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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.

Cartesian closedness of categories of completely distributive lattices

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Chinese Science Bulletin 1998年第24期43卷 2059-2063页

作者： ZHANG Dexue 1 and YANG Zhongqiang 2.1. department of Mathematics, Sichuan university, Chengdu 610064,{2. 2. department of Mathematics, Shaanxi normal university, Xi’an 710062.{2. department of Mathematics Sichuan University Chengdu China department of Mathematics Shaanxi Normal University Xi’an China

The category of completely distributive lattices with Scott continuous functions is cartesian closed. Neither the category of completely distributive lattices with arbitrary union preserving mappings nor the category ... 详细信息

关键词： completely distributive lattice continuous lattice cartesian closedness.

Dimension and measure theoretic entropy of a subshift in symbolic space

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Chinese Science Bulletin 1997年第14期42卷 1193-1196页

作者： CHEN Ercai and XIONG Jincheng1. department of Astronomy, Nanjing university, Nangjing 2.0093,{2. 2. department of Mathematics, South{2. normal university, Guangzhou 510631,{2. department of Astronomy Nanjing University Nangjing China department of Mathematics South China Normal University Guangzhou China

1 Definitions and resultsWITH the development of the theory of dynamical systems and fractal geometry, one provedthat symbolic dynamics is a powerful tool to study chaos and fractals. It is useful to study thefractal characteristics of symbolic dynamics. In the present note we shall point out the relationbetween the dimension and measure theoretic entropy of any subshift in symbolic space. Weprove here that the Bowen’s formula for Hausdorff dimension holds without Markov struc-ture. A variational principle for dimension is obtained.

关键词： symbolic space subshift measure theoretic entropy dimension.

On the Cayley-Bacharach property and the construction of vector bundles

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Science china Mathematics 2011年第9期54卷 1891-1898页

作者： SUN Hao 1,2.1 department of Mathematics and Statistics,Huazhong normal {2.,Wuhan 430079,china 2.department of Mathematics,East china normal {2.,Shanghai 2.02.1,china 1. department of Mathematics and Statistics Huazhong Normal University Wuhan 430079 China2. Department of Mathematics East China Normal University Shanghai 200241 China

We study the Cayley-Bacharach property on complex projective smooth varieties of dimension n≥2.for zero dimensional subscheme defined by the zero set of the wedge of r-n + 1 global sections of a rank r≥n vector bund... 详细信息

关键词： Cayley-Bacharach property vector bundle reflexive sheaf k-very ample

Revisiting coherent structures in low-speed turbulent boundary layers

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Applied Mathematics and Mechanics(English Edition) 2019年第2期40卷 261-272页

作者： xianyang JIANG State Key Laboratory for Turbulence and Complex Systems Peking University department of Aeronautics and Astronautics College of EngineeringPeking University

Coherent structures are essential for the momentum exchange and turbulence production in wall-bounded turbulent flows. Diversified coherent structures have been observed in turbulent boundary layers, and hairpin-based vortices dominate most of the relevant literature. However, there is no consensus yet on the origin and forming mechanism of hairpin vortices. Herein, five cornerstones pertaining to the framework of hairpin-based coherent structures are reviewed, and three different hairpin generation mechanisms are clarified. Next, the time-resolved tomographic particle image velocimetry(Tomo-PIV) is used in an early turbulent boundary layer(Re_θ= 42.) to investigate the origin of hairpin vortices. The timelines reveal a triangular bulge in the low-speed streak(LSS), and the initial roll-up occurs at two sides of it. Meanwhile, the material surfaces manifest as a three-dimensional(3D) wave structure in the LSS, which may support the model of a soliton-like coherent structure(Scs). Subsequently, the method of Lagrangian-averaged vorticity deviation is used to detect early vortices. We find that the 3D wave structure is flanked by two vortices, thus confirming the roll-up of timelines and demonstrating the advantage of the Lagrangian criteria in capturing structures in complex flows. These results suggest that various coherent structures may evolve from the metamorphosis of 3D wave structures and their later interaction. Finally, the limitations of traditional experimental and post-processing tools are discussed.

