数学最新文献

{"title":"Takashi Goda is the winner of the 2025 Joseph F. Traub Prize for Achievement in Information-Based Complexity","authors":"Erich Novak","doi":"10.1016/j.jco.2025.101947","DOIUrl":"10.1016/j.jco.2025.101947","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"89 ","pages":"Article 101947"},"PeriodicalIF":1.8,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143817477","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":"Knots and chaos in the Rössler system","authors":"Eran Igra","doi":"10.1016/j.jde.2025.113290","DOIUrl":"10.1016/j.jde.2025.113290","url":null,"abstract":"<div><div>The Rössler System is one of the best known chaotic dynamical systems, exhibiting a plethora of complex phenomena - and yet, only a few studies tackled its complexity analytically. Inspired by recent numerical studies of the Rössler System, we introduce an idealized model for the Rössler System, prove its chaoticity, and study its bifurcations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"437 ","pages":"Article 113290"},"PeriodicalIF":2.4,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143815583","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":"Finite element analysis of a pseudostress–pressure–velocity formulation of the stationary Navier–Stokes equations","authors":"M. Farhloul ,&nbsp;N. Fall ,&nbsp;I. Dione ,&nbsp;S. Léger","doi":"10.1016/j.cam.2025.116665","DOIUrl":"10.1016/j.cam.2025.116665","url":null,"abstract":"<div><div>This article is concerned with a dual-mixed formulation of the Navier–Stokes equations which is based on the introduction of the pseudostress as a new unknown. The problem is approximated by a mixed finite element method in two and three dimensions: Raviart–Thomas elements of index <span><math><mrow><mi>k</mi><mo>≥</mo><mn>0</mn></mrow></math></span> for the pseudostress tensor, and piecewise discontinuous polynomials of degree <span><math><mrow><mi>k</mi><mo>≥</mo><mn>0</mn></mrow></math></span> for the velocity and the pressure. An existence result for the finite-element solution and convergence results are proved near a nonsingular solution. Finally, quasi-optimal error estimates, which improve those existing in the literature, are provided.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"469 ","pages":"Article 116665"},"PeriodicalIF":2.1,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143808154","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":"Average pseudo-orbits and metric mean dimension with potential","authors":"Fangzhou Cai ,&nbsp;Jie Li","doi":"10.1016/j.jde.2025.113286","DOIUrl":"10.1016/j.jde.2025.113286","url":null,"abstract":"<div><div>Through a measure-theoretic approach, we show that the metric mean dimension or topological pressure of a topological dynamical system with potential can be calculated by measuring the complexity of average pseudo-orbits in the induced infinite product space with respect to the potential function. This result extends several previously known conclusions related to the topological entropy (or topological pressure, upper mean dimension with potential) and pseudo-orbits in the literature.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"437 ","pages":"Article 113286"},"PeriodicalIF":2.4,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143815711","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 diurnal cycles of an atmospheric boundary layer in a partial differential equation with a finite element model","authors":"V. Geethalakshmi ,&nbsp;R. Ravi Kumar ,&nbsp;M.K. Kalarani ,&nbsp;R. Karthikeyan ,&nbsp;R. Sivakumar ,&nbsp;N.K. Sathyamoorthy ,&nbsp;Ga. Dheebakaran","doi":"10.1016/j.chaos.2025.116367","DOIUrl":"10.1016/j.chaos.2025.116367","url":null,"abstract":"<div><div>We use the conservation laws of mass, momentum, energy, and moisture equations derived from a finite element model to assess the stability of diurnal cycles of atmospheric boundary layer flow. The results show the most accurate predictions for how temperature, pressure, and wind speed affect mesoscale flow in various domains, with isentropes remaining stable despite the dynamic influence of initial and damped boundary conditions. The degree of turbulence can fluctuate due to weak temperature and wind gradients. In order to determine which isentropes are stable in a particular area of the cold core and cyclonic system in the lower atmosphere, this work employs the numerical weather prediction (NWP) of adaptive discontinuous finite element Galerkin approach to detect temperature, pressure, wind speed, and magnitude of the turbulence oscillation mode. We select starting mesh point is longitude and latitude values (Chennai), wind speed at 2, 4, 6, 8, 10, 12 m level, temperature and relative humidity, then other nodes are treated as every 50 km distance longitude and latitude value, wind speed at 2, 4, 6, 8, 10, 12 m level, temperature and relative humidity as starting node and ending node values (Coimbatore). The computational domain is rectangular, 550 km in the horizontal and 2000 m height. In order to resolve the frontal movement reasonably well, we discretize the domain into 91 × 91 rectangular bi-quadratic elements with an effective horizontal grid spacing of 2 km, spanning a length of 30 km inland from the shore.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116367"},"PeriodicalIF":5.3,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143816729","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":"On the outdegree zeroth-order general Randić index of digraphs","authors":"Jiaxiang Yang ,&nbsp;Hechao Liu ,&nbsp;Xuesong Fu","doi":"10.1016/j.dam.2025.04.010","DOIUrl":"10.1016/j.dam.2025.04.010","url":null,"abstract":"<div><div>For any digraph <span><math><mi>D</mi></math></span> and real number <span><math><mi>α</mi></math></span>, the outdegree zeroth-order general Randić index is defined as the sum of the outdegree of each vertex raised to the power of <span><math><mi>α</mi></math></span> across all vertices in the digraph <span><math><mi>D</mi></math></span>. A cactus graph <span><math><mi>G</mi></math></span> is a connected graph in which each block of <span><math><mi>G</mi></math></span> is either an edge or a cycle. An oriented cactus is the directed variant of a cactus graph, where each edge has a specified direction. For any real number <span><math><mrow><mi>α</mi><mo>≥</mo><mn>2</mn></mrow></math></span> and positive integers <span><math><mi>n</mi></math></span>, <span><math><mi>r</mi></math></span> with <span><math><mrow><mi>n</mi><mo>&gt;</mo><mn>2</mn><mi>r</mi></mrow></math></span>, we address the problem of identifying the maximum value of the outdegree zeroth-order general Randić index among oriented cacti with <span><math><mi>n</mi></math></span> vertices and <span><math><mi>r</mi></math></span> cycles. Additionally, we determine the maximum value of the outdegree zeroth-order general Randić index over connected simple digraphs with <span><math><mi>n</mi></math></span> vertices and <span><math><mi>l</mi></math></span> arcs, where <span><math><mi>l</mi></math></span> is a positive integer. In particular, for <span><math><mrow><mi>α</mi><mo>=</mo><mn>2</mn></mrow></math></span>, we obtain some of the results obtained in Ganie and Pirzada, (2024).