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A Criterion of Nonparabolicity by the Ricci Curvature

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Chinese Annals of Mathematics,Series B 2022年第5期43卷 739-748页

作者： qing ding Xiayu DONG School of Mathematical Sciences Fudan UniversityShanghai 200433China

A complete manifold is said to be nonparabolic if it does admit a positive Green’s function. To find a sharp geometric criterion for the parabolicity/nonparbolicity is an attractive question inside the function theory on Riemannian manifolds. This paper devotes to proving a criterion for nonparabolicity of a complete manifold weakened by the Ricci curvature. For this purpose, we shall apply the new Laplacian comparison theorem established by the first author to show the existence of a non-constant bounded subharmonic function.

关键词： Nonparabolicity Subharmonic function Ricci curvature

On Geometric Realization of the General Manakov System

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Chinese Annals of Mathematics,Series B 2023年第5期44卷 753-764页

作者： qing ding Shiping ZHONG Department of Mathematics Wenzhou UniversityWenzhou 325035ZhejiangChina School of Mathematical Sciences Fudan UniversityShanghai 200433China School of Mathematics and Computer Sciences Gannan Normal UniversityGanzhou 341000JiangxiChina

It is well-known that the general Manakov system is a 2-components nonlinear Schrodinger equation with 4 nonzero real *** analytic property of the general Manakov system has been well-understood though it looks *** paper devotes to exploring geometric properties of this system via the prescribed curvature representation in the category of Yang-Mills’*** models of moving curves evolving in the symmetric Lie algebras u(2,1)=k_(α)⊕m_(α)(α=1,2)and u(3)=k_(3)⊕m_(3)are shown to be simultaneously the geometric realization of the general Manakov *** reflects a new phenomenon in geometric realization of a partial differential equation/system.

关键词： Manakov system Geometric realization Prescribed curvature representation

The complex 2-sphere in C^3 and Schrodinger flows Dedicated to Professor Hesheng Hu on the Occasion of Her 90th Birthday

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Science China Mathematics 2020年第4期63卷 777-788页

作者： qing ding Shiping Zhong School of Mathematical Sciences Fudan UniversityShanghai 200433China

By using holomorphic Riemannian geometry in C^3, the coupled Landau-Lifshitz(CLL) equation is proved to be exactly the equation of Schr¨odinger flows from R^1 to the complex 2-sphere CS^2(1) → C^***, regarded as a model of moving complex curves in C^3, the CLL equation is shown to preserve the PT symmetry if the initial data is of the P symmetry. As a consequence, the nonlocal nonlinear Schrodinger(NNLS)equation proposed recently by Ablowitz and Musslimani is proved to be gauge equivalent to the CLL equation with initial data being restricted by the P symmetry. This gives an accurate characterization of the gaugeequivalent magnetic structure of the NNLS equation described roughly by Gadzhimuradov and Agalarov(2016).

关键词： PT symmetry holomorphic Riemannian manifold gauge equivalence

The noncommutative KdV equation and its para-Kahler structure

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Science China Mathematics 2014年第7期57卷 1505-1516页

作者： ding qing HE ZhiZhou School of Mathematical Sciences Fudan University

We prove that the noncommutative(n×n)-matrix KdV equation is exactly a reduction of the geometric KdV flows from R to the symmetric para-Grassmannian manifold G2n,n=SL(2n,R)/SL(n,R)×SL(n,R)and it can also be realized geometrically as a motion of Sym-Pohlmeyer curves in the symmetric Lie algebra sl(2n,R)with initial data being suitably *** gives a para-geometric characterization of the noncommutative matrix KdV equation.

关键词： para-Kahler structure noncommutative KdV geometric realization

The Boundary Contour Method for Half-Plane Piezoelectric Media

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上海交通大学学报 2004年第z2期38卷 176-181页

作者： WANG Guoqing WANG qing LIU Zhengxing ding Haojiang Department of Engineering Mechanics Shanghai Jiaotong Univ. Shanghai200030 China Department of Engineering Mechanics Shanghai Jiaotong Univ. Shanghai200030 China Department of Engineering Mechanics Shanghai Jiaotong Univ. Shanghai200030 China Department of Civil Engineering Zhejiang Univ. Hangzhou310027 China

This paper presents a further development of the Boundary Contour Method (BCM) for half-plane piezoelectric media. Firstly, the divergence free property of the integrand of the half-plane piezoelectric boundary element is proven. Secondly, the boundary contour method formulation is derived and potential functions are obtained by introducing linear shape functions and Green's functions[1] for half-plane piezoelectric media. Finally, numerical solutions for illustrative example are compared with exact ones and that of conventional boundary element method (BEM) ones. The numerical results of BCM coincide very well with exact solution, and the feasibility and efficiency of the method are verified.

