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Splittings for $C^*$-correspondences and strong shift equivalence C^*$对应的分裂和强移位等价性
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2024-02-26 DOI: 10.7146/math.scand.a-142308
K. Brix, Alexander Mundey, Adam Rennie
{"title":"Splittings for $C^*$-correspondences and strong shift equivalence","authors":"K. Brix, Alexander Mundey, Adam Rennie","doi":"10.7146/math.scand.a-142308","DOIUrl":"https://doi.org/10.7146/math.scand.a-142308","url":null,"abstract":"We present an extension of the notion of in-splits from symbolic dynamics to topological graphs and, more generally, to $C^*$-correspondences. We demonstrate that in-splits provide examples of strong shift equivalences of $C^*$-correspondences. Furthermore, we provide a streamlined treatment of Muhly, Pask, and Tomforde's proof that any strong shift equivalence of regular $C^*$-correspondences induces a (gauge-equivariant) Morita equivalence between Cuntz-Pimsner algebras. For topological graphs, we prove that in-splits induce diagonal-preserving gauge-equivariant $*$-isomorphisms in analogy with the results for Cuntz-Krieger algebras. Additionally, we examine the notion of out-splits for $C^*$-correspondences.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140428853","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
Minimal piecewise linear cones in $mathbb{R}^4$ $mathbb{R}^4$中的最小分片线性锥体
IF 0.5 4区 数学
Mathematica Scandinavica Pub Date : 2024-02-26 DOI: 10.7146/math.scand.a-140336
Asgeir Valfells
{"title":"Minimal piecewise linear cones in $mathbb{R}^4$","authors":"Asgeir Valfells","doi":"10.7146/math.scand.a-140336","DOIUrl":"https://doi.org/10.7146/math.scand.a-140336","url":null,"abstract":"We consider three dimensional piecewise linear cones in $mathbb{R}^4$ that are mass minimal with respect to Lipschitz maps in the sense of [Almgren, F., Mem. Amer. Math. Soc. 4 (1976), no. 165] as in [Taylor, J. E., Ann. of Math. (2) 103 (1976), no. 3, 489–539]. There are three that arise naturally by taking products of $mathbb{R}$ with lower dimensional cases and earlier literature has demonstrated the existence of two with 0-dimensional singularities. We classify all possible candidates and demonstrate that there are no piecewise linear minimizers outside these five.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140429909","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
A note on $mathcal{M}$-normal embedded subgroups of finite groups 关于有限群的$mathcal{M}$-正规嵌入子群的一个注记
4区 数学
Mathematica Scandinavica Pub Date : 2023-10-26 DOI: 10.7146/math.scand.a-137337
Jian Sun, Haoran Yu
{"title":"A note on $mathcal{M}$-normal embedded subgroups of finite groups","authors":"Jian Sun, Haoran Yu","doi":"10.7146/math.scand.a-137337","DOIUrl":"https://doi.org/10.7146/math.scand.a-137337","url":null,"abstract":"In this note, we obtain a criterion for $p$-nilpotency of a finite group. We not only simplify the proofs of the main theorems of Chen et al. [On $mathcal{M}$-normal embedded subgroups and the structure of finite groups, Math. Scand. 127(2021), no. 2, 243–251] but also generalize these results.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136376476","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
Corrections to "Vanishing Morrey integrability for Riesz potentials in Morrey-Orlicz spaces" 对“Morrey- orlicz空间中Riesz势的Morrey可积性消失”的修正
4区 数学
Mathematica Scandinavica Pub Date : 2023-10-26 DOI: 10.7146/math.scand.a-140156
Yoshihiro Mizuta, Tetsu Shimomura
{"title":"Corrections to \"Vanishing Morrey integrability for Riesz potentials in Morrey-Orlicz spaces\"","authors":"Yoshihiro Mizuta, Tetsu Shimomura","doi":"10.7146/math.scand.a-140156","DOIUrl":"https://doi.org/10.7146/math.scand.a-140156","url":null,"abstract":"In this note some flaws in our recent paper by Mizuta and Shimomura (Math. Scand. 129 (2023), no.~2, 374--400) are corrected.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134907880","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
On shifting the principal eigenvalue of Dirichlet problem to infinity with non-transversal incompressible drift 带非横向不可压缩漂移的Dirichlet问题的主特征值移至无穷
4区 数学
Mathematica Scandinavica Pub Date : 2023-10-26 DOI: 10.7146/math.scand.a-139656
Brice Franke, Damak Mondher, Nassim Athmouni, Nejib Yaakoubi
{"title":"On shifting the principal eigenvalue of Dirichlet problem to infinity with non-transversal incompressible drift","authors":"Brice Franke, Damak Mondher, Nassim Athmouni, Nejib Yaakoubi","doi":"10.7146/math.scand.a-139656","DOIUrl":"https://doi.org/10.7146/math.scand.a-139656","url":null,"abstract":"We prove that it is always possible to add some divergence free drift vector field to some two dimensional spherical Dirichlet problem, such that the resulting principal eigenvalue lies above a prescribed bound. By construction those drift vector fields vanish on the boundary and their flow lines individually stay away from the boundary. The capacity of those drift vector fields to accelerate diffusivity originates from high frequency oscillation of the associated flow lines. The lower bounds for the spectrum are obtained through isoperimetric inequalities for flow invariant functions.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136377027","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
Bilinear forms, Schur multipliers, complete boundedness and duality 双线性形式，舒尔乘子，完全有界性和对偶性
4区 数学
Mathematica Scandinavica Pub Date : 2023-10-26 DOI: 10.7146/math.scand.a-140205
Erik Christensen
