数学最新文献

{"title":"Limits of saturated ideals","authors":"Joachim Jelisiejew,&nbsp;Tomasz Mańdziuk","doi":"10.1112/jlms.70188","DOIUrl":"https://doi.org/10.1112/jlms.70188","url":null,"abstract":"<p>We investigate the question of when a given homogeneous ideal is a limit of saturated ones. We provide cohomological necessary criteria for this to hold and apply them to a range of examples. In small cases, we characterise the limits. We also supply a number of auxiliary results on the classical and multigraded Hilbert schemes, for example, we prove a very general result on openness of the saturated locus and give scheme structure to ‘constant Hilbert function’ loci. Our results have applications to theory of tensors.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 6","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70188","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144206446","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":"Global attractor and robust exponential attractors for some classes of fourth-order nonlinear evolution equations","authors":"Beniamin Goldys ,&nbsp;Agus L. Soenjaya ,&nbsp;Thanh Tran","doi":"10.1016/j.nonrwa.2025.104420","DOIUrl":"10.1016/j.nonrwa.2025.104420","url":null,"abstract":"<div><div>We study the long-time behaviour of solutions to some classes of fourth-order nonlinear PDEs with non-monotone nonlinearities, which include the Landau–Lifshitz–Baryakhtar (LLBar) equation (with all relevant fields and spin torques) and the convective Cahn–Hilliard/Allen–Cahn (CH-AC) equation with a proliferation term, in dimensions <span><math><mrow><mi>d</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mrow></math></span>. Firstly, we show the global well-posedness, as well as the existence of global and exponential attractors with finite fractal dimensions for these problems. In the case of the exchange-dominated LLBar equation and the CH-AC equation without convection, an estimate for the rate of convergence of the solution to the corresponding stationary state is given. Finally, we show the existence of a robust family of exponential attractors when <span><math><mrow><mi>d</mi><mo>≤</mo><mn>2</mn></mrow></math></span>. As a corollary, exponential attractor of the LLBar equation is shown to converge to that of the Landau–Lifshitz–Bloch equation in the limit of vanishing exchange damping, while exponential attractor of the convective CH-AC equation is shown to converge to that of the convective Allen–Cahn equation in the limit of vanishing diffusion coefficient.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"87 ","pages":"Article 104420"},"PeriodicalIF":1.8,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144196149","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":"A streamline diffusion method for nonstationary incompressible magnetohydrodynamics system with variable density","authors":"Mingxia Li ,&nbsp;Qianqian Ding ,&nbsp;Shipeng Mao","doi":"10.1016/j.camwa.2025.05.020","DOIUrl":"10.1016/j.camwa.2025.05.020","url":null,"abstract":"<div><div>This paper proposes a streamline diffusion numerical method for the unsteady magnetohydrodynamic flows with variable density, in which the electric conductivity and viscosity coefficients depend on the density. We employ stable mini-elements to discretize the Navier-Stokes equations and the Nédélec edge elements to discretize the magnetic induction. In each time step, the equations for velocity and pressure are decoupled with pressure computed by solving one Poisson equation. The streamline diffusion method is applied to the continuity equation, based on which a stable finite element scheme is proposed. We show that the fully discrete numerical scheme is energy-stable and well-posed. Rigorous error estimate of all the variables is established without assuming that the density has a good approximation, which shows that this method performs as well as the constant density.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"193 ","pages":"Pages 1-19"},"PeriodicalIF":2.9,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144194453","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":"BMO estimates for Hodge–Maxwell systems with discontinuous anisotropic coefficients","authors":"Dharmendra Kumar ,&nbsp;Swarnendu Sil","doi":"10.1016/j.na.2025.113852","DOIUrl":"10.1016/j.na.2025.113852","url":null,"abstract":"<div><div>We prove up to the boundary <span><math><mi>BMO</mi></math></span> estimates for linear Maxwell–Hodge type systems for <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>-valued differential <span><math><mi>k</mi></math></span>-forms <span><math><mi>u</mi></math></span> in <span><math><mi>n</mi></math></span> dimensions <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msup><mrow><mi>d</mi></mrow><mrow><mo>∗</mo></mrow></msup><mfenced><mrow><mi>A</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>d</mi><mi>u</mi></mrow></mfenced></mtd><mtd><mo>=</mo><mi>f</mi></mtd><mtd></mtd><mtd><mtext>in</mtext><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><msup><mrow><mi>d</mi></mrow><mrow><mo>∗</mo></mrow></msup><mfenced><mrow><mi>B</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>u</mi></mrow></mfenced></mtd><mtd><mo>=</mo><mi>g</mi></mtd><mtd></mtd><mtd><mtext>in</mtext><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>with <span><math><mrow><mi>ν</mi><mo>∧</mo><mi>u</mi></mrow></math></span> prescribed on <span><math><mrow><mi>∂</mi><mi>Ω</mi><mo>,</mo></mrow></math></span> where the coefficient tensors <span><math><mrow><mi>A</mi><mo>,</mo><mi>B</mi></mrow></math></span> are only required to be bounded measurable and in a class of ‘small multipliers of BMO’. This class neither contains nor is contained in <span><math><mrow><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup><mo>.