</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"372 ","pages":"Pages 76-86"},"PeriodicalIF":1.0,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143817748","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":"Mean reflected backward stochastic differential equations with jumps in a convex domain","authors":"Hongchao Qian","doi":"10.1016/j.spl.2025.110426","DOIUrl":"10.1016/j.spl.2025.110426","url":null,"abstract":"<div><div>In this paper, we study a class of multi-dimensional mean reflected backward stochastic differential equations driven by a Brownian motion and an independent Poisson random measure. In our setting, the constraint depends on the law of the solution rather than on its paths. Specifically, the expectation of the solution takes values in a convex domain in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. The existence and uniqueness of solutions are established by a penalization method.</div></div>","PeriodicalId":49475,"journal":{"name":"Statistics & Probability Letters","volume":"223 ","pages":"Article 110426"},"PeriodicalIF":0.9,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143815702","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":"Cyclically covering subspaces of Fqn","authors":"Meng Sun,&nbsp;Changli Ma,&nbsp;Liwei Zeng","doi":"10.1016/j.ffa.2025.102625","DOIUrl":"10.1016/j.ffa.2025.102625","url":null,"abstract":"<div><div>Let <em>q</em> be a prime power, <em>n</em> be a positive integer, and <span><math><msubsup><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> be the <em>n</em>-dimensional row vector space over finite field <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span>. We say a subspace <em>U</em> of <span><math><msubsup><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> is cyclically covering if the union of the cyclic shifts of <em>U</em> is equal to <span><math><msubsup><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span>. Recently, the largest possible codimension of a cyclically covering subspace of <span><math><msubsup><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span>, denoted by <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo></math></span>, has attracted the attention of many scholars. In this paper, we introduce cyclically covering subspaces of finite field <span><math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mi>q</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></msub></math></span>. By virtue of the theory of direct sum decomposition of finite fields, we describe a method for constructing cyclically covering subspaces of <span><math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mi>q</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></msub></math></span>, and determine the value of <span><math><msub><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo></math></span> for some special <em>n</em>. In particular, we prove <span><math><msub><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mn>21</mn><mo>)</mo><mo>=</mo><mn>4</mn></math></span>. Finally, several lower bounds of <span><math><msub><mrow><mi>h</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>(</mo><mi>n</mi><mo>)</mo></math></span> are given when <span><math><mo>(</mo><mi>q</mi><mo>,</mo><mi>n</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></span>, which generalizes results of the existing results in <span><span>[2]</span></span>.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"106 ","pages":"Article 102625"},"PeriodicalIF":1.2,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143808774","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":"Elliptic equations with (p,q)-growth and competition phenomena","authors":"Nikolaos S. Papageorgiou ,&nbsp;Dongdong Qin ,&nbsp;Vicenţiu D. Rădulescu","doi":"10.1016/j.jde.2025.113304","DOIUrl":"10.1016/j.jde.2025.113304","url":null,"abstract":"<div><div>We consider a Dirichlet problem driven by a differential operator with <span><math><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span>-growth (double phase equation) and a reaction which exhibits the competing effects of “sublinear” and “superlinear” nonlinearities (concave-convex problem). Using the critical point theory, together with truncation and comparison techniques and critical groups, we prove an existence and multiplicity theorem, which is global in the parameter <span><math><mi>λ</mi><mo>&gt;</mo><mn>0</mn></math></span> (a bifurcation-type theorem).</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"435 ","pages":"Article 113304"},"PeriodicalIF":2.4,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143807210","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":"Unique Solvability and Error Analysis of a Scheme Using the Lagrange Multiplier Approach for Gradient Flows","authors":"Qing Cheng, Jie Shen, Cheng Wang","doi":"10.1137/24m1659303","DOIUrl":"https://doi.org/10.1137/24m1659303","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 63, Issue 2, Page 772-799, April 2025. <br/> Abstract. The unique solvability and error analysis of a scheme using the original Lagrange multiplier approach proposed in [Q. Cheng, C. Liu, and J. Shen, Comput. Methods Appl. Mech. Engrg., 367 (2020), 13070] for gradient flows is studied in this paper. We identify a necessary and sufficient condition that must be satisfied for the nonlinear algebraic equation arising from the original Lagrange multiplier approach to admit a unique solution in the neighborhood of its exact solution. Then we find that the unique solvability of the original Lagrange multiplier approach depends on the aforementioned condition and may be valid over a finite time period. Afterward, we propose a modified Lagrange multiplier approach to ensure that the computation can continue even if the aforementioned condition was not satisfied. Using the Cahn–Hilliard equation as an example, we prove rigorously the unique solvability and establish optimal error estimates of a second-order Lagrange multiplier scheme assuming this condition and that the time step is sufficiently small. We also present numerical results to demonstrate that the modified Lagrange multiplier approach is much more robust and can use a much larger time step than the original Lagrange multiplier approach.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"34 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143814009","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}