数学最新文献

{"title":"Variational Models with Eulerian–Lagrangian Formulation Allowing for Material Failure","authors":"Marco Bresciani,&nbsp;Manuel Friedrich,&nbsp;Carlos Mora-Corral","doi":"10.1007/s00205-024-02076-7","DOIUrl":"10.1007/s00205-024-02076-7","url":null,"abstract":"<div><p>We investigate the existence of minimizers of variational models featuring Eulerian–Lagrangian formulations. We consider energy functionals depending on the deformation of a body, defined on its reference configuration, and an Eulerian map defined on the unknown deformed configuration in the actual space. Our existence theory moves beyond the purely elastic setting and accounts for material failure by addressing free-discontinuity problems where both deformations and Eulerian fields are allowed to jump. To do this, we build upon the work of Henao and Mora-Corral regarding the variational modeling of cavitation and fracture in nonlinear elasticity. Two main settings are considered by modeling deformations as Sobolev and SBV-maps, respectively. The regularity of Eulerian maps is specified in each of these two settings according to the geometric and topological properties of the deformed configuration. We present some applications to specific models of liquid crystals, phase transitions, and ferromagnetic elastomers. Effectiveness and limitations of the theory are illustrated by means of explicit examples.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"249 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-024-02076-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142845023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multi-feature fusion for the evaluation of strategic nodes and regional importance in maritime networks","authors":"Shu Guo, Jing Lyu, Xuebin Zhu, Hanwen Fan","doi":"10.1016/j.chaos.2024.115902","DOIUrl":"https://doi.org/10.1016/j.chaos.2024.115902","url":null,"abstract":"Node importance has been a widespread research topic owing to the impact of uncertainties and accidents on supply chains during maritime transport. Although the analysis and investigation of critical nodes using complex network theory is mature and systematic, there is often a lack of multiscale node identification models and theoretical frameworks. This paper proposes a novel quantitative analysis framework and process for node importance by fusing multiple features. Node importance is determined by interdependence, risk sensitivity, and spatial conflict. These three dimensions consider the network topology, node robustness, and transportation environment stability. A case study of the Belt and Road Initiative shipping network verified the validity and feasibility of this framework. The results indicated that the importance of nodes can be represented by their heterogeneity. Critical regions strongly coincide with the distribution of major global straits and transportation routes. Notably, the similarity of results under multi-features improves the accuracy of identifying critical nodes and regions within the complex network, whereas the differences compensate for the shortcomings of the single-dimensional approach. This provides actionable insights and guidance for stakeholders to build stability in maritime supply chains.","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"79 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142857623","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":"On a new mechanism of the emergence of spatial distributions in biological models","authors":"B. Kazmierczak, V. Volpert","doi":"10.1016/j.aml.2024.109427","DOIUrl":"https://doi.org/10.1016/j.aml.2024.109427","url":null,"abstract":"Non-uniform distributions of various biological factors can be essential for tissue growth control, morphogenesis or tumor growth. The first model describing the emergence of such distributions was suggested by A. Turing for the explanation of cell differentiation in a growing embryo. In this model, diffusion-driven instability of the homogeneous in space solution appears due to the interaction of two or more morphogens described by a reaction–diffusion system of equations. In this work we suggest another mechanism of the emergence of spatial distributions in biological tissues based on local cell communication and global inhibition, and described by a nonlocal reaction–diffusion equation. Instability of the homogeneous in space solution leads to the emergence of stationary pulses and not of periodic solutions as in the case of Turing instability.","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"281 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874399","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":"Anticoncentration of Random Vectors via the Strong Perfect Graph Theorem","authors":"Tomas Juškevičius, Valentas Kurauskas","doi":"10.1007/s00493-024-00124-0","DOIUrl":"https://doi.org/10.1007/s00493-024-00124-0","url":null,"abstract":"<p>In this paper we give anticoncentration bounds for sums of independent random vectors in finite-dimensional vector spaces. In particular, we asymptotically establish a conjecture of Leader and Radcliffe (SIAM J Discrete Math 7:90–101, 1994) and a question of Jones (SIAM J Appl Math 34:1–6, 1978). The highlight of this work is an application of the strong perfect graph theorem by Chudnovsky et al. (Ann Math 164:51–229, 2006) in the context of anticoncentration.