</mo></mrow></math></span> Since the coefficients are allowed to be discontinuous, the usual Korn’s freezing trick cannot be applied. As an application, we show BMO estimates hold for the time-harmonic Maxwell system in dimension three for a class of discontinuous anisotropic permeability and permittivity tensors. The regularity assumption on the coefficient is essentially sharp.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"260 ","pages":"Article 113852"},"PeriodicalIF":1.3,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144194481","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":"Dynamic asymmetric reflective decision-making supports the evolution of cooperation","authors":"Xiaopeng Li ,&nbsp;Xiuli Zhang ,&nbsp;Zhonglin Wang ,&nbsp;Yicheng Pang","doi":"10.1016/j.chaos.2025.116583","DOIUrl":"10.1016/j.chaos.2025.116583","url":null,"abstract":"<div><div>Up to now, most previous studies have assumed that agents employed symmetric decision-updating mechanisms to investigate how cooperation evolved in selfish populations. However, dynamic and asymmetric decision-making update is overlooked. In this paper, we try our best to construct a reputation-driven dynamic asymmetric reflective decision-making model to fill in the blanks. Initially, each agent is randomly assigned a reputation value within the range [1,100], which will increase or decrease if it makes cooperative or defective decision in the process of evolution. Then, we distinguish agents as standouts or laymen by the pivotal reputation threshold <span><math><msub><mrow><mi>R</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span>. The standouts with high-reputation are cautious in updating their decisions and therefore may think more times. In sharp contrast, the laymen with low-reputation, appear too reckless and just only think once in the similar process. Simulation results show that this simple model can support the evolution of cooperation, especially expanding the threshold for cooperation annihilation. Through qualitative micro-analysis and quantitative statistical analysis, we find that standouts with high reputations play an irreplaceable role in facilitating cooperation. The robustness test further confirms that the promoting effect of this mechanism on cooperation is independent of network structures, decision update patterns, and social dilemma types. We hope that our research can deepen the understanding and cognition of the evolution of cooperation.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116583"},"PeriodicalIF":5.3,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144203042","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":"Combining deliberate study and heuristics to form opinions on interconnected questions","authors":"Ruijie Wang ,&nbsp;Yuhao Zhou ,&nbsp;Matúš Medo","doi":"10.1016/j.chaos.2025.116562","DOIUrl":"10.1016/j.chaos.2025.116562","url":null,"abstract":"<div><div>The ever-increasing complexity of the world around us challenges our ability to understand it. We study a model where an individual forms opinions about many interconnected questions. This model was shown to be challenging for a boundedly rational agent. We extend it by assuming that the individual combines a targeted study of some questions and various heuristics for the remaining ones. We find that the highest opinion accuracy is generally achieved when neither one question is studied particularly well nor when many questions are studied a little. Despite big differences in accuracy between the considered heuristics, the optimal number of questions in which the study budget is invested grows linearly with the budget for all of them. The study budget necessary to achieve the desired opinion accuracy exhibits a simple scaling with the total number of questions. In this way, we exemplify efficient learning in a complex system using simple heuristics.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116562"},"PeriodicalIF":5.3,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144203040","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":"Hybrid Morié flatbands in triple-layer superlattices via flatbands coupling","authors":"Peilong Hong ,&nbsp;Can Lu ,&nbsp;Yu Wang ,&nbsp;Changfeng Liang ,&nbsp;Liwei Zhang ,&nbsp;Peng Cheng ,&nbsp;WangPing Cheng ,&nbsp;Mingfang Yi ,&nbsp;Yi Liang","doi":"10.1016/j.chaos.2025.116598","DOIUrl":"10.1016/j.chaos.2025.116598","url":null,"abstract":"<div><div>Flatband moiré superlattices exhibit a wealth of exotic phenomena, demonstrating significant potential for groundbreaking applications across diverse fields, from condensed matter physics to photonics. In this work, we explore the intricate physics of nontrivial flatband superlattices with photonic multi-layer architectures. We introduce a universal framework for generating hybrid moiré flatbands via the strategic coupling of fundamental moiré flatbands. Following the framework, we construct series of triple-layer superlattices by stacking different pairs of double-layer superlattices, where the double-layer superlattices host two sets of fundamental moiré flatbands. Through comprehensive full-wave simulations, we validate the proposed framework by demonstrating that the coupling of different fundamental flatband pairs consistently yields hybrid flatbands, fully in agreement with our theory. Notably, we find that the flatness of the hybrid bands could be better compared to the fundamental flatbands, suggesting new opportunities for enhancing moiré localization in multi-layer configurations. Importantly, the obtained hybrid flatbands inherit the spatial features of the fundamental flatbands, offering a new degree of freedom for manipulating the field patterns of moiré localized modes. Our work establishes a new paradigm for engineering complex multi-layer superlattices with precisely tailored flatbands, paving the way for advanced on-chip light manipulation using moiré superlattice architectures.