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Illinois Journal of Mathematics最新文献

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A pointwise inequality for derivatives of solutions of the heat equation in bounded domains 有界区域内热方程解的导数的一个逐点不等式
Illinois Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.1215/00192082-10908733
Stefan Steinerberger
{"title":"A pointwise inequality for derivatives of solutions of the heat equation in bounded domains","authors":"Stefan Steinerberger","doi":"10.1215/00192082-10908733","DOIUrl":"https://doi.org/10.1215/00192082-10908733","url":null,"abstract":"Let $u(t,x)$ be a solution of the heat equation in $mathbb{R}^n$. Then, each $k-$th derivative also solves the heat equation and satisfies a maximum principle, the largest $k-$th derivative of $u(t,x)$ cannot be larger than the largest $k-$th derivative of $u(0,x)$. We prove an analogous statement for the solution of the heat equation on bounded domains $Omega subset mathbb{R}^n$ with Dirichlet boundary conditions. As an application, we give a new and fairly elementary proof of the sharp growth of the second derivatives of Laplacian eigenfunction $-Delta phi_k = lambda_k phi_k$ with Dirichlet conditions on smooth domains $Omega subset mathbb{R}^n$.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135180997","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
A note on domain monotonicity for the Neumann eigenvalues of the Laplacian 拉普拉斯算子的诺伊曼特征值的域单调性的一个注记
Illinois Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.1215/00192082-10972651
Kei Funano
{"title":"A note on domain monotonicity for the Neumann eigenvalues of the Laplacian","authors":"Kei Funano","doi":"10.1215/00192082-10972651","DOIUrl":"https://doi.org/10.1215/00192082-10972651","url":null,"abstract":"Given a convex domain and its convex sub-domain we prove a variant of domain monotonicity for the Neumann eigenvalues of the Laplacian. As an application of our method we also obtain an upper bound for Neumann eigenvalues of the Laplacian of a convex domain.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"182 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135509000","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
Critical metrics of the volume functional with pinched curvature 具有压缩曲率的体积函数的临界度量
Illinois Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.1215/00192082-10972626
H. Baltazar, C. Queiroz
{"title":"Critical metrics of the volume functional with pinched curvature","authors":"H. Baltazar, C. Queiroz","doi":"10.1215/00192082-10972626","DOIUrl":"https://doi.org/10.1215/00192082-10972626","url":null,"abstract":"","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135509002","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
Fundamental heaps for surface ribbons and cocycle invariants 表面带状和循环不变量的基本堆
Illinois Journal of Mathematics Pub Date : 2023-01-01 DOI: 10.1215/00192082-10972597
Masahico Saito, Emanuele Zappala
{"title":"Fundamental heaps for surface ribbons and cocycle invariants","authors":"Masahico Saito, Emanuele Zappala","doi":"10.1215/00192082-10972597","DOIUrl":"https://doi.org/10.1215/00192082-10972597","url":null,"abstract":"We introduce the notion of fundamental heap for compact orientable surfaces with boundary embedded in $3$-space, which is an isotopy invariant of the embedding. It is a group, endowed with a ternary heap operation, defined using diagrams of surfaces in a form of thickened trivalent graphs called surface ribbons. We prove that the fundamental heap has a free part whose rank is given by the number of connected components of the surface. We study the behavior of the invariant under boundary connected sum, as well as addition/deletion of twisted bands, and provide formulas relating the number of generators of the fundamental heap to the Euler characteristics. We describe in detail the effect of stabilization on the fundamental heap, and determine that for each given finitely presented group there exists a surface ribbon whose fundamental heap is isomorphic to it, up to extra free factors. A relation between the fundamental heap and the Wirtinger presentation is also described. Moreover, we introduce cocycle invariants for surface ribbons using the notion of mutually distributive cohomology and heap colorings. Explicit computations of fundamental heap and cocycle invariants are presented.","PeriodicalId":56298,"journal":{"name":"Illinois Journal of Mathematics","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135509004","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
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
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