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Non-local approximations of the gradient 梯度的非局部近似值
Confluentes Mathematici Pub Date : 2024-04-08 DOI: 10.5802/cml.91
H. Brezis, P. Mironescu
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引用次数: 0
On the half-trajectories of horocyclic flow on geometrically infinite hyperbolic surfaces 几何无限双曲曲面上环流的半轨迹
Confluentes Mathematici Pub Date : 2023-03-13 DOI: 10.5802/cml.89
Adamou Saidou
{"title":"On the half-trajectories of horocyclic flow on geometrically infinite hyperbolic surfaces","authors":"Adamou Saidou","doi":"10.5802/cml.89","DOIUrl":"https://doi.org/10.5802/cml.89","url":null,"abstract":"","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"287 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77590769","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: 0
A priori and a posteriori error analysis for a hybrid formulation of a prestressed shell model 预应力壳模型混合公式的先验和后验误差分析
Confluentes Mathematici Pub Date : 2023-03-13 DOI: 10.5802/cml.87
Serge Nicaise, Ismael Merabet, Rihana Rezzag Bara
{"title":"A priori and a posteriori error analysis for a hybrid formulation of a prestressed shell model","authors":"Serge Nicaise, Ismael Merabet, Rihana Rezzag Bara","doi":"10.5802/cml.87","DOIUrl":"https://doi.org/10.5802/cml.87","url":null,"abstract":"This work deals with the finite element approximation of a prestressed shell model in the case of isometrically deformed shell. Using a new formulation where the unknowns (the displacement and the rotation of fibers normal to the midsurface) are described in Cartesian and local covariant basis respectively. Due to the constraint involved in the definition of the functional space, a penalized version is then considered. We obtain a non robust a priori error estimate of this penalized formulation, but a robust one is obtained for its mixed formulation. Moreover, we present a reliable and efficient a posteriori error estimator of the penalized formulation. Numerical tests are included that confirm the efficiency of our residual a posteriori estimator.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135907496","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: 0
Infinite characters of type II on SL n (ℤ) SL n (n)上II型的无穷个字符
Confluentes Mathematici Pub Date : 2022-11-21 DOI: 10.5802/cml.80
Rémi Boutonnet
{"title":"Infinite characters of type II on SL n (ℤ)","authors":"Rémi Boutonnet","doi":"10.5802/cml.80","DOIUrl":"https://doi.org/10.5802/cml.80","url":null,"abstract":"","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84147970","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: 0
Review on Spectral asymptotics for the semiclassical Bochner Laplacian of a line bundle 线束的半经典Bochner拉普拉斯算子的谱渐近性研究
Confluentes Mathematici Pub Date : 2022-11-21 DOI: 10.5802/cml.83
L'eo Morin
{"title":"Review on Spectral asymptotics for the semiclassical Bochner Laplacian of a line bundle","authors":"L'eo Morin","doi":"10.5802/cml.83","DOIUrl":"https://doi.org/10.5802/cml.83","url":null,"abstract":". We first give a short introduction to the Bochner Laplacian on a Riemannian manifold, and explain why it acts locally as a magnetic Laplacian. Then we review recent results on the semiclassical properties of semi-excited spectrum with inhomogeneous magnetic field, including Weyl estimates and eigenvalue asymptotics. These results show under specific assumptions that the spectrum is well described by a familly of operators whose symbols are space-dependent Landau levels. Finally we discuss the strength and limitations of these theorems, in terms of possible crossings between Landau levels.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"90 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76524407","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
Towards formal Baer criteria 走向正式的贝尔标准
Confluentes Mathematici Pub Date : 2022-11-21 DOI: 10.5802/cml.82
Daniel Misselbeck-Wessel, Davide Rinaldi
{"title":"Towards formal Baer criteria","authors":"Daniel Misselbeck-Wessel, Davide Rinaldi","doi":"10.5802/cml.82","DOIUrl":"https://doi.org/10.5802/cml.82","url":null,"abstract":". Baer’s criterion helps to identify the injective objects in a category of modules by reducing the problem of map extension to a certain subclass of morphisms. Due to its notorious reliance on Zorn’s lemma, it is inherently non-constructive. However, we put Baer’s criterion on constructive grounds by couching it in point-free terms. Classical principles which will be developed alongside readily allow to gain back the conventional version. Several case studies further indicate a fair applicability.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83726755","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
