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arXiv 2024年

作者： Hua, Bobo Münch, Florentin Zhang, Haohang School of Mathematical Sciences LMNS Fudan University Shanghai200433 China Shanghai Center for Mathematical Sciences Fudan University Shanghai200438 China Faculty of Mathematics and Computer Science Leipzig University Leipzig04109 Germany Yau Mathematical Science Center Tsinghua University Beijing100084 China

For a bounded Lipschitz domain Σ in a Riemannian surface M satisfying certain curvature condition, we prove that for any k ≥ 1, we have µk+2−β1 ≤ λk, where µk (λk resp.) is the k-th Neumann (Dirichlet resp.) Laplacian eigenvalue on Σ and β1 is the first Betti number of Σ. This extends previous results on the Euclidean space to curved surfaces, including the flat cylinder, the hyperbolic plane, hyperbolic cusp, funnel, etc. The novelty of the paper lies in comparing Dirichlet and Neumann Laplacian eigenvalues via the variational principle of the Hodge Laplacian on 1-forms on a surface, extending the variational principle on vector fields in the Euclidean plane as developed by Rohleder [50]. The comparison is reduced to the existence of a distance function with appropriate curvature conditions on its level sets. Copyright © 2024, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

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DESIGNING EQUILIBRIA IN CONCURRENT GAMES WITH SOCIAL WELFARE AND TEMPORAL LOGIC CONSTRAINTS

arXiv

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arXiv 2023年

作者： Gutierrez, Julian Najib, Muhammad Perelli, Giuseppe Wooldridge, Michael Faculty of Information Technology Monash University Australia School of Mathematical and Computer Sciences Heriot-Watt University United Kingdom Department of Computer Science Sapienza University of Rome Italy Department of Computer Science University of Oxford United Kingdom

In game theory, mechanism design is concerned with the design of incentives so that a desirable outcome will be achieved under the assumption that players act rationally. In this paper, we explore the concept of equilibrium design, where incentives are designed to obtain a desirable equilibrium that satisfies a specific temporal logic property. Our study is based on a framework where system specifications are represented as temporal logic formulae, games as quantitative concurrent game structures, and players’ goals as mean-payoff objectives. We consider system specifications given by LTL and GR(1) formulae, and show that designing incentives to ensure that a given temporal logic property is satisfied on some/every Nash equilibrium of the game can be achieved in PSPACE for LTL properties and in NP/ΣP2 for GR(1) specifications. We also examine the complexity of related decision and optimisation problems, such as optimality and uniqueness of solutions, as well as considering social welfare, and show that the complexities of these problems lie within the polynomial hierarchy. Equilibrium design can be used as an alternative solution to rational synthesis and verification problems for concurrent games with mean-payoff objectives when no solution exists or as a technique to repair concurrent games with undesirable Nash equilibria in an optimal way. © 2023, CC BY.

关键词： Game theory

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PROFINITENESS OF HIGHER RANK VOLUME

arXiv

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arXiv 2024年

作者： Kammeyer, Holger Kionke, Steffen Köhl, Ralf Heinrich Heine University Düsseldorf Faculty of Mathematics and Natural Sciences Mathematical Institute Germany FernUniversität in Hagen Faculty of Mathematics and Computer Science Germany Kiel University Faculty of Mathematics and Natural Sciences Department of Mathematics Germany

We show that the covolume of an irreducible lattice in a higher rank semisimple Lie group with the congruence subgroup property is determined by the profinite completion. Without relying on CSP, we additionally show that volume is a profinite invariant of octonionic hyperbolic congruence *** Codes 22E40, 20E18 Copyright © 2024, The Authors. All rights reserved.

