数学最新文献

{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">Neck-pinching of <ns0:math> <ns0:mrow><ns0:mrow><ns0:mi>C</ns0:mi> <ns0:msup><ns0:mi>P</ns0:mi> <ns0:mn>1</ns0:mn></ns0:msup> </ns0:mrow> </ns0:mrow> </ns0:math> -structures in the <ns0:math> <ns0:mrow> <ns0:mrow><ns0:msub><ns0:mi>PSL</ns0:mi> <ns0:mn>2</ns0:mn></ns0:msub> <ns0:mi>C</ns0:mi></ns0:mrow> </ns0:mrow> </ns0:math> -character variety.","authors":"Shinpei Baba","doi":"10.1112/topo.70010","DOIUrl":"https://doi.org/10.1112/topo.70010","url":null,"abstract":"<p><p>We characterize a certain neck-pinching degeneration of (marked) <math> <mrow><mrow><mi>C</mi> <msup><mi>P</mi> <mn>1</mn></msup> </mrow> </mrow> </math> -structures on a closed oriented surface <math><mrow><mi>S</mi></mrow> </math> of genus at least two. In a more general setting, we take a path of <math> <mrow><mrow><mi>C</mi> <msup><mi>P</mi> <mn>1</mn></msup> </mrow> </mrow> </math> -structures <math> <mrow> <mrow><msub><mi>C</mi> <mi>t</mi></msub> <mspace></mspace> <mrow><mo>(</mo> <mi>t</mi> <mo>⩾</mo> <mn>0</mn> <mo>)</mo></mrow> </mrow> </mrow> </math> on <math><mrow><mi>S</mi></mrow> </math> that leaves every compact subset in its deformation space, such that the holonomy of <math> <mrow><msub><mi>C</mi> <mi>t</mi></msub> </mrow> </math> converges in the <math> <mrow> <mrow><msub><mi>PSL</mi> <mn>2</mn></msub> <mi>C</mi></mrow> </mrow> </math> -character variety as <math> <mrow><mrow><mi>t</mi> <mo>→</mo> <mi>∞</mi></mrow> </mrow> </math> . Then, it is well known that the complex structure <math> <mrow><msub><mi>X</mi> <mi>t</mi></msub> </mrow> </math> of <math> <mrow><msub><mi>C</mi> <mi>t</mi></msub> </mrow> </math> also leaves every compact subset in the Teichmüller space of <math><mrow><mi>S</mi></mrow> </math> . In this paper, under an additional assumption that <math> <mrow><msub><mi>X</mi> <mi>t</mi></msub> </mrow> </math> is pinched along a loop <math><mrow><mi>m</mi></mrow> </math> on <math><mrow><mi>S</mi></mrow> </math> , we describe the limit of <math> <mrow><msub><mi>C</mi> <mi>t</mi></msub> </mrow> </math> from different perspectives: namely, in terms of the developing maps, holomorphic quadratic differentials, and pleated surfaces. The holonomy representations of <math> <mrow><mrow><mi>C</mi> <msup><mi>P</mi> <mn>1</mn></msup> </mrow> </mrow> </math> -structures on <math><mrow><mi>S</mi></mrow> </math> are known to be nonelementary (i.e., strongly irreducible and unbounded). We also give a rather exotic example of such a path <math> <mrow><msub><mi>C</mi> <mi>t</mi></msub> </mrow> </math> whose limit holonomy is the trivial representation.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"18 1","pages":"e70010"},"PeriodicalIF":0.8,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11685183/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142916395","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":"Asymptotic Expansion of Solutions of the 2nd Order Difference Equations in an Unbounded Domain","authors":"Sofia V. Rumyantseva","doi":"10.1007/s10440-025-00706-0","DOIUrl":"10.1007/s10440-025-00706-0","url":null,"abstract":"<div><p>Difference equations play a crucial role in a wide array of mathematical and physical tasks. In this article, we focus on the analysis of a second order linear homogeneous difference equation with smooth coefficients via WKB method. It is well-known that such equations exhibit two WKB solutions in a segment devoid of turning and singular points. We establish a theorem demonstrating the existence of these solutions in an unbounded domain under certain conditions regarding the smoothness and growth behavior of the coefficients at infinity. Furthermore, using this theorem, we derive the asymptotic expansion of Laguerre polynomials for large orders and values, yielding estimates that align with existing results.