Approximate isomorphism of randomization pairs 随机化对的近似同构
Confluentes Mathematici Pub Date : 2022-02-08 DOI: 10.5802/cml.85
James Hanson, Tom'as Ibarluc'ia
{"title":"Approximate isomorphism of randomization pairs","authors":"James Hanson, Tom'as Ibarluc'ia","doi":"10.5802/cml.85","DOIUrl":"https://doi.org/10.5802/cml.85","url":null,"abstract":"We study approximate $aleph_0$-categoricity of theories of beautiful pairs of randomizations, in the sense of continuous logic. This leads us to disprove a conjecture of Ben Yaacov, Berenstein and Henson, by exhibiting $aleph_0$-categorical, $aleph_0$-stable metric theories $Q$ for which the corresponding theory $Q_P$ of beautiful pairs is not approximately $aleph_0$-categorical, i.e., has separable models that are not isomorphic even up to small perturbations of the smaller model of the pair. The theory $Q$ of randomized infinite vector spaces over a finite field is such an example. On the positive side, we show that the theory of beautiful pairs of randomized infinite sets is approximately $aleph_0$-categorical. We also prove that a related stronger property, which holds in that case, is stable under various natural constructions, and formulate our guesswork for the general case.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"66 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82788428","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: 0
Fuglede-Kadison determinants over free groups and Lehmer’s constants 自由群上的Fuglede-Kadison行列式和Lehmer常数
Confluentes Mathematici Pub Date : 2022-02-08 DOI: 10.5802/cml.79
Fathi Ben Aribi
{"title":"Fuglede-Kadison determinants over free groups and Lehmer’s constants","authors":"Fathi Ben Aribi","doi":"10.5802/cml.79","DOIUrl":"https://doi.org/10.5802/cml.79","url":null,"abstract":"Lehmer's famous problem asks whether the set of Mahler measures of polynomials with integer coefficients admits a gap at 1. In 2019, L\"uck extended this question to Fuglede-Kadison determinants of a general group, and he defined the Lehmer's constants of the group to measure such a gap. In this paper, we compute new values for Fuglede-Kadison determinants over non-cyclic free groups, which yields the new upper bound $frac{2}{sqrt{3}}$ for Lehmer's constants of all torsion-free groups which have non-cyclic free subgroups. Our proofs use relations between Fuglede-Kadison determinants and random walks on Cayley graphs, as well as works of Bartholdi and Dasbach-Lalin. Furthermore, via the gluing formula for $L^2$-torsions, we show that the Lehmer's constants of an infinite number of fundamental groups of hyperbolic 3-manifolds are bounded above by even smaller values than $frac{2}{sqrt{3}}$.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82951897","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: 0
Koszul duality in quantum field theory 量子场论中的科祖尔二象性
Confluentes Mathematici Pub Date : 2021-10-19 DOI: 10.5802/cml.88
Natalie M. Paquette, B. Williams
{"title":"Koszul duality in quantum field theory","authors":"Natalie M. Paquette, B. Williams","doi":"10.5802/cml.88","DOIUrl":"https://doi.org/10.5802/cml.88","url":null,"abstract":"In this article, we introduce basic aspects of the algebraic notion of Koszul duality for a physics audience. We then review its appearance in the physical problem of coupling QFTs to topological line defects, and illustrate the concept with some examples drawn from twists of various simple supersymmetric theories. Though much of the content of this article is well-known to experts, the presentation and examples have not, to our knowledge, appeared in the literature before. Our aim is to provide an elementary introduction for those interested in the appearance of Koszul duality in supersymmetric gauge theories with line defects and, ultimately, its generalizations to higher-dimensional defects and twisted holography.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83316891","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: 12
Exactness and faithfulness of monoidal functors 一元函子的精确性和可靠性
Confluentes Mathematici Pub Date : 2021-10-18 DOI: 10.5802/cml.86
B. Kahn
{"title":"Exactness and faithfulness of monoidal functors","authors":"B. Kahn","doi":"10.5802/cml.86","DOIUrl":"https://doi.org/10.5802/cml.86","url":null,"abstract":"Inspired by recent work of Peter O'Sullivan (arXiv:2012.15703), we give a condition under which a faithful monoidal functor between abelian $otimes$-categories is exact.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"103 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78256106","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
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