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Due to nonlinearities in weather processes, a butterfly flapping its wings in Tahiti can, in theory, produce a tornado in Kansas. This strong dependence of outcomes on very ...

Carmichael's conjecture asserts that there are an infinite number of Carmichael numbers. This was proven by Alford et al. (1994).

A special point which usually has some symmetric placement with respect to points on a curve or in a solid. The center of a circle is equidistant from all points on the ...

The coboundary polynomial chi^__G(q,t) is a bivariate graph polynomial which can be expressed in terms of the Tutte polynomial T_G(x,y) of a graph G by ...

The commutator subgroup (also called a derived group) of a group G is the subgroup generated by the commutators of its elements, and is commonly denoted G^' or [G,G]. It is ...

A product of ANDs, denoted ^ _(k=1)^nA_k. The conjunctions of a Boolean algebra A of subsets of cardinality p are the 2^p functions A_lambda= union _(i in lambda)A_i, where ...

A coordinate chart is a way of expressing the points of a small neighborhood, usually on a manifold M, as coordinates in Euclidean space. An example from geography is the ...

Given an affine variety V in the n-dimensional affine space K^n, where K is an algebraically closed field, the coordinate ring of V is the quotient ring ...

A graph is called cordial if it is possible to label its vertices with 0s and 1s so that when the edges are labeled with the difference of the labels at their endpoints, the ...

Let n points xi_1, ..., xi_n be randomly distributed on a domain S, and let H be some event that depends on the positions of the n points. Let S^' be a domain slightly ...