数学最新文献

{"title":"Analysis of multiple contact types within the framework of semi-finite element method","authors":"Ling Tao ,&nbsp;Zhongpan Li ,&nbsp;Hong Wen ,&nbsp;Simiao Yu ,&nbsp;Zhiqiang Feng","doi":"10.1016/j.amc.2025.129494","DOIUrl":"10.1016/j.amc.2025.129494","url":null,"abstract":"<div><div>Dynamic contact problems are common in engineering systems. Current dynamic contact simulations are prone to energy non-conservation and over-reliance on nodes accuracy. To address the above difficulties, a numerical algorithm based on the bipotential theory for solving the dynamic contact problems of multibody systems is proposed. Within the framework of semi-finite element method, the Uzawa iteration is embedded in Newton iteration to solve the nonlinear equation. By constructing the adaptive virtual points on the contact surface, the bipotential theory is introduced to compute the local dynamic contact force. In this work, both the interactive contact interface and the coupling contact interface are considered, and the numerical examples are extended from two-dimension line-to-line contact to three-dimension surface-to-surface contact. In addition, the influence of coupling components on the deformation and motion of each subsystem is also revealed. The numerical results show that the proposed algorithm is effective and stable, satisfies the law of energy conservation strictly and reduces the over-dependence on the nodes accuracy. This work can provide a reference for further research on balancing computation efficiency and accuracy.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"502 ","pages":"Article 129494"},"PeriodicalIF":3.5,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873981","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":"General soliton solutions to the coupled Hirota equation via the Kadomtsev–Petviashvili reduction","authors":"Changyan Shi,&nbsp;Bingyuan Liu,&nbsp;Bao-Feng Feng","doi":"10.1016/j.chaos.2025.116400","DOIUrl":"10.1016/j.chaos.2025.116400","url":null,"abstract":"<div><div>In this paper, we are concerned with various soliton solutions to the coupled Hirota equation, as well as to the Sasa–Satsuma equation which can be viewed as one reduction case of the coupled Hirota equation. First, we derive bright–bright, dark–dark, and bright–dark soliton solutions of the coupled Hirota equation by using the Kadomtsev–Petviashvili reduction method. Then, we present the bright and dark soliton solutions to the Sasa–Satsuma equation which are expressed by determinants of <span><math><mrow><mi>N</mi><mo>×</mo><mi>N</mi></mrow></math></span> instead of <span><math><mrow><mn>2</mn><mi>N</mi><mo>×</mo><mn>2</mn><mi>N</mi></mrow></math></span> in the literature. The dynamics of first-, second-order solutions are investigated in detail. It is intriguing that, for the SS equation, the bright soliton for <span><math><mrow><mi>N</mi><mo>=</mo><mn>1</mn></mrow></math></span> is also the soliton to the complex mKdV equation while the amplitude and velocity of dark soliton for <span><math><mrow><mi>N</mi><mo>=</mo><mn>1</mn></mrow></math></span> are determined by the background plane wave. For <span><math><mrow><mi>N</mi><mo>=</mo><mn>2</mn></mrow></math></span>, the bright soliton can be classified into three types: oscillating, single-hump, and double-hump ones while the dark soliton can be classified into five types: dark (single-hole), anti-dark, Mexican hat, anti-Mexican hat and double-hole. Moreover, the types of bright solitons for the Sasa–Satsuma equation can be changed due to collision.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"197 ","pages":"Article 116400"},"PeriodicalIF":5.3,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874007","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":"A generalized radial integration by parts formula and its applications to Caffarelli–Kohn–Nirenberg inequalities","authors":"Giovanni Di Fratta,&nbsp;Alberto Fiorenza","doi":"10.1007/s13324-025-01060-y","DOIUrl":"10.1007/s13324-025-01060-y","url":null,"abstract":"<div><p>This paper builds upon the Caffarelli–Kohn–Nirenberg (CKN) weighted interpolation inequalities, which are fundamental tools in partial differential equations and geometric analysis for establishing relationships between functions and their gradients when power weights are involved. Our work broadens the scope of these inequalities by generalizing them to encompass a broader class of radial weights and exponents. Additionally, we extend the application of these inequalities to the class <span>(C^{infty } ( {overline{Omega }}))</span> of smooth functions defined on bounded domains with Lipschitz boundaries. To achieve this generalization, we formulate a new integration by parts formula that accounts for more general weights, a wider range of exponents, and <span>(C^{infty }({overline{Omega }}))</span> functions. The resulting generalized CKN-type inequalities offer explicit upper bounds on the optimal constants, independent of the domain’s geometry, consistent with the scaling invariant nature of the inequalities.