Applied Mathematics and Computation最新文献

{"title":"Isomorphisms of the 4-valent generalized Cayley graphs of Z3p","authors":"Qianfen Liao , Yangming Li , Weijun Liu","doi":"10.1016/j.amc.2025.129931","DOIUrl":"10.1016/j.amc.2025.129931","url":null,"abstract":"<div><div>For an odd prime <em>p</em> ≠ 3, the cyclic group <em>Z</em><sub>3<em>p</em></sub>≅<em>Z</em><sub>3</sub> × <em>Z<sub>p</sub></em>, where <span><math><mrow><msub><mi>Z</mi><mn>3</mn></msub><mo>=</mo><mrow><mo>〈</mo><msub><mi>w</mi><mn>1</mn></msub><mo>〉</mo></mrow></mrow></math></span> and <span><math><mrow><msub><mi>Z</mi><mi>p</mi></msub><mo>=</mo><mrow><mo>〈</mo><msub><mi>w</mi><mn>2</mn></msub><mo>〉</mo></mrow></mrow></math></span>. Let <em>β</em><sub>1</sub> and <em>β</em><sub>2</sub> be involutory automorphisms of <em>Z</em><sub>3<em>p</em></sub> defined by <span><math><mrow><msup><mrow><mo>(</mo><msub><mi>w</mi><mn>1</mn></msub><mo>,</mo><msub><mi>w</mi><mn>2</mn></msub><mo>)</mo></mrow><msub><mi>β</mi><mn>1</mn></msub></msup><mo>=</mo><mrow><mo>(</mo><msubsup><mi>w</mi><mn>1</mn><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><mo>,</mo><msub><mi>w</mi><mn>2</mn></msub><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><msup><mrow><mo>(</mo><msub><mi>w</mi><mn>1</mn></msub><mo>,</mo><msub><mi>w</mi><mn>2</mn></msub><mo>)</mo></mrow><msub><mi>β</mi><mn>2</mn></msub></msup><mo>=</mo><mrow><mo>(</mo><msub><mi>w</mi><mn>1</mn></msub><mo>,</mo><msubsup><mi>w</mi><mn>2</mn><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><mo>)</mo></mrow></mrow></math></span>. Then the elements of sets <span><math><mrow><msub><mstyle><mi>Δ</mi></mstyle><mn>1</mn></msub><mo>=</mo><mrow><mo>{</mo><mrow><mo>{</mo><mrow><mo>(</mo><msub><mi>s</mi><mn>1</mn></msub><mo>,</mo><msub><mi>s</mi><mn>2</mn></msub><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><msub><mi>s</mi><mn>1</mn></msub><mo>,</mo><msubsup><mi>s</mi><mn>2</mn><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><msub><mi>s</mi><mn>1</mn></msub><mo>,</mo><msub><mi>s</mi><mn>3</mn></msub><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><msub><mi>s</mi><mn>1</mn></msub><mo>,</mo><msubsup><mi>s</mi><mn>3</mn><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><mo>)</mo></mrow><mo>}</mo></mrow><mo>∣</mo><msub><mi>s</mi><mn>1</mn></msub><mo>∈</mo><msub><mi>Z</mi><mn>3</mn></msub><mo>,</mo><msub><mi>s</mi><mn>2</mn></msub><mo>≠</mo><msub><mi>s</mi><mn>3</mn></msub><mspace></mspace><mtext>and</mtext><mspace></mspace><msub><mi>s</mi><mn>2</mn></msub><mo>,</mo><msub><mi>s</mi><mn>3</mn></msub><mo>≠</mo><msub><mi>e</mi><mn>2</mn></msub><mo>}</mo></mrow></mrow></math></span> and <span><math><mrow><msub><mstyle><mi>Δ</mi></mstyle><mn>2</mn></msub><mo>=</mo><mrow><mo>{</mo><mrow><mo>{</mo><mrow><mo>(</mo><msub><mi>w</mi><mn>1</mn></msub><mo>,</mo><msub><mi>t</mi><mn>1</mn></msub><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><msubsup><mi>w</mi><mn>1</mn><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><mo>,</mo><msub><mi>t</mi><mn>1</mn></msub><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><msub><mi>w</mi><mn>1</mn></msub><mo>,</mo><msub><mi>t</mi><mn>2</mn></msub><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><msubsup><mi>w</mi><mn>1</mn><mrow><mo>−</mo><mn>1</mn></mrow></msubsup><mo>,</mo><msub><mi>t</mi><mn>2<","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"519 ","pages":"Article 129931"},"PeriodicalIF":3.4,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886438","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":"Maximum augmented Zagreb index on polyomino chains","authors":"Manuel Montes-y-Morales,&nbsp;Saylé Sigarreta,&nbsp;Hugo Cruz-Suárez","doi":"10.1016/j.amc.2025.129929","DOIUrl":"10.1016/j.amc.2025.129929","url":null,"abstract":"<div><div>In this paper, we present a dynamic programming approach for identifying extremal polyomino chains with respect to degree–based indices. This approach provides an explicit recurrence, and a constructive algorithm that enable both the computation of an extremal polyomino chain in linear time with respect to the number of squares, and the enumeration of all maximal configurations. As a main application, we focus on the problem posed in 2016 by characterizing the polyomino chains that maximize the Augmented Zagreb Index (<em>AZI</em>) for any fixed number of squares. The results presented in this paper are aligned with previous contributions, and establish a constructive methodology for solving extremal problems in chemical graph theory. A link to the implementation code is provided in the last section.