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On equivalence of state-based potential games

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Science China(Information Sciences) 2024年第6期67卷 313-327页

作者： Han WU Jinhuan WANG institute of mathematics School of ScienceHebei University of Technology

In this paper, we explore state-based potential games using the semi-tensor product of matrices.First, applying the potential equation, we derive both a necessary and sufficient condition as well as a sufficient condition to verify whether a state-based game qualifies as a potential game. Next, we present two static equivalence conditions of state-based potential games. We then delve into dynamic equivalence. We propose a criterion that allows us to identify state-based games that are dynamically equivalent to state-based potential games and share similar dynamic properties. Ultimately, we introduce the concept of state-based networked evolutionary games. We provide a necessary and sufficient condition to ensure that a state-based networked evolutionary game can be classified as a state-based potential game.

关键词： semi-tensor product of matrices state-based potential game verification equivalence state-based networked evolutionary game

Influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel

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Applied mathematics and Mechanics(English Edition) 2024年第3期45卷 563-580页

作者： N.HUMNEKAR D.SRINIVASACHARYA Department of mathematics National Institute of TechnologyWarangal 506004TelanganaIndia

The influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel is investigated.The DarcyBrinkman model is used to characterize the fluid flow dynamics in porous materials.The analytical solutions are obtained for the unidirectional and completely developed flow.Based on a normal mode analysis,the generalized eigenvalue problem under a perturbed state is solved.The eigenvalue problem is then solved by the spectral method.Finally,the critical Rayleigh number with the corresponding wavenumber is evaluated at the assigned values of the other flow-governing parameters.The results show that increasing the Darcy number,the Lewis number,the Dufour parameter,or the Soret parameter increases the stability of the system,whereas increasing the inclination angle of the channel destabilizes the flow.Besides,the flow is the most unstable when the channel is vertically oriented.

关键词： nanofluid inclined channel variable viscosity linear stability double dif-fusion porous medium

Deformation of Rigid Conjugate Self-dual Galois Representations

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1599-1644页

作者： Yi Feng LIU Yi Chao TIAN Liang XIAO Wei ZHANG Xin Wen ZHU institute for Advanced Study in mathematics Zhejiang University Morningside Center of mathematics AMSS Chinese Academy of Sciences New Cornerstone Lab Beijing International Center for Mathematical Research Peking University Department of mathematics Massachusetts Institute of Technology Department of mathematics Stanford University

In this article, we study deformations of conjugate self-dual Galois representations. The study is twofold. First, we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite field, satisfying a certain property called rigid. Second, we study the rigidity property for the family of residue Galois representations attached to a symmetric power of an elliptic curve, as well as to a regular algebraic conjugate self-dual cuspidal representation.

关键词： Galois deformation rigid conjugate self-dual Galois representations 11F80 11F03

Stability of the Phase Separation State for Compressible Navier-Stokes/Allen-Cahn System

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 45-74页

作者： Ya-zhou Chen Hakho Hong Xiao-ding Shi Department of mathematics College of Mathematics and PhysicsBeijing University of Chemical TechnologyBeijing100029China institute of mathematics State Academy of SciencesPyongyangKorea

This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/AllenCahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global solutions and the stability of the phase separation state are proved under the small initial perturbations. Moreover, the optimal time decay rates are obtained for higher-order spatial derivatives of density,velocity and phase. Our results imply that if the immiscible two-phase flow is initially located near the phase separation state, then under small perturbation conditions, the solution exists globally and decays algebraically to the complete separation state of the two-phase flow, that is, there will be no interface fracture, vacuum, shock wave, mass concentration at any time, and the interface thickness tends to zero as the time t → +∞.

关键词： Navier-Stokes/Allen-Cahn system existence uniqueness large time behavior decay rate

Irrational-Behavior-Proof Conditions for Stochastic Games over Event Trees

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Journal of the Operations Research Society of China 2024年第1期12卷 243-263页

作者： Lei Wang Cui Liu Hong-Wei Gao Chong Lin School of Automation Institute of Complexity ScienceQingdao UniversityQingdao 266071ShandongChina School of mathematics and Statistics Institute of Applied Mathematics of ShandongQingdao UniversityQingdao 266071ShandongChina

In this paper,the irrational-behavior-proof conditions in a class of stochastic dynamic games over event trees are presented.Four kinds of irrational-behavior-proof conditions are proposed by the imputation distribution procedure,and their relationships are discussed.More specific properties for the general transformation of characteristic functions are developed,based on which,the irrational-behavior-proof conditions are proved to be true in a transformed cooperative game.

