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The nth raw moment mu_n^' (i.e., moment about zero) of a distribution P(x) is defined by mu_n^'=<x^n>, (1) where <f(x)>={sumf(x)P(x) discrete distribution; intf(x)P(x)dx ...

In order to integrate a function over a complicated domain D, Monte Carlo integration picks random points over some simple domain D^' which is a superset of D, checks whether ...

Numerical differentiation is the process of finding the numerical value of a derivative of a given function at a given point. In general, numerical differentiation is more ...

An orthonormal set is a set of normalized orthogonal vectors or functions.

Let p={a_1,a_2,...,a_n} be a permutation. Then i is a permutation ascent if a_i<a_(i+1). For example, the permutation {1,2,3,4} is composed of three ascents, namely {1,2}, ...

The index of a permutation p is defined as the sum of all subscripts j such that p_j>p_(j+1), for 1<=j<=n. MacMahon (1960) proved that the number of permutations of size n ...

The 60 Pascal lines of a hexagon inscribed in a conic section intersect three at a time through 20 Steiner points. There is a dual relationship between the 15 Plücker lines ...

For a given signal, the power spectrum gives a plot of the portion of a signal's power (energy per unit time) falling within given frequency bins. The most common way of ...

A general set of methods for integrating ordinary differential equations. Predictor-corrector methods proceed by extrapolating a polynomial fit to the derivative from the ...

A principle that was first enunciated by Jakob Bernoulli which states that if we are ignorant of the ways an event can occur (and therefore have no reason to believe that one ...