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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 {1. 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

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 {1. 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

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 {1. and Statistics Zhengzhou UniversityZhengzhou 450001China school of {1. 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

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 {1. and Engineering Shandong University the school of Statistics and {1. Shandong University of Finance and Economics IEEE the school of Management Shandong University the school of {1. 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

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 {1. and Statistics Nanjing University of Science and Technology school of Statistics and Data {1. 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： 34C20 37J40 high-dimensional weak Liouvillean KAM theory three dimensional skew-symmetric system

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 {1. Southeast University College of mathematics and Computer {1. 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 {1. 2024年第3期67卷 593-606页

作者： Guangyu An Xing Cheng Jun Sheng school of {1. 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

Study on the effective elastic performance of composites containing decagonal symmetric two-dimensional quasicrystal coatings

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Applied mathematics and Mechanics(English Edition) 2024年第9期45卷 1655-1664页

作者： Yurun WU Lu LI Lianhe LI school of {1. and science Inner Mongolia Normal UniversityHohhot 010022China Inner Mongolia Applied mathematics Center Hohhot 010022China Key Laboratory of Infinite Dimensional Hamiltonian system and Its Algorithm Application Ministry of EducationHohhot 010022China

On account of the Mori-Tanaka approach,the effective elastic performance of composites containing decagonal symmetric two-dimensional(2D)quasicrystal(QC)coatings is *** expressions for the effective elastic constants of rare-earth QC reinforced magnesium-based composites are *** discussion is presented on the effects of the volume fraction of the inclusions,the aspect ratio of the inclusions,the coating thickness,and the coating material parameters on the effective elastic constants of the *** results indicate that considering the coating increases the effective elastic constants of the composites to some extent.

关键词： Mori-Tanaka approach coated inclusion decagonal symmetric twodimensional(2D)quasicrystal(QC)

INTERFACE BEHAVIOR AND DECAY RATES OF COMPRESSIBLE NAVIER-STOKES system WITH DENSITY-DEPENDENT VISCOSITY AND A VACUUM

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Acta Mathematica Scientia 2024年第1期44卷 247-274页

作者：郭真华张学耀 school of {1. and CNS Northwest UniversityXi’an710127China school of {1. and Information science Guangxi UniversityNanning530004China

In this paper,we study the one-dimensional motion of viscous gas near a vacuum,with the gas connecting to a vacuum state with a jump in *** interface behavior,the pointwise decay rates of the density function and the expanding rates of the interface are obtained with the viscosity coefficientμ(ρ)=ρ^(α)for any 01.this includes the timeweighted boundedness from below and *** smoothness of the solution is ***,we construct a class of self-similar classical solutions which exhibit some interesting properties,such as optimal *** present paper extends the results in[Luo T,Xin Z P,Yang *** J Math Anal,2000,31.6):1.75-1.91.to the jump boundary conditions case with density-dependent viscosity.

关键词： decay rates interface Navier-Stokes equations vacuum