Search results for "Regular"

Locally convex quasi *-algebras with sufficiently many *-representations

2012

AbstractThe main aim of this paper is the investigation of conditions under which a locally convex quasi ⁎-algebra (A[τ],A0) attains sufficiently many (τ,tw)-continuous ⁎-representations in L†(D,H), to separate its points. Having achieved this, a usual notion of bounded elements on A[τ] rises. On the other hand, a natural order exists on (A[τ],A0) related to the topology τ, that also leads to a kind of bounded elements, which we call “order bounded”. What is important is that under certain conditions the latter notion of boundedness coincides with the usual one. Several nice properties of order bounded elements are extracted that enrich the structure of locally convex quasi ⁎-algebras.

On the proper homotopy invariance of the Tucker property

2006

A non-compact polyhedron P is Tucker if, for any compact subset K ⊂ P, the fundamental group π1(P − K) is finitely generated. The main result of this note is that a manifold which is proper homotopy equivalent to a Tucker polyhedron is Tucker. We use Poenaru’s theory of the equivalence relations forced by the singularities of a non-degenerate simplicial map.

Les squelettes : structures d'interaction directe et intuitive avec des formes 3D

2014

The interactions in shape creation graphic applications are far from natural. The user tends to avoid as much as possible such applications and prefer to sketch or model his/her shape.To bridge this widening gap between computer and the general public, we focus on skeletons. They are intuitive shape representation models that we propose to use as direct and intuitive interaction structures.All skeletons suffer from very low quality as shape representation models, concerning the geometry of the shape they capture, the quantity of skeletal noise they contain or the lack of useful organization of their elements. Moreover, some functionalities that must be granted to skeletons are only partiall…

On the exhaustive generation of k-convex polyominoes

2017

The degree of convexity of a convex polyomino P is the smallest integer k such that any two cells of P can be joined by a monotone path inside P with at most k changes of direction. In this paper we present a simple algorithm for computing the degree of convexity of a convex polyomino and we show how it can be used to design an algorithm that generates, given an integer k, all k-convex polyominoes of area n in constant amortized time, using space O(n). Furthermore, by applying few changes, we are able to generate all convex polyominoes whose degree of convexity is exactly k.

Extending formal language hierarchies to higher dimensions

1999

F-signature of pairs: Continuity, p-fractals and minimal log discrepancies

2011

This paper contains a number of observations on the {$F$-signature} of triples $(R,\Delta,\ba^t)$ introduced in our previous joint work. We first show that the $F$-signature $s(R,\Delta,\ba^t)$ is continuous as a function of $t$, and for principal ideals $\ba$ even convex. We then further deduce, for fixed $t$, that the $F$-signature is lower semi-continuous as a function on $\Spec R$ when $R$ is regular and $\ba$ is principal. We also point out the close relationship of the signature function in this setting to the works of Monsky and Teixeira on Hilbert-Kunz multiplicity and $p$-fractals. Finally, we conclude by showing that the minimal log discrepancy of an arbitrary triple $(R,\Delta,\b…

Circular law for sparse random regular digraphs

2020

Fix a constant $C\geq 1$ and let $d=d(n)$ satisfy $d\leq \ln^{C} n$ for every large integer $n$. Denote by $A_n$ the adjacency matrix of a uniform random directed $d$-regular graph on $n$ vertices. We show that, as long as $d\to\infty$ with $n$, the empirical spectral distribution of appropriately rescaled matrix $A_n$ converges weakly in probability to the circular law. This result, together with an earlier work of Cook, completely settles the problem of weak convergence of the empirical distribution in directed $d$-regular setting with the degree tending to infinity. As a crucial element of our proof, we develop a technique of bounding intermediate singular values of $A_n$ based on studyi…

The Existence of Solutions for Local Dirichlet (r(u),s(u))-Problems

2022

In this paper, we consider local Dirichlet problems driven by the (r(u),s(u))-Laplacian operator in the principal part. We prove the existence of nontrivial weak solutions in the case where the variable exponents r,s are real continuous functions and we have dependence on the solution u. The main contributions of this article are obtained in respect of: (i) Carathéodory nonlinearity satisfying standard regularity and polynomial growth assumptions, where in this case, we use geometrical and compactness conditions to establish the existence of the solution to a regularized problem via variational methods and the critical point theory; and (ii) Sobolev nonlinearity, somehow related to the spac…

Integration by parts on generalized manifolds and applications on quasiregular maps

2016

Astrocytic alterations in interleukin-6/Soluble interleukin-6 receptor alpha double-transgenic mice.

2000

Interleukin-6 (IL-6), a major cytokine with diverse effects on cells mainly of the immune and hematopoietic systems, has been linked to several neurological disorders such as acquired immune deficiency syndrome dementia, multiple sclerosis, and Alzheimer's disease. Central nervous system (CNS)-specific expression of IL-6 caused neurodegeneration, massive gliosis, and vascular proliferation in transgenic mice. However, the effects of systemically circulating IL-6 and its receptor IL-6Ralpha on the CNS are unknown. IL-6Ralpha is the specific component of the IL-6 receptor system and hence an important co-factor of IL-6. IL-6Ralpha is bioactive in a membrane-bound and in a soluble (s) form. We…