Search Results for ""

Let f be analytic on the unit disk, and assume that 1. |f(z)|<=1 for all z and 2. f(0)=0. Then |f(z)|<=|z| and |f^'(0)|<=1. If either |f(z)|=|z| for some z!=0 or if ...

The set St^_v-Stv, where St^_v is a closed star and Stv is a star, is called the link of v in a simplicial complex K and is denoted Lkv (Munkres 1993, p. 11).

Let K be a T2-topological space and let F be the space of all bounded complex-valued continuous functions defined on K. The supremum norm is the norm defined on F by ...

The reciprocal of the arithmetic-geometric mean of 1 and sqrt(2), G = 2/piint_0^11/(sqrt(1-x^4))dx (1) = 2/piint_0^(pi/2)(dtheta)/(sqrt(1+sin^2theta)) (2) = L/pi (3) = ...

A CW-complex is a homotopy-theoretic generalization of the notion of a simplicial complex. A CW-complex is any space X which can be built by starting off with a discrete ...

The division of two complex numbers can be accomplished by multiplying the numerator and denominator by the complex conjugate of the denominator, for example, with z_1=a+bi ...

A measure which takes values in the complex numbers. The set of complex measures on a measure space X forms a vector space. Note that this is not the case for the more common ...

Two complex numbers x=a+ib and y=c+id are multiplied as follows: xy = (a+ib)(c+id) (1) = ac+ibc+iad-bd (2) = (ac-bd)+i(ad+bc). (3) In component form, ...

Conjugation is the process of taking a complex conjugate of a complex number, complex matrix, etc., or of performing a conjugation move on a knot. Conjugation also has a ...

The operator partial^_ is defined on a complex manifold, and is called the 'del bar operator.' The exterior derivative d takes a function and yields a one-form. It decomposes ...