{"title":"Bilinear forms, Schur multipliers, complete boundedness and duality","authors":"Erik Christensen","doi":"10.7146/math.scand.a-140205","DOIUrl":"https://doi.org/10.7146/math.scand.a-140205","url":null,"abstract":"Grothendieck's inequalities for operators and bilinear forms imply some factorization results for complex $m times n$ matrices. Based on the theory of operator spaces and completely bounded maps we present norm optimal versions of these results and two norm optimal factorization results related to the Schur product. We show that the spaces of bilinear forms and of Schur multipliers are conjugate duals to each other with respect to their completely bounded norms.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134907018","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
Attainable measures for certain types of $p$-adic Duffin-Schaeffer sets 某些类型$p$一元Duffin-Schaeffer集合的可实现测度
4区 数学
Mathematica Scandinavica Pub Date : 2023-10-26 DOI: 10.7146/math.scand.a-139832
Laursen, Mathias Løkkegaard
{"title":"Attainable measures for certain types of $p$-adic Duffin-Schaeffer sets","authors":"Laursen, Mathias Løkkegaard","doi":"10.7146/math.scand.a-139832","DOIUrl":"https://doi.org/10.7146/math.scand.a-139832","url":null,"abstract":"This paper settles recent conjectures concerning the $p$-adic Haar measure applied to a family of sets defined in terms of Diophantine approximation. This is done by determining the spectrum of measure values for each family and seeing that this contradicts the corresponding conjectures.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136377032","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
Harmonic analogue of Bohr phenomenon of certain classes of univalent and analytic functions 一类一元函数和解析函数玻尔现象的调和模拟
4区 数学
Mathematica Scandinavica Pub Date : 2023-10-26 DOI: 10.7146/math.scand.a-139645
Molla Basir Ahamed, Vasudevarao Allu
{"title":"Harmonic analogue of Bohr phenomenon of certain classes of univalent and analytic functions","authors":"Molla Basir Ahamed, Vasudevarao Allu","doi":"10.7146/math.scand.a-139645","DOIUrl":"https://doi.org/10.7146/math.scand.a-139645","url":null,"abstract":"A class $ mathcal {F} $ consisting of analytic functions $ f(z)=sum _{n=0}^{infty }a_nz^n $ in the unit disk $ mathbb {D}={zin mathbb {C}:lvert zrvert <1} $ is said to satisfy Bohr phenomenon if there exists an $ r_f>0 $ such that $$ sum _{n=1}^{infty }lvert a_nrvert r^nleq d(f(0),partial mathbb {D}) $$ for every function $ fin mathcal {F} $, and $lvert zrvert =rleq r_f $. The largest radius $ r_f $ is known as the Bohr radius and the inequality $ sum _{n=1}^{infty }lvert a_nrvert r^nleq d(f(0),partial f(mathbb {D})) $ is known as the Bohr inequality for the class $ mathcal {F} $, where $d$ is the Euclidean distance. In this paper, we prove several sharp improved and refined versions of Bohr-type inequalities in terms of area measure of functions in a certain subclass of analytic and univalent (i.e. one-to-one) functions. As a consequence, we obtain several interesting corollaries on the Bohr-type inequality for the class which are the harmonic analogue of some Bohr-type inequality for the class of analytic functions.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134907524","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
Critical configurations for three projective views 三个投影视图的关键配置
4区 数学
Mathematica Scandinavica Pub Date : 2023-10-26 DOI: 10.7146/math.scand.a-139788
Martin Bråtelund
{"title":"Critical configurations for three projective views","authors":"Martin Bråtelund","doi":"10.7146/math.scand.a-139788","DOIUrl":"https://doi.org/10.7146/math.scand.a-139788","url":null,"abstract":"The problem of structure from motion is concerned with recovering the 3-dimensional structure of an object from a set of 2-dimensional images taken by unknown cameras. Generally, all information can be uniquely recovered if enough images and point correspondences are provided, yet there are certain cases where unique recovery is impossible; these are called emph{critical configurations}. We use an algebraic approach to study the critical configurations for three projective cameras. We show that all critical configurations lie on the intersection of quadric surfaces, and classify exactly which intersections constitute a critical configuration.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134907529","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
Finitely presented isomorphisms of Cuntz-Krieger algebras and continuous orbit equivalence of one-sided topological Markov shifts 有限表示的Cuntz-Krieger代数同构及单侧拓扑马尔可夫位移的连续轨道等价
4区 数学
Mathematica Scandinavica Pub Date : 2023-10-26 DOI: 10.7146/math.scand.a-139804
Kengo Matsumoto
{"title":"Finitely presented isomorphisms of Cuntz-Krieger algebras and continuous orbit equivalence of one-sided topological Markov shifts","authors":"Kengo Matsumoto","doi":"10.7146/math.scand.a-139804","DOIUrl":"https://doi.org/10.7146/math.scand.a-139804","url":null,"abstract":"We introduce the notion of finitely presented isomorphism between Cuntz–Krieger algebras, and of finitely presented isomorphic Cuntz–Krieger algebras. We prove that there exists a finitely presented isomorphism between Cuntz–Krieger algebras $mathcal{O}_A$ and $mathcal{O}_B$ if and only if their one-sided topological Markov shifts $(X_A,sigma_A)$ and $(X_B,sigma_B)$ are continuously orbit equivalent. Hence the value $det (I-A)$ is a complete invariant for the existence of a finitely presented isomorphism between isomorphic Cuntz–Krieger algebras, so that there exists a pair of Cuntz–Krieger algebras which are isomorphic but not finitely presented isomorphic.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134907178","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
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