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The Bergman number of a plane domain 平面域的伯格曼数
IF 0.6
Illinois Journal of Mathematics Pub Date : 2022-10-21 DOI: 10.1215/00192082-10678837
Christina Karafyllia
{"title":"The Bergman number of a plane domain","authors":"Christina Karafyllia","doi":"10.1215/00192082-10678837","DOIUrl":"https://doi.org/10.1215/00192082-10678837","url":null,"abstract":"Let $D$ be a domain in the complex plane $mathbb{C}$. The Hardy number of $D$, which first introduced by Hansen, is the maximal number $h(D)$ in $[0,+infty]$ such that $f$ belongs to the classical Hardy space $H^p (mathbb{D})$ whenever $0<p<h(D)$ and $f$ is holomorphic on the unit disk $mathbb{D}$ with values in $D$. As an analogue notion to the Hardy number of a domain $D$ in $mathbb{C}$, we introduce the Bergman number of $D$ and we denote it by $b(D)$. Our main result is that, if $D$ is regular, then $h(D)=b(D)$. This generalizes earlier work by the author and Karamanlis for simply connected domains. The Bergman number $b(D)$ is the maximal number in $[0,+infty]$ such that $f$ belongs to the weighted Bergman space $A^p_{alpha} (mathbb{D})$ whenever $p>0$ and $alpha>-1$ satisfy $0<frac{p}{alpha+2}<b(D)$ and $f$ is holomorphic on $mathbb{D}$ with values in $D$. We also establish several results about Hardy spaces and weighted Bergman spaces and we give a new characterization of the Hardy number and thus of the Bergman number of a regular domain with respect to the harmonic measure.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47279439","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
Subsets of rectifiable curves in Banach spaces II: Universal estimates for almost flat arcs Banach空间中可直曲线的子集Ⅱ：几乎平坦弧的普遍估计
IF 0.6
Illinois Journal of Mathematics Pub Date : 2022-08-22 DOI: 10.1215/00192082-10592390
Matthew Badger, Sean McCurdy
{"title":"Subsets of rectifiable curves in Banach spaces II: Universal estimates for almost flat arcs","authors":"Matthew Badger, Sean McCurdy","doi":"10.1215/00192082-10592390","DOIUrl":"https://doi.org/10.1215/00192082-10592390","url":null,"abstract":"We prove that in any Banach space the set of windows in which a rectifiable curve resembles two or more straight line segments is quantitatively small with constants that are independent of the curve, the dimension of the space, and the choice of norm. Together with Part I, this completes the proof of the necessary half of the Analyst's Traveling Salesman theorem with sharp exponent in uniformly convex spaces.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47675525","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: 4
Isoparametric submanifolds in Hilbert spaces and holonomy maps Hilbert空间中的等参子流形与完整映射
IF 0.6
Illinois Journal of Mathematics Pub Date : 2022-06-25 DOI: 10.1215/00192082-10450471
N. Koike
{"title":"Isoparametric submanifolds in Hilbert spaces and holonomy maps","authors":"N. Koike","doi":"10.1215/00192082-10450471","DOIUrl":"https://doi.org/10.1215/00192082-10450471","url":null,"abstract":"Let $pi:Pto B$ be a smooth $G$-bundle over a compact Riemannian manifold $B$ and $c$ a smooth loop in $B$ of constant seed $a(>0)$, where $G$ is compact semi-simple Lie group. In this paper, we prove that the holonomy map ${rm hol}_c:mathcal A_P^{H^s}to G$ is a homothetic submersion of coefficient $a$, where $s$ is a non-negative integer, $mathcal A_P^{H^s}$ is the Hilbert space of all $H^s$-connections of the bundle $P$. In particular, we prove that, if $s=0$, then ${rm hol}_c$ has minimal regularizable fibres. From this fact, we can derive that each component of the inverse image of any equifocal submanifold in $G$ by the holonomy map ${rm hol}_c:mathcal A_P^{H^0}to G$ is an isoparametric submanifold in $mathcal A_P^{H^0}$. As the result, we obtain a new systematic construction of isoparametric submanifolds in a Hilbert space.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43448523","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
Associativity and the cosmash product in operadic varieties of algebras 代数的可操作变数中的结合性与宇宙积
IF 0.6
Illinois Journal of Mathematics Pub Date : 2022-06-24 DOI: 10.1215/00192082-10678862
Ulo Reimaa, T. Linden, Corentin Vienne