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"519 ","pages":"Article 129929"},"PeriodicalIF":3.4,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886384","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":"A second-order unconditionally energy stable scheme for the Lifshitz-Petrich model integrated with observational data","authors":"Xiaochuan Hu ,&nbsp;Junseok Kim ,&nbsp;Yibao Li","doi":"10.1016/j.amc.2025.129914","DOIUrl":"10.1016/j.amc.2025.129914","url":null,"abstract":"<div><div>In this paper, we introduce a modified Lifshitz-Petrich model that incorporates a data assimilation term. This model is used to investigate the nucleation of quasicrystalline structures in polycrystalline materials by leveraging information from observational data. Guided by the principle of feedback control, the data assimilation term drives the solution toward the observational data sampled from the reference process. Using the second-order backward differentiation formula and the scalar auxiliary variable method, we introduce an efficient numerical scheme for the modified Lifshitz-Petrich model. We employ the Fourier spectral method to achieve second-order accuracy and high computational efficiency. And we prove the numerical discrete energy is unconditionally stable. A series of numerical experiments are conducted to evaluate the efficiency and robustness of the proposed method.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"518 ","pages":"Article 129914"},"PeriodicalIF":3.4,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842454","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":"Impact of interaction diversity and interlayer coupling on the evolution of human-AI cooperation","authors":"Bo Gao ,&nbsp;Pengfei Zuo ,&nbsp;Chengyi Xia ,&nbsp;Tianyi Zhang ,&nbsp;Suyalatu Dong ,&nbsp;Chunyang Liu","doi":"10.1016/j.amc.2025.129894","DOIUrl":"10.1016/j.amc.2025.129894","url":null,"abstract":"<div><div>In the context of a digitized society characterized by profound human-artificial intelligence (AI) interaction, the evolutionary dynamics of cooperative behavior confront novel challenges. This study develops a two-layer network evolutionary game model that couples a human decision-making layer with an AI system layer, aiming to investigate how bidirectional interlayer coupling mechanisms influence the emergence and sustainability of cooperation. We find that interlayer coupling facilitates the emergence and stabilization of cooperative behavior across both the AI and human layers. However, the efficacy of this facilitative effect is highly contingent upon the relative dependency configurations between two networks. When interaction diversity (link-strategy) is introduced within the AI layer, the system’s resilience to the temptation of defection is markedly enhanced, resulting in elevated levels of cooperation. Conversely, excessive interaction diversity within the human layer may, under certain conditions, undermine cooperative coordination, particularly in scenarios characterized by high interlayer dependency. Moreover, the AI layer exhibits substantial adaptive capacity, maintaining relatively stable behavioral patterns across varying human decision-making regimes, thereby enabling the emergence of a robust mixed equilibrium of cooperation and defection. This study proposes a computational model to explore the evolutionary dynamics of cooperation in human-AI collaborative environments, offering new insights into AI governance, multi-agent system design, and related domains.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"518 ","pages":"Article 129894"},"PeriodicalIF":3.4,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145885776","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":"A posteriori-driven adaptive strategy for solving inverse Cauchy problems in diffusion-reaction models","authors":"Hafida Hamdi ,&nbsp;Mourad Nachaoui ,&nbsp;Amal Bergam ,&nbsp;Abdeljalil Nachaoui","doi":"10.1016/j.amc.2025.129902","DOIUrl":"10.1016/j.amc.2025.129902","url":null,"abstract":"<div><div>This work addresses the inverse Cauchy problem for the modified Helmholtz equation using an alternating iterative approach. The central contribution lies in the design of novel local error indicators based on a posteriori analysis, which simultaneously assess the accuracy of the spatial discretization and the convergence behavior of the iterative algorithm. Unlike standard methods, our strategy leverages a comparative assessment of these indicators to drive an adaptive mesh refinement process. This adaptive framework ensures a more balanced distribution of computational resources, significantly reducing the numerical cost while maintaining high solution accuracy. The proposed methodology is validated through a series of synthetic and application-driven numerical experiments, demonstrating both its effectiveness and robustness in reconstructing inaccessible boundary data.