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"195 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142976442","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":"Proof of the transverse instability of Stokes waves","authors":"Ryan P. Creedon,&nbsp;Huy Q. Nguyen,&nbsp;Walter A. Strauss","doi":"10.1007/s40818-024-00188-7","DOIUrl":"10.1007/s40818-024-00188-7","url":null,"abstract":"<div><p>A Stokes wave is a traveling free-surface periodic water wave that is constant in the direction transverse to the direction of propagation. In 1981 McLean discovered via numerical methods that Stokes waves at infinite depth are unstable with respect to transverse perturbations of the initial data. Even for a Stokes wave that has very small amplitude <span>(varepsilon )</span>, we prove rigorously that transverse perturbations, after linearization, will lead to exponential growth in time. To observe this instability, extensive calculations are required all the way up to order <span>(O(varepsilon ^3))</span>. All previous rigorous results of this type were merely two-dimensional, in the sense that they only treated long-wave perturbations in the longitudinal direction. This is the first rigorous proof of three-dimensional instabilities of Stokes waves.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"11 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142976668","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":"Exponential Stability of Highly Nonlinear Hybrid Neutral Pantograph Stochastic Systems with Multiple Delays","authors":"Abdellatif Ben Makhlouf,&nbsp;Aws Ben Hamed,&nbsp;Lassaad Mchiri,&nbsp;Mohamed Rhaima","doi":"10.1007/s10440-025-00705-1","DOIUrl":"10.1007/s10440-025-00705-1","url":null,"abstract":"<div><p>This paper addresses the existence and exponential stability problem of highly nonlinear hybrid neutral pantograph stochastic equations with multiple delays (HNPSDEswMD). By Lyapunov functional method and without laying down a linear growth condition, the above problem of the exact solution is shown. We end up with two numerical examples that corroborates our theoretical findings.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"195 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142976409","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":"New limits of the Lie product formula type in Banach algebras","authors":"Dumitru Popa","doi":"10.1007/s13324-024-01002-0","DOIUrl":"10.1007/s13324-024-01002-0","url":null,"abstract":"<div><p>We find new limits of the Lie product formula type in Banach algebras with unit. Some sample results: Let <i>X</i>, <i>Y</i>, <i>Z</i> be Banach algebras with unit, <span>( left( x_{n},y_{n}right) _{nin mathbb {N}}subset Xtimes Y)</span> convergent sequences with <span>(lim nolimits _{nrightarrow infty }x_{n}=x)</span>, <span>( lim nolimits _{nrightarrow infty }y_{n}=y)</span> and <span>(T:Xtimes Yrightarrow Z)</span> a continuous bilinear operator with <span>(Tleft( textbf{1},textbf{1}right) = textbf{1})</span>. Then for all sequences of natural numbers <span>(left( a_{n}right) _{nin mathbb {N}})</span> with <span>(lim nolimits _{nrightarrow infty }a_{n}=infty )</span> we have </p><div><div><span>$$begin{aligned} lim limits _{nrightarrow infty }left[ Tleft( prod limits _{k=1}^{n}e^{ frac{x_{k}}{a_{n}left( k+nright) left( k+2nright) }},prod limits _{k=1}^{n}e^{frac{y_{k}}{a_{n}left( k+2nright) left( k+3nright) } }right) right] ^{a_{n}}=e^{left( ln frac{4}{3}right) Tleft( x,textbf{ 1}right) +left( ln 2right) Tleft( textbf{1},yright) }; end{aligned}$$</span></div></div><div><div><span>$$begin{aligned} lim limits _{nrightarrow infty }left[ Tleft( prod limits _{k=1}^{n}cos frac{x_{k}}{a_{n}sqrt{nleft( n+kright) }},prod limits _{k=1}^{n}cos frac{ky_{k}}{na_{n}sqrt{n^{2}+k^{2}}}right) right] ^{na_{n}^{2}} end{aligned}$$</span></div></div><div><div><span>$$begin{aligned} =e^{-frac{left( ln 2right) Tleft( x^{2},textbf{1}right) +left( 1- frac{pi }{4}right) Tleft( textbf{1},y^{2}right) }{2}}. end{aligned}$$</span></div></div></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-01002-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142976575","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":"Issue Information ‐ TOC","authors":"","doi":"10.1002/cpa.22210","DOIUrl":"https://doi.org/10.1002/cpa.22210","url":null,"abstract":"","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":"45 