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Summation by parts for discrete variables is the equivalent of integration by parts for continuous variables Delta^(-1)[v(x)Deltau(x)]=u(x)v(x)-Delta^(-1)[Eu(x)Deltav(x)], ...

A topological groupoid over B is a groupoid G such that B and G are topological spaces and alpha,beta, and multiplication are continuous maps. Here, alpha and beta are maps ...

A topological partial algebra is a pair (A,tau), where A=(A,(f_i^A)_(i in I)) is a partial algebra and each of the operations f_i^A is continuous in the product topology. ...

The probability law on the space of continuous functions g with g(0)=0, induced by the Wiener process.

Let f(x) be a real continuous monotonic strictly increasing function on the interval [0,a] with f(0)=0 and b<=f(a), then ab<=int_0^af(x)dx+int_0^bf^(-1)(y)dy, where f^(-1)(y) ...

If f is a function on an open set U, then the zero set of f is the set Z={z in U:f(z)=0}. A subset of a topological space X is called a zero set if it is equal to f^(-1)(0) ...

Differential Geometry

A general type of statistical distribution which is related to the gamma distribution. Beta distributions have two free parameters, which are labeled according to one of two ...

The Cantor function F(x) is the continuous but not absolutely continuous function on [0,1] which may be defined as follows. First, express x in ternary. If the resulting ...

A category consists of three things: a collection of objects, for each pair of objects a collection of morphisms (sometimes call "arrows") from one to another, and a binary ...