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Restricted Arc-Connectivity of Harary Digraphs

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Journal of the Operations Research Society of China 2024年第2期12卷 540-547页

作者： Jun-Hao Zhang Ji-Xiang Meng College of mathematics and system science Xinjiang UniversityUrumqi 830046XinJiangChina

The h-restricted arc-connectivity of a digraph is an important parameter to measure fault-tolerance of interconnection *** paper determines that the h-restricted arc-connectivity of the Harary digraph D=G(n;1,2,.:,k)i... 详细信息

关键词： Restricted arc-connectivity λ_(h)(D) Super-λ_(h) λ_(h)-Atom λ_(h)-Superatom

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

Predicted Critical State Based on Invariance of the Lyapunov Exponent in Dual Spaces

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Chinese Physics Letters 2024年第1期41卷 68-76页

作者：刘通夏旭 Department of Applied Physics School of ScienceNanjing University of Posts and TelecommunicationsNanjing 210003China Academy of mathematics and system sciences Chinese Academy of SciencesBeijing 100190China

Critical states in disordered systems,fascinating and subtle eigenstates,have attracted a lot of research ***,the nature of critical states is difficult to describe quantitatively,and in general,it cannot predict a system that hosts the critical *** propose an explicit criterion whereby the Lyapunov exponent of the critical state should be 0 simultaneously in dual spaces,namely the Lyapunov exponent remains invariant under the Fourier *** this criterion,we can exactly predict a one-dimensional quasiperiodic model which is not of self-duality,but hosts a large number of critical ***,we perform numerical verification of the theoretical prediction and display the self-similarity of the critical *** to computational complexity,calculations are not performed for higher dimensional ***,since the description of extended and localized states by the Lyapunov exponent is universal and dimensionless,utilizing the Lyapunov exponent of dual spaces to describe critical states should also be ***,we conjecture that some kind of connection exists between the invariance of the Lyapunov exponent and conformal invariance,which can promote the research of critical phenomena.

关键词： state exponent critical

GLOBAL UNIQUE SOLUTIONS FOR THE INCOMPRESSIBLE MHD EQUATIONS WITH VARIABLE DENSITY AND ELECTRICAL CONDUCTIVITY

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Acta Mathematica Scientia 2024年第5期44卷 1747-1765页

作者： Xueli KE school of mathematics and Computational science Xiangtan UniversityXiangtan411105China school of mathematics and Information science Henan Polytechnic UniversityJiaozuo454000China

We study the global unique solutions to the 2-D inhomogeneous incompressible MHD equations,with the initial data(u0,B0)being located in the critical Besov space■and the initial densityρ0 being close to a positive *** using weighted global estimates,maximal regularity estimates in the Lorentz space for the Stokes system,and the Lagrangian approach,we show that the 2-D MHD equations have a unique global solution.

关键词： inhomogeneous MHD equations electrical conductivity global unique solutions

Kriging Model Averaging Based on Leave-One-Out Cross-Validation Method

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Journal of systems science & Complexity 2024年第5期37卷 2132-2156页

作者： FENG Ziheng ZONG Xianpeng XIE Tianfa ZHANG Xinyu school of mathematics Statistics and Mechanics Beijing University of Technology Academy of mathematics and systems science Chinese Academy of Sciences

In recent years, Kriging model has gained wide popularity in various fields such as space geology, econometrics, and computer experiments. As a result, research on this model has *** this paper, the authors propose a model averaging estimation based on the best linear unbiased prediction of Kriging model and the leave-one-out cross-validation method, with consideration for the model uncertainty. The authors present a weight selection criterion for the model averaging estimation and provide two theoretical justifications for the proposed method. First, the estimated weight based on the proposed criterion is asymptotically optimal in achieving the lowest possible prediction ***, the proposed method asymptotically assigns all weights to the correctly specified models when the candidate model set includes these models. The effectiveness of the proposed method is verified through numerical analyses.

关键词： Asymptotic optimality best linear unbiased prediction cross-validation Kriging model model averaging

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