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Retrieving Yang–Mills–Higgs fields in Minkowski space from active local measurements 从主动局部测量找回闵科夫斯基空间的杨-米尔斯-希格斯场
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-30 DOI: 10.1007/s00208-024-02980-z
Xi Chen, Matti Lassas, Lauri Oksanen, Gabriel P. Paternain
{"title":"Retrieving Yang–Mills–Higgs fields in Minkowski space from active local measurements","authors":"Xi Chen, Matti Lassas, Lauri Oksanen, Gabriel P. Paternain","doi":"10.1007/s00208-024-02980-z","DOIUrl":"https://doi.org/10.1007/s00208-024-02980-z","url":null,"abstract":"<p>We show that we can retrieve a Yang–Mills potential and a Higgs field (up to gauge) from source-to-solution type data associated with the classical Yang–Mills–Higgs equations in Minkowski space <span>({mathbb {R}}^{1+3})</span>. We impose natural non-degeneracy conditions on the representation for the Higgs field and on the Lie algebra of the structure group which are satisfied for the case of the Standard Model. Our approach exploits the non-linear interaction of waves generated by sources with values in the centre of the Lie algebra showing that abelian components can be used effectively to recover the Higgs field.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"37 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Spectrum invariance dilemma for nonuniformly kinematically similar systems 非均匀运动学相似系统的频谱不变性困境
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-29 DOI: 10.1007/s00208-024-02969-8
Néstor Jara, Claudio A. Gallegos
{"title":"Spectrum invariance dilemma for nonuniformly kinematically similar systems","authors":"Néstor Jara, Claudio A. Gallegos","doi":"10.1007/s00208-024-02969-8","DOIUrl":"https://doi.org/10.1007/s00208-024-02969-8","url":null,"abstract":"<p>We unveil instances where nonautonomous linear systems manifest distinct nonuniform <span>(mu )</span>-dichotomy spectra despite admitting nonuniform <span>((mu , varepsilon ))</span>-kinematic similarity. Exploring the theoretical foundations of this lack of invariance, we discern the pivotal influence of the parameters involved in the property of nonuniform <span>(mu )</span>-dichotomy such as in the notion of nonuniform <span>((mu , varepsilon ))</span>-kinematic similarity. To effectively comprehend these dynamics, we introduce the stable and unstable optimal ratio maps, along with the <span>(varepsilon )</span>-neighborhood of the nonuniform <span>(mu )</span>-dichotomy spectrum. These new concepts provide a framework for understanding scenarios governed by the noninvariance of the nonuniform <span>(mu )</span>-dichotomy spectrum.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"24 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Idempotents and homology of diagram algebras 图代数的幂等性和同源性
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-28 DOI: 10.1007/s00208-024-02960-3
Guy Boyde
{"title":"Idempotents and homology of diagram algebras","authors":"Guy Boyde","doi":"10.1007/s00208-024-02960-3","DOIUrl":"https://doi.org/10.1007/s00208-024-02960-3","url":null,"abstract":"<p>This paper provides a systematization of some recent results in homology of algebras. Our main theorem gives criteria under which the homology of a diagram algebra is isomorphic to the homology of the subalgebra on diagrams having the maximum number of left-to-right connections. From this theorem, we deduce the ‘invertible-parameter’ cases of the Temperley–Lieb and Brauer results of Boyd–Hepworth and Boyd–Hepworth–Patzt. We are also able to give a new proof of Sroka’s theorem that the homology of an odd-strand Temperley–Lieb algebra vanishes, as well as an analogous result for Brauer algebras and an interpretation of both results in the even-strand case. Our proofs are relatively elementary: in particular, no auxiliary chain complexes or spectral sequences are required. We briefly discuss the relationship to cellular algebras in the sense of Graham–Lehrer.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"6 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Balanced measures, sparse domination and complexity-dependent weight classes 平衡度量、稀疏支配和取决于复杂性的权重等级
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-28 DOI: 10.1007/s00208-024-02961-2
José M. Conde Alonso, Jill Pipher, Nathan A. Wagner
