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A tree having four branches at each node. Quadtrees are used in the construction of some multidimensional databases (e.g., cartography, computer graphics, and image ...

A power series sum^(infty)c_kx^k will converge only for certain values of x. For instance, sum_(k=0)^(infty)x^k converges for -1<x<1. In general, there is always an interval ...

A positive number k such that a lamina or solid body with moment of inertia about an axis I and mass m is given by I=mk^2. Pickover (1995) defines a generalization of k as a ...

Ramsey's theorem is a generalization of Dilworth's lemma which states for each pair of positive integers k and l there exists an integer R(k,l) (known as the Ramsey number) ...

The space of currents arising from rectifiable sets by integrating a differential form is called the space of two-dimensional rectifiable currents. For C a closed bounded ...

A crossing in a knot diagram for which there exists a circle in the projection plane meeting the diagram transversely at that crossing, but not meeting the diagram at any ...

The numerators and denominators obtained by taking the ratios of adjacent terms in the triangular array of the number of +1 "bordered" alternating sign matrices A_n with a 1 ...

Let the true value of a quantity be x and the measured or inferred value x_0. Then the relative error is defined by deltax=(Deltax)/x=(x_0-x)/x=(x_0)/x-1, where Deltax is the ...

Let G be a graph, and suppose each edge of G is independently deleted with fixed probability 0<=p<=1. Then the probability that no connected component of G is disconnected as ...

A removable singularity is a singular point z_0 of a function f(z) for which it is possible to assign a complex number in such a way that f(z) becomes analytic. A more ...