数学最新文献

{"title":"Resilience prediction and tipping point control of multilayer ecological networks based on dimensionality reduction method","authors":"Dongli Duan, Xingjie Zhao, Zhiqiang Cai, Ning Wang","doi":"10.1016/j.chaos.2024.115914","DOIUrl":"https://doi.org/10.1016/j.chaos.2024.115914","url":null,"abstract":"The collapse of ecosystems often leads to irreversible and catastrophic outcomes. Analyzing and controlling these collapses are challenging due to the complex nature, high dimensionality, multilayer structure, and dynamic behavior of ecosystems, influenced by factors such as interaction topology. While dimensionality reduction techniques can simplify system dynamics, most existing methods focus on individual interaction, hindering comprehensive analysis of diverse species and interactions in complex ecological networks. This paper presents a framework for a plant–pollinator–parasite multilayer network that incorporates mutualistic and parasitic interactions using diagonal coupling. A downscaling approach is devised to transform the high-dimensional system into a low-dimensional effective system with overall variables and layer structure variables. The simplified model accurately captures the fundamental characteristics and dynamics of the original system. Through this framework, we systematically elucidate the resilience patterns of multilayer networks under coupled interactions and the collapse scenarios of three species types, highlighting hysteresis phenomena, multiple tipping points, and first-order or multistage phase transitions within the system. Additionally, two control strategies are introduced to manage collapse critical points via intra- and inter-layer influence, with a low-dimensional model employed to forecast control outcomes. The study demonstrates that the low-dimensional model and control measures are instrumental in evaluating, foreseeing, and controlling the resilience and collapse tipping points of multilayer ecosystems. This framework is versatile and can be extended to diverse multilayer dynamic networks, exposing the fundamental mechanisms and resilience phenomena of these systems.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"25 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887306","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":"The Ekström–Persson conjecture regarding random covering sets","authors":"Esa Järvenpää,&nbsp;Maarit Järvenpää,&nbsp;Markus Myllyoja,&nbsp;Örjan Stenflo","doi":"10.1112/jlms.70058","DOIUrl":"https://doi.org/10.1112/jlms.70058","url":null,"abstract":"<p>We consider the Hausdorff dimension of random covering sets formed by balls with centres chosen independently at random according to an arbitrary Borel probability measure on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mi>d</mi>\u0000 </msup>\u0000 <annotation>$mathbb {R}^d$</annotation>\u0000 </semantics></math> and radii given by a deterministic sequence tending to zero. We prove, for a certain parameter range, the conjecture by Ekström and Persson concerning the exact value of the dimension in the special case of radii <span></span><math>\u0000 <semantics>\u0000 <msubsup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>n</mi>\u0000 <mrow>\u0000 <mo>−</mo>\u0000 <mi>α</mi>\u0000 </mrow>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>=</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <mi>∞</mi>\u0000 </msubsup>\u0000 <annotation>$(n^{-alpha })_{n=1}^infty$</annotation>\u0000 </semantics></math>. For balls with an arbitrary sequence of radii, we find sharp bounds for the dimension and show that the natural extension of the Ekström–Persson conjecture is not true in this case. Finally, we construct examples demonstrating that there does not exist a dimension formula involving only the lower and upper local dimensions of the measure and a critical parameter determined by the sequence of radii.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70058","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142868872","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":"Unconditional superconvergence analysis of a novel energy dissipation nonconforming Crank-Nicolson FEM for Sobolev equations with high order Burgers' type nonlinearity","authors":"Tiantian Liang, Dongyang Shi","doi":"10.1016/j.camwa.2024.12.010","DOIUrl":"https://doi.org/10.1016/j.camwa.2024.12.010","url":null,"abstract":"A novel energy dissipation Crank-Nicolson (C-N) fully discrete scheme is established by low order nonconforming <mml:math altimg=\"si1.svg\"><mml:mi>E</mml:mi><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:math> element for solving the Sobolev equations with high order Burgers' type nonlinearity. Firstly, the boundedness of the discrete solution in the broken <mml:math altimg=\"si2.svg\"><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math>-norm is achieved directly by the energy dissipation property without using the known time-space splitting technique in the existing literatures, and its well-posedness is demonstrated by the Brouwer fixed point theorem. Secondly, by utilizing the special characters of nonconforming <mml:math altimg=\"si1.svg\"><mml:mi>E</mml:mi><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>r</mml:mi><mml:mi>o</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:math> element, the unconditional superclose result of order <mml:math altimg=\"si3.svg\"><mml:mi>O</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msup><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo