数学最新文献

{"title":"Space-time finite element analysis of the advection-diffusion equation using Galerkin/least-square stabilization","authors":"Biswajit Khara ,&nbsp;Kumar Saurabh ,&nbsp;Robert Dyja ,&nbsp;Anupam Sharma ,&nbsp;Baskar Ganapathysubramanian","doi":"10.1016/j.camwa.2025.02.020","DOIUrl":"10.1016/j.camwa.2025.02.020","url":null,"abstract":"<div><div>We present a full space-time numerical solution of the advection-diffusion equation using a continuous Galerkin finite element method on conforming meshes. The Galerkin/least-square method is employed to ensure stability of the discrete variational problem. In the full space-time formulation, time is considered another dimension, and the time derivative is interpreted as an additional advection term of the field variable. We derive <em>a priori</em> error estimates and illustrate spatio-temporal convergence with several numerical examples. We also derive <em>a posteriori</em> error estimates, which coupled with adaptive space-time mesh refinement provide efficient and accurate solutions. The accuracy of the space-time solutions is illustrated by comparing against analytical solutions as well as against numerical solutions using a conventional time-marching algorithm.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"185 ","pages":"Pages 52-75"},"PeriodicalIF":2.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519113","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":"Classifying smashing ideals in derived categories of valuation domains","authors":"Scott Balchin ,&nbsp;Florian Tecklenburg","doi":"10.1016/j.jpaa.2025.107917","DOIUrl":"10.1016/j.jpaa.2025.107917","url":null,"abstract":"<div><div>Building on results of Bazzoni–Št'ovíček, we give a complete classification of the frame of smashing ideals for the derived category of a finite dimensional valuation domain. In particular, we give an explicit construction of an infinite family of commutative rings such that the telescope conjecture fails and which generalise an example of Keller. As a consequence, we deduce that the Krull dimension of the Balmer spectrum and the Krull dimension of the smashing spectrum can differ arbitrarily for rigidly-compactly generated tensor-triangulated categories.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 3","pages":"Article 107917"},"PeriodicalIF":0.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509541","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":"Path eccentricity of k-AT-free graphs and application on graphs with the consecutive ones property","authors":"Paul Bastide ,&nbsp;Claire Hilaire ,&nbsp;Eileen Robinson","doi":"10.1016/j.disc.2025.114449","DOIUrl":"10.1016/j.disc.2025.114449","url":null,"abstract":"<div><div>The central path problem is a variation on the single facility location problem. The aim is to find, in a given connected graph <em>G</em>, a path <em>P</em> minimizing its eccentricity, which is the maximal distance from <em>P</em> to any vertex of the graph <em>G</em>. The <em>path eccentricity</em> of <em>G</em> is the minimal eccentricity achievable over all paths in <em>G</em>. In this article we consider the path eccentricity of the class of the <em>k-AT-free graphs</em>. They are graphs in which any set of three vertices contains a pair for which every path between them uses at least one vertex of the closed neighborhood at distance <em>k</em> of the third. We prove that they have path eccentricity bounded by <em>k</em>.</div><div>Moreover, we answer a question of Gómez and Gutiérrez asking if there is a relation between path eccentricity and the <em>consecutive ones property</em>. The latter is the property for a binary matrix to admit a permutation of the rows placing the 1's consecutively on the columns. It was already known that graphs whose adjacency matrices have the consecutive ones property have path eccentricity at most 1, and that the same remains true when the augmented adjacency matrices (with ones on the diagonal) have the consecutive ones property. We generalize these results as follow. We study graphs whose adjacency matrices can be made to satisfy the consecutive ones property after changing some values on the diagonal, and show that those graphs have path eccentricity at most 2, by showing that they are 2-AT-free.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 7","pages":"Article 114449"},"PeriodicalIF":0.7,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511942","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":"On the dynamics of coupled envelope structures for barotropic–baroclinic interaction with Bottom Topography","authors":"Jie Wang,&nbsp;Ruigang Zhang,&nbsp;Quansheng Liu,&nbsp;Liangui Yang","doi":"10.1016/j.chaos.2025.116179","DOIUrl":"10.1016/j.chaos.2025.116179","url":null,"abstract":"<div><div>Nonlinear barotropic–baroclinic interaction is of great theoretical importance in gaining a deeper understanding of the physical mechanisms of atmospheric or oceanic motions. Based on the classical two-layer quasi-geostrophic potential vorticity (2LQGPV) conservation model, this paper