关键词： Lie groups

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On continuum real trees of circle maps and their graphs

arXiv

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arXiv 2024年

作者： Gröger, Maik Troscheit, Sascha Faculty of Mathematics and Computer Science Jagiellonian University Kraków Poland Mathematical Sciences Research Unit University of Oulu PO Box 8000 Oulu90014 Finland

The Brownian continuum tree was extensively studied in the 90s as a universal random metric space. One construction obtains the continuum tree by a change of metric from an excursion function (or continuous circle mapping) on [0,1]. This change of metric can be applied to all excursion functions, and generally to continuous circle mappings. In 2008, Picard proved that the dimension theory of the tree is connected to its associated contour function: the upper box dimension of the continuum tree coincides with the variation index of the contour function. In this article we give a short and direct proof of Picard’s theorem through the study of packings. We develop related and equivalent notions of variations and variation indices and study their basic properties. Finally, we link the dimension theory of the tree with the dimension theory of the graph of its contour function. © 2024, CC BY.

关键词： Mapping

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An Efficient Non-standard Finite Difference Scheme for Solving Distributed Order Time Fractional Reaction–Diffusion Equation

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International Journal of Applied and Computational Mathematics 2022年第2期8卷 1-17页

作者： Taghipour, M. Aminikhah, H. Department of Applied Mathematics and Computer Science Faculty of Mathematical Sciences University of Guilan P.O. Box 1914 Rasht 41938 Iran Center of Excellence for Mathematical Modelling Optimization and Combinational Computing (MMOCC) University of Guilan P.O. Box 1914 Rasht 41938 Iran

In this article, a nonstandard finite difference scheme is proposed for solving the distributed order time-fractional reaction–diffusion equation. In this equation, the time-fractional derivative is defined in the Caputo sense. We decompose the equation into two sub-equations and use the exact finite difference scheme with the Clenshaw–Curtis quadrature for sub-equations, then combine them to obtain the numerical method. The term involving the time distributed-order derivative is discretized using the Clenshaw–Curtis quadrature, and the Caputo fractional derivative is approximated by the Grünwald difference operator. We show that the presented scheme is uniquely solvable, unconditionally stable, and convergent. Numerical experiments are carried out to inspect the effectiveness of the presented scheme. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.

关键词： Caputo derivative Clenshaw–Curtis quadrature Distributed order fractional differential equation Non-standard finite difference scheme Reaction–diffusion equation Stability and convergence

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Optimally Combined Incentive for Cooperation Among Interacting Agents in Population Games

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IEEE Transactions on Automatic Control 2025年

作者： Wang, Shengxian Cao, Ming Chen, Xiaojie Anhui Normal University School of Computer and Information Wuhu241002 China University of Electronic Science and Technology of China School of Mathematical Sciences Chengdu611731 China University of Groningen ENTEG Faculty of Science and Engineering Groningen9747 AG Netherlands

Combined prosocial incentives, integrating reward for cooperators and punishment for defectors, are effective tools to promote cooperation among competing agents in population games. Existing research concentrated on how to adjust reward or punishment, as two mutually exclusive tools, during the evolutionary process to achieve the desired proportion of cooperators in the population, and less attention has been given to exploring a combined incentive-based control policy that can steer the system to the full cooperation state at the lowest cost. In this work we propose a combined incentive scheme in a population of agents whose conflicting interactions are described by the prisoner's dilemma game on complete graphs and regular networks, respectively. By devising an index function for quantifying the implementation costs of the combined incentives, we analytically construct the optimally combined incentive protocol by using optimal control theory. By means of theoretical analysis, we identify the mathematical conditions, under which the optimally combined incentive scheme requires the minimal amount of cost. In addition to numerical calculations, we further perform computer simulations to verify our theoretical results and explore their robustness on different types of network structures. © 1963-2012 IEEE.