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":"39 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142832150","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":"Protocol-based H∞ estimation for Markovian jumping delayed systems with partially unknown transition probability","authors":"Guixiu Liu, Bing Li","doi":"10.1016/j.amc.2024.129247","DOIUrl":"https://doi.org/10.1016/j.amc.2024.129247","url":null,"abstract":"This article pays attention to estimation issue for the state of a particular kind of Markovian jumping delayed systems (MJDSs) with exogenous disturbances. The transition probability of Markovian process is assumed to be partially unknown for accurately reflecting the real complexity of mode switching. To avoid data collision while retaining the necessary requirement of information updating, a scheduling named MEF-TOD protocol is adopted to dynamically allocate access authorization of sensor nodes to estimator. By virtue of binary delta operator, a mode-dependent estimator is built to asymptotically approximate the real state of original system. Through taking a suitable energy functional and exploiting stochastic analysis method, several novel approaches are given to sufficiently make the error asymptotically stable under constraint of <mml:math altimg=\"si1.svg\"><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mo>∞</mml:mo></mml:mrow></mml:msub></mml:math> performance. The gain matrices for estimator are ultimately formed through settling a series of inequalities of matrix. At last, a numerical instance exhibits the validity of proposed results.","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"31 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142874071","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":"Continuous Time q-Learning for Mean-Field Control Problems","authors":"Xiaoli Wei,&nbsp;Xiang Yu","doi":"10.1007/s00245-024-10205-7","DOIUrl":"10.1007/s00245-024-10205-7","url":null,"abstract":"<div><p>This paper studies the q-learning, recently coined as the continuous time counterpart of Q-learning by Jia and Zhou (J Mach Learn Res 24:1–61, 2023), for continuous time mean-field control problems in the setting of entropy-regularized reinforcement learning. In contrast to the single agent’s control problem in Jia and Zhou (J Mach Learn Res 24:1–61, 2023), we reveal that two different q-functions naturally arise in mean-field control problems: (i) the integrated q-function (denoted by <i>q</i>) as the first-order approximation of the integrated Q-function introduced in Gu et al. (Oper Res 71(4):1040–1054, 2023), which can be learnt by a weak martingale condition using all test policies; and (ii) the essential q-function (denoted by <span>(q_e)</span>) that is employed in the policy improvement iterations. We show that two q-functions are related via an integral representation. Based on the weak martingale condition and our proposed searching method of test policies, some model-free learning algorithms are devised. In two examples, one in LQ control framework and one beyond LQ control framework, we can obtain the exact parameterization of the optimal value function and q-functions and illustrate our algorithms with simulation experiments.\u0000</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":"91 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142826395","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":"Stability for a stochastic fractional differential variational inequality with Lévy jump","authors":"Yue Zeng, Yao-jia Zhang, Nan-jing Huang","doi":"10.1016/j.cnsns.2024.108533","DOIUrl":"https://doi.org/10.1016/j.cnsns.2024.108533","url":null,"abstract":"The main goal of this paper is to investigate the multi-parameter stability result for a stochastic fractional differential variational inequality with Lévy jump (SFDVI with Lévy jump) under some mild conditions. We verify that Mosco convergence of the perturbed set implies point convergence of the projection onto the Hilbert space consisting of special stochastic processes whose range is the perturbed set. Moreover, by using the projection method and some inequality techniques, we establish a strong convergence result for the solution of SFDVI with Lévy jump when the mappings and constraint set are both perturbed. Finally, we apply the stability results to the spatial price equilibrium problem and the multi-agent optimization problem in stochastic