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The ordered pair (s,t), where s is the number of real embeddings of the number field and t is the number of complex-conjugate pairs of embeddings. The degree of the number ...

A subset S of a topological space X is compact if for every open cover of S there exists a finite subcover of S.

Doob (1996) defines a stochastic process as a family of random variables {x(t,-),t in J} from some probability space (S,S,P) into a state space (S^',S^'). Here, J is the ...

Let Omega be a bounded open set in R^d whose boundary partialOmega is at least C^1 smooth and let T:C_c^1(Omega^_)->L^p(partialOmega) (1) be a linear operator defined by ...

A random matrix is a matrix of given type and size whose entries consist of random numbers from some specified distribution. Random matrix theory is cited as one of the ...

The generalized law of sines applies to a simplex in space of any dimension with constant Gaussian curvature. Let us work up to that. Initially in two-dimensional space, we ...

A nonnegative matrix is a real or integer matrix (a)_(ij) for which each matrix element is a nonnegative number, i.e., a_(ij)>=0 for all i, j. Nonnegative matrices are ...

In Minkowski space, a twistor may be defined as a pair consisting of a spinor field and a complex conjugate spinor field satisfying the twistor equation.

Consider any star of n line segments through one point in space such that no three lines are coplanar. Then there exists a polyhedron, known as a zonohedron, whose faces ...

Sylvester's line problem, known as the Sylvester-Gallai theorem in proved form, states that it is not possible to arrange a finite number of points so that a line through ...