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142975084","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":"Continuous Dependence Result for a Class of Evolutionary Variational-Hemivariational Inequalities with Application to a Dynamic Thermo-Viscoelastic Contact Problem","authors":"Abdelhafid Ouaanabi,&nbsp;Mohammed Alaoui,&nbsp;Mustapha Bouallala,&nbsp;El Hassan Essoufi","doi":"10.1007/s10440-025-00707-z","DOIUrl":"10.1007/s10440-025-00707-z","url":null,"abstract":"<div><p>In the present paper, we consider a mathematical model describing the dynamic Coulomb’s frictional contact between a thermo-viscoelastic body and a thermally conductive rigid foundation. We employ the nonlinear constitutive viscoelastic law with long-term memory and thermal effects. We describe some contact and thermal conditions with the Clarke subdifferential boundary conditions. We derive the weak formulation of the problem as a system coupling two variational-hemivariational inequalities. We provide results on the existence and uniqueness of a weak solution to the model by using recent results from the theory of variational-hemivariational inequalities. Finally, the continuous dependence of the solution on the data is derived by applying an abstract result that we demonstrate.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"195 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142976565","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":"Grand-Canonical Optimal Transport","authors":"Simone Di Marino,&nbsp;Mathieu Lewin,&nbsp;Luca Nenna","doi":"10.1007/s00205-024-02080-x","DOIUrl":"10.1007/s00205-024-02080-x","url":null,"abstract":"<div><p>We study a generalization of the multi-marginal optimal transport problem, which has no fixed number of marginals <i>N</i> and is inspired of statistical mechanics. It consists in optimizing a linear combination of the costs for all the possible <i>N</i>’s, while fixing a certain linear combination of the corresponding marginals.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142976459","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":"An Energy-Stable Parametric Finite Element Method for the Planar Willmore Flow","authors":"Weizhu Bao, Yifei Li","doi":"10.1137/24m1633893","DOIUrl":"https://doi.org/10.1137/24m1633893","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 1, Page 103-121, February 2025. <br/> Abstract. We propose an energy-stable parametric finite element method (PFEM) for the planar Willmore flow and establish its unconditional energy stability of the full discretization scheme. The key lies in the introduction of two novel geometric identities to describe the planar Willmore flow: the first involves the coupling of the outward unit normal vector [math] and the normal velocity [math], and the second concerns the time derivative of the mean curvature [math]. Based on these, we derive a set of new geometric partial differential equations for the planar Willmore flow, leading to our new fully discretized and unconditionally energy-stable PFEM. Our stability analysis is also based on the two new geometric identities. Extensive numerical experiments are provided to illustrate our PFEM’s efficiency and validate its unconditional energy stability.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"9 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142967963","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":"On LCD skew group codes","authors":"Mohammed El Badry, Abdelfattah Haily, Ayoub Mounir","doi":"10.1007/s10623-024-01561-0","DOIUrl":"https://doi.org/10.1007/s10623-024-01561-0","url":null,"abstract":"<p>In this paper we study skew group codes as left ideals in some skew group rings. We have constructed a large class of LCD codes and a class of an LCD MDS codes. An important interest is given to the construction of idempotents generators of these codes.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"76 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142974807","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}