies of a ...

A collection B of subsets of a set X forming a topological basis.

One baud is defined as the state of a signal in a communication channel changing once per second.

The orthogonal polynomials on the interval [-1,1] associated with the weighting functions w(x) = (1-x^2)^(-1/2) (1) w(x) = (1-x^2)^(1/2) (2) w(x) = sqrt((1-x)/(1+x)), (3) ...