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A theorem, also known as Bachet's conjecture, which Bachet inferred from a lack of a necessary condition being stated by Diophantus. It states that every positive integer can ...

Laguerre-Gauss quadrature, also called Gauss-Laguerre quadrature or Laguerre quadrature, is a Gaussian quadrature over the interval [0,infty) with weighting function ...

An algebra <L; ^ , v > is called a lattice if L is a nonempty set, ^ and v are binary operations on L, both ^ and v are idempotent, commutative, and associative, and they ...

Given a square complex or real matrix A, a matrix norm ||A|| is a nonnegative number associated with A having the properties 1. ||A||>0 when A!=0 and ||A||=0 iff A=0, 2. ...

Modular arithmetic is the arithmetic of congruences, sometimes known informally as "clock arithmetic." In modular arithmetic, numbers "wrap around" upon reaching a given ...

Newton's method for finding roots of a complex polynomial f entails iterating the function z-[f(z)/f^'(z)], which can be viewed as applying the Euler backward method with ...

An error which is superimposed on top of a true signal. Noise may be random or systematic. Noise can be greatly reduced by transmitting signals digitally instead of in analog ...

Informally, a function f is a one-way function if 1. The description of f is publicly known and does not require any secret information for its operation. 2. Given x, it is ...

Hadamard matrices H_n can be constructed using finite field GF(p^m) when p=4l-1 and m is odd. Pick a representation r relatively prime to p. Then by coloring white ...

A system of equation types obtained by generalizing the differential equation for the normal distribution (dy)/(dx)=(y(m-x))/a, (1) which has solution y=Ce^((2m-x)x/(2a)), ...