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Quarterly Journal of Mathematics最新文献

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Well-Posedness and Stability of a Generalized Micropolar Thermoelastic Body With Infinite Memory 无限记忆广义微极热弹性体的适定性和稳定性
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.1093/qmath/haab014
A Guesmia;J E MuÑoz Rivera;M A Sepúlveda CortÉs;O Vera VillagrÁn
{"title":"Well-Posedness and Stability of a Generalized Micropolar Thermoelastic Body With Infinite Memory","authors":"A Guesmia;J E MuÑoz Rivera;M A Sepúlveda CortÉs;O Vera VillagrÁn","doi":"10.1093/qmath/haab014","DOIUrl":"https://doi.org/10.1093/qmath/haab014","url":null,"abstract":"We study in this paper the well-posedness and stability of a linear system of a thermoelastic Cosserat medium with infinite memory, where the Cosserat medium is a continuum in which each point has the degrees of freedom of a rigid body.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qmath/haab014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49978798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Second Moment Of Dirichlet L-Functions, Character Sums Over Subgroups And Upper Bounds On Relative Class Numbers Dirichlet l -函数的二阶矩、子群上的字符和及相对类数上的上界
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.1093/qmath/haab010
Stéphane R Louboutin;Marc Munsch
{"title":"Second Moment Of Dirichlet L-Functions, Character Sums Over Subgroups And Upper Bounds On Relative Class Numbers","authors":"Stéphane R Louboutin;Marc Munsch","doi":"10.1093/qmath/haab010","DOIUrl":"https://doi.org/10.1093/qmath/haab010","url":null,"abstract":"We prove an asymptotic formula for the mean-square average of L-functions associated with subgroups of characters of sufficiently large size. Our proof relies on the study of certain character sums \u0000<tex>${mathcal{A}}(p,d)$</tex>\u0000 recently introduced by E. Elma, where p ≥ 3 is prime and d ≥ 1 is any odd divisor of p − 1. We obtain an asymptotic formula for \u0000<tex>${mathcal{A}}(p,d),$</tex>\u0000 which holds true for any odd divisor d of p − 1, thus removing E. Elma's restrictions on the size of d. This answers a question raised in Elma's paper. Our proof relies on both estimates on the frequency of large character sums and techniques from the theory of uniform distribution. As an application, in the range \u0000<tex>$1leq dleqfrac{log p}{3loglog p}$</tex>\u0000, we obtain a significant improvement \u0000<tex>$h_{p,d}^- leq 2(frac{(1+o(1))p}{24})^{m/4}$</tex>\u0000 over the trivial bound \u0000<tex>$h_{p,d}^- ll (frac{dp}{24} )^{m/4}$</tex>\u0000 on the relative class numbers of the imaginary number fields of conductor \u0000<tex>$pequiv 1mod{2d}$</tex>\u0000 and degree \u0000<tex>$m=(p-1)/d$</tex>\u0000, where d ≥ 1 is odd.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qmath/haab010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49978794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Pullback of the Normal Module of Ideals with Low Codimension 低余维理想正规模的拉回
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.1093/qmath/haaa065
Cleto B Miranda-Neto
{"title":"Pullback of the Normal Module of Ideals with Low Codimension","authors":"Cleto B Miranda-Neto","doi":"10.1093/qmath/haaa065","DOIUrl":"10.1093/qmath/haaa065","url":null,"abstract":"The normal module (or sheaf) of an ideal is a celebrated object in commutative algebra and algebraic geometry. In this paper, we prove results about its pullback under the natural projection, focusing on subtle numerical invariants such as, for instance, the reduction number. For certain codimension 2 perfect ideals, we show that the pullback has reduction number two. This is of interest since the determination of this invariant in the context of modules (even for special classes) is a mostly open, difficult problem. The analytic spread is also computed. Finally, for codimension 3 Gorenstein ideals, we determine the depth of the pullback, and we also consider a broader class of ideals provided that the Auslander transpose of the conormal module is almost Cohen–Macaulay.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49664747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Transversal Hard Lefschetz Theorem on Transversely Symplectic Foliations 横向辛叶上的横向硬Lefschetz定理
