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High-order Soliton Matrix for the Third-order Flow Equation of the Gerdjikov-Ivanov Hierarchy Through the Riemann-Hilbert Method

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 358-378页

作者： Jin-yan ZHU Yong CHEN school of mathematical sciences Shanghai Key Laboratory of Pure Mathematics and Mathematical PracticeEast China Normal UniversityShanghai 200062China College of mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China

The Gerdjikov-Ivanov(GI)hierarchy is derived via recursion operator,in this article,we mainly investigate the third-order flow GI equation.In the framework of the Riemann-Hilbert method,the soliton matrices of the third-order flow GI equation with simple zeros and elementary high-order zeros of Riemann-Hilbert problem are constructed through the standard dressing process.Taking advantage of this result,some properties and asymptotic analysis of single soliton solution and two soliton solution are discussed,and the simple elastic interaction of two soliton are proved.Compared with soliton solution of the classical second-order flow,we find that the higher-order dispersion term affects the propagation velocity,propagation direction and amplitude of the soliton.Finally,by means of a certain limit technique,the high-order soliton solution matrix for the third-order flow GI equation is derived.

关键词： Gerdjikov-Ivanov hierarchy third-order flow GI equation Riemann-Hilbert method high-order soliton

Integral Operators Between Fock Spaces

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Chinese Annals of mathematics,Series B 2024年第2期45卷 265-278页

作者： Yongqing LIU Shengzhao HOU school of mathematics and statistics Changshu Institute of TechnologySuzhou 215006JiangsuChina school of mathematical sciences Soochow UniversitySuzhou 215006JiangsuChina

In this paper,the authors study the integral operator■induced by a kernel functionφ(z,·)∈F_α~∞between Fock spaces.For 1≤p≤∞,they prove that S_φ:F_α^(1)→F_α^(p)is bounded if and only if■where k_(a)is the ... 详细信息

关键词： Fock spaces Integral operators Normalized reproducing kernel

Threshold Selection and Resource Allocation for Quantized Identification

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Journal of Systems Science & Complexity 2024年第1期37卷 204-229页

作者： WANG Ying LI Xin ZHAO Yanlong ZHANG Ji-Feng key laboratory of Systems and Control Institute of Systems ScienceAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China school of mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

This paper is concerned with the optimal threshold selection and resource allocation problems of quantized identification, whose aims are improving identification efficiency under limited resources. Firstly, the first-order asymptotically optimal quantized identification theory is extended to the weak persistent excitation condition. Secondly, the characteristics of time and space complexities are established based on the Cramér-Rao lower bound of quantized systems. On these basis, the optimal selection methods of fixed thresholds and adaptive thresholds are established under aperiodic signals, which answer how to achieve the best efficiency of quantized identification under the same time and space complexity. In addition, based on the principle of maximizing the identification efficiency under a given resource, the optimal resource allocation methods of quantized identification are given for the cases of fixed thresholds and adaptive thresholds, respectively, which show how to balance time and space complexity to realize the best identification efficiency of quantized identification.

关键词： Quantized output resource allocation system identification threshold selection.

UNIFORM ERROR BOUNDS OF A CONSERVATIVE COMPACT FINITE DIFFERENCE METHOD FOR THE QUANTUM ZAKHAROV SYSTEM IN THE SUBSONIC LIMIT REGIME

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Journal of Computational mathematics 2024年第1期42卷 289-312页

作者： Gengen Zhang Chunmei Su school of mathematics and statistics Yunnan UniversityKunming 650504China Yau mathematical sciences Center Tsinghua UniversityBeijing 100084China

In this paper,we consider a uniformly accurate compact finite difference method to solve the quantum Zakharov system(QZS)with a dimensionless parameter 0<ε≤1,which is inversely proportional to the acoustic speed.In the subsonic limit regime,i.e.,when 0<ε?1,the solution of QZS propagates rapidly oscillatory initial layers in time,and this brings significant difficulties in devising numerical algorithm and establishing their error estimates,especially as 0<ε?1.The solvability,the mass and energy conservation laws of the scheme are also discussed.Based on the cut-off technique and energy method,we rigorously analyze two independent error estimates for the well-prepared and ill-prepared initial data,respectively,which are uniform in both time and space forε∈(0,1]and optimal at the fourth order in space.Numerical results are reported to verify the error behavior.

