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Consider the plane quartic curve X defined by x^3y+y^3z+z^3x=0, where homogeneous coordinates have been used here so that z can be considered a parameter (the plot above ...

There are several functions called "Lommel functions." One type of Lommel function appear in the solution to the Lommel differential equation and are given by ...

The product of primes p_n#=product_(k=1)^np_k, (1) with p_n the nth prime, is called the primorial function, by analogy with the factorial function. Its logarithm is closely ...

Thurston's conjecture proposed a complete characterization of geometric structures on three-dimensional manifolds. Before stating Thurston's geometrization conjecture in ...

Let S be a collection of subsets of a finite set X. A subset Y of X that meets every member of S is called the vertex cover, or hitting set. A vertex cover of a graph G can ...

A one-person game played on a rectangular lattice of lamps which can be turned on and off. A move consists of flipping a "switch" inside one of the squares, thereby toggling ...

A theorem proved by É. Cartan in 1913 which classifies the irreducible representations of complex semisimple Lie algebras.

If V and W are Banach spaces and T:V->W is a bounded linear operator, the T is said to be a compact operator if it maps the unit ball of V into a relatively compact subset of ...

A surface S is n-embeddable if it can be placed in R^n-space without self-intersections, but cannot be similarly placed in any R^k for k<n. A surface so embedded is said to ...

Five point geometry is a finite geometry subject to the following three axioms: 1. there exist exactly five points, 2. each two distinct points have exactly one line on both ...