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∞-Tilting Subcategories in Extriangulated Categories

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Chinese Annals of mathematics,Series B 2024年第1期45卷 151-160页

作者： Zhen ZHANG Jiaqun WEI Shance WANG Department of mathematics Qilu Normal UniversityJinan 250200China Institution of mathematics School of Mathematics ScienceNanjing Normal UniversityNanjing 210023China

In this paper, the authors introduce a new definition of ∞-tilting(resp. cotilting) subcategories with infinite projective dimensions(resp. injective dimensions) in an extriangulated category. They give a Bazzoni characterization of ∞-tilting(resp. cotilting)subcategories. Also, they obtain a partial Auslander-Reiten correspondence between ∞-tilting(resp. cotilting) subcategories and coresolving(resp. resolving) subcategories with an E-projective generator(resp. E-injective cogenerator) in an extriangulated category.

关键词： Extriangulated category ∞-Tilting subcategory Auslander-Reiten correspondence Bazzoni characterization

Lyapunov Conditions for Finite-Time Input-to-State Stability of Impulsive Switched Systems

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IEEE/CAA Journal of Automatica Sinica 2024年第4期11卷 1057-1059页

作者： Taixiang Zhang Jinde Cao Xiaodi Li the school of mathematics Southeast UniversityNanjing 210096China the school of mathematics and Statistics Shandong Normal UniversityJinan 250014Chi

Dear Editor,This letter studies finite-time input-to-state stability(FTISS)for impulsive switched systems.A set of Lyapunov-based conditions are established for guaranteeing FTISS *** constituent modes governing continuous dynamics are FTISS and discrete dynamics involving impulses are destabilizing,the FTISS can be retained if impulsive-switching signals satisfy an average dwell-time(ADT)condition.

关键词： property impulsive satisfy

THE EXACT MEROMORPHIC SOLUTIONS OF SOME NONLINEAR DIFFERENTIAL EQUATIONS

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Acta Mathematica Scientia 2024年第1期44卷 103-114页

作者：刘慧芳毛志强 school of mathematics and Statistics Jiangxi Normal UniversityNanchang330022China school of mathematics and Computer Jiangxi Science and Technology Normal UniversityNanchang330038China

We find the exact forms of meromorphic solutions of the nonlinear differential equations■,n≥3,k≥1,where q,Q are nonzero polynomials,Q■Const.,and p_(1),p_(2),α_(1),α_(2)are nonzero constants withα_(1)≠α_(2).Compared with previous results on the equation p(z)f^(3)+q(z)f"=-sinα(z)with polynomial coefficients,our results show that the coefficient of the term f^((k))perturbed by multiplying an exponential function will affect the structure of its solutions.

关键词： Nevanlinna theory nonlinear differential equations meromorphic functions entire functions

GLOBAL WEAK SOLUTIONS FOR AN ATTRACTION-REPULSION CHEMOTAXIS SYSTEM WITH p-LAPLACIAN DIFFUSION AND LOGISTIC SOURCE

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Acta Mathematica Scientia 2024年第3期44卷 909-924页

作者：王晓闪王忠谦贾哲 Department of mathematics Luoyang Normal UniversityLuoyang471934China school of mathematics Science Jiangsu Second Normal UniversityNanjing210013China school of mathematics and Statistics Linyi UniversityLinyi276005China

This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ ■ R^(n)(n≥2),with χ,ξ,α,β,γ,δ,k_(1),k_(2)> 0,p> *** addition,the function f is smooth and satisfies that f(s)≤κ-μs~l for all s≥0,with κ ∈ R,μ> 0,l> *** is shown that(ⅰ)if l> max{2k_(1),(2k_(1)n)/(2+n)+1/(p-1)},then system possesses a global bounded weak solution and(ⅱ)if k_(2)> max{2k_(1)-1,(2k_(1)n)/(2+n)+(2-p)/(p-1)} with l> 2,then system possesses a global bounded weak solution.