关键词： Quantum Zakharov system Subsonic limit Compact finite difference method Uniformly accurate Error estimate

Boundary points, minimal L^(2) integrals and concavity property Ⅱ: Weakly pseudoconvex Kähler manifolds

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Science China mathematics 2024年第7期67卷 1665-1718页

作者： Qi’an Guan Zhitong Mi Zheng Yuan school of mathematical sciences Peking UniversityBeijing100871China school of mathematics and statistics Beijing Jiaotong UniversityBeijing100044China Institute of mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing100190China

In this paper, we consider minimal L^(2) integrals on the sublevel sets of plurisubharmonic functions on weakly pseudoconvex K?hler manifolds with Lebesgue measurable gain related to modules at boundary points of the sublevel sets, and establish a concavity property of the minimal L^(2) integrals. As applications, we present a necessary condition for the concavity degenerating to linearity, a concavity property related to modules at inner points of the sublevel sets, an optimal support function related to modules, a strong openness property of modules and a twisted version, and an effectiveness result of the strong openness property of modules.

关键词： minimal L^(2)integrals plurisubharmonic functions boundary points weakly pseudoconvex K?hler manifold

Spontaneous Infection and Periodic Evolving of Domain in a Diffusive SIS Epidemic Model

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 164-191页

作者： Qiang Wen Guo-qiang Ren Bin Liu school of mathematics and statistics Huazhong University of Science and TechnologyWuhan430074China hubei key laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan430074China

In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the uniform boundedness of solution is established. In addition, the spatial-temporal risk index R0(ρ) depending on the domain evolution rate ρ(t) as well as its analytical properties are discussed. The monotonicity of R0(ρ)with respect to the diffusion coefficients of the infected dI, the spontaneous infection rate η(ρ(t)y) and interval length L is investigated under appropriate conditions. Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method. Finally, some numerical simulations are presented to illustrate our analytical results. Our results provide valuable information for disease control and prevention.

关键词： diffusive SIS model spontaneous infection periodically evolving domain periodic endemic equilibrium

Almost Periodic Type Group Actions on Compact Quantum Metric Spaces

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Acta Mathematica Sinica,English Series 2024年第2期40卷 568-594页

作者： Bo Tao LONG Wei WU College of mathematics MIIT Key Laboratory of Mathematical Modelling and High Performance Computing of Air VehiclesNanjing University of Aeronautics and AstronauticsNanjing 211106P.R.China school of mathematical sciences Shanghai Key Laboratory of Pure Mathematics and Mathematical PracticeEast China Normal UniversityShanghai 200241P.R.China

A compact quantum metric space is a complete order unit space A endowed with a Lipnorm L.We give some characterizations of almost periodic type group actions on a compact quantum metric space(A,L)by means of several kinds of subsets of A,its induced equicontinuous actions on several important subsets of the dual Banach space A*,and the Lip-norm L with its induced metric space structures on the state space S(A)of A.

关键词： Lip-norm compact quantum metric space Lipschitz isomorphism almost periodicity Arzela-Ascoli theorem metric set

F_(p) as a Discrete Metric Space

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Algebra Colloquium 2024年第1期31卷 165-180页

作者： Zezhou Zhang school of mathematical sciences MOE key laboratory of mathematics and Complex Systems Beijing Normal University Beijing 100875China

We define a metric that makes the algebraic closure of a finite field F_(p) into a UDBG(uniformly discrete with bounded geometry)metric space.This metric stems from algebraic properties of F_(p).From this perspective,for F_(p)we explore common research themes in metric spaces,reveal how peculiar properties naturally arise,and present it as a new type of example for certain well-studied questions.

关键词： algebraic closure of finite field discrete metric space non-expanding Falner

Equilibrium Reinsurance Strategy and Mean Residual Life Function

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Acta Mathematicae Applicatae Sinica 2024年第3期40卷 758-777页

作者： Dan-ping LI Lv CHEN Lin-yi QIAN Wei WANG school of statistics Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOEEast China Normal UniversityShanghai 200062China Academy of statistics and Interdisciplinary sciences Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOEEast China Normal UniversityShanghai 200062China school of mathematics and statistics Ningbo UniversityNingbo 315211China

In this paper,we analyze the relationship between the equilibrium reinsurance strategy and the tail of the distribution of the risk.Since Mean Residual Life(MRL)has a close relationship with the tail of the distribution,we consider two classes of risk distributions,Decreasing Mean Residual Life(DMRL)and Increasing Mean Residual Life(IMRL)distributions,which can be used to classify light-tailed and heavy-tailed distributions,respectively.We assume that the underlying risk process is modelled by the classical CramérLundberg model process.Under the mean-variance criterion,by solving the extended Hamilton-Jacobi-Bellman equation,we derive the equilibrium reinsurance strategy for the insurer and the reinsurer under DMRL and IMRL,respectively.Furthermore,we analyze how to choose the reinsurance premium to make the insurer and the reinsurer agree with the same reinsurance strategy.We find that under the case of DMRL,if the distribution and the risk aversions satisfy certain conditions,the insurer and the reinsurer can adopt a reinsurance premium to agree on a reinsurance strategy,and under the case of IMRL,the insurer and the reinsurer can only agree with each other that the insurer do not purchase the reinsurance.

关键词： mean residual life excess-of-loss reinsurance insurer reinsurer stochastic control