关键词： boundary contour method piezoelectricity half-plane shape function

On Differential Equations Describing 3-Dimensional Hyperbolic Spaces

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Communications in Theoretical Physics 2006年第1期45卷 135-142页

作者： WU Jun-Yi ding qing Keti Tenenblat Institute of Mathematics Fudan University Shanghai 200433 China Key Laboratory of Mathematics for Nonlinear Sciences l~hdan University Shanghai 200433 China Department of Mathematics Brasilia University Brasilia DF 70910-900 Brazil

In this paper, we introduce the notion of a （2＋1）-dimenslonal differential equation describing three-dimensional hyperbolic spaces （3-h.s.）. The （2＋1）-dimensional coupled nonlinear Schrodinger equation and its sister equation, the （2＋1）-dimensional coupled derivative nonlinear Schrodinger equation, are shown to describe 3-h.s, The （2 ＋ 1 ）-dimensional generalized HF model：St=（1/2i[S,Sy]＋2iσS）x,σx=-1/4i tr（SSxSy）, in which S ∈ GLc（2）/GLc（1）×GLc（1）,provides another example of （2＋1）-dimensional differential equations describing 3-h.s. As a direct con-sequence, the geometric construction of an infinire number of conservation lairs of such equations is illustrated. Furthermore we display a new infinite number of conservation lairs of the （2＋1）-dimensional nonlinear Schrodinger equation and the （2＋1）-dimensional derivative nonlinear Schrodinger equation by a geometric way.

关键词： (2+1)-dimensional integrable systems differential equations describing 3-dimensional hyperbolic spaces conservation laws

Some Remarks on Projective Generators and Injective Cogenerators

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Acta Mathematica Sinica,English Series 2014年第12期30卷 2063-2078页

作者： Li LIANG Nan qing ding Gang YANG School of Mathematics and Physics Lanzhou Jiaotong University Department of Mathematics Nanjing University

In this paper,we give a relationship between projective generators（resp.,injective cogenerators） in the category of R-modules and the counterparts in the category of complexes of *** a consequence,we get that complexes of W^--Gorenstein modules are actually W-Gorenstein complexes whenever W is a subcategory of R-modules satisfying W⊥W,where W^- is the subcategory of exact complexes with all cycles in *** also study when all cycles of a W-Gorenstein complexes are W^--Gorenstein modules.

关键词： W-Gorenstein modules Gorenstein projective complexes Gorenstein injective complexes projective generators injective cogenerators

Testing for Serial Correlation in Three-dimensional Panel Data Models

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Acta Mathematicae Applicatae Sinica 2017年第1期33卷 239-250页

作者： Jian-hong WU qing ding Jin-xu QIN College of Mathematics and Science Shanghai Normal University Shanghai 200234 China

This paper studies serial correlation testing for a general three-dimensional panel data model. As a step for hypothesis testing, the robust within estimation of parameter coefficients is investigated, and shown to asymptotically consistent and normal under some mild conditions. A residual-based statistic is then constructed to test for serial correlation in the idiosyncratic errors, which is based on the parameter estimates for an artificial autoregression modeled by centering and differencing residuals. The test can be shown to asymptotically chisquare distributed under the null hypothesis. Power study shows that the test can detect local alternatives distinct at the parametric rate from the null hypothesis. The test needs no distribution assumptions of the error components, and is robust to the misspecification of various specific effects. Monte Carlo simulations are carried out for illustration.

关键词： three-dimensional panel data serial correlation residual-based test

THE DECAY OF SWIRLING FLOWS IN A TYPE OF CROSS-SECTION-VARYING PIPES

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Applied Mathematics and Mechanics(English Edition) 2001年第8期22卷 983-988页

作者： XIONG Ao-kui(熊鳌魁) WEI qing-ding(魏庆鼎) Department of Mechanics and Engineering Science Peking UniversityBeijing 100871 P R China Department of Mechanics and Engineering Science Peking UniversityBeijing 100871 P R China

The decay of weakly swirling flows in a type of cross-section-varying pipes was discussed analytically. For laminar swirling flow, the feature of exponential decay was demonstrated. For turbulent swirling flow, in spite of the decay of circulation flux, a necessary condition for local circulation to amplify along downstream was obtained under the Boussinesq's hypothesis.

关键词： swirling flow decay analysis of fluid flows