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A hyperbolic knot is a knot that has a complement that can be given a metric of constant curvature -1. All hyperbolic knots are prime knots (Hoste et al. 1998). A prime knot ...

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 ...

The divided difference f[x_0,x_1,x_2,...,x_n], sometimes also denoted [x_0,x_1,x_2,...,x_n] (Abramowitz and Stegun 1972), on n+1 points x_0, x_1, ..., x_n of a function f(x) ...

A linear transformation between two vector spaces V and W is a map T:V->W such that the following hold: 1. T(v_1+v_2)=T(v_1)+T(v_2) for any vectors v_1 and v_2 in V, and 2. ...

A Steiner quadruple system is a Steiner system S(t=3,k=4,v), where S is a v-set and B is a collection of k-sets of S such that every t-subset of S is contained in exactly one ...

A sequence of functions {f_n}, n=1, 2, 3, ... is said to be uniformly convergent to f for a set E of values of x if, for each epsilon>0, an integer N can be found such that ...

A uniform distribution, sometimes also known as a rectangular distribution, is a distribution that has constant probability. The probability density function and cumulative ...

Milnor (1956) found more than one smooth structure on the seven-dimensional hypersphere. Generalizations have subsequently been found in other dimensions. Using surgery ...

The regular decagon is constructible 10-sided regular polygon with Schläfli symbol {10}. The inradius r, circumradius R, and area can be computed directly from the formulas ...

A shuffle-exchange graph is a nonsimple graph (due to the existence of graph loops) whose vertices are length n binary strings with an edge from w to w^' if 1. w^' differs ...