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Geometry of holomorphic invariant strongly pseudoconvex complex Finsler metrics on the classical domains

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Science China Mathematics 2024年第8期67卷 1827-1864页

作者： Xiaoshu Ge Chunping Zhong school of mathematical sciences Xiamen UniversityXiamen 361005China

In this paper,a class of holomorphic invariant metrics is introduced on the irreducible classical domains of typesⅠ-Ⅳ,which are strongly pseudoconvex complex Finsler metrics in the strict sense of Abate and Patrizio(1994).These metrics are of particular interest in several complex variables since they are holomorphic invariant complex Finsler metrics found in the literature which enjoy good regularity as well as strong pseudoconvexity and can be explicitly expressed to admit differential geometry *** are,however,not necessarily Hermitian quadratic as the Bergman *** metrics are explicitly constructed via deformation of the corresponding Bergman metric on the irreducible classical domains of typesⅠ-Ⅳ,respectively,and they are all proved to be complete K?hler-Berwald *** enjoy very similar curvature properties as those of the Bergman metric on the irreducible classical domains,i.e.,their holomorphic sectional curvatures are bounded between two negative constants and their holomorphic bisectional curvatures are always nonpositive and bounded below by negative constants,*** the viewpoint of complex analysis,these metrics are analogs of Bergman metrics in complex Finsler geometry which do not necessarily have Hermitian quadratic restrictions in the sense of Chern(1996).

关键词： holomorphic invariant metric Kahler-Berwald metric irreducible classical domains

Gorenstein projective modules over rings of Morita contexts

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Science China Mathematics 2024年第11期67卷 2453-2484页

作者： Qianqian Guo Changchang Xi school of mathematical sciences Capital Normal University school of mathematical sciences Laboratory of Mathematics and Complex Systems(Ministry of Education of China)Beijing Normal University school of Mathematics and Statistics Shaanxi Normal University

Under semi-weak and weak compatibility conditions of bimodules,we establish necessary and sufficient conditions of Gorenstein-projective modules over rings of Morita contexts with one bimodule homomorphism *** extends greatly the results on triangular matrix Artin algebras and on Artin algebras of Morita contexts with two bimodule homomorphisms zero in the literature,where only sufficient conditions are given under a strong assumption of compatibility of *** application is provided to describe Gorenstein-projective modules over noncommutative tensor products arising from Morita *** results are proved under a general setting of noetherian rings and modules instead of Artin algebras and modules.

关键词： Gorenstein-projective module noetherian ring noncommutative tensor product totally exact complex weakly compatible bimodule

Soliton resolution and asymptotic stability of N-solutions for the defocusing Kundu–Eckhaus equation with nonzero boundary conditions

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Communications in Theoretical Physics 2024年第1期76卷 1-6页

作者： Engui Fan Yanxi Zhang school of mathematical sciences and Key Laboratory of Mathematics for Nonlinear Science Fudan UniversityShanghai200433China Tianjin Xinhua High school No.99 machang RoadTianjin300204China

In this paper,we address interesting soliton resolution,asymptotic stability of N-soliton solutions and the Painleve asymptotics for the Kundu-Eckhaus(KE)equation with nonzero boundary conditions iq_(t)+q_(xx)-2(l|q|^(2)-1)q+4β^(2)(lql^(4)-1)q+4iβ(lql^(2))_(x)q=0,q(x,0)=q_(0)(x)-±1,x→±∞.The key to proving these results is to establish the formulation of a Riemann-Hilbert(RH)problem associated with the above Cauchy problem and find its connection with the RH problem of the defocusing NLS *** the■-steepest descent method and the results of the defocusing NLS equation,we find complete leading order approximation formulas for the defocusing KE equation on the whole(x,t)half-plane including soliton resolution and asymptotic stability of N-soliton solutions in a solitonic region,Zakharov-Shabat asymptotics in a solitonless region and the Painlevéasymptotics in two transition regions.

关键词： defocusing Kundu-Eckhaus equation Riemann-Hilbert problems steepest descent method soliton resolution asymptotic stability Painleve transcendents

Global classical solutions for 3D compressible magneto-micropolar fluids without resistivity and spin viscosity in a strip domain

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Science China Mathematics 2024年第11期67卷 2485-2514页

作者： Zefu Feng Guangyi Hong Changjiang Zhu school of mathematical sciences Chongqing Normal University school of Mathematics South China University of Technology

In this paper,we consider 3D compressible magneto-micropolar fluids without resistivity and spin viscosity in a strip *** prominent character of the governing model is the presence of the microstructure,a linear coupling structure involving derivatives of the velocity fields,which along with the lack of spin viscosity brings several challenges to the *** exploiting the two-tier energy method developed in Guo and Tice(Arch Ration Mech Anal,2013),we prove the global existence of classical solutions to the governing model around a uniform magnetic field that is non-parallel to the horizontal ***,we show that the solution converges to the steady state at an almost exponential rate as time goes to *** of the main ingredients in our analysis,compared with previous works on micropolar fluids,is that we deal with the microstructure by establishing some delicate estimates based on the analysis of the div-curl decomposition,and the coupling between the fluid velocity and the vorticity of angular velocity.

