Search Results for ""

The following conditions are equivalent for a conservative vector field on a particular domain D: 1. For any oriented simple closed curve C, the line integral ∮_CF·ds=0. 2. ...

Let alpha(G) denote the independence number of a graph G. Then the Shannon capacity Theta(G), sometimes also denoted c(G), of G is defined as ...

A transformation which is one-to-one and a surjection (i.e., "onto").

The integral transform defined by (Kphi)(x)=int_0^infty(x^2-t^2)_+^(lambda/2)P_nu^lambda(t/x)phi(t)dt, where y_+^alpha is the truncated power function and P_nu^lambda(x) is ...

A C^*-algebra is a Banach algebra with an antiautomorphic involution * which satisfies (x^*)^* = x (1) x^*y^* = (yx)^* (2) x^*+y^* = (x+y)^* (3) (cx)^* = c^_x^*, (4) where ...

A subset of a topological group which is closed as a subset and also a subgroup.

Given n sets of variates denoted {X_1}, ..., {X_n} , the first-order covariance matrix is defined by V_(ij)=cov(x_i,x_j)=<(x_i-mu_i)(x_j-mu_j)>, where mu_i is the mean. ...

The largest cube dividing a positive integer n. For n=1, 2, ..., the first few are 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, ... (OEIS A008834).

A robust nonparametric test which is an alternative to the paired t-test. This test makes the basic assumption that there is information only in the signs of the differences ...

A collection of equations satisfies the Hasse principle if, whenever one of the equations has solutions in R and all the Q_p, then the equations have solutions in the ...