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Given the sum-of-factorials function Sigma(n)=sum_(k=1)^nk!, SW(p) is the smallest integer for p prime such that Sigma[SW(p)] is divisible by p. If pSigma(n) for all n<p, ...

A correction to a discrete binomial distribution to approximate a continuous distribution. P(a<=X<=b) approx P((a-1/2-np)/(sqrt(np(1-p)))<=z<=(b+1/2-np)/(sqrt(np(1-p)))), ...

A two-dimensional planar closed surface L which has a mass M and a surface density sigma(x,y) (in units of mass per areas squared) such that M=int_Lsigma(x,y)dxdy. The center ...

P_y(nu)=lim_(T->infty)2/T|int_(-T/2)^(T/2)[y(t)-y^_]e^(-2piinut)dt|^2, (1) so int_0^inftyP_y(nu)dnu = lim_(T->infty)1/Tint_(-T/2)^(T/2)[y(t)-y^_]^2dt (2) = <(y-y^_)^2> (3) = ...

Defined for samples x_i, i=1, ..., N by alpha_r=1/Nsum_(i=1)^Nz_i^r=(mu_r)/(sigma^r), (1) where z_i=(x_i-x^_)/(s_x). (2) The first few are alpha_1 = 0 (3) alpha_2 = 1 (4) ...

The Gibbs phenomenon is an overshoot (or "ringing") of Fourier series and other eigenfunction series occurring at simple discontinuities. It can be reduced with the Lanczos ...

Let E be a Euclidean space, (beta,alpha) be the dot product, and denote the reflection in the hyperplane P_alpha={beta in E|(beta,alpha)=0} by ...

Relations in the definition of a Steenrod algebra which state that, for i<2j, Sq^i degreesSq^j(x)=sum_(k=0)^(|_i/2_|)(j-k-1; i-2k)Sq^(i+j-k) degreesSq^k(x), where f degreesg ...

The infinitesimal algebraic object associated with a Lie groupoid. A Lie algebroid over a manifold B is a vector bundle A over B with a Lie algebra structure [,] (Lie ...

In an exterior algebra ^ V, a top-dimensional form has degree n where n=dimV. Any form of higher degree must be zero. For example, if V=R^4 then alpha=e_1 ^ e_2 ^ e_3 ^ e_4 ...