数学最新文献

{"title":"Quadratic & additive mappings on operator commuting elements in ({textrm{JBW}}^*)-algebras","authors":"Gerardo M. Escolano, Jan Hamhalter, Antonio M. Peralta, Armando R. Villena","doi":"10.1007/s13324-026-01277-5","DOIUrl":"10.1007/s13324-026-01277-5","url":null,"abstract":"<div><p>Let <span>(mathfrak {A})</span> and <span>(mathfrak {B})</span> be <span>({textrm{JBW}}^*)</span>-algebras whose sets of unitaries are denoted by <span>(mathscr {U}(mathfrak {A}))</span> and <span>(mathscr {U}(mathfrak {B}))</span>, respectively. We show that <span>(mathscr {U}(mathfrak {A}))</span> is closed for Jordan products of operator commuting pairs inside itself. Let <span>(mathfrak {A})</span> and <span>(mathfrak {B})</span> be <span>({textrm{JBW}}^*)</span>-algebras without direct summands of type <span>(I_1)</span> or <span>(I_2)</span>, and let <span>(Phi : mathscr {U}(mathfrak {A}) rightarrow mathscr {U}(mathfrak {B}))</span> be a bicontinuous bijection satisfying <span>(Phi (u circ v) = Phi (u)circ Phi (v))</span> whenever <i>u</i> and <i>v</i> are operator commuting unitaries in <span>(mathfrak {A})</span>. We prove that there exist a linear Jordan <span>({phantom {a}}^*)</span>-isomorphism <span>(theta : mathfrak {A} rightarrow mathfrak {B})</span>, a real linear mapping <span>(beta : mathfrak {A_{sa}}rightarrow Z(mathfrak {B}_{sa}))</span>, and an invertible central element <span>(c in mathfrak {B}_{sa})</span> such that </p><div><div><span>$$begin{aligned} Phi (e^{i a}) = e^{i beta (a)}circ e^{i ccirc theta (a)} = e^{i beta (a)} circ theta left( e^{i theta ^{-1}( c )circ a}right) , end{aligned}$$</span></div></div><p>for all <span>(ain mathfrak {A}_{sa})</span>. The conclusion improves when <span>(mathfrak {A})</span> is a <span>({textrm{JBW}}^*)</span>-algebra factor not of type <span>(I_2)</span>. Assuming that <span>(mathfrak {A})</span> has no direct summands of type <span>(I_2)</span>, we show that any mapping <span>(Phi : mathfrak {A}_{sa} rightarrow mathfrak {B}_{sa})</span> satisfying the following conditions: </p><ol>\u0000 <li>\u0000 <span>(a)</span>\u0000 \u0000 <p><span>(Phi big (U_a(b)big ) = U_{Phi (a)}big (Phi (b)big ))</span> whenever <i>a</i> and <i>b</i> operator commute in <span>(mathfrak {A}_{sa})</span>,</p>\u0000 \u0000 </li>\u0000 <li>\u0000 <span>(b)</span>\u0000 \u0000 <p><span>(Phi )</span> is additive on pairs of operator commuting elements,</p>\u0000 \u0000 </li>\u0000 </ol><p> enjoys the following properties: First, <span>(Phi (textbf{1}))</span> is a tripotent in <span>(mathfrak {B}_{sa})</span>, the Peirce-2 subspace <span>(mathfrak {B}_2!left( Phi (textbf{1})right) )</span> carries a natural structure of <span>({textrm{JBW}}^*)</span>-algebra whose self-adjoint part contains the range of <span>(Phi )</span>, and makes the corresponding mapping <span>(Phi : mathfrak {A}_{sa} rightarrow mathfrak {B}_2!left( Phi (textbf{1})right) _{sa})</span> a unital (real linear) Jordan homomorphism. Furthermore, if <span>(Phi )</span> is bijective, then <span>(Phi (textbf{1}))</span> is a central symmetry in <span>(mathfrak {B})</span>, and <span>(Phi )</span>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"16 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189289","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}

