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For |q|<1, the Rogers-Ramanujan identities are given by (Hardy 1999, pp. 13 and 90), sum_(n=0)^(infty)(q^(n^2))/((q)_n) = 1/(product_(n=1)^(infty)(1-q^(5n-4))(1-q^(5n-1))) ...

Given an arrangement of points, a line containing just two of them is called an ordinary line. Dirac (1951) conjectured that every sufficiently set of n noncollinear points ...

Codimension is a term used in a number of algebraic and geometric contexts to indicate the difference between the dimension of certain objects and the dimension of a smaller ...

The following conditions are equivalent for a conservative vector field on a particular domain D: 1. For any oriented simple closed curve C, the line integral ∮_CF·ds=0. 2. ...

On a measure space X, the set of square integrable L2-functions is an L^2-space. Taken together with the L2-inner product with respect to a measure mu, <f,g>=int_Xfgdmu (1) ...

Let T be a linear operator on a separable Hilbert space. The spectrum sigma(T) of T is the set of lambda such that (T-lambdaI) is not invertible on all of the Hilbert space, ...

A number of areas of mathematics have the notion of a "dual" which can be applies to objects of that particular area. Whenever an object A has the property that it is equal ...

The number 163 is very important in number theory, since d=163 is the largest number such that the imaginary quadratic field Q(sqrt(-d)) has class number h(-d)=1. It also ...

A class of knots containing the class of alternating knots. Let c(K) be the link crossing number. Then for knot sum K_1#K_2 which is an adequate knot, ...

An almost alternating link with a single component.