发布求助
文献互助 智能选刊 最新文献

Mathematika最新文献

筛选
英文 中文
On orthogonal and staircase connectedness in the plane 平面上的正交连通性和阶梯连通性
IF 0.8 3区 数学
Mathematika Pub Date : 2025-04-29 DOI: 10.1112/mtk.70021
Julia Q. Du, Liping Yuan, Tudor Zamfirescu
{"title":"On orthogonal and staircase connectedness in the plane","authors":"Julia Q. Du,&nbsp;Liping Yuan,&nbsp;Tudor Zamfirescu","doi":"10.1112/mtk.70021","DOIUrl":"https://doi.org/10.1112/mtk.70021","url":null,"abstract":"<p>In this paper, we introduce <i>o</i>-extreme points defined by using orthogonal paths in orthogonally connected sets. We investigate their properties and obtain Minkowski-type theorems involving orthogonally connected sets. Using <i>o</i>-extreme points, we give some characterizations of staircase connectedness.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143888809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A note on limsup sets of annuli 关于环空的limsup组的注释
IF 0.8 3区 数学
Mathematika Pub Date : 2025-04-28 DOI: 10.1112/mtk.70023
Mumtaz Hussain, Benjamin Ward
{"title":"A note on limsup sets of annuli","authors":"Mumtaz Hussain,&nbsp;Benjamin Ward","doi":"10.1112/mtk.70023","DOIUrl":"https://doi.org/10.1112/mtk.70023","url":null,"abstract":"<p>We consider the set of points in infinitely many max-norm annuli centred at rational points in <span></span><math></math>. We give Jarník–Besicovitch-type theorems for this set in terms of Hausdorff dimension. Interestingly, we find that if the outer radii are decreasing sufficiently slowly, dependent only on the dimension <span></span><math></math>, and the thickness of the annuli is decreasing rapidly, then the dimension of the set tends towards <span></span><math></math>. We also consider various other forms of annuli including rectangular annuli and quasi-annuli described by the difference between balls of two different norms. Our results are deduced through a novel combination of a version of Cassel's scaling lemma and a generalisation of the Mass Transference Principle, namely the Mass transference principle from rectangles to rectangles due to Wang and Wu (Math. Ann. 2021).</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143880056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Minimal periodic foams with fixed inradius 最小周期泡沫与固定半径
IF 0.8 3区 数学
Mathematika Pub Date : 2025-04-22 DOI: 10.1112/mtk.70020
Annalisa Cesaroni, Matteo Novaga
{"title":"Minimal periodic foams with fixed inradius","authors":"Annalisa Cesaroni,&nbsp;Matteo Novaga","doi":"10.1112/mtk.70020","DOIUrl":"https://doi.org/10.1112/mtk.70020","url":null,"abstract":"<p>In this note, we show existence and regularity of periodic tilings of the Euclidean space into equal cells containing a ball of fixed radius, which minimize either the classical or the fractional perimeter. We also discuss some qualitative properties of minimizers in dimensions 3 and 4.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143861591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 0
Spherical functions and Stolarsky's invariance principle 球面函数与斯托拉斯基不变性原理
IF 0.8 3区 数学
Mathematika Pub Date : 2025-04-21 DOI: 10.1112/mtk.70019
M. M. Skriganov
{"title":"Spherical functions and Stolarsky's invariance principle","authors":"M. M. Skriganov","doi":"10.1112/mtk.70019","DOIUrl":"https://doi.org/10.1112/mtk.70019","url":null,"abstract":"<p>In the previous paper (Skriganov, <i>J. Complexity</i> 56 (2020), 101428), Stolarsky's invariance principle, known in the literature for point distributions on Euclidean spheres, has been extended to the real, complex, and quaternionic projective spaces and the octonionic projective plane. Geometric features of these spaces as well as their models in terms of Jordan algebras have been used very essentially in the proof. In the present paper, a new pure analytic proof of the extended Stolarsky's invariance principle is given, relying on the theory of spherical functions on compact Riemannian symmetric manifolds of rank one.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143853058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On the determinants of matrices with elements from arbitrary sets 关于元素来自任意集合的矩阵的行列式
IF 0.8 3区 数学
Mathematika Pub Date : 2025-04-04 DOI: 10.1112/mtk.70018
Ilya D. Shkredov, Igor E. Shparlinski
{"title":"On the determinants of matrices with elements from arbitrary sets","authors":"Ilya D. Shkredov,&nbsp;Igor E. Shparlinski","doi":"10.1112/mtk.70018","DOIUrl":"https://doi.org/10.1112/mtk.70018","url":null,"abstract":"<p>Recently there have been several works estimating the number of <span></span><math></math> matrices with elements from some finite sets <span></span><math></math> of arithmetic interest and of a given determinant. Typically such results are compared with the trivial upper bound <span></span><math></math>, where <span></span><math></math> is the cardinality of <span></span><math></math>. Here we show that even for arbitrary sets <span></span><math></math>, some recent results from additive combinatorics enable us to obtain a stronger bound with a power saving.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143770450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On a Gallai-type problem and illumination of spiky balls and cap bodies 关于尖球和帽体的盖莱型问题及其说明
IF 0.8 3区 数学
Mathematika Pub Date : 2025-03-25 DOI: 10.1112/mtk.70017
Andrii Arman, Andriy Bondarenko, Andriy Prymak, Danylo Radchenko
