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A repeated integral is an integral taken multiple times over a single variable (as distinguished from a multiple integral, which consists of a number of integrals taken with ...

In the directed graph above, pick any vertex and follow the arrows in sequence blue-red-red three times. You will finish at the green vertex. Similarly, follow the sequence ...

For a set of n numbers or values of a discrete distribution x_i, ..., x_n, the root-mean-square (abbreviated "RMS" and sometimes called the quadratic mean), is the square ...

A row-convex polyomino is a self-avoiding convex polyomino such that the intersection of any horizontal line with the polyomino has at most two connected components. A ...

A Saunders graphic is a plot of the dth base-b digits of a function f(x,y) as a function of x and y. The plots above show Saunders graphics for the functions ...

The semigroup algebra K[S], where K is a field and S a semigroup, is formally defined in the same way as the group algebra K[G]. Similarly, a semigroup ring R[S] is a ...

Take the Helmholtz differential equation del ^2F+k^2F=0 (1) in spherical coordinates. This is just Laplace's equation in spherical coordinates with an additional term, (2) ...

A standard basis, also called a natural basis, is a special orthonormal vector basis in which each basis vector has a single nonzero entry with value 1. In n-dimensional ...

For two random variates X and Y, the correlation is defined bY cor(X,Y)=(cov(X,Y))/(sigma_Xsigma_Y), (1) where sigma_X denotes standard deviation and cov(X,Y) is the ...

The superellipsoid is a generalization of the ellipsoid by allowing different exponents of the variables in the algebraic representation. It is similarly a generalization of ...