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"15 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-025-01060-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875296","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":"Convergence rate of nonlinear delayed neutral McKean-Vlasov SDEs driven by fractional Brownian motions","authors":"Shengrong Wang ,&nbsp;Jie Xie ,&nbsp;Li Tan","doi":"10.1016/j.amc.2025.129478","DOIUrl":"10.1016/j.amc.2025.129478","url":null,"abstract":"<div><div>The primary objective of this paper is to explore the strong convergence for a neutral McKean-Vlasov stochastic differential equation with super-linear delay driven by fractional Brownian motion with Hurst exponent <span><math><mi>H</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>. After giving uniqueness and existence for the exact solution, we analyze the properties including boundedness of moment and propagation of chaos. Besides, we give the Euler-Maruyama (EM) scheme and show that the numerical solution convergent to the true solution strongly. Furthermore, a related example is given to illustrate the theory.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"502 ","pages":"Article 129478"},"PeriodicalIF":3.5,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873906","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":"Completely independent spanning trees in kth power of 2-connected graphs","authors":"Xia Hong ,&nbsp;Zhizheng Zhang","doi":"10.1016/j.dam.2025.04.051","DOIUrl":"10.1016/j.dam.2025.04.051","url":null,"abstract":"<div><div>Let <span><math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></math></span> be spanning trees of a graph <span><math><mi>G</mi></math></span>. For any two vertices <span><math><mrow><mi>u</mi><mo>,</mo><mi>v</mi></mrow></math></span> of <span><math><mi>G</mi></math></span>, if the paths from <span><math><mi>u</mi></math></span> to <span><math><mi>v</mi></math></span> in these <span><math><mi>k</mi></math></span> trees are pairwise openly disjoint, then we say that <span><math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></math></span> are completely independent. Let <span><math><mrow><mi>G</mi><mo>≇</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span>, where <span><math><mrow><mi>n</mi><mo>=</mo><mi>q</mi><mi>k</mi><mo>+</mo><mn>2</mn><mo>,</mo><mi>k</mi><mo>≥</mo><mn>6</mn><mo>,</mo><mi>q</mi><mo>≥</mo><mn>3</mn></mrow></math></span>. In this paper, we prove that the <span><math><mi>k</mi></math></span>th power of any 2-connected graph <span><math><mi>G</mi></math></span> on <span><math><mrow><mi>n</mi><mo>≥</mo><mn>2</mn><mi>k</mi><mrow><mo>(</mo><mi>k</mi><mo>≥</mo><mn>4</mn><mo>)</mo></mrow></mrow></math></span> vertices has <span><math><mi>k</mi></math></span> completely independent spanning trees, unless <span><math><mrow><mi>G</mi><mo>≅</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span> where <span><math><mrow><mi>n</mi><mo>=</mo><mi>k</mi><mi>q</mi><mo>+</mo><mi>r</mi><mo>,</mo><mi>r</mi><mo>∈</mo><mrow><mo>{</mo><mn>3</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>k</mi><mo>−</mo><mn>1</mn><mo>}</mo></mrow></mrow></math></span> or <span><math><mrow><mi>n</mi><mo>=</mo><mn>2</mn><mi>k</mi><mo>+</mo><mn>2</mn><mo>,</mo><mi>k</mi><mo>≥</mo><mn>6</mn></mrow></math></span>. The work of this paper improves the results of Hong (2018).</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"372 ","pages":"Pages 268-273"},"PeriodicalIF":1.0,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874386","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":"When all directed cycles have length three","authors":"Paul Seymour","doi":"10.1016/j.ejc.2025.104161","DOIUrl":"10.1016/j.ejc.2025.104161","url":null,"abstract":"<div><div>We give a construction to build all digraphs with the property that every directed cycle has length three.</div></div>","PeriodicalId":50490,"journal":{"name":"European Journal of Combinatorics","volume":"127 ","pages":"Article 104161"},"PeriodicalIF":1.0,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873957","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":"Fast reaction limit for a Leslie–Gower model including preys, meso-predators and top-predators","authors":"L. Desvillettes ,&nbsp;L. Fiorentino ,&nbsp;T. Mautone","doi":"10.1016/j.na.2025.113817","DOIUrl":"10.1016/j.na.2025.113817","url":null,"abstract":"<div><div>We consider a system of three reaction–diffusion equations modeling the interaction between a prey species and two predators species including functional responses of Holly type-II and Leslie–Gower type. We propose a reaction–diffusion model with five equations with simpler functional responses which, in the fast reaction limit, allows to recover the zero-th order terms of the initially considered system. The diffusive part of the initial equations is however modified and cross diffusion terms pop up. We first study the equilibria of this new system and show that no Turing instability appears. We then rigorously prove a partial result of convergence for the fast reaction limit (in 1D and 2D).