{"title":"On a Gallai-type problem and illumination of spiky balls and cap bodies","authors":"Andrii Arman,&nbsp;Andriy Bondarenko,&nbsp;Andriy Prymak,&nbsp;Danylo Radchenko","doi":"10.1112/mtk.70017","DOIUrl":"https://doi.org/10.1112/mtk.70017","url":null,"abstract":"<p>We show that any finite family of pairwise intersecting balls in <span></span><math></math> can be pierced by <span></span><math></math> points improving the previously known estimate of <span></span><math></math>. As a corollary, this implies that any 2-illuminable spiky ball in <span></span><math></math> can be illuminated by <span></span><math></math> directions. For the illumination number of convex spiky balls, that is, cap bodies, we show an upper bound in terms of the sizes of certain related spherical codes and coverings. For large dimensions, this results in an upper bound of <span></span><math></math>, which can be compared with the previous <span></span><math></math> established only for the centrally symmetric cap bodies. We also prove the lower bounds of <span></span><math></math> for the three problems above.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70017","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143698904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 0
A sharp higher order Sobolev embedding 一个高阶索博列夫嵌入
IF 0.8 3区 数学
Mathematika Pub Date : 2025-03-12 DOI: 10.1112/mtk.70012
Raul Hindov, Shahaf Nitzan, Jan-Fredrik Olsen, Eskil Rydhe
{"title":"A sharp higher order Sobolev embedding","authors":"Raul Hindov,&nbsp;Shahaf Nitzan,&nbsp;Jan-Fredrik Olsen,&nbsp;Eskil Rydhe","doi":"10.1112/mtk.70012","DOIUrl":"https://doi.org/10.1112/mtk.70012","url":null,"abstract":"<p>We obtain sharp embeddings from the Sobolev space <span></span><math></math> into the space <span></span><math></math> and determine the extremal functions. This improves on a previous estimate of the sharp constants of these embeddings due to Kalyabin.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 0
An exotic calculus of Berezin–Toeplitz operators Berezin-Toeplitz算子的奇异演算
IF 0.8 3区 数学
Mathematika Pub Date : 2025-03-08 DOI: 10.1112/mtk.70016
Izak Oltman
{"title":"An exotic calculus of Berezin–Toeplitz operators","authors":"Izak Oltman","doi":"10.1112/mtk.70016","DOIUrl":"https://doi.org/10.1112/mtk.70016","url":null,"abstract":"<p>We develop a calculus of Berezin–Toeplitz operators quantizing exotic classes of smooth functions on compact Kähler manifolds and acting on holomorphic sections of powers of positive line bundles. These functions (classical observables) are exotic in the sense that their derivatives are allowed to grow in ways controlled by local geometry and the power of the line bundle. The properties of this quantization are obtained via careful analysis of the kernels of the operators using Melin and Sjöstrand's method of complex stationary phase. We obtain a functional calculus result, a trace formula, and a parametrix construction for this larger class of functions. These results are crucially used in proving a probabilistic Weyl-law for randomly perturbed (standard) Berezin–Toeplitz operators in Oltman (arXiv:2207.09599).</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70016","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 0
Youden's demon is Sylvester's problem 尤登的恶魔是西尔维斯特的问题
IF 0.8 3区 数学
Mathematika Pub Date : 2025-02-18 DOI: 10.1112/mtk.70015
Florian Frick, Andrew Newman, Wesley Pegden
{"title":"Youden's demon is Sylvester's problem","authors":"Florian Frick,&nbsp;Andrew Newman,&nbsp;Wesley Pegden","doi":"10.1112/mtk.70015","DOIUrl":"https://doi.org/10.1112/mtk.70015","url":null,"abstract":"<p>If four people with Gaussian-distributed heights stand at Gaussian positions on the plane, the probability that there are exactly two people whose height is above the average of the four is exactly the same as the probability that they stand in convex position; both probabilities are <span></span><math></math>. We show that this is a special case of a more general phenomenon: The problem of determining the position of the mean among the order statistics of Gaussian random points on the real line (Youden's demon problem) is the same as a natural generalization of Sylvester's four point problem to Gaussian points in <span></span><math></math>. Our main tool is the observation that the Gale dual of independent samples in <span></span><math></math> itself can be taken to be a set of independent points (translated to have barycenter at the origin) when the distribution of the points is Gaussian.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143431696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
A four-dimensional peabody of constant width 宽度恒定的四维体
IF 0.8 3区 数学
Mathematika Pub Date : 2025-02-13 DOI: 10.1112/mtk.70014
Isaac Arelio, Luis Montejano, Deborah Oliveros
{"title":"A four-dimensional peabody of constant width","authors":"Isaac Arelio,&nbsp;Luis Montejano,&nbsp;Deborah Oliveros","doi":"10.1112/mtk.70014","DOIUrl":"https://doi.org/10.1112/mtk.70014","url":null,"abstract":"<p>In this paper, we present a unique four-dimensional body of constant width based on the classical notion of focal conics.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"71 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143404474","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 0
下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信