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The Bargmann Symmetry Constraint and Binary Nonlinearization of the Super Dirac Systems

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Chinese Annals of mathematics,Series B 2010年第3期31卷 361-372页

作者： Jing YU Jingsong HE Wenxiu MA Yi CHENG School of science Hangzhou Dianzi University Hangzhou 310018 China department of mathematics University of Science and Technology of China Hefei 230026 China department of mathematics University of Science and Technology of China Hefei 230026 China department of mathematics Ningbo University Ningbo 315211 Zhejiang China. department of mathematics and Statistics University of South Florida Florida 33620-5700 USA.

An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super Dirac systems. Under the obtained symmetry constraint, the n-th flow of the super Dirac hierarchy is decomposed into two super finite-diinensional integrable Hamiltonian systems, defined over the super- symmetry manifold R^4N{2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.

关键词： Symmetry constraints Binary nonlinearization Super Dirac systems Super finite-dimensional integrable Hamiltonian systems

STRONG CONSISTENCY OF M-ESTIMATES OF MULTIPLE REGRESSION COEFFICIENTS

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Systems science and Mathematical sciences 1995年第1期8卷 82-87页

作者： CHEN Xiru (Graduate School of the Chinese Academy of sciences, Beijing 100039, china)ZHAO Lincheng (department of mathematics, university of science and technology of china, hefei 230026, china)

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关键词： Linear regression M-estimate strong consistency.

EXISTENCE AND NONEXISTENCE OF POSITIVE RADIAL SOLUTIONS FOR A CLASS OF SEMILINEAR ELLIPTIC SYSTEMS

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Journal of Systems science & Complexity 2004年第3期17卷 325-331页

作者： ZHONGJinbiao CHENZuchi departmentofmathematics UniversityofScienceandTechnologyofChinaHefei230026China

In this paper an existence theorem of positive radial solutions to a class of semilinear elliptic systems is proved by the Leray-Schauder degree theorem. Also, a nonexistence theorem is obtained. As an application of ... 详细信息

关键词： leray-schauder degree positive radial solution completely continuousoperator

HARDY-SOBOLEV INEQUALITIES WITH GENERAL WEIGHTS AND REMAINDER TERMS

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Acta Mathematica Scientia 2008年第3期28卷 469-478页

作者：陈志辉沈尧天 School of Mathematical sciences South China University of Technology

The Hardy-Sobolev inequality with general weights is established, and it is shown that the constant is optimal. The two weights in this inequality are determined by a Bernoulli equation. In addition, the authors obtain the Hardy-Sobolev inequality with general weights and remainder terms. By choosing special weights, it turns to be many versions of the Hardy-Sobolev inequality and the Caffarelli-Kohn-Nirenberg inequality with remainder terms in the literature.

关键词： Hardy-Sobolev inequality general weight best constant

The Lax Representation and Darboux Transformation for Constrained Flows of the AKNS Hierarchy

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Acta Mathematica Sinica,English Series 1996年第2期12卷 217-224页

作者： Zeng Yunbo Li Yishen Zeng Yunbo department of Applied mathematics Tsinghua university Beijing,100084 chinaLi Yishen department of mathematics university of science and technology of china hefei,230026 china Tsinghua university university of science and technology of china

By using a general scheme for decomposing a zero-curvature equation into two commut- ing x-and t_n-finite-dimensional integrable Hamiltonian systems (FDIHS),a systematic deduction of the Lax representation for all constrained flows of the AKNS hierarchy from the adjoint repre- sentation of the two auxiliary linear problems is *** Darboux transformation for these FDIHSs is derived.

关键词： Constrained flow Lax representation Adjoint representation Darboux transformation

The Spaces bp with 0 < p < 1

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Chinese Quarterly Journal of mathematics 2004年第4期19卷 331-337页

作者： HU Zhang-jian, LIU Tai-shun(1.department of mathematics, university of science and technology of china, hefei 230026, china 2.department of mathematics, Huzhou Teacher's College, Huzhou 313000, china ) department of mathematics University of Science and Technology of China Hefei 230026China department of mathematics Huzhou Teacher's College Huzhou 313000China department of mathematics University of Science and Technology of China Hefei 230026China

Let 0 < p < 1. In this paper we prove that the Bergman norm on the p-th Bergman space bp(H) is equivalent to certain "normal direction norm" as well as certain "tangential direction norm", where H = Rn-1 × R+ is the ... 详细信息

关键词： Bergman space upper half space harmonic conjugation

Weighted estimation of single index models with right censored responses

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science china mathematics 2011年第3期54卷 479-514页

作者： WANG YanHua1, LI XiaYan2, WANG QiHua3 & HE ShuYuan4 1School of sciences, Beijing Institute of technology, Beijing 100081, china 2department of mathematics, university of science and technology of china, hefei 230026, china 3Chinese Academy of mathematics and System science, Beijing 100080, china 4School of Mathematical sciences, Capital Normal university, Beijing 100048, china School of sciences Beijing Institute of Technology Beijing China department of mathematics University of Science and Technology of China Hefei China Chinese Academy of mathematics and System science Beijing China School of Mathematical sciences Capital Normal University Beijing China

In this paper, the unknown link function, the direction parameter, and the heteroscedastic variance in single index models are estimated by the random weight method under the random censorship, respectively. The central limit theory and the convergence rate of the law of the iterated logarithm for the estimator of the direction parameter are derived, respectively. The optimal convergence rates for the estimators of the link function and the heteroscedastic variance are obtained. Simulation results support the theoretical results of the paper.

关键词： single index models random censorship central limit theorem law of the iterated logarithm weighted least squares unknown link function

Applications of interval arithmetic in solving polynomial equations by Wu's elimination method

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science china mathematics 2005年第9期 110-123页

作者： CHEN Falai & YANG Wu department of mathematics,university of science and technology of china,hefei 230026,china

Wu’s elimination method is an important method for solving multivariate poly- nomial *** this paper,we apply interval arithmetic to Wu’s method and convert the problem of solving polynomial equations into that of solving interval polynomial equa- *** results such as zero-decomposition theorem are obtained for interval poly- nomial *** advantages of the new approach are two-folds:First,the problem of the numerical instability arisen from floating-point arithmetic is largely ***, the low efficiency of the algorithm caused by large intermediate coefficients introduced by exact compaction is dramatically *** examples are provided to illustrate the effectiveness of the proposed algorithm.

关键词： mathematical mechanization Wu’s method polynomial equation interval arithmetic

A HIERARCHY OF INTEGRABLE HAMILTONIAN SYSTEMS WITH NEUMANN TYPE CONSTRAINT

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Chinese Annals of mathematics,Series B 1992年第3期13卷 327-340页

作者：曾云波李翊神陈登远 department of mathematics University of Science and Technology of ChinaHefeiAuhui 230026 China.

A hierarchy of integrable Hamiltonian systems with Neumann type constraint isobtained by restricting a hierarchy of evolution equations associated with λφxx+uiλiφ=λmφ to aninvariant subspace of their recursion *** independentintegrals of motion and Hamiltonian functions for these Hamiltonian systems areconstructed by using relevant reeursion formula and are shown to be in *** Hamiltonian systems are completely integrable and commute with each other.

关键词： Hamiltonian integrable hierarchy constraint Neumann subspace tangent trained details guarantees