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GROUP COVERS, o-MINIMALITY, AND CATEGORICITY 组覆盖，极小性和分类性
Confluentes Mathematici Pub Date : 2010-09-26 DOI: 10.1142/S1793744210000259
A. Berarducci, Y. Peterzil, A. Pillay
{"title":"GROUP COVERS, o-MINIMALITY, AND CATEGORICITY","authors":"A. Berarducci, Y. Peterzil, A. Pillay","doi":"10.1142/S1793744210000259","DOIUrl":"https://doi.org/10.1142/S1793744210000259","url":null,"abstract":"We study the model theory of \"covers\" of groups H definable in an o-minimal structure M. We pose the question of whether any finite central extension G of H is interpretable in M, proving some cases (such as when H is abelian) as well as stating various equivalences. When M is an o-minimal expansion of the reals (so H is a definable Lie group) this is related to Milnor's conjecture [15], and many cases are known. We also prove a strong relative Lω1, ω-categoricity theorem for universal covers of definable Lie groups, and point out some notable differences with the case of covers of complex algebraic groups (studied by Zilber and his students).","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"39 1","pages":"473-496"},"PeriodicalIF":0.0,"publicationDate":"2010-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75150024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
LAPLACIENS DE GRAPHES INFINIS I-GRAPHES MÉTRIQUEMENT COMPLETS 无限图的拉普拉斯图对称完全i图
Confluentes Mathematici Pub Date : 2010-06-25 DOI: 10.1142/S179374421000020X
Nabila Torki-Hamza
{"title":"LAPLACIENS DE GRAPHES INFINIS I-GRAPHES MÉTRIQUEMENT COMPLETS","authors":"Nabila Torki-Hamza","doi":"10.1142/S179374421000020X","DOIUrl":"https://doi.org/10.1142/S179374421000020X","url":null,"abstract":"We introduce the weighted graph Laplacian Δω,c and the notion of Schrodinger operator of the form Δ1,a + W on a locally finite graph G. Concerning essential self-adjointness, we extend Wojciechowski's and Dodziuk's results for graphs with vertex constant weight. The main result in this work states that on any metrically complete weighted graph with bounded degree, the Laplacian Δω,c is essentially self-adjoint and the same holds for Schrodinger operators provided the associated quadratic form is bounded from below. We construct for the proof a strictly positive and harmonic function which allows us to write any Schrodinger operator Δ1,a + W as a Laplacian Δω,c modulo a unitary transform. On introduit le Laplacien Δω,c d'un graphe G localement fini pondere a la fois sur les sommets et sur les aretes, ainsi que la notion d'operateur de Schrodinger Δ1,a + W. Pour les graphes a poids constants sur les sommets, on etend un resultat de Wojciechowski pour le Laplacien et un resultat de Dodziuk pour les operateurs de Schrodinger concernant le caractere essentiellement auto-adjoint. Le resultat principal de ce travail etablit que pour les graphes ponderes a valence bornee et metriquement complets, le Laplacien Δω,c est essentiellement auto-adjoint, et il en va de meme pour l'operateur Δ1,a + W pourvu que la forme quadratique associee soit minoree. La preuve fait appel a la construction d'une fonction harmonique strictement positive qui permet d'ecrire l'operateur de Schrodinger Δ1,a + W comme un Laplacien a poids Δω,c a transformation unitaire pres.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"os-23 1","pages":"333-350"},"PeriodicalIF":0.0,"publicationDate":"2010-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87038037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 48
SOBOLEV MAPS INTO THE PROJECTIVE LINE WITH BOUNDED TOTAL VARIATION Sobolev映射到总变分有界的射影线上
Confluentes Mathematici Pub Date : 2010-06-01 DOI: 10.1142/S179374421000017X
D. Mucci
{"title":"SOBOLEV MAPS INTO THE PROJECTIVE LINE WITH BOUNDED TOTAL VARIATION","authors":"D. Mucci","doi":"10.1142/S179374421000017X","DOIUrl":"https://doi.org/10.1142/S179374421000017X","url":null,"abstract":"Variational problems for Sobolev maps with bounded total variation that take values into the one-dimensional projective space are studied. We focus on the different features from the case of Sobolev maps with bounded conformal p-energy that take values into the p-dimensional projective space, for p ≥ 2 integer, recently studied in [19].","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"9 1","pages":"181-216"},"PeriodicalIF":0.0,"publicationDate":"2010-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77742280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A STRIKING CORRESPONDENCE BETWEEN THE DYNAMICS GENERATED BY THE VECTOR FIELDS AND BY THE SCALAR PARABOLIC EQUATIONS 由矢量场和标量抛物方程产生的动力学之间有惊人的对应关系
