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Tunisian Journal of Mathematics最新文献

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Asymptotics for the rotating fluids and primitive systems with large ill-prepared initial data in critical spaces 临界空间中初始数据不充分的旋转流体和原始系统的渐近性
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2022-04-12 DOI: 10.2140/tunis.2023.5.171
Frédéric Charve
{"title":"Asymptotics for the rotating fluids and primitive systems with large ill-prepared initial data in critical spaces","authors":"Frédéric Charve","doi":"10.2140/tunis.2023.5.171","DOIUrl":"https://doi.org/10.2140/tunis.2023.5.171","url":null,"abstract":"In this article we study the lifespan and asymptotics (in the large rotation and stratification regime) for the Primitive system for highly ill-prepared initial data in critical spaces. Compared to our previous works, we simplified the proof and made it adaptable to the Rotating fluids system with highly ill-prepared initial data decomposed as a sum of 2D horizontal part and a very large 3D part. We also provide explicit convergence rates.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42178182","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
Quasi-2-Segal sets Quasi-2-Segal集
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2022-04-05 DOI: 10.2140/tunis.2023.5.327
M. Feller
{"title":"Quasi-2-Segal sets","authors":"M. Feller","doi":"10.2140/tunis.2023.5.327","DOIUrl":"https://doi.org/10.2140/tunis.2023.5.327","url":null,"abstract":"We show that the 2-Segal spaces (also called decomposition spaces) of Dyckerhoff-Kapranov and G'alvez-Kock-Tonks have a natural analogue within simplicial sets, which we call quasi-2-Segal sets, and that the two ideas enjoy a similar relationship as the one Segal spaces have with quasi-categories. In particular, we construct a model structure on the category of simplicial sets whose fibrant objects are the quasi-2-Segal sets which is Quillen equivalent to a model structure for complete 2-Segal spaces (where our notion of completeness comes from one of the equivalent characterizations of completeness for Segal spaces). We also prove a path space criterion, which says that a simplicial set is a quasi-2-Segal set if and only if its path spaces (also called d'ecalage) are quasi-categories, as well as an edgewise subdivision criterion.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":"58 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68571915","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: 3
Partially algebraic maps and operator algebras 部分代数映射与算子代数
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2022-03-30 DOI: 10.2140/tunis.2022.4.1
M. Karoubi
{"title":"Partially algebraic maps and operator algebras","authors":"M. Karoubi","doi":"10.2140/tunis.2022.4.1","DOIUrl":"https://doi.org/10.2140/tunis.2022.4.1","url":null,"abstract":"","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43290791","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
Uniformity of rational points: an up-date and corrections 有理点的一致性:更新和修正
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2022-03-30 DOI: 10.2140/tunis.2022.4.183
L. Caporaso, J. Harris, B. Mazur
{"title":"Uniformity of rational points: an up-date and corrections","authors":"L. Caporaso, J. Harris, B. Mazur","doi":"10.2140/tunis.2022.4.183","DOIUrl":"https://doi.org/10.2140/tunis.2022.4.183","url":null,"abstract":"In [2] it is asserted that, assuming the truth of the Strong Lang Conjecture (Conjecture 1 below), a very strong form of boundedness holds: for every g ≥ 2 there is a finite bound N(g)—not depending on K!—such that for any number field K there are only finitely many isomorphism classes of curves of genus g defined over K with more than N(g) K-rational points. The issue is, in that statement do we mean finitely many isomorphism classes over K, or over the algebraic closure K? The paper asserts the statement in the stronger form—up to isomorphism over K—but the proof establishes only the weaker statement that there are finitely many curves with more than N(g) points up to isomorphism over K.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68572262","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
Constructibilité générique et uniformité enℓ 通用可建性和统一性,ℓ
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2022-03-30 DOI: 10.2140/tunis.2022.4.159
L. Illusie
{"title":"Constructibilité générique et uniformité en\u0000ℓ","authors":"L. Illusie","doi":"10.2140/tunis.2022.4.159","DOIUrl":"https://doi.org/10.2140/tunis.2022.4.159","url":null,"abstract":"","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44974532","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
Uniform observation of semiclassicalSchrödinger eigenfunctions on an interval 区间上半经典薛定谔本征函数的一致观测
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2022-03-07 DOI: 10.2140/tunis.2023.5.125
Camille Laurent, Matthieu Léautaud