关键词： Dynamic cooperative game Event tree Irrational-behavior-proof condition Imputation distribution procedure Transformation of characteristic function

A DIRECT DISCONTINUOUS GALERKIN METHOD FOR TIME FRACTIONAL DIFFUSION EQUATIONS WITH FRACTIONAL DYNAMIC BOUNDARY CONDITIONS

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Journal of Computational mathematics 2024年第1期42卷 156-177页

作者： Jingjun Zhao Wenjiao Zhao Yang Xu School of mathematics Harbin Institute of TechnologyHarbin 150001China

This paper deals with the numerical approximation for the time fractional diffusion problem with fractional dynamic boundary conditions.The well-posedness for the weak solutions is studied.A direct discontinuous Galerkin approach is used in spatial direction under the uniform meshes,together with a second-order Alikhanov scheme is utilized in temporal direction on the graded mesh,and then the fully discrete scheme is constructed.Furthermore,the stability and the error estimate for the full scheme are analyzed in detail.Numerical experiments are also given to illustrate the effectiveness of the proposed method.

关键词： Time fractional diffusion equation Numerical stability Convergence

Identification of Linear Systems Using Binary Sensors with Random Thresholds

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Journal of Systems Science & Complexity 2024年第3期37卷 907-923页

作者： HUANG Zhiyong SONG Qijiang School of mathematics Renmin University of ChinaBeijing 100872China School of mathematics Sino-French InstituteRenmin University of ChinaBeijing 100872China

In this paper,the problem of identifying autoregressive-moving-average systems under random threshold binary-valued output measurements is considered.With the help of stochastic approximation algorithms with expanding truncations,the authors give the recursive estimates for the parameters of both the linear system and the binary sensor.Under reasonable conditions,all constructed estimates are proved to be convergent to the true values with probability one,and the convergence rates are also established.A simulation example is provided to justify the theoretical results.

关键词： α-mixing binary sensor quantized system stochastic approximation stochastic thresh-old strongly consistent system identification

The KAM theorem on the modulus of continuity about parameters

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Science China mathematics 2024年第3期67卷 577-592页

作者： Zhicheng Tong Jiayin Du Yong Li School of mathematics Jilin UniversityChangchun 130012China institute of mathematics Jilin UniversityChangchun 130012China School of mathematics and Statistics Center for Mathematics and Interdisciplinary SciencesNortheast Normal UniversityChangchun 130024China

In this paper,we study the Hamiltonian systems H(y,x,ξ,ε)=〈ω(ξ),y〉+εP(y,x,ξ,ε),where ω and P are continuous about ξ.We prove that persistent invariant tori possess the same frequency as the unperturbed tori,under a certain transversality condition and a weak convexity condition for the frequency mapping ω.As a direct application,we prove a Kolmogorov-Arnold-Moser(KAM) theorem when the perturbation P holds arbitrary Holder continuity with respect to the parameter ξ.The infinite-dimensional case is also considered.To our knowledge,this is the first approach to the systems with the only continuity in the parameter beyond H?lder's type.

关键词： Hamiltonian systems invariant tori frequency-preserving weak regularity

2-local unstable homotopy groups of indecomposable A32-complexes

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Science China mathematics 2024年第3期67卷 607-626页

作者： Zhongjian Zhu Jianzhong Pan College of mathematics and Physics Wenzhou University Hua Loo-Keng Key Laboratory of mathematics Institute of MathematicsAcademy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences

In this paper,we calculate the 2-local unstable homotopy groups of indecomposable A32-complexes.The main technique used is analysing the homotopy property of J(A,X),defined by Gray(1973) for a CW-pair(X,A),which is ho... 详细信息

关键词： homotopy groups A 2 n -complexes fibration sequence relative James construction 55P15