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A discrete group is a topological group with the discrete topology. Often in practice, discrete groups arise as discrete subgroups of continuous Lie groups acting on a ...

The disk model is the standard Boolean-Poisson model in two-dimensional continuum percolation theory. In particular, the disk model is characterized by the existence of a ...

The dominance relation on a set of points in Euclidean n-space is the intersection of the n coordinate-wise orderings. A point p dominates a point q provided that every ...

If q_n is the nth prime such that M_(q_n) is a Mersenne prime, then q_n∼(3/2)^n. It was modified by Wagstaff (1983) to yield Wagstaff's conjecture, q_n∼(2^(e^(-gamma)))^n, ...

In real and functional analysis, equicontinuity is a concept which extends the notion of uniform continuity from a single function to collection of functions. Given ...

The extended mean-value theorem (Anton 1984, pp. 543-544), also known as the Cauchy mean-value theorem (Anton 1984, pp. 543) and Cauchy's mean-value formula (Apostol 1967, p. ...

A module M over a unit ring R is called faithfully flat if the tensor product functor - tensor _RM is exact and faithful. A faithfully flat module is always flat and ...

Let J_A, J_B, and J_C be the vertices of the outer Soddy triangle, and also let E_A, E_B, and E_C be the pairwise contact points of the three tangent circles. Then the lines ...

Also called the Tait flyping conjecture. Given two reduced alternating projections of the same knot, they are equivalent on the sphere iff they are related by a series of ...

The frame bundle on a Riemannian manifold M is a principal bundle. Over every point p in M, the Riemannian metric determines the set of orthonormal frames, i.e., the possible ...