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"518 ","pages":"Article 129902"},"PeriodicalIF":3.4,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145814360","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":"An alternating direction implicit method for 2D nonlinear Schrödinger equation with accelerated evaluation of Caputo derivative","authors":"Himanshu Kumar Dwivedi ,&nbsp;Rajeev ,&nbsp;Shengda Zeng","doi":"10.1016/j.amc.2025.129905","DOIUrl":"10.1016/j.amc.2025.129905","url":null,"abstract":"<div><div>We propose an efficient time-space discretization for nonlinear fractional Schrödinger equations involving Caputo tempered derivatives. A new tempered Alikhanov scheme with parameter <em>λ</em> is introduced, together with a fast sum-of-exponentials (SOE) implementation, reducing complexity to <span><math><mrow><mi>O</mi><mo>(</mo><mi>M</mi><msub><mi>K</mi><mi>t</mi></msub><mi>log</mi><msub><mi>K</mi><mi>t</mi></msub><mo>)</mo></mrow></math></span> and memory to <span><math><mrow><mi>O</mi><mo>(</mo><mi>M</mi><mi>log</mi><msub><mi>K</mi><mi>t</mi></msub><mo>)</mo></mrow></math></span>. Spatial derivatives are approximated using a compact scheme, and an alternating direction implicit formulation is derived with perturbation terms for stability. A graded time mesh resolves the initial singularity, while adaptive time-stepping ensures long-time efficiency. Stability and maximum-norm error bounds are established via a discrete Grönwall inequality. Numerical tests confirm the theoretical convergence and demonstrate substantial savings in CPU time and storage over classical methods. This work presents a novel nonuniform tempered Alikhanov time-stepping framework for nonlinear tempered fractional Schrödinger equation(NL-TFSEs), combining robustness, high accuracy, and computational scalability.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"518 ","pages":"Article 129905"},"PeriodicalIF":3.4,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842452","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":"Efficient diffusion for high order non-oscillatory entropy stable schemes","authors":"Anuradha Sahu ,&nbsp;Prashant Kumar Pandey ,&nbsp;Ritesh Kumar Dubey","doi":"10.1016/j.amc.2025.129901","DOIUrl":"10.1016/j.amc.2025.129901","url":null,"abstract":"<div><div>This paper proposes an efficient approach to construct non-oscillatory entropy stable fluxes (<span><math><mover><mi>F</mi><mo>^</mo></mover></math></span>) by adding an efficient diffusion term to the entropy conservative fluxes. Computation of proposed diffusion term does not require restrictive and logically expensive sign stability condition on high order reconstruction process or flux sign stability on high order fluxes. The diffusion term is defined as the absolute difference of non-oscillatory (<span><math><mover><mi>F</mi><mo>˘</mo></mover></math></span>) and entropy conservative fluxes (<span><math><mover><mi>F</mi><mo>˜</mo></mover></math></span>) multiplied with sign of jump in entropy variable. The amount of diffusion is adjusted using a limiter function without compromising the entropy stability of the resulting scheme which exhibits both high resolution and the non-oscillatory property. The proposed approach is tested on various standard benchmark test problems. Numerical results demonstrate the effectiveness of the method in achieving high resolution entropy stable schemes, Moreover the scheme maintains formal order of accuracy of the lower order flux used in defining the diffusion term.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"518 ","pages":"Article 129901"},"PeriodicalIF":3.4,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842451","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-time trajectory tracking of multi-agent systems via higher-order dynamic networks with channel damage","authors":"Junfeng Mao ,&nbsp;Lilan Tu ,&nbsp;Xianjia Wang ,&nbsp;Fujuan Gao ,&nbsp;Qiuyue Zhao","doi":"10.1016/j.amc.2025.129918","DOIUrl":"10.1016/j.amc.2025.129918","url":null,"abstract":"<div><div>For multi-agent trajectory tracking, strong communication channels between agents are crucial for group motion. In this paper, using undirected and directed higher-order complex networks described by second-order simplicial complexes, we investigated finite-time trajectory tracking of multi-agent systems when communication channels are damaged. By introducing the effective and damaged rates to the first-order and second-order channels of