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Continuum percolation can be thought of as a continuous, uncountable version of percolation theory-a theory which, in its most studied form, takes place on a discrete, ...

The Jacobi theta functions are the elliptic analogs of the exponential function, and may be used to express the Jacobi elliptic functions. The theta functions are ...

The partial differential equation u_(xy)+(alphau_x-betau_y)/(x-y)=0.

J_m(x)=(x^m)/(2^(m-1)sqrt(pi)Gamma(m+1/2))int_0^1cos(xt)(1-t^2)^(m-1/2)dt, where J_m(x) is a Bessel function of the first kind and Gamma(z) is the gamma function. Hankel's ...

The function K(alpha,t) in an integral or integral transform g(alpha)=int_a^bf(t)K(alpha,t)dt. Whittaker and Robinson (1967, p. 376) use the term nucleus for kernel.

The commutation operation [a,b]=ab-ba corresponding to the Lie product.

The partial differential equation u_(xt)=sinhu, which contains u_(xt) instead of u_(xx)-u_(tt) and sinhu instead to sinu, as in the sine-Gordon equation (Grauel 1985; ...

In statistics, a trial is a single performance of well-defined experiment (Papoulis 1984, p. 25), such as the flipping of a coin, the generation of a random number, the ...

The problem of finding the connection between a continuous function f on the boundary partialR of a region R with a harmonic function taking on the value f on partialR. In ...

A second-order partial differential equation, i.e., one of the form Au_(xx)+2Bu_(xy)+Cu_(yy)+Du_x+Eu_y+F=0, (1) is called elliptic if the matrix Z=[A B; B C] (2) is positive ...