environments.","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"114 1","pages":""},"PeriodicalIF":3.9,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142849247","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":"Non-Abelian Extensions of Groupoids and Their Groupoid Rings","authors":"Natã Machado,&nbsp;Johan Öinert,&nbsp;Stefan Wagner","doi":"10.1007/s10485-024-09795-8","DOIUrl":"10.1007/s10485-024-09795-8","url":null,"abstract":"<div><p>We present a geometrically oriented classification theory for non-Abelian extensions of groupoids generalizing the classification theory for Abelian extensions of groupoids by Westman as well as the familiar classification theory for non-Abelian extensions of groups by Schreier and Eilenberg-MacLane. As an application of our techniques we demonstrate that each extension of groupoids <span>({mathcal {N}}rightarrow {mathcal {E}}rightarrow {mathcal {G}})</span> gives rise to a groupoid crossed product of <span>({mathcal {G}})</span> by the groupoid ring of <span>({mathcal {N}})</span> which recovers the groupoid ring of <span>({mathcal {E}})</span> up to isomorphism. Furthermore, we make the somewhat surprising observation that our classification methods naturally transfer to the class of groupoid crossed products, thus providing a classification theory for this class of rings. Our study is motivated by the search for natural examples of groupoid crossed products.</p></div>","PeriodicalId":7952,"journal":{"name":"Applied Categorical Structures","volume":"33 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10485-024-09795-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142826110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modular representations of the Yangian \u0000 \u0000 \u0000 Y\u0000 2\u0000 \u0000 $Y_2$","authors":"Hao Chang,&nbsp;Jinxin Hu,&nbsp;Lewis Topley","doi":"10.1112/jlms.70056","DOIUrl":"https://doi.org/10.1112/jlms.70056","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>Y</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$Y_2$</annotation>\u0000 </semantics></math> be the Yangian associated to the general linear Lie algebra <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>gl</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$mathfrak {gl}_2$</annotation>\u0000 </semantics></math>, defined over an algebraically closed field <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$mathbb {k}$</annotation>\u0000 </semantics></math> of characteristic <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$p&gt;0$</annotation>\u0000 </semantics></math>. In this paper, we study the representation theory of the restricted Yangian <span></span><math>\u0000 <semantics>\u0000 <msubsup>\u0000 <mi>Y</mi>\u0000 <mn>2</mn>\u0000 <mrow>\u0000 <mo>[</mo>\u0000 <mi>p</mi>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 </msubsup>\u0000 <annotation>$Y^{[p]}_2$</annotation>\u0000 </semantics></math>. This leads to a description of the representations of <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>gl</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$mathfrak {gl}_{2n}$</annotation>\u0000 </semantics></math>, whose <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-character is nilpotent with Jordan type given by a two-row partition <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>,</mo>\u0000 <mi>n</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(n, n)$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70056","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142861583","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":"Online multiple one way non-preemptive time series search with interrelated prices","authors":"Jinghan Zhao, Yongxi Cheng, Jan Eube, Haodong Liu","doi":"10.1007/s10878-024-01247-2","DOIUrl":"https://doi.org/10.1007/s10878-024-01247-2","url":null,"abstract":"<p>This paper studies the online multiple time series search problem with interrelated prices (MTSS-ip). This perspective narrows the distance between the problem and the reality of market prices with limited variation. In MTSS-ip, the products arrive periodically, and the decision maker has a limited storage size without knowing future prices. The prices of two adjacent periods are interrelated. This study proposes an online zero-inventory algorithm (ZIA) and proves an upper bound of <span>(K+1-frac{K}{theta _2})</span> on the competitive ratio of ZIA. In addition, a lower bound on the competitive ratio of problem MTSS-ip for any deterministic online algorithm is established. For the case with a large storage size <i>K</i>, a lower bound of <span>(frac{K}{48log _{theta _2} K})</span> on the competitive ratio for MTSS-ip is proved.</p>","PeriodicalId":50231,"journal":{"name":"Journal of Combinatorial Optimization","volume":"27 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142832113","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}