Confluentes Mathematici Pub Date : 2010-05-11 DOI: 10.1142/S1793744211000369
R. Joly, G. Raugel
{"title":"A STRIKING CORRESPONDENCE BETWEEN THE DYNAMICS GENERATED BY THE VECTOR FIELDS AND BY THE SCALAR PARABOLIC EQUATIONS","authors":"R. Joly, G. Raugel","doi":"10.1142/S1793744211000369","DOIUrl":"https://doi.org/10.1142/S1793744211000369","url":null,"abstract":"The purpose of this paper is to enhance a correspondence between the dynamics of the differential equations ẏ(t) = g(y(t)) on ℝd and those of the parabolic equations on a bounded domain Ω. We give details on the similarities of these dynamics in the cases d = 1, d = 2 and d ≥ 3 and in the corresponding cases Ω = (0, 1), Ω = 𝕋1 and dim(Ω) ≥ 2 respectively. In addition to the beauty of such a correspondence, this could serve as a guideline for future research on the dynamics of parabolic equations.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"49 1","pages":"471-493"},"PeriodicalIF":0.0,"publicationDate":"2010-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90366207","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
POSITIVE LIOUVILLE THEOREMS AND ASYMPTOTIC BEHAVIOR FOR p-LAPLACIAN TYPE ELLIPTIC EQUATIONS WITH A FUCHSIAN POTENTIAL 具有FUCHSIAN势的p- laplace型椭圆方程的正LIOUVILLE定理和渐近性
Confluentes Mathematici Pub Date : 2010-03-29 DOI: 10.1142/S1793744211000321
M. Fraas, Y. Pinchover
{"title":"POSITIVE LIOUVILLE THEOREMS AND ASYMPTOTIC BEHAVIOR FOR p-LAPLACIAN TYPE ELLIPTIC EQUATIONS WITH A FUCHSIAN POTENTIAL","authors":"M. Fraas, Y. Pinchover","doi":"10.1142/S1793744211000321","DOIUrl":"https://doi.org/10.1142/S1793744211000321","url":null,"abstract":"We study positive Liouville theorems and the asymptotic behavior of positive solutions of p-Laplacian type elliptic equations of the form -Δp(u) + V|u|p-2 u = 0 in X, where X is a domain in ℝd, d ≥ 2 and 1 < p < ∞. We assume that the potential V has a Fuchsian type singularity at a point ζ, where either ζ = ∞ and X is a truncated C2-cone, or ζ = 0 and ζ is either an isolated point of ∂X or belongs to a C2-portion of ∂X.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"26 1","pages":"291-323"},"PeriodicalIF":0.0,"publicationDate":"2010-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84611825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 22
HILBERT SPACE-VALUED INTEGRAL OF OPERATOR-VALUED FUNCTIONS 算子值函数的希尔伯特空间值积分
Confluentes Mathematici Pub Date : 2010-03-01 DOI: 10.1142/S1793744210000144
V. Tesko
{"title":"HILBERT SPACE-VALUED INTEGRAL OF OPERATOR-VALUED FUNCTIONS","authors":"V. Tesko","doi":"10.1142/S1793744210000144","DOIUrl":"https://doi.org/10.1142/S1793744210000144","url":null,"abstract":"In this paper we construct and study an integral of operator-valued functions with respect to Hilbert space-valued measures generated by a resolution of identity. Our integral generalizes the Ito stochastic integral with respect to normal martingales and the Ito integral on a Fock space.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"12 1","pages":"135-157"},"PeriodicalIF":0.0,"publicationDate":"2010-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89525966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
METABELIAN GROUPS WITH QUADRATIC DEHN FUNCTION AND BAUMSLAG–SOLITAR GROUPS 具有二次dehn函数的元群与baumslag -孤子群
Confluentes Mathematici Pub Date : 2010-02-28 DOI: 10.1142/S1793744210000235
Yves Cornulier, R. Tessera
{"title":"METABELIAN GROUPS WITH QUADRATIC DEHN FUNCTION AND BAUMSLAG–SOLITAR GROUPS","authors":"Yves Cornulier, R. Tessera","doi":"10.1142/S1793744210000235","DOIUrl":"https://doi.org/10.1142/S1793744210000235","url":null,"abstract":"We prove that metabelian locally compact groups in a certain class have quadratic Dehn function. As an application, we embed the solvable Baumslag–Solitar groups in finitely presented metabelian groups with quadratic Dehn function. Also, we prove that Baumslag's finitely presented metabelian groups, in which the lamplighter groups embed, have quadratic Dehn function.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"15 1","pages":"431-443"},"PeriodicalIF":0.0,"publicationDate":"2010-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75557425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 27
