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A family quantization formula for symplectic manifolds with boundary

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Science China mathematics 2001年第5期44卷 599-609页

作者：冯惠涛张伟平胡文传 nankai institute of mathematics Nankai University Tianjin China

This paper generalizes the family quantization formula of Zhang to the case of manifolds with boundary. As an application, Tian-Zhang’s analytic version of the Guillemin-Kalkman-Martin residue formula is generalized ... 详细信息

关键词： Hamiltonian action family quantization higher spectral flow.

Solutions of the Generalized Lennard-Jones System

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Acta Mathematica Sinica,English Series 2018年第2期34卷 139-170页

作者： Bowen LIU Yiming LONG Chongchun ZENG Chern institute of mathematics Nankai University Chern institute of mathematics and LPMC Nankai University School of mathematics Georgia Institute of Technology

In this paper, we study solution structures of the following generalized Lennard-Jones system in R^n,x（-α/｜x｜α＋2＋β/｜x｜β＋2）xwith 0 〈 α 〈β. Considering periodic solutions with zero angular momentum, we prove that the corre- sponding problem degenerates to I-dimensional and possesses infinitely many periodic solutions which must be oscillating line solutions or constant solutions. Considering solutions with non-zero angular momentum, we compute Morse indices of the circular solutions first, and then apply the mountain pass theorem to show the existence of non-circular solutions with non-zero topological degrees. We further prove that besides circular solutions the system possesses in fact countably many periodic solutions with arbitrarily large topological degree, infinitely many quasi-periodic solutions, and infinitely many asymptotic solutions.

关键词： Generalized Lennard-Jones system mountain pass solutions periodic solutions quasi- periodic solutions asymptotic solutions

CRITERION FOR SL(2,Z)-MATRIX TO BE CONJUGATE TO ITS INVERSE

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Chinese Annals of mathematics,Series B 2002年第4期23卷 455-460页

作者： LONG YIMINGnankai institute of mathematics, nankai University, Tianjin 300071, China. E-mail: longym@***. nankai institute of mathematics Nankai University Tianjin 300071 China

This paper gives a necessary and sufficient condition for a matrix in SL(2, Z) to be conjugateto its inverse. This condition reduces the determination of the conjugation to solving some indeterminate equation of second degree. It yields an algorithm to determine this conjugation in finite steps based on the elementary number theory.

关键词： SL(2 Z) matrix Inverse Mixed stability

Convex Functions, Subdifferentiability and Renormings

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Acta Mathematica Sinica,English Series 1998年第1期14卷 47-56页

作者： Cheng Lixin Wu Congxin Xue Xiaoping Yao Xiaobo nankai institute of mathematics, nankai University, Tianjin 300071, China Department of mathematics, Harbin institute of Technology, Harbin 150006, China nankai institute of mathematics Nankai University Tianjin China Department of mathematics Harbin Institute of Technology Harbin China

This paper through discussing subdifferentiability and convexity of convex functions shows that a Banach space admits an equivalent uniformly [locally uniformly, strictly] convex norm if and only if there exists a continuous uniformly [locally uniformly, strictly] convex function on some nonempty open convex subset of the space and presents some characterizations of super-reflexive Banach spaces.

关键词： Convex function Differentiabilit Renorming Uniformly convex Banach space

Stability of Symmetric Closed Characteristics on Symmetric Compact Convex Hypersurfaces in R^(2n) under a Pinching Condition

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Acta Mathematica Sinica,English Series 2012年第5期28卷 885-900页

作者： Hui LIU Chern institute of mathematics Nankai University

In this paper, let ∑ R2n be a symmetric compact convex hypersurface which is （r, R）-pinched with. Then Z carries at least two elliptic symmetric closed characteristics; moreover,∑ carries at least E[n-1/2] ＋ E[n-... 详细信息

关键词： Symmetric compact convex hypersurfaces symmetric closed characteristics Hamiltonian systems index iteration stability

Property T^(**) for C~*-algebras

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Acta Mathematica Sinica,English Series 2012年第9期28卷 1845-1850页

作者： Dan LI Chern institute of mathematics Nankai University

Extending the notion of property T of finite von Neumann algebras to general yon Neu- mann algebras, we define and study in this paper property T＊＊ for （possibly non-unital） C＊-algebras. We obtain several results of property T＊＊ parallel to those of property T for unital C＊-algebras. Moreover, we show that a discrete group F has property T if and only if the group C＊-algebra C＊（F）（or equivalently, the reduced group C＊-algebra C＊（F）） has property T＊＊. We also show that the compact operators K（g2） has property T＊＊ but co does not have property T＊＊.

关键词： Property T** C*-algebras Hilbert bimodules

ON THE MINIMAL PERIOD FOR PERIODIC SOLUTION PROBLEM OF NONLINEAR HAMILTONIAN SYSTEMS

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Chinese Annals of mathematics,Series B 1997年第4期18卷 481-484页

作者： LONG YIMING  nankai institute of mathematics Nankai University Tianjin 300071 China

The author proves a sharper estimate on the minimal period for periodic solutions of autonomous second order Hamiltonian systems under precisely Rabinowitz' superquadratic condition.

关键词： Hamiltonian systems Z 2 symmetry Index interation inequality Minimal period Even solution Superquadratic condition Non convexity

CHARACTERIZATION OF THE UPPER SUBDERIVATIVE AND ITS CONSEQUENCES IN NONSMOOTH ANALYSIS

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Chinese Annals of mathematics,Series B 1991年第4期12卷 480-494页

作者：王运通 nankai institute of mathematics Nankai University Tianjin China

It is proved that the upper subderivative of a lower semicontinuous function on a Banach space is upper semicontinuous for the first variable as x′→f x, i. e., x′-x, f(x′)-f(x). By taking account of the work of Treiman. it is further shown that the upper subderivative of a 1. s. c. function is the upper limit of the contingent directtional derivatives around the concorned point. This new characterization of the upper suoberivative allows simple derivations and natural extension of many results' in nonsmooth analysis.

关键词：七气任才二阳 notions neighborhood 拍脚 Hadamard Regular translate 云一

Dative B–N bonds weaven toward two-dimensional purely organic materials for single crystals

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Science China Chemistry 2025年第1期68卷 12-14页

作者： Wei-Lei Zhou Siwei Wang Yong Chen College of Chemistry and Materials Science Inner Mongolia Key Laboratory of Chemistry for Nature Products and Synthesis for Functional Molecules Innovation Team of Optical Functional Molecular Devices Inner Mongolia Minzu University College of Chemistry Nankai University

Molecular topology is one of the important topics to study and understand the relationship between molecular structure and properties [1]. Particularly, two-dimensional (2D) materials with extremely high surface area and ultra-thin morphology have attracted considerable attention due to their unexpected properties in materials and chemistry [2,3].

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