{"title":"Uniform observation of semiclassical\u0000Schrödinger eigenfunctions on an interval","authors":"Camille Laurent, Matthieu Léautaud","doi":"10.2140/tunis.2023.5.125","DOIUrl":"https://doi.org/10.2140/tunis.2023.5.125","url":null,"abstract":"We consider eigenfunctions of a semiclassical Schr{\"o}dinger operator on an interval, with a single-well type potential and Dirichlet boundary conditions. We give upper/lower bounds on the L^2 density of the eigenfunctions that are uniform in both semiclassical and high energy limits. These bounds are optimal and are used in an essential way in a companion paper in application to a controllability problem. The proofs rely on Agmon estimates and a Gronwall type argument in the classically forbidden region, and on the description of semiclassical measures for boundary value problems in the classically allowed region. Limited regularity for the potential is assumed.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41339095","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
Hodge properties of Airy moments Airy矩的Hodge性质
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2021-12-26 DOI: 10.2140/tunis.2023.5.215
C. Sabbah, Jeng-Daw Yu
{"title":"Hodge properties of Airy moments","authors":"C. Sabbah, Jeng-Daw Yu","doi":"10.2140/tunis.2023.5.215","DOIUrl":"https://doi.org/10.2140/tunis.2023.5.215","url":null,"abstract":"We consider the complex analogues of symmetric power moments of cubic exponential sums. These are symmetric powers of the classical Airy differential equation. We show that their de Rham cohomologies underlie an arithmetic Hodge structure in the sense of Anderson and we compute their Hodge numbers by means of the irregular Hodge filtration, which is indexed by rational numbers, on their realizations as exponential mixed Hodge structures. The main result is that all Hodge numbers are either zero or one.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47281831","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
Singular limit of an Allen–Cahn equation withnonlinear diffusion 具有非线性扩散的Allen–Cahn方程的奇异极限
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2021-12-24 DOI: 10.2140/tunis.2022.4.719
Perla El Kettani, T. Funaki, D. Hilhorst, Hyunjoo Park, S. Sethuraman
{"title":"Singular limit of an Allen–Cahn equation with\u0000nonlinear diffusion","authors":"Perla El Kettani, T. Funaki, D. Hilhorst, Hyunjoo Park, S. Sethuraman","doi":"10.2140/tunis.2022.4.719","DOIUrl":"https://doi.org/10.2140/tunis.2022.4.719","url":null,"abstract":"We consider an Allen-Cahn equation with nonlinear diffusion, motivated by the study of the scaling limit of certain interacting particle systems. We investigate its singular limit and show the generation and propagation of an interface in the limit. The evolution of this limit interface is governed by mean curvature flow with a novel, homogenized speed in terms of a surface tension-mobility parameter emerging from the nonlinearity in our equation.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42585553","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: 3
Rigidity aspects of singular patches in stratified flows 分层流动中奇异斑块的刚性方面
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2021-11-14 DOI: 10.2140/tunis.2022.4.465
T. Hmidi, Haroune Houamed, M. Zerguine
{"title":"Rigidity aspects of singular patches in stratified flows","authors":"T. Hmidi, Haroune Houamed, M. Zerguine","doi":"10.2140/tunis.2022.4.465","DOIUrl":"https://doi.org/10.2140/tunis.2022.4.465","url":null,"abstract":"We explore the local well-posedness theory for the 2d inviscid Boussinesq system when the vorticity is given by a singular patch. We give a significant improvement of cite{Hassainia-Hmidi} by replacing their compatibility assumption on the density with a constraint on its platitude degree on the singular set. The second main contribution focuses on the same issue for the partial viscous Boussinesq system. We establish a uniform LWP theory with respect to the vanishing conductivity. This issue is much more delicate than the inviscid case and one should carefully deal with various difficulties related to the diffusion effects which tend to alter some local structures. The weak a priori estimates are not trivial and refined analysis on transport-diffusion equation subject to a logarithmic singular potential is required. Another difficulty stems from some commutators arising in the control of the co-normal regularity that we counterbalance in part by the maximal smoothing effects of transport-diffusion equation advected by a velocity field which scales slightly below the Lipschitz class.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43233694","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: 3
Moduli of local shtukas and Harris’sconjecture 局部shtukas模与Harri猜想
IF 0.9
Tunisian Journal of Mathematics Pub Date : 2021-10-20 DOI: 10.2140/tunis.2021.3.749
D. Hansen
{"title":"Moduli of local shtukas and Harris’s\u0000conjecture","authors":"D. Hansen","doi":"10.2140/tunis.2021.3.749","DOIUrl":"https://doi.org/10.2140/tunis.2021.3.749","url":null,"abstract":"We prove, under a certain assumption of “Hodge-Newton reducibility”, a strong form of a conjecture of Harris on the cohomology of moduli spaces of mixed-characteristic local shtukas for GLn. Our strategy is roughly based on a previous strategy developed by Mantovan in the setting of p-divisible groups, but the arguments are completely different. In particular, we reinterpret and generalize the Hodge-Newton filtration of a p-divisible group in terms of modified vector bundles on the Fargues-Fontaine curve. We also compute the dualizing complex and compactly supported étale cohomology of any positive Banach-Colmez space over any base; this should be of independent interest.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49594738","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
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