{"title":"Associativity and the cosmash product in operadic varieties of algebras","authors":"Ulo Reimaa, T. Linden, Corentin Vienne","doi":"10.1215/00192082-10678862","DOIUrl":"https://doi.org/10.1215/00192082-10678862","url":null,"abstract":"In this article, we characterise the operadic variety of commutative associative algebras over a field via a (categorical) condition: the associativity of the so-called cosmash product. This condition, which is closely related to commutator theory, is quite strong: for example, groups do not satisfy it. However, in the case of commutative associative algebras, the cosmash product is nothing more than the tensor product; which explains why in this case it is associative. We prove that in the setting of operadic varieties of algebras over a field, it is the only example. Further examples in the non-operadic case are also discussed.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45151541","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
Prime power order circulant determinants 幂次循环行列式
IF 0.6
Illinois Journal of Mathematics Pub Date : 2022-05-25 DOI: 10.1215/00192082-10596890
Michael J. Mossinghoff, Christopher G. Pinner
{"title":"Prime power order circulant determinants","authors":"Michael J. Mossinghoff, Christopher G. Pinner","doi":"10.1215/00192082-10596890","DOIUrl":"https://doi.org/10.1215/00192082-10596890","url":null,"abstract":"Newman showed that for primes $pgeq 5$ an integral circulant determinant of prime power order $p^t$ cannot take the value $p^{t+1}$ once $tgeq 2.$ We show that many other values are also excluded. In particular, we show that $p^{2t}$ is the smallest power of $p$ attained for any $tgeq 3$, $pgeq 3.$ We demonstrate the complexity involved by giving a complete description of the $25times 25$ and $27times 27$ integral circulant determinants. The former case involves a partition of the primes that are $1bmod5$ into two sets, Tanner's textit{perissads} and textit{artiads}, which were later characterized by E. Lehmer.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41803368","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: 4
Widening of inequalities in COVID-19 years of life lost from 2020 to 2021: a Scottish Burden of Disease Study. 2020 年至 2021 年 COVID-19 生命损失年数不平等的扩大：苏格兰疾病负担研究。
Illinois Journal of Mathematics Pub Date : 2022-05-25 DOI: 10.1136/jech-2022-219090
Grant M A Wyper, Eilidh Fletcher, Ian Grant, Oliver Harding, Maria Teresa de Haro Moro, Gerry McCartney, Diane L Stockton
{"title":"Widening of inequalities in COVID-19 years of life lost from 2020 to 2021: a Scottish Burden of Disease Study.","authors":"Grant M A Wyper, Eilidh Fletcher, Ian Grant, Oliver Harding, Maria Teresa de Haro Moro, Gerry McCartney, Diane L Stockton","doi":"10.1136/jech-2022-219090","DOIUrl":"10.1136/jech-2022-219090","url":null,"abstract":"<p><strong>Background: </strong>Previous studies have highlighted the large extent of inequality in adverse COVID-19 health outcomes. Our aim was to monitor changes in overall, and inequalities in, COVID-19 years of life lost to premature mortality (YLL) in Scotland from 2020 and 2021.</p><p><strong>Methods: </strong>Cause-specific COVID-19 mortality counts were derived at age group and area deprivation level using Scottish death registrations for 2020 and 2021. YLL was estimated by multiplying mortality counts by age-conditional life expectancy from the Global Burden of Disease 2019 reference life table. Various measures of absolute and relative inequality were estimated for triangulation purposes.</p><p><strong>Results: </strong>There were marked inequalities in COVID-19 YLL by area deprivation in 2020, which were further exacerbated in 2021; confirmed across all measures of absolute and relative inequality. Half (51%) of COVID-19 YLL was attributable to inequalities in area deprivation in 2021, an increase from 41% in 2020.</p><p><strong>Conclusion: </strong>Despite a highly impactful vaccination programme in preventing mortality, COVID-19 continues to represent a substantial area of fatal population health loss for which inequalities have widened. Tackling systemic inequalities with effective interventions is required to mitigate further unjust health loss in the Scottish population from COVID-19 and other causes of ill-health and mortality.</p>","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88136926","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
Weingarten flows in Riemannian manifolds 黎曼流形中的Weingarten流
IF 0.6
Illinois Journal of Mathematics Pub Date : 2022-05-19 DOI: 10.1215/00192082-10817329
R. F. Lima