关键词： global weak solutions attraction-repulsion p-Laplacian logistic source

Bipartite consensus problems of Lurie multi-agent systems over signed graphs: A contraction approach

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Chinese Physics B 2024年第7期33卷 137-145页

作者：张晓娇吴祥 school of mathematics and Information Science Nanchang Normal UniversityNanchang 330032China school of Mathematical Sciences Guizhou Normal UniversityGuiyang 550001China

This paper examines the bipartite consensus problems for the nonlinear multi-agent systems in Lurie dynamics form with cooperative and competitive communication between different agents. Based on the contraction theory, some new conditions for the nonlinear Lurie multi-agent systems reaching bipartite leaderless consensus and bipartite tracking consensus are presented. Compared with the traditional methods, this approach degrades the dimensions of the conditions, eliminates some restrictions of the system matrix, and extends the range of the nonlinear function. Finally, two numerical examples are provided to illustrate the efficiency of our results.

关键词： contraction theory virtual system bipartite consensus Lurie multi-agent systems

Eventually homological isomorphisms and Gorenstein projective modules

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Science China mathematics 2024年第8期67卷 1719-1734页

作者： Yongyun Qin Dawei Shen school of mathematics Yunnan Normal UniversityKunming 650500China school of mathematics and Statistics Henan UniversityKaifeng 475004China

We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity categories,Gorenstein defect categories and stable categories of Gorenstein projective ***,we show that the Auslander-Reiten conjecture and the Gorenstein symmetry conjecture can be reduced by eventually homological *** these results to arrow removal and vertex removal,we describe the Gorenstein projective modules over some non-monomial algebras and verify the Auslander-Reiten conjecture for certain algebras.

关键词： singularity categories Gorenstein defect categories Gorenstein projective modules AuslanderReiten conjecture Gorenstein symmetry conjecture eventually homological isomorphisms

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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MULTIPLE SOLUTIONS TO CRITICAL MAGNETIC SCHRODINGER EQUATIONS

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Acta Mathematica Scientia 2024年第4期44卷 1373-1393页

作者： Ruijiang WEN Jianfu YANG school of mathematics and Statistics Jiangri Normal UniversityNanchang 330022China

In this paper,we are concerned with the existence of multiple solutions to the critical magnetic Schrödinger equation(-i▽-a(x))^(2)u+⒂λV(x)u=p|u|^(p-2)u+(∫R(n)|u(y)|^(2)_(a)^(*)/|x-y|^(a)dy)|u|2_(a)^(*)-2_(u)in R^(N),(0.1)where N≥4,2≤p0,μ∈R,A(x)=(A_(1)(x),A_(2)(x),…,A_(N)(x))is a real local Hölder continuous vector function,i is the imaginary unit,and V(x)is a real valued potential function on R^(N).Supposing thatΩ=int V^(-1)(0)■R^(N)is bounded,we show that problem(0.1)possesses at least cat_(Ω)(Ω)nontrivial solutions ifλis large.

关键词： critical magnetic Schrödinger equation multiple solutions Ljusternik-Schnirelman theory

THE SUPERCLOSENESS OF THE FINITE ELEMENT METHOD FOR A SINGULARLY PERTURBED CONVECTION-DIFFUSION PROBLEM ON A BAKHVALOV-TYPE MESH IN 2D

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Acta Mathematica Scientia 2024年第4期44卷 1572-1593页

作者： Chunxiao ZHANG Jin ZHANG school of mathematics and Statistics Shandong Normal UniversityJinan 250014China

For singularly perturbed convection-diffusion problems,supercloseness analysis of the finite element method is still open on Bakhvalov-type meshes,especially in the case of *** difficulties arise from the width of the mesh in the layer adjacent to the transition point,resulting in a suboptimal estimate for *** analysis techniques cannot handle these difficulties *** fill this gap,here a novel interpolation is designed delicately for the smooth part of the solution,bringing about the optimal supercloseness result of almost order 2 under an energy norm for the finite element *** theoretical result is uniform in the singular perturbation parameterεand is supported by the numerical experiments.

关键词： singularly perturbed convection-diffusion finite element method supercloseness Bakhvalov-type mesh