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.1093/qmath/haaa071
Jesús A Álvarez López;Seoung Dal Jung
{"title":"Transversal Hard Lefschetz Theorem on Transversely Symplectic Foliations","authors":"Jesús A Álvarez López;Seoung Dal Jung","doi":"10.1093/qmath/haaa071","DOIUrl":"https://doi.org/10.1093/qmath/haaa071","url":null,"abstract":"We study the transversal hard Lefschetz theorem on a transversely symplectic foliation. This article extends the results of transversally symplectic flows (H.K. Pak, “Transversal harmonic theory for transversally symplectic flows”, J. Aust. Math. Soc. 84 (2008), 233–245) to general transversely symplectic foliations.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qmath/haaa071","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49947645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The Maximum Entropy of a Metric Space 度量空间的最大熵
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.1093/qmath/haab003
Tom Leinster;Emily Roff
{"title":"The Maximum Entropy of a Metric Space","authors":"Tom Leinster;Emily Roff","doi":"10.1093/qmath/haab003","DOIUrl":"https://doi.org/10.1093/qmath/haab003","url":null,"abstract":"We define a one-parameter family of entropies, each assigning a real number to any probability measure on a compact metric space (or, more generally, a compact Hausdorff space with a notion of similarity between points). These entropies generalise the Shannon and Renyi entropies of information theory. We prove that on any space X, there is a single probability measure maximising all these entropies simultaneously. Moreover, all the entropies have the same maximum value: the maximum entropy of X. As X is scaled up, the maximum entropy grows; its asymptotics determine geometric information about X, including the volume and dimension. We also study the large-scale limit of the maximising measure itself, arguing that it should be regarded as the canonical or uniform measure on X. Primarily we work not with entropy itself but its exponential, called diversity and (in its finite form) used as a measure of biodiversity. Our main theorem was first proved in the finite case by Leinster and Meckes.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8016816/9690900/09690907.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49947669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
A Unified Approach to the Arens Regularity and Related Problems for a Class of Banach Algebras Associated with Locally Compact Groups 一类与局部紧群相关的Banach代数的Arens正则性及相关问题的统一研究
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.1093/qmath/haab005
Anthony to-Ming Lau;Ali Ülger
{"title":"A Unified Approach to the Arens Regularity and Related Problems for a Class of Banach Algebras Associated with Locally Compact Groups","authors":"Anthony to-Ming Lau;Ali Ülger","doi":"10.1093/qmath/haab005","DOIUrl":"https://doi.org/10.1093/qmath/haab005","url":null,"abstract":"Based on Katznelson–Tzafriri Theorem on power bounded operators, we prove in this paper a theorem, which applies to the most of the classical Banach algebras of harmonic analysis associated with locally compact groups, to deal with the problems when a given Banach algebra A is Arens regular and when A is an ideal in its bidual. In the second part of the paper, we study the topological center of the bidual of a class of Banach algebras with a multiplier bounded approximate identity.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qmath/haab005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49947670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Gaussian Primes in Narrow Sectors 窄扇区中的高斯素数
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.1093/qmath/haab009
Joshua Stucky
{"title":"Gaussian Primes in Narrow Sectors","authors":"Joshua Stucky","doi":"10.1093/qmath/haab009","DOIUrl":"https://doi.org/10.1093/qmath/haab009","url":null,"abstract":"We generalize a Theorem of Ricci and count Gaussian primes \u0000<tex>$mathfrak{p}$</tex>\u0000 with short interval restrictions on both the norm and the argument of \u0000<tex>$mathfrak{p}$</tex>\u0000. We follow Heath-Brown's method for counting rational primes in short intervals.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49978793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Space of Traces in Symmetric Monoidal Infinity Categories 对称单无穷范畴中的迹空间