</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"258 ","pages":"Article 113817"},"PeriodicalIF":1.3,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874392","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":"Some digraph classes that meet the directed path partition conjecture","authors":"Jiawen Bo ,&nbsp;Zhipeng Gao ,&nbsp;Xiaopan Lian ,&nbsp;Jianing Liu","doi":"10.1016/j.dam.2025.04.048","DOIUrl":"10.1016/j.dam.2025.04.048","url":null,"abstract":"<div><div>Let <span><math><mrow><mi>λ</mi><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow></mrow></math></span> denote the order of a longest path in a digraph <span><math><mi>D</mi></math></span>. For disjoint <span><math><mrow><mi>A</mi><mo>,</mo><mi>B</mi><mo>⊆</mo><mi>V</mi><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow></mrow></math></span>, if <span><math><mrow><mi>A</mi><mo>∪</mo><mi>B</mi><mo>=</mo><mi>V</mi><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow></mrow></math></span>, we say that <span><math><mrow><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></mrow></math></span> is a partition of <span><math><mi>D</mi></math></span>. The Directed Path Partition Conjecture (DPPC) states that for every digraph <span><math><mi>D</mi></math></span> and every integer <span><math><mi>q</mi></math></span> with <span><math><mrow><mi>q</mi><mo>&lt;</mo><mi>λ</mi><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow></mrow></math></span>, there is a partition <span><math><mrow><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></mrow></math></span> of <span><math><mi>D</mi></math></span> such that <span><math><mrow><mi>λ</mi><mrow><mo>(</mo><mi>D</mi><mrow><mo>[</mo><mi>A</mi><mo>]</mo></mrow><mo>)</mo></mrow><mo>≤</mo><mi>q</mi></mrow></math></span> and <span><math><mrow><mi>λ</mi><mrow><mo>(</mo><mi>D</mi><mrow><mo>[</mo><mi>B</mi><mo>]</mo></mrow><mo>)</mo></mrow><mo>≤</mo><mi>λ</mi><mrow><mo>(</mo><mi>D</mi><mo>)</mo></mrow><mo>−</mo><mi>q</mi></mrow></math></span>.</div><div>Arroyo and Galeana-Sánchez (2013) proved that every strong 3-quasi-transitive digraph satisfies the DPPC. They also showed that the DPPC holds for compositions over an acyclic digraph with digraphs that meet the DPPC. In the paper, we show that non-strong 3-quasi-transitive digraphs and strong 4-transitive digraphs also satisfy the DPPC. Additionally, we show that the DPPC holds for the compositions over a unicyclic digraph with digraphs that satisfy the DPPC and certain other conditions. Furthermore, by applying different arguments, we show that the compositions over a cycle with arbitrary digraphs meets the DPPC.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"372 ","pages":"Pages 260-267"},"PeriodicalIF":1.0,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874385","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":"Chaotic guided local search algorithm for solving global optimization and engineering problems","authors":"Anis Naanaa","doi":"10.1007/s10878-025-01281-8","DOIUrl":"https://doi.org/10.1007/s10878-025-01281-8","url":null,"abstract":"<p>Chaos optimization algorithm (COA) is an interesting alternative in a global optimization problem. Due to the non-repetition and ergodicity of chaos, it can explore the global search space at higher speeds than stochastic searches that depend on probabilities. To adjust the solution obtained by COA, guided local search algorithm (GLS) is integrated with COA to form a hybrid algorithm. GLS is a metaheuristic optimization algorithm that combines elements of local search with strategic guidance to efficiently explore the solution space. This study proposes a chaotic guided local search algorithm to search for global solutions. The proposed algorithm, namely COA-GLS, contributes to optimization problems by providing a balance between quick convergence and good solution quality. Its combination of local refinement, strategic guidance, diversification strategies, and adaptability makes it a powerful metaheuristic capable of efficiently navigating complex solution spaces and finding high-quality solutions in a relatively short amount of time. Simulation results show that the present algorithms significantly outperform the existing methods in terms of convergence speed, numerical stability, and a better optimal solution than other algorithms.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"53 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143876098","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":"A class of time-dependent quasi-variational–hemivariational inequalities with applications","authors":"Yongjian Liu ,&nbsp;Stanisław Migórski ,&nbsp;Sylwia Dudek","doi":"10.1016/j.nonrwa.2025.104385","DOIUrl":"10.1016/j.nonrwa.2025.104385","url":null,"abstract":"<div><div>In this paper a class of time-dependent multivalued quasi-variational inequalities of elliptic type with a solution dependent constraint set, is studied. Its solvability and the closedness of the solution set are proved. Then, the results are applied to constrained quasi-variational–hemivariational inequalities for which the relaxed monotonicity condition is not required. Finally, the abstract results are illustrated by two applications. The first one is a time-dependent frictional contact problem with locking materials, and the second one is the stationary incompressible Navier–Stokes equation which models a generalized Newtonian fluid of Bingham type. Results on existence and the closedness of the solution sets are established for both applications.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"86 ","pages":"Article 104385"},"PeriodicalIF":1.8,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143874274","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}