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Incentive Feedback Stackelberg Strategy in Mean-Field Type Stochastic Difference Games

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Journal of Systems Science & Complexity 2024年第4期37卷 1425-1445页

作者： GAO Wenhui LIN Yaning ZHANG Weihai School of mathematics and statistics Shandong University of TechnologyZibo 255000China college of Electrical Engineering and Automation Shandong University of Science and TechnologyQingdao 266590China

This paper designs an incentive Stackelberg strategy for the discrete-time stochastic systems with mean-field *** conditions for the existence of such a design are ***,the incentive strategy is obtained as a feedback form including the deviation of the state and its mathematical ***,the stability analysis is *** is found that the stability can be guaranteed by the *** addition,the specific algorithm is proposed and its effectiveness is checked by two examples.

关键词： Discrete-time mean-field stochastic systems incentive strategy Stackelberg game teamoptimal solution

Global Zero-relaxation Limit Problem of the Electro-diffusion Model Arising in Electro-Hydrodynamics

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 241-268页

作者： Ming-hua Yang Si-ming Huang Jin-yi Sun Department of mathematics Jiangxi University of Finance and EconomicsNanchang330032China School of Public Administration Guangdong University of Foreign StudiesGuangzhou510006China college of mathematics and statistics Northwest Normal UniversityLanzhou730070China

In this paper,we study a global zero-relaxation limit problem of the electro-diffusion model arising in electro-hydrodynamics which is the coupled Planck-Nernst-Poisson and Navier-Stokes *** is,the paper deals with a singular limit problem of{u^(∈)_(t)+u^(∈)·▽u^(∈)-Δu^(∈)+▽P^(∈)=Δφ^(∈)▽φ^(∈),in R^(3)×(0,∞),▽·u^(∈)=0,in R^(3)×(0,∞),n^(∈)_(t)+u^(∈)·▽n^(∈)-Δn^(∈)=-▽·(n^(∈)▽φ^(∈)),in R^(3)×(0,∞),ct+u^(∈)·▽c^(∈)-Δc^(∈)=▽·(c^(∈)▽φ^(∈)),in R^(3)×(0,∞),∈^(-1)φ^(∈)_(t)=Δφ^(∈)-n^(∈)+c^(∈),in R^(3)×(0,∞),(u^(∈),n^(∈),c^(∈),φ^(∈))|t=0=(u0,n0,c0,φ0),in R^(3) involving with a positive,large parameter^(∈).The present work show a case that(u^(∈),n^(∈),c^(∈))stabilizes to(u^(∞),n∞,c∞):=(u,n,c)uniformly with respect to the time variable as^(∈)→+∞with respect to the strong topology in a certain Fourier-Herz space.

关键词： fourier-Herz space littlewood-Paley decomposition stability limit dissipative system

Receding Horizon Control-Based Stabilization of Singular Stochastic Systems with State Delay

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Journal of Shanghai Jiaotong university(Science) 2024年第3期29卷 436-449页

作者：王晓静刘晓华高荣 college of Engineering Yantai Nanshan UniversityYantai 265706ShandongChina School of mathematics and statistics Science Ludong UniversityYantai 264025ShandongChina

For a class of discrete-time singular stochastic systems with multi-state delay,the stabilization problem of receding horizon control(RHC)is *** to the difficulty in solving the proposed optimization problem,the RHC stabilization for such systems has not been *** adopting the forward and backward equation technique,the optimization problem is solved completely.A sufficient and necessary condition for the optimization controller to have a unique solution is given when the regularization and pulse-free conditions are *** on this controller,an RHC stabilization condition is derived,which is in the form of linear matrix *** is proved that the singular stochastic system with multi-state delay is stable in the mean-square sense under appropriate assumptions when the terminal weighting matrix satisfies the given *** examples show that the proposed RHC method is effective in stabilizing singular stochastic systems with multi-state delay.

关键词： receding horizon control(RHC) singular stochastic system state delay stabilization

Decompositions of the Kadomtsev-Petviashvili equation and their symmetry reductions

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Chinese Physics B 2024年第3期33卷 150-159页

作者：陈孜童贾曼郝夏芝楼森岳 School of mathematics and statistics Ningbo UniversityNingbo 315211China School of Physical Science and Technology Ningbo UniversityNingbo 315211China college of Science Zhejiang University of TechnologyHangzhou 310014China

Starting with a decomposition conjecture,we carefully explain the basic decompositions for the Kadomtsev-Petviashvili(KP)equation as well as the necessary calculation procedures,and it is shown that the KP equation allows the Burgers-STO(BSTO)decomposition,two types of reducible coupled BSTO decompositions and the BSTO-KdV ***,we concentrate ourselves on pointing out the main idea and result of Bäcklund transformation of the KP equation based on a special superposition principle in the particular context of the BSTO *** the framework of standard Lie point symmetry theory,these decompositions are studied and the problem of computing the corresponding symmetry constraints is treated.