linebreak=\"badbreak\" linebreakstyle=\"after\">+</mml:mo><mml:msup><mml:mrow><mml:mi>τ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=\"false\">)</mml:mo></mml:math> in the broken <mml:math altimg=\"si2.svg\"><mml:msup><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math>-norm is gained strictly with no restrictions between the spatial partition parameter <ce:italic>h</ce:italic> and the time step <ce:italic>τ</ce:italic>. Moreover, the corresponding global superconvergent error estimate of order <mml:math altimg=\"si3.svg\"><mml:mi>O</mml:mi><mml:mo stretchy=\"false\">(</mml:mo><mml:msup><mml:mrow><mml:mi>h</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo linebreak=\"badbreak\" linebreakstyle=\"after\">+</mml:mo><mml:msup><mml:mrow><mml:mi>τ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=\"false\">)</mml:mo></mml:math> is proved by applying an interpolation post-processing approach. Thirdly, an application to some different finite elements and nonlinear PDEs is discussed, which shows that the proposed scheme and the analysis presented herein can be considered as a general framework to cope with. Lastly, the theoretical results are validated by four numerical examples.","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"32 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142884407","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":"Residualities and uniform ergodicities of Markov semigroups","authors":"Nazife Erkurşun-Özcan,&nbsp;Farrukh Mukhamedov","doi":"10.1007/s43034-024-00398-x","DOIUrl":"10.1007/s43034-024-00398-x","url":null,"abstract":"<div><p>The primary objective of this research is to use an extended Dobrushin ergodicity coefficient to explore residualities of the set of uniform <i>P</i>-ergodic Markov semigroups defined on abstract state spaces. Moreover, we investigate uniform mean ergodicities of Markov semigroups under the Doeblin’s Condition.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142859410","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":"Central limit theorem for smooth statistics of one-dimensional free fermions","authors":"Alix Deleporte,&nbsp;Gaultier Lambert","doi":"10.1112/jlms.70045","DOIUrl":"https://doi.org/10.1112/jlms.70045","url":null,"abstract":"<p>We consider the determinantal point processes associated with the spectral projectors of a Schrödinger operator on <span></span><math>\u0000 <semantics>\u0000 <mi>R</mi>\u0000 <annotation>$mathbb {R}$</annotation>\u0000 </semantics></math>, with a smooth confining potential. In the semiclassical limit, where the number of particles tends to infinity, we obtain a Szegő-type central limit theorem for the fluctuations of smooth linear statistics. More precisely, the Laplace transform of any statistic converges without renormalisation to a Gaussian limit with a <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$H^{1/2}$</annotation>\u0000 </semantics></math>-type variance, which depends on the potential. In the one-well (one-cut) case, using the quantum action-angle theorem and additional micro-local tools, we reduce the problem to the asymptotics of Fredholm determinants of certain approximately Toeplitz operators. In the multi-cut case, we show that for generic potentials, a similar result holds and the contributions of the different wells are independent in the limit.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70045","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142868975","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":"Axial-torsional coupling vibration model and nonlinear behavior of drill string system in oil and gas wells","authors":"Xiaoqiang Guo, Zhichen Qiu, Mingming Li, Xinye Li, Ning Hu, Libin Zhao, Chengyang Ye","doi":"10.1016/j.cnsns.2024.108560","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108560","url":null,"abstract":"In response to the failure problem of axial-torsional coupling vibration of drill string in oil &amp; gas wells, an axial-torsional coupling nonlinear vibration model of drill string is established using the finite element method, which can effectively simulate the coupling vibration of actual wellbore drill string multi-body systems and the real-time rock breaking effect. Moreover, the correctness and effectiveness of the theoretical model verified by a similar experiment of tubing vibration. Finally, the influences of feed rate and rotary drilling speed on the nonlinear behavior of the vibration of the drill string are investigated. The results obtained demonstrate that, the axial vibration response of the drill string system shows an overall trend of quasi-periodic-chaotic change with the increase of feed rate, and the torsional vibration of the drill string shows the trend of quasi periodic-chaotic. When the feed rate is high, the vibration of the drill string system is mainly for the irregular and complex hybrid motion. Therefore, the appropriate reduction of feed speed can increase the stability of the drill string on-site, and reduce the jump drilling and stick-slip vibration of the drill string. When the rotary drilling speed is 90–210 rpm, the torsional vibration response of the drill string shows a chaotic-quasi-periodic trend and the complexity of the torsional vibration of the drill string decreases with the increase of rotary drilling speed. The axial vibration response of the drill string shows a chaotic-quasi-periodic-chaotic trend with the increase of the rotary drilling speed. When the rotary drilling speed increases to 400–410 rpm, the axial vibration of the drill string becomes a quasi-periodic motion. Therefore, increasing the rotary drilling speed within a certain range can reduce the complexity of the vibration of the drill string and reduce the skip and stick-slip vibration of the drill string.