{"title":"Balanced measures, sparse domination and complexity-dependent weight classes","authors":"José M. Conde Alonso, Jill Pipher, Nathan A. Wagner","doi":"10.1007/s00208-024-02961-2","DOIUrl":"https://doi.org/10.1007/s00208-024-02961-2","url":null,"abstract":"<p>We study sparse domination for operators defined with respect to an atomic filtration on a space equipped with a general measure <span>(mu )</span>. In the case of Haar shifts, <span>(L^p)</span>-boundedness is known to require a weak regularity condition, which we prove to be sufficient to have a sparse domination-like theorem. Our result allows us to characterize the class of weights where Haar shifts are bounded. A surprising novelty is that said class depends on the complexity of the Haar shift operator under consideration. Our results are qualitatively sharp.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"35 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Classification of non-CSC extremal Kähler metrics on K-surfaces $$S^2_{{alpha }}$$ and $$S^2_{{alpha ,beta }}$$ K 曲面 $$S^2_{{alpha }}$ 和 $$S^2_{{alpha ,beta }}$ 上的非 CSC 极值凯勒度量的分类
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-27 DOI: 10.1007/s00208-024-02967-w
Yingjie Meng, Zhiqiang Wei
{"title":"Classification of non-CSC extremal Kähler metrics on K-surfaces $$S^2_{{alpha }}$$ and $$S^2_{{alpha ,beta }}$$","authors":"Yingjie Meng, Zhiqiang Wei","doi":"10.1007/s00208-024-02967-w","DOIUrl":"https://doi.org/10.1007/s00208-024-02967-w","url":null,"abstract":"<p>We commonly refer to an extremal Kähler metric with finitely many singularities on a compact Riemann surface as a metric where the Hessian of the curvature of the Metric is Umbilical, known as an HCMU metric. In this study, we specifically classify non-CSC HCMU metrics on the K-surfaces <span>(S^2_{{alpha }})</span> and <span>(S^2_{{alpha ,beta }})</span>.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"141 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Long-time dynamics and singular limit of a shear beam model 剪切梁模型的长时动力学和奇异极限
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-27 DOI: 10.1007/s00208-024-02978-7
M. M. Freitas, D. S. Almeida, A. J. A. Ramos, M. J. Dos Santos, R. Q. Caljaro
{"title":"Long-time dynamics and singular limit of a shear beam model","authors":"M. M. Freitas, D. S. Almeida, A. J. A. Ramos, M. J. Dos Santos, R. Q. Caljaro","doi":"10.1007/s00208-024-02978-7","DOIUrl":"https://doi.org/10.1007/s00208-024-02978-7","url":null,"abstract":"<p>This paper is dedicated to studying the long-term dynamics of a beam model known as the Shear beam model (without rotary inertia). Unlike the classical Timoshenko beam model, which combines bending moment and shear force, the Shear beam model has only one wave speed without blow-up at lower frequencies. This distinction has a significant impact on the analysis of long-term dynamic properties. We prove that the Euler–Bernoulli beam equation can be obtained as a singular limit of the Shear beam model when the shear elasticity modulus <span>(kappa )</span> tends to infinity. By introducing a dissipative mechanism in the vertical displacement equation, we prove the existence of a smooth global attractor with finite fractal dimension. Finally, we demonstrate that the global attractor for the Shear beam model converges upper-semicontinuously to the global attractor for the Euler–Bernoulli equation as <span>(kappa rightarrow infty )</span>.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"27 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 Euler–Dierkes–Huisken variational problem 论欧拉-迪尔克斯-惠斯肯变分问题
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-24 DOI: 10.1007/s00208-024-02970-1
Hongbin Cui, Xiaowei Xu
{"title":"On Euler–Dierkes–Huisken variational problem","authors":"Hongbin Cui, Xiaowei Xu","doi":"10.1007/s00208-024-02970-1","DOIUrl":"https://doi.org/10.1007/s00208-024-02970-1","url":null,"abstract":"<p>In this paper, we study the stability and minimizing properties of higher codimensional surfaces in Euclidean space associated with the <i>f</i>-weighted area-functional </p><span>$$begin{aligned} mathcal {E}_f(M)=int _M f(x); d mathcal {H}_k end{aligned}$$</span><p>with the density function <span>(f(x)=g(|x|))</span> and <i>g</i>(<i>t</i>) is non-negative, which develop the recent works by U. Dierkes and G. Huisken (Math Ann, 20 October 2023) on hypersurfaces with the density function <span>(|x|^alpha )</span>. Under suitable assumptions on <i>g</i>(<i>t</i>), we prove that minimal cones with globally flat normal bundles are <i>f</i>-stable, and we also prove that the minimal cones satisfy the Lawlor curvature criterion, the determinantal varieties and the Pfaffian varieties without some