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A codimension one foliation F of a 3-manifold M is said to be taut if for every leaf lambda in the leaf space L of F, there is a circle gamma_lambda transverse to F (i.e., a ...

A transition function describes the difference in the way an object is described in two separate, overlapping coordinate charts, where the description of the same set may ...

The degree of a graph vertex v of a graph G is the number of graph edges which touch v. The vertex degrees are illustrated above for a random graph. The vertex degree is also ...

Voronin (1975) proved the remarkable analytical property of the Riemann zeta function zeta(s) that, roughly speaking, any nonvanishing analytic function can be approximated ...

The first of the Hardy-Littlewood conjectures. The k-tuple conjecture states that the asymptotic number of prime constellations can be computed explicitly. In particular, ...

The Ackermann function is the simplest example of a well-defined total function which is computable but not primitive recursive, providing a counterexample to the belief in ...

The Cantor set T_infty, sometimes also called the Cantor comb or no middle third set (Cullen 1968, pp. 78-81), is given by taking the interval [0,1] (set T_0), removing the ...

Given a planar graph G, a geometric dual graph and combinatorial dual graph can be defined. Whitney showed that these are equivalent (Harary 1994), so that one may speak of ...

Consider a first-order ODE in the slightly different form p(x,y)dx+q(x,y)dy=0. (1) Such an equation is said to be exact if (partialp)/(partialy)=(partialq)/(partialx). (2) ...

A fusene is a simple planar 2-connected graph embedded in the plane with all vertices of degree 2 or 3, all bounded faces (not necessarily regular) hexagons, and all vertices ...