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.1093/qmath/haab013
Jan Steinebrunner
{"title":"The Space of Traces in Symmetric Monoidal Infinity Categories","authors":"Jan Steinebrunner","doi":"10.1093/qmath/haab013","DOIUrl":"https://doi.org/10.1093/qmath/haab013","url":null,"abstract":"We define a tracelike transformation to be a natural family of conjugation invariant maps \u0000<tex>$T_{x,mathtt{C}}:hom_mathtt{C}(x, x) to hom_mathtt{C}(unicode{x1D7D9},unicode{x1D7D9})$</tex>\u0000 for all dualizable objects x in any symmetric monoidal \u0000<tex>$infty$</tex>\u0000-category \u0000<tex>$mathtt{C}$</tex>\u0000. This generalizes the trace from linear algebra that assigns a scalar \u0000<tex>$operatorname{Tr}(,f,) in k$</tex>\u0000 to any endomorphism f : V → V of a finite-dimensional k-vector space. Our main theorem computes the moduli space of tracelike transformations using the one-dimensional cobordism hypothesis with singularities. As a consequence, we show that the trace \u0000<tex>$operatorname{Tr}$</tex>\u0000 can be uniquely extended to a tracelike transformation up to a contractible space of choices. This allows us to give several model-independent characterizations of the \u0000<tex>$infty$</tex>\u0000-categorical trace.By restricting the aforementioned notion of tracelike transformations from endomorphisms to automorphisms one can in particular recover a theorem of Toën and Vezzosi. Other examples of tracelike transformations are for instance given by \u0000<tex>$f mapsto operatorname{Tr}(,f^{,n})$</tex>\u0000. Unlike for \u0000<tex>$operatorname{Tr}$</tex>\u0000, the relevant connected component of the moduli space is not contractible, but rather equivalent to \u0000<tex>$Bmathbb{Z}/nmathbb{Z}$</tex>\u0000 or BS\u0000<sup>1</sup>\u0000 for n = 0. As a result, we obtain a \u0000<tex>$mathbb{Z}/nmathbb{Z}$</tex>\u0000-action on \u0000<tex>$operatorname{Tr}(,f^{,n})$</tex>\u0000 as well as a circle action on \u0000<tex>$operatorname{Tr}(operatorname{id}_x)$</tex>\u0000.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qmath/haab013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49978797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Definable Regularity Lemmas for Nip Hypergraphs Nip超图的可定义正则引理
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.1093/qmath/haab011
Artem Chernikov;Sergei Starchenko
{"title":"Definable Regularity Lemmas for Nip Hypergraphs","authors":"Artem Chernikov;Sergei Starchenko","doi":"10.1093/qmath/haab011","DOIUrl":"https://doi.org/10.1093/qmath/haab011","url":null,"abstract":"We present a systematic study of the regularity phenomena for NIP hypergraphs and connections to the theory of (locally) generically stable measures, providing a model-theoretic hypergraph version of the results of Alon-Fischer-Newman and Lovász-Szegedy for graphs of bounded VC-dimension. We also consider the two extremal cases of regularity for stable and distal hypergraphs, improving and generalizing the corresponding results for graphs in the literature. Finally, we consider a related question of the existence of large (approximately) homogeneous definable subsets of NIP hypergraphs and provide some positive results and counterexamples, in particular for graphs definable in the p-adics.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49978795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 25
Presentations for Temperley–Lieb Algebras Temperley-Lieb代数的表示
IF 0.7 4区 数学
Quarterly Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.1093/qmath/haab001
James East
{"title":"Presentations for Temperley–Lieb Algebras","authors":"James East","doi":"10.1093/qmath/haab001","DOIUrl":"https://doi.org/10.1093/qmath/haab001","url":null,"abstract":"We give a new and conceptually straightforward proof of the well-known presentation for the Temperley–Lieb algebra, via an alternative new presentation. Our method involves twisted semigroup algebras, and we make use of two apparently new submonoids of the Temperley–Lieb monoid.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qmath/haab001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49947646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
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