If given n ∈ N and Γ, a multiplicatively closed subset of Zn, then the set HΓ = {n ∈ Z : x ∈ N : x + nZ ∈ Γ} ∪ {1} is a multiplicative submonoid of N0 known as a congruence monoid. Much work has been done to characterize the factorial (every element has unique factorization) and half-factorial (lengths of irreducible factorizations of an element remain constant) properties of such objects. Our ...

We prove that for any semi-Dirichlet form (ε, D(ε)) on a measurable Lusin space E there exists a Lusin topology with the given σ-algebra as the Borel σ-algebra so that (ε, D(ε)) becomes quasi–regular. However one has to enlarge E by a zero set. More generally a corresponding result for arbitrary L-resolvents is proven.

We expect generative models of language to correctly predict surface forms from underlying forms, but morphologically complex words, especially compounds, can exhibit idiosyncratic outputs, which require an extra lexical listing. This results in (a) a poorer Minimum Description Length of our model (Goldsmith 2011) and (b) failure of a grammar to capture patterning among exceptions. To solve an ...

This paper describes a method to construct semi-regular meshes for a surface S de ned by the zero set of a trivariate function F(x,y,z), representing a distance eld de nition of S. An adaptive distance eld (ADF) de nition of S is obtained by constructing, adaptively, an octree decomposition of F's domain. The vertices of the octree-based de nition of S lie either on the positive or negative sid...

In this paper we introduce a new mesh refinement method for subdivision surfaces. It generates a semiregular 4-direction hierarchical structure from control meshes representing 2D manifolds of arbitrary topology. The main advantage of this structure is that it allows the extraction of conforming variable-resolution meshes based on spatially varying adaptation functions. We also present a smooth...

. On considère une classe de systèmes non-linéaires pour lesquels la technique de synthèse par backstepping n’est pas applicable. On présente un critère pour la synthèse d’une commande hybride faisant l’union d’une commande par backstepping et d’une commande locale. Cette commande hybride rend le système bouclé globalement asymptotiquement stable. Le critère de sélection repose sur le choix de ...

It is well known that the internal suplattices in the topos of sheaves on a locale are precisely the modules on that locale. Using enriched category theory and a lemma on KZ doctrines we prove (the generalization of) this fact in the case of ordered sheaves on a small quantaloid. Comparing module-equivalence with sheaf-equivalence for quantaloids and using the notion of centre of a quantaloid, ...

A reduction system for regular expressions is presented. For a regular expression t, the reduction system is proved to terminate in a state where the most-reduced expression readily yields a semi-linear representation for the Parikh image of the language of t.

Rendering high quality digital terrains at interactive rates requires carefully crafted algorithms and data structures able to balance the competing requirements of realism and frame rates, while taking into account the memory and speed limitations of the underlying graphics platform. In this survey, we analyze multi-resolution approaches that exploit a certain semi-regularity of the data. Thes...

Semi-regular meshes describe surface models that exhibit a structural regularity that facilitates many geometric processing algorithms. We introduce a technique to construct semi-regular, quad-only meshes from input surface meshes of arbitrary polygonal type and genus. The algorithm generates a quad-only model through subdivision of the input polygons, then simplifies to a base domain that is h...