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Nonlinear ergodic theorem for semitopological semigroups of non-Lipschitzian mappings in Banach spaces

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Chinese Science Bulletin 1997年第1期42卷 8-11页

作者： LI Gang and MA Jipu1. department of mathematics, Yangzhou {2. College, Yangzhou 2.5002. China 2. department of mathematics, Nanjing university, Nanjing 2.0093, China department of mathematics Yangzhou Normal College Yangzhou China department of mathematics Nanjing University Nanjing China

LET G be a semitopological semigroup, i. e. G is a semigroup with a Hausdorff topology such that for each s∈G the mapping s|→s·t and s|→t·s from G to G are continuous. G is called right reversible if any two closed left ideals of G have non-void intersection. In this case, (G,≤) is a directed system when the binary relation '≤' on G is defined by a≤b if and only if Let E be the uniformly convex Banach space

关键词： nonlinear semigroup ergodic theorem non-Lipschitzian mapping.

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, {2. of Science and Technology of China, Hefei 2.002., China 2. department of mathematics, Beijing normal {2., Beijing 100875, China 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.

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, China {2., South China normal university, Guangzhou 510631, China 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.

Density functional study on enantioselective reduction of keto oxime ether with borane catalyzed by oxazaborolidine

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Science China Chemistry 2006年第4期49卷 296-307页

作者： LI Ming1, ZHENG Wenxu2.& TIAN Anmin2.1. department of Chemistry, Southwest-China normal {2., Chongqing 400715, China 2. department of Chemistry, Sichuan {2., Chengdu 610064, China department of Chemistry Southwest-China Normal University Chongqing China department of Chemistry Sichuan University Chengdu China

The enantioselective reduction of keto oxime ether with borane catalyzed by oxazaborolidine is discussed by the density functional theory (DFT) method. The main intermediates and transition states for this reaction are optimized completely at the B3LYP/6-31g(d) level, and the transition states are verified by vibrational modes. As shown, the chirality-controlled steps for this re- action are the hydride transfer from borane to carbonyl carbon and oxime carbon of keto oxime ether, and the chirality for the reduced products is determined in these two reaction steps. In all examined reaction paths, the first hydride is transferred via a six-membered ring and the second hydride via a five-membered ring or a four-membered ring.

关键词： keto oxime ether, oxazaborolidine, enantioselective reduction, DFT.

Boundedness of solutions and existence of invariant tori for generalized pendulum type equation

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Chinese Science Bulletin 1997年第20期42卷 1673-1675页

作者： HUANG Hai and YUAN Rong1. Institute of mathematics, Chinese Academy of Sciences, Beijing 100080, China 2. department of mathematics, Beijing {2. university, Beijing 100875, China Institute of mathematics Chinese Academy of Sciences Beijing China department of mathematics Beijing Normal University Beijing China

MOTIVATED by various significant applications to non-Newtonian fluid theory, diffusion offlows in porous media, nonlinear elasticity, and theory of capillary surfaces, several authors(see refs.[1,2. and references cited therein ) have recently studied the existence of periodicsolutions and other properties for the following differential equation:

关键词： boundeduess of solutions invariant tori quasiperlodic solutions Moser’s small twist theorem.

Effects of annealing on structural, optical and electrical properties of Al-doped ZnO thin films

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Science China(Physics,Mechanics & Astronomy) 2004年第5期47卷 588-596页

作者： CHEN Yanwei1,2. YU Wenhua1 & LIU Yichun1,2.1. Centre for Advanced Optoelectronic Functional Material Research, northeast normal university, changchun 13.02., China 2. Key Laboratory of Excited State Processes, {2. Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, changchun 13.02., China Centre for Advanced Optoelectronic Functional Material Research Northeast Normal University Changchun China Key Laboratory of Excited State Processes Changchun Institute of Optics Fine Mechanics and Physics Chinese Academy of Sciences Changchun China

In this paper, the structural, electrical and optical properties of Al-doped zinc oxide (ZnO: Al) thin films onto quartz substrates prepared by electron beam evaporation technique were studied. All samples are polycrystal with a hexagonal structure andc-axis preferred orientation. The intense UV emissions and weak deep-level green emissions were observed. The films show high transparency, conductivity and high carrier concentration. Van der Pauw measurements show that the films are n-type degenerate semiconductor. The lowest resistivity is 6.7×10?4 Ω⊙cm at room temperature. These films exhibit a carrier density above 102. cm?3. The conduction mechanism was discussed. The behavior of metallic conduction can be observed in the high temperature range.

关键词： ZnO: Al thin film, photoluminescence, electrical properties, structural properties, Van der Pauw measurement.

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 {2. university,Wuhan 430079,China 2.department of mathematics,East China {2. university,Shanghai 2.02.1,China department of mathematics and Statistics Huazhong Normal University Wuhan China department of mathematics East China Normal University Shanghai 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

The influence of laser pulse on the photoabsorption spectra of Li atom in strong external field

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Science China(Physics,Mechanics & Astronomy) 2006年第2期49卷 178-186页

作者： WANG Dehua1 & LIN Shenglu2.1. School of Physics and Electronic Engineering, Yantai normal university, Yantai 2.402., China 2. {2. of Physics, Shandong normal university, Jinan 2.0014, China School of Physics and Electronic Engineering Yantai Normal University Yantai China department of Physics Shandong Normal University Jinan China

Using the time-dependent perturbation theory and the calculation formula of the single- and double-pulse absorption spectra of the atom in strong external fields, we calculate the single- and double-pulse absorption spectra of Li atom in strong magnetic field for different pulse widths. The results show that a pulse of some width can reduce the contribution of the short period closed orbits and eliminate the contribution of the long period orbits. Compared with the single-pulse absorption spectra, we found that for some phase differences, the double-pulse laser absorption spectra are strengthened; while for others, they are reduced. Therefore, we can use the pulse laser to control the oscillation of the absorption spectra and obtain the optimization object.

关键词： laser pulse closed orbit absorption spectra.

LARGE TIME BEHAVIOR OF SOLUTIONS TO NEWTONIAN FILTRATION EQUATIONS WITH SOURCES

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Acta Mathematica Scientia 2010年第3期30卷 968-974页

作者：王路生尹景学王泽佳 department of mathematics Jilin University department of mathematics South China Normal University

This article is concerned with large time behavior of solutions to the Neumann or Dirichlet problem for a class of Newtonian filtration equations ｜x｜λ＋Эt^-Эu=div（｜x｜^k∨u^m）＋｜x｜λ＋ku^p with 0 〈 m 〈 1,p 〉 1,λ≥0, k ∈ R. An interesting phenomenon is that there exist two thresholds k∞ and kl for the exponent k, such that the critical Fujita exponent pc for p exists and is finite if k E （k∞, k1）, otherwise, pc is infinite or does not exist.

关键词： Newtonian filtration equation critical exponent exterior problem Thresh -old