the multi-agent networks, and employing Lyapunov stability theory, and finite-time control techniques, we proposed several theoretical sufficient conditions that enable multiple agents in the response networks with damaged channels to track the trajectories of multiple agents in the drive networks within finite time. Extensive numerical simulations were conducted not only to verify the feasibility and effectiveness of the proposed theoretical results, but also to explore the effects of first-order channel, second-order channel, random damage, deliberate damage, one-time damage, and cascade damage on the finite-time tracking performance of multi-agent systems. We found that damage to first-order channels significantly impacts the tracking performance of multi-agent systems, while damage to second-order channels has a comparatively smaller impact. Deliberate damage is more detrimental to multi-agent systems than random damage. Random damage triggers significant phase fluctuations in tracking time. The directionality makes the network more vulnerable to channel damage.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"518 ","pages":"Article 129918"},"PeriodicalIF":3.4,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842453","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 2-distance integral Cayley graphs","authors":"Xiaoqian Zhang,&nbsp;Weijun Liu,&nbsp;Lu Lu","doi":"10.1016/j.amc.2025.129893","DOIUrl":"10.1016/j.amc.2025.129893","url":null,"abstract":"<div><div>The distance splitting field of distance matrix associated with a graph is the smallest field extension of <span><math><mi>Q</mi></math></span> that contains all of its distance eigenvalues. The extension degree is called its distance algebraic degree. A graph Γ is called <em>k</em>-distance integral if distance algebraic degree is equal to <em>k</em>. In this paper, we prove that the normal Cayley graph is distance algebraically integral over field <em>K</em> if and only if it is algebraically integral over <em>K</em>, and the Cayley graphs over cyclic groups is 2-distance integral if and only if it is 2-integral. Moreover, we construct <em>k</em>-distance integral Cayley graphs over cyclic groups, and classify the 2-distance integral abelian Cayley graphs with valency 2, 3, 4 and 5.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"517 ","pages":"Article 129893"},"PeriodicalIF":3.4,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145712288","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":"Memory-based evolutionary prisoner’s dilemma game with neighbor screening mechanism","authors":"Jinlong Ma ,&nbsp;Guanghui Wang","doi":"10.1016/j.amc.2025.129903","DOIUrl":"10.1016/j.amc.2025.129903","url":null,"abstract":"<div><div>Memory effects of individuals have been demonstrated to significantly promote cooperation, attracting widespread attention among scholars exploring the underlying dynamics of cooperative behavior. In this paper, we build a strategy updating framework by proposing a neighbor screening mechanism and combining particle swarm optimization algorithm in memory-based evolutionary prisoners’ dilemma game. Under the proposed mechanism, individuals may not imitate a neighbor with the only highest payoff from the current round when updating their strategy. Instead, individual evaluates the historical performance by his/her neighbors’ the frequency of choosing cooperation strategy and being chosen as an optimal neighbor and screen out the neighbors who do not meet the defined initial threshold. Moreover, a threshold adjustment parameter <em>α</em> is introduced to strengthen the flexible of the threshold. In addition, the proposed mechanism is compared in two situations: fixed memory and dynamic memory. Specifically, in the neighbor screening mechanism with dynamic memory, each individual’s memory will decay or remain unchanged according to the relationship between their current payoff and average payoff of all players in the local group. The simulation results reveal that the advantages of short memory length and dynamic memory in promoting cooperation. Furthermore, the synergistic effect between initial threshold and memory length better promotes cooperation. Additionally, a slight increase in the threshold adjustment parameter <em>α</em> promotes cooperation when the initial threshold is low. These findings shed light on how cooperation can be enhanced through specific rules.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"517 ","pages":"Article 129903"},"PeriodicalIF":3.4,"publicationDate":"2026-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784752","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}