DIFFERENTIABILITY-FREE CONDITIONS ON THE FREE-ENERGY FUNCTION IMPLYING LARGE DEVIATIONS 自由能函数的无微条件意味着大的偏差
Confluentes Mathematici Pub Date : 2009-10-01 DOI: 10.1142/S1793744209000079
H. Comman
{"title":"DIFFERENTIABILITY-FREE CONDITIONS ON THE FREE-ENERGY FUNCTION IMPLYING LARGE DEVIATIONS","authors":"H. Comman","doi":"10.1142/S1793744209000079","DOIUrl":"https://doi.org/10.1142/S1793744209000079","url":null,"abstract":"Let (μα) be a net of Radon sub-probability measures on ℝ, and (tα) be a net in ]0, 1] converging to 0. Assuming that the generalized log-moment generating function L(λ) exists for all λ in a nonempty open interval G, we give conditions on the left or right derivatives of L|G, implying a vague (and thus narrow when 0 ∈ G large deviation principle. The rate function (which can be nonconvex) is obtained as an abstract Legendre–Fenchel transform. This allows us to strengthen the Gartner–Ellis theorem by weakening the essential smoothness assumption. A related question of R. S. Ellis is solved.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"17 1","pages":"181-196"},"PeriodicalIF":0.0,"publicationDate":"2009-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76106746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
QUANTUM TRAJECTORIES IN RANDOM ENVIRONMENT: THE STATISTICAL MODEL FOR A HEAT BATH 随机环境中的量子轨迹:热浴的统计模型
Confluentes Mathematici Pub Date : 2009-08-19 DOI: 10.1142/S1793744209000109
I. Nechita, C. Pellegrini
{"title":"QUANTUM TRAJECTORIES IN RANDOM ENVIRONMENT: THE STATISTICAL MODEL FOR A HEAT BATH","authors":"I. Nechita, C. Pellegrini","doi":"10.1142/S1793744209000109","DOIUrl":"https://doi.org/10.1142/S1793744209000109","url":null,"abstract":"In this paper, we derive the stochastic master equations corresponding to the statistical model of a heat bath. These stochastic differential equations are obtained as continuous time limits of discrete models of quantum repeated measurements. Physically, they describe the evolution of a small system in contact with a heat bath undergoing continuous measurement. The equations obtained in the present work are qualitatively different from the ones derived in [6], where the Gibbs model of heat bath has been studied. It is shown that the statistical model of a heat bath has a clear physical interpretation in terms of emissions and absorptions of photons. Our approach yields models of random environment and unravelings of stochastic master equations. The equations are rigorously obtained as solutions of martingale problems using the convergence of Markov generators.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"36 1","pages":"249-289"},"PeriodicalIF":0.0,"publicationDate":"2009-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86392198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
UNRAVELING OPEN QUANTUM SYSTEMS: CLASSICAL REDUCTIONS AND CLASSICAL DILATIONS OF QUANTUM MARKOV SEMIGROUPS 解开量子系统:量子马尔可夫半群的经典约简和经典膨胀
Confluentes Mathematici Pub Date : 2009-05-01 DOI: 10.1142/S1793744209000055
R. Rebolledo
{"title":"UNRAVELING OPEN QUANTUM SYSTEMS: CLASSICAL REDUCTIONS AND CLASSICAL DILATIONS OF QUANTUM MARKOV SEMIGROUPS","authors":"R. Rebolledo","doi":"10.1142/S1793744209000055","DOIUrl":"https://doi.org/10.1142/S1793744209000055","url":null,"abstract":"A number of results connecting quantum and classical Markov semigroups, as well as their dilations is reported. The method presented here is based on the analysis of the structure of the semigroup generator. In particular, measure-valued processes appear as a combination of classical reduction and classical dilation of a given quantum Markov semigroup.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"164 1","pages":"123-167"},"PeriodicalIF":0.0,"publicationDate":"2009-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76608975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
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