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"41 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142886814","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":"Simplest transistor-based chaotic circuit with extreme events: Statistical characterization, synchronization, and analogy with interictal spikes","authors":"Léandre Kamdjeu Kengne, Vitrice Ruben Folifack Signing, Davide Rossi Sebastiano, Raoul Blaise Wafo Tekam, Joakim Vianney Ngamsa Tegnitsap, Manyu Zhao, Qingshi Bao, Jacques Kengne, Pedro Antonio Valdes-Sosa, Ludovico Minati","doi":"10.1016/j.chaos.2024.115894","DOIUrl":"https://doi.org/10.1016/j.chaos.2024.115894","url":null,"abstract":"This paper investigates the simplest autonomous chaotic circuit capable of generating extreme events, comprising a DC voltage source, a series resistor, a capacitor, three inductors, and two bipolar transistors. The statistical properties and synchronization of the extreme events generated by the system are characterized using a simplified equation model, realistic SPICE simulations, and experimental circuit measurements. Heavy-tailed amplitude distributions and Poisson-like inter-event intervals are uncovered, confirming the existence and uncorrelated nature of the extreme events generated in this elementary circuit. Furthermore, a regime is identified where the extreme events synchronize significantly more strongly than the underlying lower-amplitude continuous activity that paces the dynamics, and a novel approach to visualize this situation is introduced. By drawing a tentative parallel with the interictal spikes observed in the neuroelectrical recordings of epilepsy patients, the study proposes that the analog chaotic circuit under consideration could, in the future, serve as a physical model for studying epileptic-like dynamics in electronic networks.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"202 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142887286","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 construction of optimal quasi-cyclic locally recoverable codes using constituent codes","authors":"Gustavo Terra Bastos, Angelynn Álvarez, Zachary Flores, Adriana Salerno","doi":"10.1007/s10623-024-01532-5","DOIUrl":"https://doi.org/10.1007/s10623-024-01532-5","url":null,"abstract":"<p>A locally recoverable code of locality <i>r</i> over <span>(mathbb {F}_{q})</span> is a code where every coordinate of a codeword can be recovered using the values of at most <i>r</i> other coordinates of that codeword. Locally recoverable codes are efficient at restoring corrupted messages and data which make them highly applicable to distributed storage systems. Quasi-cyclic codes of length <span>(n=mell )</span> and index <span>(ell )</span> are linear codes that are invariant under cyclic shifts by <span>(ell )</span> places. In this paper, we decompose quasi-cyclic locally recoverable codes into a sum of constituent codes where each constituent code is a linear code over a field extension of <span>(mathbb {F}_q)</span>. Using these constituent codes with set parameters, we propose conditions which ensure the existence of almost optimal and optimal quasi-cyclic locally recoverable codes with increased dimension and code length.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"20 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142867030","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 approximation spaces and Greedy-type bases","authors":"Pablo M. Berná,&nbsp;Hùng Việt Chu,&nbsp;Eugenio Hernández","doi":"10.1007/s43034-024-00397-y","DOIUrl":"10.1007/s43034-024-00397-y","url":null,"abstract":"<div><p>The purpose of this paper is to introduce <span>(omega )</span>-Chebyshev–Greedy and <span>(omega )</span>-partially greedy approximation classes and study their relation with <span>(omega )</span>-approximation spaces, where the latter are a generalization of the classical approximation spaces. The relation gives us sufficient conditions of when certain continuous embeddings imply different greedy-type properties. Along the way, we generalize a result by P. Wojtaszczyk as well as characterize semi-greedy Schauder bases in quasi-Banach spaces, generalizing a previous result by the first author.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142859652","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":"Uniqueness and stability of traveling vortex pairs for the incompressible Euler equation","authors":"Daomin Cao,&nbsp;Guolin Qin,&nbsp;Weicheng Zhan,&nbsp;Changjun Zou","doi":"10.1007/s40818-024-00191-y","DOIUrl":"10.1007/s40818-024-00191-y","url":null,"abstract":"<div><p>In this paper, we establish the uniqueness and nonlinear stability of concentrated symmetric traveling vortex patch-pairs for the 2D Euler equation. We also prove the uniqueness of concentrated rotating polygons as well. The proofs are achieved by a combination of the local Pohozaev identity, a detailed description of asymptotic behaviors of the solutions and some symmetry properties obtained by the method of moving planes.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"11 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142859697","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}