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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 ...

Involving two variables, as opposed to many (multivariate), or one (univariate).

A function that joins univariate distribution functions to form multivariate distribution functions. A two-dimensional copula is a function C:I^2->I such that C(0,t)=C(t,0)=0 ...

Let H be a two-dimensional distribution function with marginal distribution functions F and G. Then there exists a copula C such that H(x,y)=C(F(x),G(y)). Conversely, for any ...

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 ...

A temporal point process is a random process whose realizations consist of the times {tau_j}_(j in J) of isolated events. Note that in some literature, the values tau_j are ...