关键词： magneto-micropolar fluids compressible global existence large-time behavior

Data-Driven Direct Adaptive Risk-Sensitive Control of Stochastic Systems

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Journal of Systems Science & Complexity 2024年第4期37卷 1446-1469页

作者： QIAO Nan LI Tao school of mathematical sciences East China Normal UniversityShanghai 200241China Shanghai Key Laboratory of Pure Mathematics and mathematical Practice School of Mathematical SciencesEast China Normal UniversityShanghai 200241China

The authors propose a data-driven direct adaptive control law based on the adaptive dynamic programming(ADP) algorithm for continuous-time stochastic linear systems with partially unknown system dynamics and infinite horizon quadratic risk-sensitive *** authors use online data of the system to iteratively solve the generalized algebraic Riccati equation(GARE) and to learn the optimal control law *** the case with measurable system noises,the authors show that the adaptive control law approximates the optimal control law as time goes *** the case with unmeasurable system noises,the authors use the least-square solution calculated only from the measurable data instead of the real solution of the regression equation to iteratively solve the *** authors also study the influences of the intensity of the system noises,the intensity of the exploration noises,the initial iterative matrix,and the sampling period on the convergence of the ADP ***,the authors present two numerical simulation examples to demonstrate the effectiveness of the proposed algorithms.

关键词： Adaptive dynamic programming direct adaptive control generalized algebraic Riccati equation risk-sensitive control

On entire solutions of some Fermat type differential-difference equations

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Applied Mathematics(A Journal of Chinese Universities) 2024年第1期39卷 69-88页

作者： LONG Jian-ren QIN Da-zhuan school of mathematical sciences Guizhou Normal UniversityGuiyang 550025China

On one hand,we study the existence of transcendental entire solutions with finite order of the Fermat type difference *** the other hand,we also investigate the existence and growth of solutions of nonlinear different... 详细信息

关键词： entire solutions differential-difference equations existence finite order

THE EXISTENCE AND UNIQUENESS OF TIME-PERIODIC SOLUTIONS TO THE NON-ISOTHERMAL MODEL FOR COMPRESSIBLE NEMATIC LIQUID CRYSTALS IN A PERIODIC DOMAIN

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Acta Mathematica Scientia 2024年第3期44卷 947-972页

作者：陈爽郭闪闪许秋菊 school of mathematical sciences Chongqing Normal UniversityChongqing401331China

In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic *** some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree *** also prove a uniqueness result via energy estimates.

关键词： compressible nematic liquid crystals time-periodic solution topological degree theory energy estimates

Maximal operators of pseudo-differential operators with rough symbols

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Applied Mathematics(A Journal of Chinese Universities) 2024年第1期39卷 174-180页

作者： Ramla Benhamoud ZHU Xiang-rong school of mathematical sciences Zhejiang Normal UniversityJinhua 321004China

Consider a pseudo-differential operator T_(a)f(x)=∫_(R^(n))e^(ix,ζ)a(x,ζ)f(ζ)dζwhere the symbol a is in the rough Hormander class L^(∞)S_(ρ)^(m)with m∈R andρ∈[0,1].In this note,when 1≤p≤2,if n(ρ-1)/p and a∈L^(∞)S_(ρ)^(m),then for any f∈S(R^(n))and x∈R^(n),we prove that M(T_(a)f)(x)≤C(M(|f|^(p))(x))^(1/p) where M is the Hardy-Littlewood maximal *** theorem improves the known results and the bound on m is sharp,in the sense that n(ρ-1)/p can not be replaced by a larger constant.

关键词： pseudo-differential operator rough Hormander class H-L maximal operator

ON THE STABILITY OF PERIODIC SOLUTIONS OF PIECEWISE SMOOTH PERIODIC DIFFERENTIAL EQUATIONS

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Acta Mathematica Scientia 2024年第4期44卷 1524-1535页

作者： Maoan HAN Yan YE school of mathematical sciences Zhejiang Normal UniversityJinhua 321000China

In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential *** studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic *** also present... 详细信息

关键词： periodic solution Poincarémap periodic equation stability