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The ratio of the independence number of a graph G to its vertex count is known as the independence ratio of G (Bollobás 1981). The product of the chromatic number and ...

A ring that is commutative under multiplication, has a multiplicative identity element, and has no divisors of 0. The integers form an integral domain.

The infinitesimal algebraic object associated with a Lie groupoid. A Lie algebroid over a manifold B is a vector bundle A over B with a Lie algebra structure [,] (Lie ...

A function f is said to have a lower bound c if c<=f(x) for all x in its domain. The greatest lower bound is called the infimum.

Given a marked point process Phi of the form Phi=(T,Y)=((T_n)_(n>=1),(Y_n)_(n>=1)), the space Y=(Y_n)_(n>=1) is said to be the mark space of Phi.

A geometry in which Archimedes' axiom does not hold.

An algebra in which the associator (x,x,x)=0. The subalgebra generated by one element is associative.

A scalar which reverses sign under inversion is called a pseudoscalar. For example, the scalar triple product A·(BxC) is a pseudoscalar since A·(BxC)=-[-A·((-B)x(-C))].

"The rationals" refers to the set of rational numbers and is commonly denoted Q.

Let P be a prime ideal in D_m not containing m. Then (Phi(P))=P^(sumtsigma_t^(-1)), where the sum is over all 1<=t<m which are relatively prime to m. Here D_m is the ring of ...