关键词： Game theory

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mathematical modeling of mixed convective MHD Falkner-Skan squeezed Sutterby multiphase flow with non-Fourier heat flux theory and porosity

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Applied Mathematics and Mechanics(English Edition) 2023年第11期44卷 2005-2018页

作者： Shuguang LI M.I.KHAN F.ALI S.S.ABDULLAEV S.SAADAOUI HABIBULLAH School of Computer Science and Technology Shandong Technology and Business UniversityYantai 264005Shandong ProvinceChina Department of Mechanics and Engineering Science Peking UniversityBeijing 100871China Department of Mechanical Engineering Lebanese American UniversityBeirut 11020Lebanon Department of Mathematical Sciences Federal Urdu University of ArtsSciences&TechnologyGulshan-e-IqbalKarachi 75300Pakistan Faculty of Chemical Engineering New Uzbekistan UniversityTashkent 100070Uzbekistan Department of Science and Innovation Tashkent State Pedagogical University named after NizamiTashkent 100070Uzbekistan Department of Physics Faculty of Science and ArtsMohayel AserKing Khalid UniversityAbha 61421Saudi Arabia State Key Laboratory of Turbulence and Complex System Collaborative Innovative Center for Advanced Aero-EnginesPeking UniversityBeijing 100871China

In a wide variety of mechanical and industrial applications,e.g.,space cooling,nuclear reactor cooling,medicinal utilizations(magnetic drug targeting),energy generation,and heat conduction in tissues,the heat transfer phenomenon is ***’s law of heat conduction has been used as the foundation for predicting the heat transfer behavior in a variety of real-world *** model’s production of a parabolic energy expression,which means that an initial disturbance would immediately affect the system under investigation,is one of its main ***,numerous researchers worked on such problem to resolve this *** last,this problem was resolved by Cattaneo by adding relaxation time for heat flux in Fourier’s law,which was defined as the time required to establish steady heat conduction once a temperature gradient is *** offered a material invariant version of Cattaneo’s model by taking into account the upper-connected derivative of the Oldroyd ***,both models are combinedly known as the Cattaneo-Christov(CC)*** this attempt,the mixed convective MHD Falkner-Skan Sutterby nanofluid flow is addressed towards a wedge surface in the presence of the variable external magnetic *** CC model is incorporated instead of Fourier’s law for the examination of heat transfer features in the energy expression.A two-phase nanofluid model is utilized for the implementation of *** nonlinear system of equations is tackled through the bvp4c technique in the MATLAB software *** influence of pertinent flow parameters is discussed and displayed through different *** and important results are summarized in the conclusion ***,in both cases of wall-through flow(i.e.,suction and injection effects),the porosity parameters increase the flow speed,and decrease the heat transport and the influence of drag forces.

关键词： sporosity Cattaneo-Christov(CC)heat flux model Falkner-Skan Sutterby nanofluid mixed convection stagnation point

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A novel fault-tolerant scheduling approach for collaborative workflows in an edge-IoT environment

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Digital Communications and Networks 2022年第6期8卷 911-922页

作者： Tingyan Long Yong Ma Lei Wu Yunni Xia Ning Jiang Jianqi Li Xiaodong Fu Xiangmi You Bo Zhang College of Computer Science Chongqing UniversityChongqing400030China School of Computer and Information Engineering Jiangxi Normal UniversityJiangxi330022China School of Mathematical Sciences University of Electronic Science and Technology of ChinaChengdu611731China Mashang Consumer Finance Co. Ltd.(MSCF)Chongqing401129China Global Energy Interconnection Research Institute Co.Ltd. Beijing102209China Faculty of Information Engineering and Automation Kunming University of Science and TechnologyYunnan650500China CISDI Research&Development CO. LTDChongqing401122China

