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An AB percolation is a discrete percolation model in which the underlying point lattice graph L has the properties that each of its graph vertices is occupied by an atom ...

In the original formulation, a quantity associated with ideal class groups. According to Chevalley's formulation, a Grössencharakter is a multiplicative character of the ...

A linear functional defined on a subspace of a vector space V and which is dominated by a sublinear function defined on V has a linear extension which is also dominated by ...

With a large enough sample, any outrageous thing is likely to happen (Diaconis and Mosteller 1989). Littlewood (1986) considered an event which occurs one in a million times ...

A semi-Riemannian manifold M=(M,g) is said to be Lorentzian if dim(M)>=2 and if the index I=I_g associated with the metric tensor g satisfies I=1. Alternatively, a smooth ...

A partially ordered set (or poset) is a set taken together with a partial order on it. Formally, a partially ordered set is defined as an ordered pair P=(X,<=), where X is ...

A presheaf C of categories consists of the following data: 1. For every local homeomorphism f:Y->X of topological spaces X, Y, a category C(f:Y->X); 2. For every diagram f ...

A quasiperfect number, called a "slightly excessive number" by Singh (1997), is a "least" abundant number, i.e., one such that sigma(n)=2n+1. Quasiperfect numbers are ...

The Sendov conjecture, proposed by Blagovest Sendov circa 1958, that for a polynomial f(z)=(z-r_1)(z-r_2)...(z-r_n) with n>=2 and each root r_k located inside the closed unit ...

Let any finite or infinite set of points having no finite limit point be prescribed, and associate with each of its points a definite positive integer as its order. Then ...