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The h-statistic h_r is the unique symmetric unbiased estimator for a central moment of a distribution <h_r>=mu_r. (1) In addition, the variance var(h_r)=<(h_r-mu_r)^2> (2) is ...

The base-4 method of counting in which only the digits 0, 1, 2, and 3 are used. The illustration above shows the numbers 0 to 63 represented in quaternary, and the following ...

The contraction of a tensor is obtained by setting unlike indices equal and summing according to the Einstein summation convention. Contraction reduces the tensor rank by 2. ...

The double sphere is the degenerate quartic surface (x^2+y^2+z^2-r^2)^2=0 obtained by squaring the left-hand side of the equation of a usual sphere x^2+y^2+z^2-r^2=0.

The Scarabaeus curve is a sextic curve given by the equation (x^2+y^2)(x^2+y^2+ax)^2-b^2(x^2-y^2)^2=0 and by the polar equation r=bcos(2theta)-acostheta where a,b!=0.

p^x is an infinitary divisor of p^y (with y>0) if p^x|_(y-1)p^y, where d|_kn denotes a k-ary Divisor (Guy 1994, p. 54). Infinitary divisors therefore generalize the concept ...

If f(x) is an odd function, then a_n=0 and the Fourier series collapses to f(x)=sum_(n=1)^inftyb_nsin(nx), (1) where b_n = 1/piint_(-pi)^pif(x)sin(nx)dx (2) = ...

A related rates problem is the determination of the rate at which a function defined in terms of other functions changes. Related rates problems can be solved by computing ...

A shuffle-exchange graph is a nonsimple graph (due to the existence of graph loops) whose vertices are length n binary strings with an edge from w to w^' if 1. w^' differs ...

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 ...