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116598"},"PeriodicalIF":5.3,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144196285","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":"Design and application of spatial multi-structure hidden attractors in memristor-coupled heterogeneous neural networks","authors":"Jie Zhang,&nbsp;Liu Yang,&nbsp;Jiangang Zuo,&nbsp;Xiaodong Wei,&nbsp;Nana Cheng","doi":"10.1016/j.chaos.2025.116662","DOIUrl":"10.1016/j.chaos.2025.116662","url":null,"abstract":"<div><div>Biomimetic modeling, through memristors coupling different numbers of heterogeneous neurons, holds extraordinary significance for exploring brain science. To expand the diversity of models related to multi-structure attractors, this paper first proposes a novel multi-segment memristor, and then uses it to couple a 4D Hopfield neural network (HNN) and a 2D Hindmarsh-Rose (HR) neuron. This coupling method simulates the electromagnetic induction effect and mutual-synapses between neurons, thereby constructing a new type of memristor-coupled heterogeneous neural network (MCH-NN) with multi-structure chaotic attractors. This innovative model provides a new perspective for exploring multi-structure behaviors in neural networks. Theoretical research and numerical simulations indicate: (1) In the analysis of the generation mechanism of multi-structure chaotic attractors, its rare hidden characteristics are revealed. (2) This is the first time that arbitrarily controllable quantities of 1D (unidirectional)-, 2D (grid)-, and 3D (spatial)- multi-structure hidden attractors (MSHAs) have been detected in heterogeneous neural networks. Notably, the number of MSHAs is determined by the control parameters of the memristor. (3) The coupling strength significantly affects the dynamic evolution of MCH-NN, and dual-parameter dynamic evolution analysis further confirms this. (4) MCH-NN exhibits rich hidden dynamic characteristics, such as spatial initial offset and spatial amplitude control. Interestingly, mirror-symmetric and mirror-asymmetric MSHAs were also discovered when adjusting the amplitude control parameters. Furthermore, its practical feasibility is validated through analog circuit and digital hardware experiments. Finally, based on MCH-NN, incorporating adaptive filtering denoising technology and spread spectrum communication technology, a novel chaos shift keying (CSK) secure communication scheme is designed, and is intended for binary digital information transmission under low signal-to-noise ratio (SNR) environments. The results demonstrate that this scheme has strong anti-noise performance and excellent communication capabilities.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116662"},"PeriodicalIF":5.3,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144196287","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 mixed finite element method for pricing American options and Greeks in the Heston model","authors":"Youness Mezzan ,&nbsp;Moulay Hicham Tber","doi":"10.1016/j.camwa.2025.05.023","DOIUrl":"10.1016/j.camwa.2025.05.023","url":null,"abstract":"<div><div>In this paper, we propose a numerical algorithm for solving a complementarity system associated with pricing American options. More precisely, we consider the stochastic volatility Heston's model. Our method is based on a semi-Lagrangian approach that couples mixed finite elements with a discretization of the material derivative along the characteristics. A primal dual active set solver is developed to handle the complementarity saddle point system obtained at the discrete level. To demonstrate the precision and effectiveness of our method, numerical examples are provided.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"193 ","pages":"Pages 20-33"},"PeriodicalIF":2.9,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144194640","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":"Transverse-freeness in finite geometries","authors":"Charlie Bruggemann ,&nbsp;Vera Choi ,&nbsp;Brian Freidin ,&nbsp;Jaedon Whyte","doi":"10.1016/j.ffa.2025.102663","DOIUrl":"10.1016/j.ffa.2025.102663","url":null,"abstract":"<div><div>We study the interplay between combinatorial and algebraic geometry via projective curves and hypersurfaces defined over a finite field that are tangent to every member of a class of low-degree varieties. Extending the 2-dimensional work of Asgarli, we first explore the lowest degrees attainable by smooth hypersurfaces in <em>n</em>-dimensional projective space that are tangent to every <em>k</em>-dimensional subspace, for some values of <em>n</em> and <em>k</em>. We then study projective surfaces that serve as models of finite inversive and hyperbolic planes, finite analogs of spherical and hyperbolic geometries. In these surfaces, we prove existence results for low-degree curves tangent to each of the lowest degree curves defined over the base field.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"108 ","pages":"Article 102663"},"PeriodicalIF":1.2,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144203078","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}