关键词： coherent structure hairpin vortex soliton-like coherent structure(Scs)

Fuzzy controllers based on some fuzzy implication operators and their response functions

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Progress in Natural Science:Materials International 2004年第1期14卷 16-21页

作者： LI Hongxing 1*, YOU Fei 1 and PENG Jiayin 2.1. department of Mathematics, Beijing normal {2., Beijing 100875, china 2. department of Mathematics, Neijiang Teacher's College, Neijiang 641112. china) Beijing normal Univ Dept Math Beijing 100875 Peoples R China

The fuzzy controllers constructed by 2. fuzzy implication operators based on CRI algorithm and their response functions are discussed. The conclusions show that the fuzzy controllers constructed by 9 fuzzy implication operators are universal approximators to continuous functions and can be used in practical fuzzy control systems. And these 9 fuzzy implication operators except for Einstein operator intersection are all the adjoint pairs of some fuzzy implication operators. Besides, there are 3 other fuzzy controllers formed by fuzzy implication operators being regarded approximately as fitted functions.

关键词： fuzzy implication operators CRI algorithm fuzzy controllers response functions universal approximators

An equality on Hochschild homology groups

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Chinese Science Bulletin 1997年第8期42卷 624-627页

作者： ZHANG Pu and LIU Shaoxue1. department of Mathematics, university of Science and Technology of{2., Hefei 2.002.,{2. 2. department of Mathematics, Beijing normal university, Beijing 100875,{2. department of Mathematics University of Science and Technology of China Hefei China department of Mathematics Beijing Normal University Beijing China

LET A be finite-dimensional algebra over field k,and Ae the enveloping algebra of A,i.e.Ae=A kAop,where Aop is the opposite algebra of *** A-bimodule has a natural left Ae-module structure as follows:

关键词： finite-dimensional algebra Hochschild homology groups dimensions.

Joint density of hitting time and point to an ellipse for Brownian motion

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Chinese Science Bulletin 1997年第24期42卷 2054-2058页

作者： YIN Chuancun ZHAO Xuelei department of Mathematics, Qufu normal {2., Qufu 2.3165, china 2. Institute of Mathematics, Shantou {2., Shantou 515063, china department of Mathematics Qufu Normal University Qufu 273165 China

IT is well known that the distribution of hitting time, hitting point, last exiting time, and lastexiting point for Brownian motion to balls has been extensively studied. A similar investi-gation of rectangles or cubes has also been well done. However, analogous questions for Brow-nian motion to ellipsoid are rarely concerned. Bai and Cai obtained the distribution of

关键词： Brownian motion hitting time hitting point ellipse.

Superconductivity of small metal grains

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Science china(phys.cs,Mechanics & Astronomy) 2005年第4期48卷 431-441页

作者： ZHENG Renrong1 CHEN Zhiqian2.& ZHU Shunquan1,3 1. department of phys.cs, Shanghai {2. university, Shanghai 2.02.4, china 2. department of phys.cs, Southwest {2. university, Chongqing 400715, china 3. department of Computer and Electric Technology, Shanghai Business School, Shanghai 2.1400, china 1. department of phys.cs Shanghai Normal University 200234 Shanghai China 2. department of phys.cs Southwest Normal University 400715 Chongqing China 3. department of Computer and Electric Technology Shanghai Business School 201400 Shanghai China

The formulas of the energy gap and superconducting critical temperature appropriate for systems with both odd and even number of electrons are derived; the bases of the derivations are Bcs theory and energy level statistics. Numerical results qualitatively agree with the experimental phenomena. i.e., the superconductivity of small metallic grains will first enhance then decrease to zero when the grain are getting smaller and smaller. The calculations indicate that the above phenomena happen in the metallic grains belonging to Gaussian Orthogonal Ensemble (GOE) and Gaussian Unitary ensemble (GUE) with zero spin; The superconductivity of small metallic grains in Gaussian Symplectic Ensemble (GSE) will monotonically decrease to zero with the decreasing of the grain size. The analyses suggest that the superconductivity enhancements come from pairing and the balance of the strengths between spin-orbital coupling and external magnetic field. In order to take the latter into account, it is necessary to include the level statistics given by Random Matrix Theory (RMT) in describing small metallic grains.

关键词： size effect, superconductivity enhancements, small metallic grains.