As a newly emerging computing paradigm, edge computing shows great capability in supporting and boosting 5G and Internet-of-Things (IoT) oriented applications, e.g., scientific workflows with low-latency, elastic, and on-demand provisioning of computational resources. However, the geographically distributed IoT resources are usually interconnected with each other through unreliable communications and ever-changing contexts, which brings in strong heterogeneity, potential vulnerability, and instability of computing infrastructures at different levels. It thus remains a challenge to enforce high fault-tolerance of edge-IoT scientific computing task flows, especially when the supporting computing infrastructures are deployed in a collaborative, distributed, and dynamic environment that is prone to faults and failures. This work proposes a novel fault-tolerant scheduling approach for edge-IoT collaborative workflows. The proposed approach first conducts a dependency-based task allocation analysis, then leverages a Primary-Backup (PB) strategy for tolerating task failures that occur at edge nodes, and finally designs a deep Q-learning algorithm for identifying the near-optimal workflow task scheduling scheme. We conduct extensive simulative case studies on multiple randomly-generated workflow and real-world edge-IoT server position datasets. Results clearly suggest that our proposed method outperforms the state-of-the-art competitors in terms of task completion ratio, server active time, and resource utilization.

关键词： Edge computing Fault tolerance DQN algorithm Primary-backup model

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Periodic cosmic evolution in f(Q)gravity formalism

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Communications in Theoretical Physics 2022年第12期74卷 97-107页

作者： Parbati Sahoo Avik De Tee-How Loo P K Sahoo Astrophysics and Cosmology Research Unit School of MathematicsStatistics and Computer ScienceUniversity of KwaZulu–NatalPrivate Bag X54001Durban 4000South Africa Department of Mathematics(SAS) Vellore Institute of Technology-Andhra Pradesh UniversityAndhra Pradesh—522237India Department of Mathematical and Actuarial Sciences Universiti Tunku Abdul RahmanJalan Sungai Long43000 CherasMalaysia Institute of Mathematical Sciences Faculty of ScienceUniversiti Malaya50603 Kuala LumpurMalaysia Department of Mathematics Birla Institute of Technology and Science-PilaniHyderabad CampusHyderabad-500078India

We study the periodic cosmic transit behavior of the accelerated universe in the framework of symmetric teleparallelism. The exact solution of field equations is obtained by employing a wellknown deceleration parameter(DP) called periodic varying DP, q =m coskt-1. The viability and physical reliability of the DP are studied by using observational constraints. The dynamics of periodicity and singularity are addressed in detail with respect to time and redshift *** energy conditions are discussed in this setting.

关键词： f(Q)gravity deceleration parameter energy conditions Hubble parameter

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Shewhart Median Scheme with Estimated Process Parameters Using Median Run Length for Smart Manufacturing 10

Shewhart Median Scheme with Estimated Process Parameters Usi...

引用

10th IEEE Asia-Pacific Conference on Applied Electromagnetics, APACE 2024

作者： Chong, Zhi Lin Teoh, Wei Lin Ng, Peh Sang Yeong, Wai Chung Teh, Sin Yin Universiti Tunku Abdul Rahman Faculty of Engineering and Green Technology Department of Electronic Engineering Kampar31900 Malaysia Heriot-Watt University Malaysia School of Mathematical and Computer Sciences Jalan Venna P5/2 Precinct 5 Putrajaya62200 Malaysia Universiti Tunku Abdul Rahman Faculty of Science Department of Physical and Mathematical Science Perak Kampar31900 Malaysia Monash University School of Science Jalan Lagoon Selatan Bandar Sunway Selangor Subang Jaya47500 Malaysia Universiti Sains Malaysia School of Management Penang 11800 Malaysia

ISBN: (纸本)9798350364163

The exclusive reliance on the average run length (ARL) as a control scheme's performance metric has drawn a lot of criticisms in the literature. This is because the form and skewness of the run length distribution changes depending on the amount of the mean shift in any process, making interpretation based only on the ARL potentially inaccurate. Therefore, when the process parameters are estimated (U-Case), we take into account the median run length (MRL) performance metric for the Shewhart median scheme. To demonstrate how to apply the U-Case Shewhart median scheme, we provide an example for smart manufacturing using a dataset related to the forged piston ring manufacturing process. © 2024 IEEE.

关键词： Smart manufacturing

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