{"title":"Weingarten flows in Riemannian manifolds","authors":"R. F. Lima","doi":"10.1215/00192082-10817329","DOIUrl":"https://doi.org/10.1215/00192082-10817329","url":null,"abstract":"Given orientable Riemannian manifolds $M^n$ and $bar M^{n+1},$ we study flows $F_t:M^nrightarrowbar M^{n+1},$ called Weingarten flows,in which the hypersurfaces $F_t(M)$ evolve in the direction of their normal vectors with speed given by a function $W$ of their principal curvatures,called a Weingarten function, which is homogeneous, monotonic increasing with respect to any of its variables, and positive on the positive cone. We obtain existence results for flows with isoparametric initial data, in which the hypersurfaces $F_t:M^nrightarrowbar M^{n+1}$ are all parallel, and $bar M^{n+1}$ is either a simply connected space form or a rank-one symmetric space of noncompact type. We prove that the avoidance principle holds for Weingarten flows defined by odd Weingarten functions, and also that such flows are embedding preserving.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46232637","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
Labor and Art 劳动与艺术
Illinois Journal of Mathematics Pub Date : 2022-05-01 DOI: 10.5622/illinois/9780252044397.003.0013
Rebekah Bryer, Thomas E. MacMillan
{"title":"Labor and Art","authors":"Rebekah Bryer, Thomas E. MacMillan","doi":"10.5622/illinois/9780252044397.003.0013","DOIUrl":"https://doi.org/10.5622/illinois/9780252044397.003.0013","url":null,"abstract":"This chapter discusses the controversy surrounding the removal of the Maine Labor Mural, an eleven-panel piece of public art, by Maine governor Paul LePage in 2011. Removed as part of a wider conflict over labor rights, the mural's disappearance is analyzed in conjunction with the fight over labor legislation and pro-austerity measures. The mural controversy's ramifications are addressed, as is its return to public display at the Maine State Museum in 2013. The chapter concludes with a discussion of the legacy of labor and public art in Maine.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"1 1","pages":"207-222"},"PeriodicalIF":0.0,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147911568","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
Lipschitz metric isometries between outer spaces of virtually free groups 虚拟自由群外空间之间的Lipschitz度量等距
IF 0.6
Illinois Journal of Mathematics Pub Date : 2022-03-17 DOI: 10.1215/00192082-10592435
Rylee Alanza Lyman
{"title":"Lipschitz metric isometries between outer spaces of virtually free groups","authors":"Rylee Alanza Lyman","doi":"10.1215/00192082-10592435","DOIUrl":"https://doi.org/10.1215/00192082-10592435","url":null,"abstract":"Dowdall and Taylor observed that given a finite-index subgroup of a free group, taking covers induces an embedding from the Outer Space of the free group to the Outer Space of the subgroup, that this embedding is an isometry with respect to the (asymmetric) Lipschitz metric, and that the embedding sends folding paths to folding paths. The purpose of this note is to extend this result to virtually free groups. We further extend a result Francaviglia and Martino, proving the existence of\"candidates\"for the Lipschitz distance between points in the Outer Space of the virtually free group. Additionally we identify a deformation retraction of the spine of the Outer Space for the virtually free group with the space considered by Krsti'c and Vogtmann.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48082774","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
Vanishing of (co)homology of Burch and related submodules Burch及其相关子模的（共）同调的消失
IF 0.6
Illinois Journal of Mathematics Pub Date : 2022-01-04 DOI: 10.1215/00192082-10429128
Souvik Dey, Toshinori Kobayashi
{"title":"Vanishing of (co)homology of Burch and related submodules","authors":"Souvik Dey, Toshinori Kobayashi","doi":"10.1215/00192082-10429128","DOIUrl":"https://doi.org/10.1215/00192082-10429128","url":null,"abstract":"We introduce the notion of Burch submodules and weakly $mathfrak m$-full submodules of modules over local rings and study their properties. One of our main results shows that Burch submodules satisfy 2-Tor rigid and test property. We also show that over a local ring $(R,mathfrak m)$ a submodule $M$ of a finitely generated $R$-module $X$, such that either $M=mathfrak m X$ or $M(subseteq mathfrak m X$) is weakly $mathfrak m$-full in $X$, is 1-Tor rigid and a test module provided that $X$ is faithful (and $X/M$ has finite length when $M$ is weakly $mathfrak m$-full). As an application, we give a new class of rings such that a conjecture of Huneke and Wiegand is affirmative over them.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46224949","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: 5
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