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Arnold's theorem on properly degenerate systems with the Russmann nondegeneracy

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Science china mathematics 2005年第12期48卷 1656-1669页

作者： HAN Yuecai & LI Yong College of mathematics, jilin university, changchun 130012. china 1. College of mathematics Jilin University 130012 Changchun China

In this paper, we investigate the persistence of invariant tori for the nearly in-tegrable Hamiltonian system H(x,y) = h(y) + εp(x,y) + ε2Q(x,y), where h(y) and εp(x,y) satisfy the Russmann non-degenerate condition. Mainly we overcome the difficulties that the order of the parameter E in the perturbation ε2Q(x,y) is not enough and that the measure estimate involves in parts of frequencies with small parameter.

关键词： Arnold’s theorem the Russmann non-degenerate condition.

A scheme for the RCP pattern of the nano-structure

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Communications in Nonlinear Science and Numerical Simulation 2001年第4期6卷 201-204页

作者： Guangwu YAN, Hongxue QU and Bing YAN Department of mathematics, jilin university, changchun 130012. china institute of Atomic and Molecular Physics, jilin university. changchun 130023, china Department of mathematics Juin University Changchun 130012 China Inst. of Atom. and Molecular Physics Jilin University Changchun 130023 China

A new scheme for the Random-Continuous-Pile (RCP) pattern is proposed to simulate a two-dimensional structure The RCP pattern is plotted.

关键词： RCP pattern. Maxwell distribution balls-filling

A hybrid method for inverse cavity scattering problem for shape

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Applied mathematics(A Journal of Chinese Universities) 2010年第2期25卷 127-136页

作者： LIU Juan MA Fu-ming School of mathematics, jilin university, changchun 130012. china. School of mathematics Jilin University Changchun China

In this paper, we give a hybrid method to numerically solve the inverse open cavity scattering problem for cavity shape, given the scattered solution on the opening of the cavity. This method is a hybrid between an iterative method and an integral equations method for solving the Cauchy problem. The idea of this hybrid method is simple, the operation is easy, and the computation cost is small. Numerical experiments show the feasibility of this method, even for cases with noise.

关键词： Open cavity Cauchy problem Helmholtz equation integral equations system method iterativehybrid method.

INSTANTANEOUS SHRINKING AND LOCALIZATION OF FUNCTIONS IN Y_λ(m,p,q,N) AND THEIR APPLICATIONS

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Chinese Annals of mathematics,Series B 2001年第3期22卷 361-380页

作者： YUAN HONGJUN institute of mathematics, jilin university, changchun 130023, china. institute of mathematics Jilin University Changchun 130023 China

The aim of this paper is to discuss the instantaneous shrinking and localization of the support of functions in Yλ(m,p,q,N) and their applications to some nonlinear parabolic equations including the porous medium equation ut = △um-uq, m > 0, q > 0 and the p-Laplace equation ut = div(|△u|p-2△u)-uq, P > 1, q > 0. In particular, as an application of the results, the necessary and sufficient condition for the solutious of the above p-Laplace equation with nonnegative finite Borel measures as initial conditions to have the instantaneous shrinking property of the support is obtained. This is an answer to an open problem posed by R. Kersner and A. Shishkov.

关键词： Porous medium equation p-Laplace equation Instantaneous shrinking Localization property Support

Quantifying quantum entanglement via machine learning models

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Communications in Theoretical Physics 2024年第7期76卷 52-56页

作者： changchun Feng Lin Chen LMIB(Beihang university) Ministry of EducationBeijing 100191China School of Mathematical Sciences Beihang UniversityBeijing 100191China International Research institute for Multidisciplinary Science Beihang UniversityBeijing 00191China

Quantifying entanglement measures for quantum states with unknown density matrices is a challenging *** learning offers a new perspective to address this *** training machine learning models using experimentally measurable data,we can predict the target entanglement *** this study,we compare various machine learning models and find that the linear regression and stack models perform better than *** investigate the model's impact on quantum states across different dimensions and find that higher-dimensional quantum states yield better ***,we investigate which measurable data has better predictive power for target entanglement *** correlation analysis and principal component analysis,we demonstrate that quantum moments exhibit a stronger correlation with coherent information among these data features.