{"title":"Proper affine deformations of positive representations","authors":"Jean-Philippe Burelle,&nbsp;Neža Žager Korenjak","doi":"10.1112/topo.70102","DOIUrl":"https://doi.org/10.1112/topo.70102","url":null,"abstract":"<p>We define, for every positive Anosov representation of a nonabelian free group into <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>SO</mi>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 <mo>,</mo>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{SO}(2n,2n-1)$</annotation>\u0000 </semantics></math>, a family of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$mathbb {R}^{4n-1}$</annotation>\u0000 </semantics></math>-valued cocycles which induce proper affine actions on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$mathbb {R}^{4n-1}$</annotation>\u0000 </semantics></math>. We construct fundamental domains in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$mathbb {R}^{4n-1}$</annotation>\u0000 </semantics></math> bounded by generalized crooked planes for these affine actions, and deduce that the quotient manifolds are homeomorphic to handlebodies.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"19 4","pages":""},"PeriodicalIF":1.6,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70102","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149177278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Expected value of the Sackin index under biased speciation models.","authors":"Daniel J Bauman, Noah A Rosenberg","doi":"10.1007/s00285-026-02465-4","DOIUrl":"10.1007/s00285-026-02465-4","url":null,"abstract":"<p><p>Models of random phylogenetic trees are important mathematical tools in phylogenetic data analysis; tree balance is a property of phylogenetic trees that helps describe and compare their shapes. Here, we investigate the Sackin index, one of the oldest and most widely used tree balance measures, under a variety of phylogenetic models beyond the standard Yule and Uniform models. The general biased speciation model is a biologically interpretable tree-generating model in which species branch into pairs of descendants according to an intrinsic branching rate, which is then split between the pair of descendants. The proportion of the branching rate of the parent that is assigned to a specific descendant, the split fraction, is a model parameter. Our main result is a formula for the expected value of the Sackin index under the general biased speciation model. Special cases of the general biased speciation model include a case that sets the split fraction to be a constant for each branching event, and two special cases inspired by the Aldous beta-splitting model: a random choice of split fraction is sampled independently at each branching event and drawn from a symmetric beta distribution in the Blum-François beta-splitting model or an asymmetric beta distribution in the Sainudiin-Véber beta-splitting model. As a corollary of our main result, we find formulas for the expected value of the Sackin index under these three cases of the general biased speciation model. We use the formulas to study how the balance of trees depends on the model parameters. Finally, because the Yule model is a special case of the Blum-François beta-splitting model, we find a new proof for the classical result describing the expected value of the Sackin index under the Yule model.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"93 5","pages":""},"PeriodicalIF":2.7,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13669139/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149185686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Murmurations via Petersson trace formula","authors":"Chan Ieong Kuan,&nbsp;Didier Lesesvre","doi":"10.1112/mtk.70135","DOIUrl":"https://doi.org/10.1112/mtk.70135","url":null,"abstract":"<p>We prove the murmuration phenomenon, which is a correlation between signs of functional equations and Fourier coefficients, in the case of modular forms in the weight aspect. We in particular improve the range of visibility of murmurations compared to previous results. This is the first approach to the murmuration phenomenon using a relative trace formula, showing its robustness.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":"72 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/mtk.70135","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205854","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}

{"title":"Inferring Hub Nodes on Differential Score Matching Graphical Models","authors":"Peiyao Cai,Junwei Lu,Kean Ming Tan","doi":"10.1080/10618600.2026.2748567","DOIUrl":"https://doi.org/10.1080/10618600.2026.2748567","url":null,"abstract":"","PeriodicalId":15422,"journal":{"name":"Journal of Computational and Graphical Statistics","volume":"32 1","pages":"1-20"},"PeriodicalIF":2.4,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208874","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}