derives the nonlinear Schrödinger equation describing the Rossby wave amplitude evolution under the <span><math><mi>β</mi></math></span>-plane approximation, combined with multiscale analysis and small-parameter expansion methods. The influence of different forms of bottom topography on the evolution mechanism of the nonlinear barotropic–baroclinic interaction and the blockage effect is highlighted. The results show that the barotropic stream function dominates the generation process of the baroclinic stream function, and at the same time the baroclinic stream function has a perturbing effect on the barotropic stream function. Topography is an essential factor for dipole excitation or decay, with up-convex topography more likely to cause dipole blockage, while sloped topography and down-concave topography have a weaker effect. This finding reveals the significant influence of topography in wave–wave interactions. These results further enrich the theory of nonlinear barotropic–baroclinic interactions and provide a new theoretical framework and explanation for understanding wave–wave and wave-stream interactions.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116179"},"PeriodicalIF":5.3,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143511416","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":"Influences of the graphene reinforcements on the natural vibrational properties, nonlinear flutter responses, and the chaotic motions of the FG-GR laminated composite cantilever rectangular variable cross-section plate in the supersonic flow","authors":"Y. Jiang ,&nbsp;Y. Wang ,&nbsp;W. Zhang ,&nbsp;Y.F. Zhang ,&nbsp;S.F. Lu ,&nbsp;X. Du","doi":"10.1016/j.chaos.2025.116221","DOIUrl":"10.1016/j.chaos.2025.116221","url":null,"abstract":"<div><div>Due to the excellent mechanical and lightweight properties of the graphene-reinforced composite structure, it can meet the design requirements of modern aircraft comments. In this paper, the aircraft wings with low aspect ratio are modelled as the functionally graded graphene-reinforced laminated composite cantilever rectangular (FG-GRLCCR) variable cross-section plate. The influences of the graphene reinforcements on the natural vibrational properties, the nonlinear flutter responses, and the chaotic motions of the FG-GRLCCR variable cross-section plate are investigated. The extended Halpin-Tsai model is used to calculate the mechanical parameters for the graphene-reinforced composite materials. The first-order piston theory is applied to simulate the aerodynamic force on the FG-GRLCCR variable cross-section plate in supersonic flow. Considering the classical laminated theory, the von Karman large deformation theory, and the simple harmonic excitation, the dynamic partial differential equations for the FG-GRLCCR variable cross-section plate are derived by the Hamilton principle. The nonlinear ordinary partial equations of the system are given based on the Galerkin truncation technique. The frequency loci veering phenomenon and vibrational mode interaction for the FG-GRLCCR variable cross-section plate are obtained by the Rayleigh-Ritz method. The nonlinear flutter responses of the FG-GRLCCR variable cross-section plate are analyzed before and after critical flutter pressure. The bifurcation diagrams, Maximum Lyapunov exponent diagram, phase diagram, waveform diagram, and Poincaré cross-section diagram of the system are depicted for investigating the influence the graphene reinforcements on the nonlinear dynamic responses. The results showed that the graphene reinforcements and distributed patterns can change the frequency loci veering phenomenon, improve the critical flutter pressure and reduce the occurrence of chaotic motions of the FG-GRLCCR variable cross-section plate.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"194 ","pages":"Article 116221"},"PeriodicalIF":5.3,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143520049","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":"Quasi-exponential stability of non-autonomous integro-differential systems with infinite delay","authors":"Liguang Xu ,&nbsp;Hongxiao Hu","doi":"10.1016/j.aml.2025.109520","DOIUrl":"10.1016/j.aml.2025.109520","url":null,"abstract":"<div><div>The current article focuses on the quasi-exponential stability analysis of non-autonomous integro-differential systems characterized by infinite delay. By developing a novel generalized Halanay inequality, sufficient conditions for the quasi-exponential stability of non-autonomous integro-differential systems with infinite delay are presented for the systems.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"166 ","pages":"Article 109520"},"PeriodicalIF":2.9,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526859","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":"Level set estimates for the periodic Schrödinger maximal function on T1","authors":"Ciprian Demeter","doi":"10.1016/j.aim.2025.110186","DOIUrl":"10.1016/j.aim.2025.110186","url":null,"abstract":"<div><div>We prove (essentially) sharp <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> level set estimates for the periodic Schrödinger maximal operator in a certain range of the cut-off parameter.