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The field of all rational and irrational numbers is called the real numbers, or simply the "reals," and denoted R. The set of real numbers is also called the continuum, ...

A hypergeometric class of orthogonal polynomials defined by R_n(lambda(x);alpha,beta,gamma,delta) =_4F_3(-n,n+alpha+beta+1,-x,x+gamma+delta+1; alpha+1,beta+delta+1,gamma+1;1) ...

Let E be a linear space over a field K. Then the vector space tensor product tensor _(lambda=1)^(k)E is called a tensor space of degree k. More specifically, a tensor space ...

Liouville's constant, sometimes also called Liouville's number, is the real number defined by L=sum_(n=1)^infty10^(-n!)=0.110001000000000000000001... (OEIS A012245). ...

A codimension one foliation F of a 3-manifold M is said to be taut if for every leaf lambda in the leaf space L of F, there is a circle gamma_lambda transverse to F (i.e., a ...

The field of semidefinite programming (SDP) or semidefinite optimization (SDO) deals with optimization problems over symmetric positive semidefinite matrix variables with ...

A copositive matrix is a real n×n square matrix A=(a_(ij)) that makes the corresponding quadratic form f(x)=x^(T)Ax nonnegative for all nonnegative n-vectors x. Copositive ...

There are certain optimization problems that become unmanageable using combinatorial methods as the number of objects becomes large. A typical example is the traveling ...

Mathematics is a broad-ranging field of study in which the properties and interactions of idealized objects are examined. Whereas mathematics began merely as a calculational ...

In the field of percolation theory, the term percolation threshold is used to denote the probability which "marks the arrival" (Grimmett 1999) of an infinite connected ...