A finite simplicial graph Γ determines a right-angled Artin group GΓ, with generators corresponding to the vertices of Γ, and with a relation vw = wv for each pair of adjacent vertices. We compute the lower central series quotients, the Chen quotients, and the (first) resonance variety of GΓ, directly from the graph Γ.

We propose a direct method to control the first order fractional difference quotients of solutions to quasilinear subelliptic equations in the Heisenberg group. In this way we implement iteration methods on fractional difference quotients to obtain weak differentiability in the T -direction and then second order weak differentiability in the horizontal directions.

The category, or class of algebras, in the title is denoted by $bf W$. A hull operator (ho) in $bf W$ is a reflection in the category consisting of $bf W$ objects with only essential embeddings as morphisms. The proper class of all of these is $bf hoW$. The bounded monocoreflection in $bf W$ is denoted $B$. We classify the ho's by their interaction with $B$ as follows. A ``word'' is a function ...

Let a and m be integers such that (a, m) = 1. Let qa = aφ(m)−1 m . We call qa the Euler Quotient of m with base a. This is called the Fermat Quotient when m is a prime. We consider some properties of the matrix of Euler Quotients reduced modulo m and show that these quotients are uniformly distributed modulo m.

Interpretability logic is a modal description of the interpretability predicate. The modal system IL is an extension of the provability logic GL (Gödel–Löb). Bisimulation quotients and largest bisimulations have been well studied for Kripke models. We examine interpretability logic and consider how these results extend to Veltman models. REPORTS ON MATHEMATICAL LOGIC 40 (2006), 59–73 Domagoj VR...

This paper gives a partial desingularisation construction for hyperkähler quotients and a criterion for the surjectivity of an analogue of the Kirwan map to the cohomology of hyperkähler quotients. This criterion is applied to some linear actions on hyperkähler vector spaces.

We present and compare two different implementations of quotient types in Intensional Type Theory. We first introduce quotients as particular inductive-like types following Martin Hofmann’s extension of Calculus of Constructions with quotient types [6]. Then we give an impredicative encoding of quotients. This implementation is reminiscent of Church numerals and more generally of encodings of i...

For any given real number α with bounded partial quotients, we construct explicitly continuum many real numbers β with bounded partial quotients for which the pair (α, β) satisfies a strong form of the Littlewood conjecture. Our proof is elementary and rests on the basic theory of continued fractions.