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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 ***, 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

An integrable generalization of the Fokas–Lenells equation:Darboux transformation, reduction and explicit soliton solutions

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Chinese Physics B 2024年第7期33卷 117-124页

作者：魏姣耿献国王鑫 school of mathematics and Statistics Zhengzhou UniversityZhengzhou 450001China school of mathematics and Information science Zhongyuan University of TechnologyZhengzhou 450007China

Under investigation is an integrable generalization of the Fokas–Lenells equation, which can be derived from the negative power flow of a 2 × 2 matrix spectral problem with three potentials. Based on the gauge transformation of the matrix spectral problem, one kind of Darboux transformation with multi-parameters for the three-component coupled Fokas–Lenells system is constructed. As a reduction, the N-fold Darboux transformation for the generalized Fokas–Lenells equation is obtained, from which the N-soliton solution in a compact Vandermonde-like determinant form is given. Particularly,the explicit one-and two-soliton solutions are presented and their dynamical behaviors are shown graphically.

关键词： Darboux transformation soliton solutions generalized Fokas–Lenells equation

Detecting the core of a network by the centralities of the nodes

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Chinese Physics B 2024年第8期33卷 615-621页

作者：马佩杰任学藻朱军芳蒋艳群 school of mathematics and science Southwest University of Science and TechnologyMianyang 621010China

Many networks exhibit the core/periphery ***/periphery structure is a type of meso-scale structure that consists of densely connected core nodes and sparsely connected peripheral *** nodes tend to be well-connected,both among themselves and to peripheral nodes,which tend not to be well-connected to other *** this brief report,we propose a new method to detect the core of a network by the centrality of each *** is discovered that such nodes with non-negative centralities often consist in the core of the *** simulation is carried out on different real *** results are checked by the objective *** checked results may show the effectiveness of the simulation results by the centralities of the nodes on the real ***,we discuss the characters of networks with the single core/periphery structure and point out the scope of the application of our method at the end of this paper.

关键词： complex network core/periphery structure the objective function

A Mean-Field Game for a Forward-Backward Stochastic System With Partial Observation and Common Noise

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IEEE/CAA Journal of Automatica Sinica 2024年第3期11卷 746-759页

作者： Pengyan Huang Guangchen Wang Shujun Wang Hua Xiao the school of Control science and Engineering Shandong University the school of Statistics and mathematics Shandong University of Finance and Economics IEEE the school of Management Shandong University the school of mathematics and Statistics Shandong University

This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals and observation ***,to reduce the complexity of solving the meanfield game,a limiting control problem is *** virtue of the decomposition approach,an admissible control set is *** a filter technique and dimensional-expansion technique,a decentralized control strategy and a consistency condition system are derived,and the related solvability is also ***,we discuss an approximate Nash equilibrium property of the decentralized control ***,we work out a financial problem with some numerical simulations.

关键词： Decentralized control strategy ϵ-Nash equilibrium forward-backward stochastic system mean-field game partial observation

Ambarzumyan's Theorem for the Dirac Operator on Equilateral Tree Graphs

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 568-576页

作者： Dong-Jie WU Xin-Jian XU Chuan-Fu YANG Department of mathematics School of Mathematics and StatisticsNanjing University of Science and TechnologyNanjing 210094China

The classical Ambarzumyan’s theorem states that if the Neumann eigenvalues of the Sturm-Liouville operator-d^(2)/dx^(2)+q with an integrable real-valued potential q on[0,π] are {n^(2):n≥0},then q=0 for almost all x∈[0,π].In this work,the classical Ambarzumyan’s theorem is extended to the Dirac operator on equilateral tree *** prove that if the spectrum of the Dirac operator on graphs coincides with the unperturbed case,then the potential is identically zero.

关键词： dirac operator quantum graph Ambarzumyan’s theorem inverse spectral problem

Reducibility of Three Dimensional Skew Symmetric System with High Dimensional Weak Liouvillean Frequencies

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Acta Mathematica Sinica,English Series 2024年第10期40卷 2388-2410页

作者： Jie LIU Yuan SHAN Jing WANG school of mathematics and Statistics Nanjing University of Science and Technology school of Statistics and Data science Nanjing Audit University

In this paper, we consider the reducibility of three-dimensional skew symmetric *** obtain a reducibility result if the base frequency is high-dimensional weak Liouvillean and the parameter is sufficiently small. The ... 详细信息

关键词： 3.C20 3.J40 high-dimensional weak Liouvillean KAM theory three dimensional skew-symmetric system

Impact of different interaction behavior on epidemic spreading in time-dependent social networks

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Chinese Physics B 2024年第3期33卷 190-195页

作者：黄帅陈杰李梦玉徐元昊胡茂彬 school of Engineering science University of Science and Technology of ChinaHefei 230026China school of mathematics Southeast UniversityNanjing 210096China

We investigate the impact of pairwise and group interactions on the spread of epidemics through an activity-driven model based on time-dependent *** effects of pairwise/group interaction proportion and pairwise/group interaction intensity are explored by extensive simulation and theoretical *** is demonstrated that altering the group interaction proportion can either hinder or enhance the spread of epidemics,depending on the relative social intensity of group and pairwise *** the group interaction proportion decreases,the impact of reducing group social intensity *** ratio of group and pairwise social intensity can affect the effect of group interaction proportion on the scale of infection.A weak heterogeneous activity distribution can raise the epidemic threshold,and reduce the scale of *** results benefit the design of epidemic control strategy.

关键词： epidemic transmission complex network time-dependent networks social interaction

Critical observability of partially observed discrete event systems under cyber attacks

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science China(Information sciences) 2024年第2期67卷 333-334页

作者： Liyun TONG Jinling LIANG Yang LIU Department of mathematics School of SciencesHangzhou Dianzi University school of mathematics Southeast University College of mathematics and Computer science Zhejiang Normal University

The discrete event system(DES) is a dynamic system driven by asynchronous/sudden events and has been widely used in many critical infrastructures, such as electric transportation networks and intelligent transportatio...

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Cohomology groups of a new class of Kadison-Singer algebras

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science China mathematics 2024年第3期67卷 593-606页

作者： Guangyu An Xing Cheng Jun Sheng school of mathematics and Data science Shaanxi University of Science and TechnologyXi’an 710021China

Let N be a maximal discrete nest on an infinite-dimensional separable Hilbert space H,ξ=∑^(∞)_(n=1)en/2n be a separating vector for the commutant N',E_(ξ)be the projection from H onto the subspace[Cξ]spanned by the vectorξ,and Q be the projection from K=H⊕H⊕H onto the closed subspace{(η,η,η)^(T):η∈H}.Suppose that L is the projection lattice generated by the projections(E_(ξ) 0 0 0 0 0 0 0 0),{(E 0 0 0 0 0 0 0 0):E∈N},(I 0 0 0 I 0 0 0 0) and *** show that L is a Kadison-Singer lattice with the trivial ***,we prove that every n-th bounded cohomology group H~n(AlgL,B(K))with coefficients in B(K)is trivial for n≥1.

关键词： Kadison-Singer algebra Kadison-Singer lattice derivation cohomology group