关键词： quantum information entanglement predict machine learning coherence

THE STABILITY AND CONVERGENCE OF COMPUTINGLONG-TIME BEHAVIOUR

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Journal of Computational mathematics 1999年第4期17卷 397-418页

作者： HaI-jun Wu Rong-hua Li(institute of mathematics, jilin university, changchun 130023, china) 吉林大学数学系吉林长春 130023 吉林大学数学系吉林长春

The object of this paper is to establish the relation between stability and convergence of the numerical methods for the evolution equation u(t) - Au - f(u) = g(t) on Banach space V, and to prove the long-time error estimates for the approximation solutions. At first, we give the definition of long-time stability, and then prove the fact that stability and compatibility imply the uniform convergence on the infinite time region. Thus, we establish a general frame in order to prove the long-time convergence. This frame includes finite element methods and finite difference methods of the evolution equations, especially the semilinear parabolic and hyperbolic partial differential equations. As applications of these results we prove the estimates obtained by Larsson [5] and Sanz-serna and Stuart [6].

关键词： stability compatibility covergence reaction-diffusion equation long-time error estimates

Finite-time composite learning control for nonlinear teleoperation systems under networked time-varying delays

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Science china(Information Sciences) 2024年第6期67卷 279-296页

作者： Yana YANG Huixin JIANG changchun HUA Junpeng LI institute of Electrical Engineering Yanshan University

The robust finite-time synchronization control problem is investigated for master-slave networked nonlinear telerobotics systems(NNTSs) in this article. Although there have been some research achievements on finite-time control for the NNTSs, these studies are based on the strong assumptions of communication time delays or can only achieve finite-time bounded convergence even when the external forces are *** and in view of the importance of these issues, a novel robust composite learning adaptive control scheme rendering the finite-time master-slave synchronization is proposed in this paper. In particular, the influence of time delays on finite-time convergence of the system is analyzed by employing the multi-dimension finite-time small-gain framework. Meanwhile, in order to achieve accurate and fast estimation of uncertain parameters of the system, both the online historical and the instantaneous data of the estimation data are explored to derive the new parameter adaptive law under a more realizable interval-excitation(IE) ***, the convergence of the position/force synchronization errors and the adaptive parameter estimation errors is obtained in finite time, and enhanced robustness of the closed-loop system will also be ***, the superior performance of the proposed control algorithms is validated by numerical simulations and hardware experiments.

关键词： networked teleoperation systems finite-time control exact parameter estimation small-gain theorem unknown communication delays

Transitivity, mixing and chaos for a class of set-valued mappings

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Science china mathematics 2006年第1期49卷 1-8页

作者： LIAO Gongfu, WANG Lidong & ZHANG Yucheng institute of mathematics, jilin university, changchun 130012. china institute of Nonlinear Information Technology, Dalian Nations university, Dalian 116600, china Department of mathematics, university of Science and Technology of china, Hefei 230026, china 1. institute of mathematics Jilin University Changchun 130012 China 2. institute of Nonlinear Information Technology Dalian Nations University Dalian 116600 China 3. Department of mathematics University of Science and Technology of China Hefei 230026 China

Consider the continuous map f : x → X and the continuous map f of K,(X) into itself induced by f, where X is a metric space and K(X) the space of all non-empty compact subsets of x endowed with the Hausdorff metric. According to the questions whether the chaoticity of f implies the chaoticity of f posed by Roman-Flores and when the chaoticity of f implies the chaoticity of f posed by Fedeli, we investigate the relations between f and f in the related dynamical properties such as transitivity, weakly mixing and mixing, etc. And by using the obtained results, we give the satisfied answers to Roman-Flores's question and Fedeli's question.

关键词： set-valued mapping, transitivity, weak mixing, mixing, chaos.

Localization for a Fast Diffusion Equation with Absorption

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Communications in Mathematical Research 1999年第2期 27-32页

作者： Yuan Hongjun (institute of mathematics, jilin university, changchun, 130012.

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒｗｅｃｏｎｓｉｄｅｒｔｈｅｆａｓｔｄｉｆｕｓｉｏｎｅｑｕａｔｉｏｎｗｉｔｈａｂｓｏｒｐｔｉｏｎｕｔ＝Δｕｍ－ｕｐ（１）ｉｎＱ＝Ｒｎ×（０，＋∞）ｗｉｔｈｔｈｅｉｎｉ... 详细信息

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒｗｅｃｏｎｓｉｄｅｒｔｈｅｆａｓｔｄｉｆｕｓｉｏｎｅｑｕａｔｉｏｎｗｉｔｈａｂｓｏｒｐｔｉｏｎｕｔ＝Δｕｍ－ｕｐ（１）ｉｎＱ＝Ｒｎ×（０，＋∞）ｗｉｔｈｔｈｅｉｎｉｔｉａｌｃｏｎｄｉｔｉｏｎｕ（ｘ，...

关键词： Localization Nonlinear Diffusion Equation Fast Diffusion Equation