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In order to integrate a function over a complicated domain D, Monte Carlo integration picks random points over some simple domain D^' which is a superset of D, checks whether ...

A multidimensional point process is a measurable function from a probability space (Omega,A,P) into (X,Sigma) where X is the set of all finite or countable subsets of R^d not ...

Rational numbers are countable, so an order can be placed on them just like the natural numbers. Although such an ordering is not obvious (nor unique), one such ordering can ...

If the coefficients of the polynomial d_nx^n+d_(n-1)x^(n-1)+...+d_0=0 (1) are specified to be integers, then rational roots must have a numerator which is a factor of d_0 and ...

A triangle cubic is a curve that can be expressed in trilinear coordinates such that the highest degree term in the trilinears alpha, beta, and gamma is of order three. Wells ...

A Tychonoff plank is a topological space that is an example of a normal space which has a non-normal subset, thus showing that normality is not a hereditary property. Let ...

Let L be a language of first-order predicate logic, let I be an indexing set, and for each i in I, let A_i be a structure of the language L. Let u be an ultrafilter in the ...

Let any finite or infinite set of points having no finite limit point be prescribed, and associate with each of its points a definite positive integer as its order. Then ...

The graph diameter of a graph is the length max_(u,v)d(u,v) of the "longest shortest path" (i.e., the longest graph geodesic) between any two graph vertices (u,v), where ...

The Shrikhande graph is a strongly regular graph on 16 nodes. It is cospectral with the rook graph L_(4,4), so neither of the two is determined by spectrum. The Shrikhande ...