{"title":"Persistent Homology of Function Spaces","authors":"Jonathan Block,Fedor Manin,Shmuel Weinberger","doi":"10.1007/s00039-026-00752-2","DOIUrl":"https://doi.org/10.1007/s00039-026-00752-2","url":null,"abstract":"","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"236 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149210377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"MaxTDA: Robust Statistical Inference for Maximal Persistence in Topological Data Analysis","authors":"Sixtus Dakurah,Jessi Cisewski-Kehe","doi":"10.1080/10618600.2026.2748028","DOIUrl":"https://doi.org/10.1080/10618600.2026.2748028","url":null,"abstract":"","PeriodicalId":15422,"journal":{"name":"Journal of Computational and Graphical Statistics","volume":"11 1","pages":"1-26"},"PeriodicalIF":2.4,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208875","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}

{"title":"Linear converters of majorization to row majorization and vice versa","authors":"Erfan Yazdan,Ali Armandnejad","doi":"10.1080/03081087.2026.2747256","DOIUrl":"https://doi.org/10.1080/03081087.2026.2747256","url":null,"abstract":"","PeriodicalId":49905,"journal":{"name":"Linear & Multilinear Algebra","volume":"32 1","pages":"1-9"},"PeriodicalIF":1.1,"publicationDate":"2026-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149208915","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}

{"title":"Homoclinic Quasiperiodic Orbits and Emergence of Strange Nonchaotic Attractors in a Discontinuous Piecewise Smooth Map","authors":"Jicheng Duan,&nbsp;Laura Gardini,&nbsp;Zhouchao Wei,&nbsp;Iryna Sushko,&nbsp;Yiwen Chen","doi":"10.1111/sapm.70326","DOIUrl":"https://doi.org/10.1111/sapm.70326","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper investigates the formation and evolution of strange nonchaotic attractors (SNAs) in a discontinuous noninvertible piecewise-smooth map subjected to quasiperiodic forcing. The system is formulated as a two-dimensional skew-product, combining a piecewise-smooth one-dimensional base map with an irrational rotation. The notion of quasiperiodic homoclinic and heteroclinic orbits is introduced, and their potential relevance to the transition from smooth tori to SNAs is explored. Forward images of critical lines are shown to reflect key changes in the attractor and its basin, including disconnected components and the formation of holes. Discontinuities in the attractor are found to result from direct contact with the discontinuity line of the map. Through a set of representative examples, we identify three main routes to SNA formation: (i) contact between the attractor and its basin boundary leading to homoclinic orbits, (ii) contact between the attractor and a repeller, leading to homoclinic orbits, and (iii) contact between the attractor and the discontinuity set. These results clarify how different types of critical curves shape the dynamics, and contribute to the understanding of attractor evolution in discontinuous noninvertible quasiperiodically forced systems.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"157 4","pages":""},"PeriodicalIF":2.4,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205420","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}

{"title":"Stability of the Catenoid for the Hyperbolic Vanishing Mean Curvature Equation in 4 Spatial Dimensions","authors":"Ning Tang","doi":"10.1007/s40818-026-00256-0","DOIUrl":"10.1007/s40818-026-00256-0","url":null,"abstract":"<div><p>We establish the asymptotic stability of the catenoid, as a nonflat stationary solution to the hyperbolic vanishing mean curvature (HVMC) equation in Minkowski space <img> for <span>(n = 4)</span>. Our main result is under a “codimension-1” assumption on initial perturbation, modulo suitable translation and boost (i.e. modulation), without any symmetry assumptions. In comparison to the <span>(n ge 5)</span> case addressed by Lührmann–Oh–Shahshahani [40], proving catenoid stability in 4 dimensions shares additional difficulties with its 3 dimensional analog, namely the slower spatial decay of the catenoid and slower temporal decay of waves. To overcome these difficulties in the <span>(n = 3)</span> case, the strong Huygens principle, as well as a miraculous cancellation in the source term, plays an important role in [50] to obtain strong late time tails. In <span>(n = 4)</span> dimensions, without these special structural advantages, our novelty is to introduce an appropriate commutator vector field to derive a new hierarchy of estimates with higher <span>(r^p)</span>-weights so that an improved pointwise decay can be established. We expect this to be applicable for proving improved late time tails of other quasilinear wave equations in even dimensions or wave equations with inverse square potential.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"12 2","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-026-00256-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}