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On contactomorphism group of contact structure overtwisted at infinity on R^3

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Science China mathematics 2007年第8期50卷 1087-1092页

作者： Li YU department of mathematics,{2. university,{2. 2.0093,China department of mathematics Nanjing University Nanjing 210093 China

We compute all the homotopy groups of the compactly supported contactomorphism group of a contact structure on R^3 which is overtwisted at infinity.

关键词： contactomorphism overtwisted contact structure

On critical values concerning the evolution of the long period families

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Chinese Journal of Astronomy and Astrophysics 2009年第4期9卷 494-500页

作者： Xi-Yun Hou1,2. Astronomy department, nanjing university,{2., China 2.Institute of Space Environment and Astronautics, nanjing university,{2., China Astronomy department Nanjing University Nanjing 210093 China Institute of Space Environment and Astronautics Nanjing University Nanjing 210093 China

In a previous paper, we proposed another special critical value concerning the evolution of the long period family around the equilateral equilibrium points, besides the two values given by Henrard. Are there any other special critical values？ After studying the stability curves of the long period family carefully, we gave a negative answer. During the study, we found an interesting family of periodic orbits which we called the homo family. We studied the evolution of this family following the increase of μ. With these findings, we were able to explain the origin of the four branches of periodic families emanating from L4 and the stability results of the equilateral equilibrium points.

关键词： celestial mechanics

Characteristic analysis for a polynomial-like iterative equation

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Chinese Science Bulletin 1998年第3期43卷 192-196页

作者： Janusz Matkowski 1 and ZHANG Weinian 2.1. department of mathematics, Technical{2., 43_300 Bielsko_Biala, Poland 2. department of mathematics, Sichuan Union{2., Chengdu 610064, China department of mathematics Technical University Bielsko-Biala Poland department of mathematics Sichuan Union University Chengdu China

In the light of Euler’s idea for differential equations,a polynomial_like n _order iterative equation is discussed through analyzing its characteristic polynomial. An unproved result is verified rigorously for the fi... 详细信息

关键词： iterative dynamics functional equation characteristic.

SOLVING TRUST REGION PROBLEM IN LARGE SCALEOPTIMIZATION

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Journal of Computational mathematics 2000年第1期18卷 1-12页

作者： Bing-sheng He(department of mathematics,{2., Naming 2.0093, China) 南京大学江苏南京 210093

Presents a study which introduced a method for solving trust region problem in scale minimization. Review of the conjugate gradient method (CG) and the projection and contraction (PC) method; Convergence behavior of t... 详细信息

关键词： trust region problem conjugate gradient method projection and contraction method

K-uniformly rotund spaces and k-uniformly smooth spaces

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Chinese Science Bulletin 1998年第2期43卷 92-95页

作者： Suyalatu 1 and WU Congxin 2.1. department of mathematics,Inner Mongolia Normal{2., Huhhot 01002., China 2. department of mathematics, Harbin Institute of Technology, Harbin 150006, China department of mathematics Inner Mongolia Normal University Huhhot China department of mathematics Harbin Institute of Technology Harbin China

The conception of k_uniform smoothness (KUS) is introduced. It is the extension of the conception of uniform smoothness. It is proved that the k_uniform smoothness and Sullivan’s K_uniform rotundity (KUR) are the daul notions. X+* is a KUR space if and only if X is a KUS space, X+* is a KUS space if and only if X is a KUR space. If X is a KUS space, then X is a (K+1)US space. It is also proved that the KUS space includes the Nan’s k_strongly smooth space.

关键词： K_uniform smoothness K_uniform convexity.

Completely regular paracompact reflection of locales

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Science China mathematics 2006年第6期49卷 820-826页

作者： HE Wei & LUO Maokang department of mathematics,{2. Normal university,{2. 2.0097, China department of mathematics, Sichuan university, Chengdu 610064, China department of mathematics Nanjing Normal University Nanjing 210097 China department of mathematics Sichuan University Chengdu 610064 China

We give an explicit construction of the completely regular paracompact reflection pL of a completely regular locale L described as a sublocale of the Stone-tech compactification βL of L.