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"467 ","pages":"Article 110186"},"PeriodicalIF":1.5,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510837","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":"Construction of solutions of the Riemann problem for a two-dimensional Keyfitz-Kranzer type model governing a thin film flow","authors":"Anamika Pandey ,&nbsp;Rahul Barthwal ,&nbsp;T. Raja Sekhar","doi":"10.1016/j.amc.2025.129378","DOIUrl":"10.1016/j.amc.2025.129378","url":null,"abstract":"<div><div>This article is concerned with constructing solutions involving nonlinear waves to a three-constant two-dimensional Riemann problem for a reduced hyperbolic model describing a thin film flow of a perfectly soluble anti-surfactant solution. Here, we solve the Riemann problem without the limitation that each jump of the initial data emanates exactly one planar elementary wave. We obtain ten topologically distinct solutions using the generalized characteristic analysis. Our analysis explores the intricate interaction between classical and non-classical waves. Furthermore, in order to validate our solutions we thoroughly compare the obtained analytical solutions with numerical results through the second-order Local Lax Friedrichs scheme which is implemented in numerical simulation.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"498 ","pages":"Article 129378"},"PeriodicalIF":3.5,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526705","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":"Symmetry and the Buchanan-Lillo conjecture: A resolution of the mixed feedback case","authors":"Elena Braverman ,&nbsp;John Ioannis Stavroulakis","doi":"10.1016/j.amc.2025.129376","DOIUrl":"10.1016/j.amc.2025.129376","url":null,"abstract":"<div><div>Buchanan and Lillo both conjectured that oscillatory solutions of the first-order delay differential equation with positive feedback <span><math><msup><mrow><mi>x</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>p</mi><mo>(</mo><mi>t</mi><mo>)</mo><mi>x</mi><mo>(</mo><mi>τ</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>)</mo></math></span>, <span><math><mi>t</mi><mo>≥</mo><mn>0</mn></math></span>, where <span><math><mn>0</mn><mo>≤</mo><mi>p</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>≤</mo><mn>1</mn></math></span>, <span><math><mn>0</mn><mo>≤</mo><mi>t</mi><mo>−</mo><mi>τ</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>≤</mo><mn>2.75</mn><mo>+</mo><mi>ln</mi><mo>⁡</mo><mn>2</mn><mo>,</mo><mi>t</mi><mo>∈</mo><mi>R</mi></math></span>, are asymptotic to a shifted multiple of a unique periodic solution. This special solution can also be described from the more general perspective of the mixed feedback case (sign-changing <em>p</em>), thanks to its symmetry (antiperiodicity). The analogue of this conjecture for negative feedback, <span><math><mi>p</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>≤</mo><mn>0</mn></math></span>, was resolved by Lillo, and the mixed feedback analog was recently set as an open problem. In this paper, we resolve the case of mixed feedback, obtaining results in support of the conjecture of Buchanan and Lillo, underlining its link to the symmetry of the periodic solution. In particular, we obtain and describe the optimal estimates on the necessary delay for existence of periodic (more generally, nonvanishing) solutions, with respect to the period (oscillation speed). These apply to almost any first-order delay system, as we consider the general nonautonomous case, under minimal assumptions of measurability of the parameters. We furthermore discuss and elucidate the relations between the periodic and the nonautonomous case.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"498 ","pages":"Article 129376"},"PeriodicalIF":3.5,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526706","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":"Maker–Breaker domination game critical graphs","authors":"Athira Divakaran ,&nbsp;Tanja Dravec ,&nbsp;Tijo James ,&nbsp;Sandi Klavžar ,&nbsp;Latha S Nair","doi":"10.1016/j.dam.2025.02.038","DOIUrl":"10.1016/j.dam.2025.02.038","url":null,"abstract":"<div><div>The Maker–Breaker domination game (MBD game) is a two-player game played on a graph <span><math><mi>G</mi></math></span> by Dominator and Staller. They alternately select unplayed vertices of <span><math><mi>G</mi></math></span>. The goal of Dominator is to form a dominating set with the set of vertices selected by him while that of Staller is to prevent this from happening. In this paper MBD game critical graphs are studied. Their existence is established and critical graphs are characterized for most of the cases in which the first player can win the game in one or two moves.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"368 ","pages":"Pages 126-134"},"PeriodicalIF":1.0,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143512585","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}