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Fuglede (1974) conjectured that a domain Omega admits an operator spectrum iff it is possible to tile R^d by a family of translates of Omega. Fuglede proved the conjecture in ...

A function is a relation that uniquely associates members of one set with members of another set. More formally, a function from A to B is an object f such that every a in A ...

A genetic algorithm is a class of adaptive stochastic optimization algorithms involving search and optimization. Genetic algorithms were first used by Holland (1975). The ...

A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight ...

The geometric distribution is a discrete distribution for n=0, 1, 2, ... having probability density function P(n) = p(1-p)^n (1) = pq^n, (2) where 0<p<1, q=1-p, and ...

A graph H is a minor of a graph G if a copy of H can be obtained from G via repeated edge deletion and/or edge contraction. The Kuratowski reduction theorem states that any ...

The set of graph eigenvalues of the adjacency matrix is called the spectrum of the graph. (But note that in physics, the eigenvalues of the Laplacian matrix of a graph are ...

Consider two mutually tangent (externally) spheres A and B together with a larger sphere C inside which A and B are internally tangent. Then construct a chain of spheres each ...

A hyperbolic paraboloid is the quadratic and doubly ruled surface given by the Cartesian equation z=(y^2)/(b^2)-(x^2)/(a^2) (1) (left figure). An alternative form is z=xy (2) ...

One of the most useful tools in nonstandard analysis is the concept of a hyperfinite set. To understand a hyperfinite set, begin with an arbitrary infinite set X whose ...