关键词： completely regular paracompact locale, nucleus.

Tribological Properties of Dimpled Surface Alloying Layer on Carbon Steel

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Journal of Wuhan university of Technology(Materials Science) 2009年第2期24卷 218-222页

作者：万轶 department of Materials Science & Engineering Nanjing University of Science and Technology department of Mechanical and Electrical Engineering Yingtian College

The effect of surface structure and coating on tribological properties of 45^# carbon steel disc was analyzed. A Nd：YAG laser was used to generate rnicrodirnples on steel surfaces. Dimples with diameter of 150 rn and depth of 50 rn were distributed in an orbicular array on disc surface. Then the alloying element Mo was sputtered to 45# carbon steel disc surface by means of double glow plasma technology. Diffusion Mo alloying layer with 30min thickness and high hardness up to 0.02. was formed on the disc surface. Tribological experiments of three types samples （smooth, texturing and texturing＋alloying） were conducted with a pin-on-disc tribometer. It is found that the dimpled-samples are most effective for reducing friction in comparison with smooth steel surthces, improving the lubricating state from boundary to hydrodynamic region.

关键词： laser surface texturing double glow plasma surface alloying technology carbon steel tribological performance lubricating state

Application of ERS-1 scatterometer data to studying land surfaces ──Distributive characteristic of backscattering coefficient over China land surfaces

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Chinese Science Bulletin 1998年第23期43卷 1950-1955页

作者： WANG Xiangyun 1, WANG Chao 2. GUO Huadong 2.and SHI Yangshen 1 1. department of Earth Sciences, nanjing university,{2., China 2. Institute of Remote Sensing Applications, Chinese Academy of Sciences, Beijing 100101, China department of Earth Sciences Nanjing University Nanjing 210093 China Inst. of Remote Sensing Applications Chinese Academy of Sciences Beijing 100101 China

ERS 1 WSC data were obtained by international cooperation. The distributive characteristics of radar backscattering coefficient image of China land surface are analyzed and the research results are presented. The capability of ERS 1 WSC data for monitoring land surfaces is investigated. The results show that the radar backscattering coefficient images can reveal the natural landform features of China land. Using the WSC data can discriminate six types of major land coverage, including evergreen vegetation and snow covered region, vegetation and crops, mountains, grassland, desert and grassland, desert. On the whole, the radar backscattering coefficient image of China land is the synthesis of the vegetation map and terrain map. Statistical study of the typical terrain shows that the radar backscatter coefficients of China land range from -2. dB to -5 dB. The lowest value corresponds to the deserts of Badain Jaran, Takla Makan, and Tengger. The highest value corresponds to snow covered regions of Himalaya Mountains and Tianshan Mountains.

关键词： ERS 1 WSC radar backscattering coefficient land surfaces coverage.

A three level linearized compact difference scheme for the Cahn-Hilliard equation

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Science China mathematics 2012年第4期55卷 805-826页

作者： LI Juan 1,2.,SUN ZhiZhong 1,& ZHAO Xuan 1 1 department of mathematics,Southeast{2.,nanjing 2.0096,China 2.Yingtian College,nanjing 2.0046,China 1. department of mathematics Southeast University Nanjing 210096 China2. Yingtian College Nanjing 210046 China

This article is devoted to the study of high order accuracy difference methods tor the Cahn-rnmara equation. A three level linearized compact difference scheme is derived. The u^ique solvability and uaconditional convergence of the difference solution are proved. The convergence order is O（T2.h4） in the maximum norm. The mass conservation and the non-increase of the total energy are also verified. Some numerical examples are given to demonstrate the theoretical results.

关键词： Cahn-Hilliard equation compact difference scheme convergence solvability conservation energynon-increase