Search Results for ""

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♯. Then A is a left Hilbert algebra if A has an inner product <·,·> satisfying: 1. ...

A group theoretic operation which is useful in the study of complex atomic spectra. A plethysm takes a set of functions of a given symmetry type {mu} and forms from them ...

Generalizes the secant method of root finding by using quadratic 3-point interpolation q=(x_n-x_(n-1))/(x_(n-1)-x_(n-2)). (1) Then define A = ...

In general, there is no unique matrix solution A to the matrix equation y=Ax. Even in the case of y parallel to x, there are still multiple matrices that perform this ...

A real number that is b-normal for every base 2, 3, 4, ... is said to be absolutely normal. As proved by Borel (1922, p. 198), almost all real numbers in [0,1) are absolutely ...

The fundamental theorem of arithmetic states that every positive integer (except the number 1) can be represented in exactly one way apart from rearrangement as a product of ...

A necessary and sufficient condition for a sequence S_i to converge. The Cauchy criterion is satisfied when, for all epsilon>0, there is a fixed number N such that ...

A Lehmer number is a number generated by a generalization of a Lucas sequence. Let alpha and beta be complex numbers with alpha+beta = sqrt(R) (1) alphabeta = Q, (2) where Q ...

Petersson considered the absolutely converging Dirichlet L-series phi(s)=product_(p)1/(1-c(p)p^(-s)+p^(2k-1)p^(-2s)). (1) Writing the denominator as ...

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♭. Then A is a right Hilbert algebra if A has an inner product <·,·> satisfying: 1. ...