exceptional cases are <i>f</i>-minimizing. As an application, we show that <i>k</i>-dimensional cones over product of spheres are <span>(|x|^alpha )</span>-stable for <span>(alpha ge -k+2sqrt{2(k-1)})</span>, the oriented stable minimal hypercones are <span>(|x|^alpha )</span>-stable for <span>(alpha ge 0)</span>, and we also show that the cones over product of spheres <span>(mathcal {C}=C left( S^{k_1} times cdots times S^{k_{m}}right) )</span> are <span>(|x|^alpha )</span>-minimizing for <span>(dim mathcal {C} ge 7)</span>, <span>(k_i&gt;1)</span> and <span>(alpha ge 0)</span>, the Simons cones <span>(C(S^{p} times S^{p}))</span> are <span>(|x|^alpha )</span>-minimizing for <span>(alpha ge 1)</span>, which relaxes the assumption <span>(1le alpha le 2p)</span> in Dierkes and Huisken ( Math Ann, https://doi.org/10.1007/s00208-023-02726-3, 2023). Recently, Dierkes (Rend Sem Mat Univ Padova, 2024) prove that <span>(C(S^{p} times S^{p}))</span> are <span>(|x|^alpha )</span>-minimizing for <span>(alpha ge 3-p)</span>, which has improved our assumption <span>(alpha ge 1)</span> for <span>(pge 3)</span>.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"74 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Relative assembly maps and the K-theory of Hecke algebras in prime characteristic 素特性中的相对集合映射与赫克代数的 K 理论
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-23 DOI: 10.1007/s00208-024-02966-x
W. Lück
{"title":"Relative assembly maps and the K-theory of Hecke algebras in prime characteristic","authors":"W. Lück","doi":"10.1007/s00208-024-02966-x","DOIUrl":"https://doi.org/10.1007/s00208-024-02966-x","url":null,"abstract":"<p>We investigate the relative assembly map from the family of finite subgroups to the family of virtually cyclic subgroups for the algebraic <i>K</i>-theory of twisted group rings of a group <i>G</i> with coefficients in a regular ring <i>R</i> or, more generally, with coefficients in a regular additive category. They are known to be isomorphisms rationally. We show that it suffices to invert only those primes <i>p</i> for which <i>G</i> contains a non-trivial finite <i>p</i>-group and <i>p</i> is not invertible in <i>R</i>. The key ingredient is the detection of Nil-terms of a twisted group ring of a finite group <i>F</i> after localizing at <i>p</i> in terms of the <i>p</i>-subgroups of <i>F</i> using Verschiebungs and Frobenius operators. We construct and exploit the structure of a module over the ring of big Witt vectors on the Nil-terms. We analyze the algebraic <i>K</i>-theory of the Hecke algebras of subgroups of reductive <i>p</i>-adic groups in prime characteristic.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"62 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Iterative scheme generating method beyond Ishikawa iterative method 石川迭代法之外的迭代方案生成法
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-23 DOI: 10.1007/s00208-024-02977-8
Atsumasa Kondo
{"title":"Iterative scheme generating method beyond Ishikawa iterative method","authors":"Atsumasa Kondo","doi":"10.1007/s00208-024-02977-8","DOIUrl":"https://doi.org/10.1007/s00208-024-02977-8","url":null,"abstract":"<p>We propose an iterative scheme generating method to address common fixed point problems. Our approach yields diverse iterative schemes for finding common fixed points. The derivative results include the Ishikawa iterative method and its variations. An application to the variational inequality problem is provided to illustrate the usefulness of our method. The class of mappings we target is general. This category includes nonexpansive mappings and various other types, even those that lack continuity.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"31 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Monodromy and mapping class groups of 3-dimensional hypersurfaces 三维超曲面的单色性和映射类群
IF 1.4 2区 数学
Mathematische Annalen Pub Date : 2024-08-21 DOI: 10.1007/s00208-024-02951-4
Oscar Randal-Williams
{"title":"Monodromy and mapping class groups of 3-dimensional hypersurfaces","authors":"Oscar Randal-Williams","doi":"10.1007/s00208-024-02951-4","DOIUrl":"https://doi.org/10.1007/s00208-024-02951-4","url":null,"abstract":"<p>We describe the subgroup of the mapping class group of a hypersurface in <span>(mathbb{C}mathbb{P}^4)</span> consisting of those diffeomorphisms which can be realised by monodromy.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"41 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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