Search Results for ""

The Cartesian product of two sets A and B (also called the product set, set direct product, or cross product) is defined to be the set of all points (a,b) where a in A and b ...

If f(z) is analytic in some simply connected region R, then ∮_gammaf(z)dz=0 (1) for any closed contour gamma completely contained in R. Writing z as z=x+iy (2) and f(z) as ...

A moment mu_n of a univariate probability density function P(x) taken about the mean mu=mu_1^', mu_n = <(x-<x>)^n> (1) = int(x-mu)^nP(x)dx, (2) where <X> denotes the ...

Given a subset A of a larger set, the characteristic function chi_A, sometimes also called the indicator function, is the function defined to be identically one on A, and is ...

Chebyshev-Gauss quadrature, also called Chebyshev quadrature, is a Gaussian quadrature over the interval [-1,1] with weighting function W(x)=(1-x^2)^(-1/2) (Abramowitz and ...

The metric properties discovered for a primitive figure remain applicable, without modifications other than changes of signs, to all correlative figures which can be ...

A contravariant tensor is a tensor having specific transformation properties (cf., a covariant tensor). To examine the transformation properties of a contravariant tensor, ...

Covariance provides a measure of the strength of the correlation between two or more sets of random variates. The covariance for two random variates X and Y, each with sample ...

A covariant tensor, denoted with a lowered index (e.g., a_mu) is a tensor having specific transformation properties. In general, these transformation properties differ from ...

Differential geometry is the study of Riemannian manifolds. Differential geometry deals with metrical notions on manifolds, while differential topology deals with nonmetrical ...