关键词： Kadomtsev-Petviashvili(KP)equation decomposition Bäcklund transformation symmetry reduction

Balanced Subeulerian Signed Graphs and Signed Line Graphs

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Journal of Mathematical Research with Applications 2024年第1期44卷 7-17页

作者： Juan LIU Hong YANG Xindong ZHANG Hongjian LAI college of Big Data statistics Guizhou University of Finance and Economics college of mathematics and System Sciences Xinjiang University Department of mathematics West Virginia University

A signed graph S =(Su, σ) has an underlying graph Suand a function σ : E(Su)-→{+,-}. Let E-(S) denote the set of negative edges of S. Then S is eulerian signed graph(or subeulerian signed graph, or balanced eulerian signed graph, respectively) if Suis eulerian(or subeulerian, or eulerian and |E-(S)| is even, respectively). We say that S is balanced subeulerian signed graph if there exists a balanced eulerian signed graph S′ such that S′ is spanned by *** signed line graph L(S) of a signed graph S is a signed graph with the vertices of L(S) being the edges of S, where an edge eiej is in L(S) if and only if the edges ei and ej of S have a vertex in common in S such that an edge eiej in L(S) is negative if and only if both edges ei and ej are negative in S. In this paper, two families of signed graphs S and S ′ are identified, which are applied to characterize balanced subeulerian signed graphs and balanced subeulerian signed line graphs. In particular, it is proved that a signed graph S is balanced subeulerian if and only if S?S, and that a signed line graph of signed graph S is balanced subeulerian if and only if S?S ′.

关键词： signed graph signed line graph balanced eulerian balanced subeulerian

Stability Analysis of Inverse Lax-Wendroff Procedure for a High order Compact Finite Difference Schemes

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Communications on Applied mathematics and Computation 2024年第1期6卷 142-189页

作者： Tingting Li Jianfang Lu Pengde Wang School of mathematics and statistics Henan UniversityKaifeng475004HenanChina School of mathematics South China University of TechnologyGuangzhou510641GuangdongChina college of mathematics and Information Science Henan University of Economics and LawZhengzhou450046HenanChina

This paper considers the finite difference(FD)approximations of diffusion operators and the boundary treatments for different boundary *** proposed schemes have the compact form and could achieve arbitrary even order of *** main idea is to make use of the lower order compact schemes recursively,so as to obtain the high order compact schemes ***,the schemes can be implemented efficiently by solving a series of tridiagonal systems recursively or the fast Fourier transform(FFT).With mathematical induction,the eigenvalues of the proposed differencing operators are shown to be bounded away from zero,which indicates the positive definiteness of the *** obtain numerical boundary conditions for the high order schemes,the simplified inverse Lax-Wendroff(SILW)procedure is adopted and the stability analysis is performed by the Godunov-Ryabenkii method and the eigenvalue spectrum visualization *** numerical experiments are provided to demonstrate the effectiveness and robustness of our algorithms.

关键词： Compact scheme Diffusion operators Inverse Lax-Wendroff(ILW) Fourier analysis Eigenvalue analysis

Left-invariant metrics on a class of solvable Lie Groups

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Acta Mathematica Sinica,English Series 2024年

作者： Zhi Qi CHEN Ke YAN Hui ZHANG School of mathematics and statistics Guangdong University of Technology college of Science National University of Defense Technology School of mathematics Southeast University

Left-invariant Riemannian metrics on Lie groups G_(RHn-1)×R and GRH2×Rn-2（n ≥ 3） have been classified by Hiroshi, Takahara and Tamaru. It is easily seen that G_(RHn-1)×R and GRH2×Rn-2（n ≥ 3） have the same automorphism group, which is denoted by L_n. In this paper, we first classify n-dimensional simply connected Lie groups with automorphism group L_n, then we classify the leftinvariant Riemannian metrics on such Lie groups. As an application, we get the m-quasi Einstein metrics.

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Some Simple Groups Which are Determined by Their Orders and Degree-Patterns

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Algebra Colloquium 2024年第2期31卷 341-346页

作者： Qinghong Guo Weijun Liu Genghua Fan School of mathematics and statistics HNP-LAMACentral South University Changsha 410083China college of General Education Guangdong University of Science and Technology DongguanGuangdong 523083China 不详

Let G be a finite group and Irr(G)the set of all irreducible complex characters of *** cd(G)be the set of all irreducible complex character degrees of G and denote byρ(G)the set of all primes which divide some character degree of *** character-prime graphΓ(G)associated to G is a simple undirected graph whose vertex set isρ(G)and there is an edge between two distinct primes p and q if and only if the product p q divides some character degree of *** show that the finite nonabelian simple groups A_(7),J_(1),J_(3),J_(4),L_(3)(3)and U_(3)(4)are uniquely determined by their degree-patterns and orders.

关键词： irreducible complex character character-prime graph finite nonabelian simple group

Ergodicity of 3D Stochastic Burgers Equation

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Acta Mathematica Sinica,English Series 2024年第2期40卷 498-510页

作者： Zhao DONG Jiang Lun WU Guo Li ZHOU RCSDS Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190P.R.China Department of mathematics Computational FoundrySwansea UniversitySwansea SA18ENUK college of mathematics and statistics Chongqing UniversityChongqing 400044P.R.China

3D Burgers equation is an important model for *** is natural to expect the long-time behaviour for this hydrodynamics ***,there is no result about the long-time behaviour for this deterministic ***,if the system is perturbed by stochastic noise,we establish the existence and uniqueness of invariant measure for 3D stochastic Burgers equation.

关键词： 3D stochastic Burgers equations maximum principle ergodicity