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There are several types of integrals which go under the name of a "Dirichlet integral." The integral D[u]=int_Omega|del u|^2dV (1) appears in Dirichlet's principle. The ...

Using disk point picking, x = sqrt(r)costheta (1) y = sqrt(r)sintheta (2) for r in [0,1], theta in [0,2pi), choose two points at random in a unit disk and find the ...

The dot product can be defined for two vectors X and Y by X·Y=|X||Y|costheta, (1) where theta is the angle between the vectors and |X| is the norm. It follows immediately ...

The eban numbers are the sequence of numbers whose names (in English) do not contain the letter "e" (i.e., "e" is "banned"). The name was coined by N. J. A. Sloane around ...

A (p,q)-graph is edge-graceful if the edges can be labeled 1 through q in such a way that the labels induced on the vertices by summing over incident edges modulo p are ...

There are (at least) two graphs associated with Ellingham and Horton. These graphs on 54 and 78 nodes respectively, illustrated above, are examples of 3-connected bicubic ...

For an ellipse with parametric equations x = acost (1) y = bsint, (2) the negative pedal curve with respect to the origin has parametric equations x_n = ...

The Euler polynomial E_n(x) is given by the Appell sequence with g(t)=1/2(e^t+1), (1) giving the generating function (2e^(xt))/(e^t+1)=sum_(n=0)^inftyE_n(x)(t^n)/(n!). (2) ...

Euler's series transformation is a transformation that sometimes accelerates the rate of convergence for an alternating series. Given a convergent alternating series with sum ...

Given a Poisson distribution with rate of change lambda, the distribution of waiting times between successive changes (with k=0) is D(x) = P(X<=x) (1) = 1-P(X>x) (2) = ...