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Pole assignment in descriptor periodic systems

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Science china mathematics 2005年第10期48卷 1309-1332页

作者： FAN Hung-Yuan~1 LIN Wen-Wei~1 & XU Shufang~2.1. department of mathematics,Tsing Hua University,Hsinchu 30043,{2. 2. LMAM,School of Mathematical Sciences,Peking University,Beijing 100871,{2. 1. department of mathematics Tsing Hua University 30043 Hsinchu China 2. LMAM School of Mathematical Sciences Peking University 100871 Beijing China

In this paper a pole assignment problem is considered for the descriptor linear discrete-time periodic systems, which is using the periodic proportional-derivative feedback to modify a given system such that the closed loop system has a specified selfconjugate set of eigenvalues. It is shown that the complete reachability of an open loop periodic system is equivalent to the possibility of assigning an arbitrary set of the eigenvalues to the system by choosing the suitable periodic proportional-derivative feedback.A computational approach is also proposed to solve the problem, which uses the reliable numerical techniques based on the orthogonal transformations. Numerical examples are presented to illustrate the effectiveness of the proposed approach.

关键词： descriptor linear periodic system, pole assignment, proportional and derivative feedback, numerical method, periodic Schur decomposition.

Assessment of biochemical concentrations of vegetation using remote sensing technology

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Journal of Geographical Sciences 2002年第3期12卷 321-330页

作者： DING Shengyan, GU Jidong, QIAN Lexiang(1. College of Environment and Planning, henan University, kaifeng 475001,{2. 2. department of Ecology & Biodiversity, The University of Hong Kong, Hong Kong,{2.) College of Environment and Planning Henan University Kaifeng 475001 department of Ecology & Biodiversity The University of Hong Kong 香港

The main biochemicals (such as lignin, protein, cellulose, sugar, starch, chlorophyll and water) of vegetation are directly or indirectly involved in major ecological processes, such as the functions of terrestrial ecosystems (i.e., nutrient-cycling processes, primary production, and decomposition). Remote sensing techniques provide a very convenient way of data acquisition capable of covering a large area several times during one season, so it can play a unique and essential role provided that we can relate remote sensing measurements to the biochemical characteristics of the Earth surface in a reliable and operational way. The application of remote sensing techniques for the estimation of canopy biochemicals was reviewed. Three methods of estimating biochemical concentrations of vegetation were included in this paper: index, stepwise multiple linear regression, and stepwise multiple linear regression based on a model of the forest crown. In addition, the vitality and potential applying value are stress

关键词： biochemicals vegetation remote sensing techniques

Some Invariant Properties of Semi-symmetric Metric Recurrent Connections and Curvature Tensor Expressions

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Chinese Quarterly Journal of mathematics 2004年第4期19卷 355-361页

作者： ZHAO Pei-biao, SONG Hong-zao, YANG Xiao-ping(1. department of Applied mathematics, Nanjing University of Science and Technology, Nanjing 2.0094,{2. 2. College of Mathematic and Information Science, henan University , kaifeng 475001,{2.) department of Applied mathematics Nanjing University of Science and Technology Nanjing 210094China College of Mathematic and Information Science Henan University Kaifeng 475001 China

The projective transformation of the special semi-symmetric metric recurrent connection is studied in this paper. First of all, an invariant under this transformation is granted; Secondly, by inducing of the invariant and making use of the properties that the corresponding covariant derivative keeps being fixed under the distinctness connection, the curvature tensor expression of the Riemannian manifold is posed at the same time.

关键词： projective transformation semi-symmetric metric connection metric recurrent connection invariant curvature tensor expression covariant derivative

Direct numerical simulation of a supersonic turbulent boundary layer on a flat plate and its analysis

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Science china(Physics,Mechanics & Astronomy) 2005年第5期48卷 626-640页

作者： HUANG Zhangfeng1, ZHOU Heng1,2.& LUO Jisheng1,2.1. department of Mechanics, Tianjin University, Tianjin 300072. china 2. Liu-Hui Center of Applied {2., Nankai University and Tianjin University, Tianjin 300072. china 1. department of Mechanics Tianjin University 300072 Tianjin China 2. Liu-Hui Center of Applied mathematics Nankai University and Tianjin University 300072 Tianjin China

Temporal mode direct numerical simulation (DNS) has been done for a supersonic turbulent boundary layer on a flat plate with Mach number 4.5. It was found that the mean flow profile, the normal-wise distribution of turbulent Mach number and the root mean square (RMS) of the fluctuations of various variables, as well as the Reynolds stresses, bore similarity in nature, when the turbulence reached a fully developed state. But the compressibility effect was strong and must be considered. The strong Reynolds analogy (SRA) and the Morkovin hypothesis were no longer valid. From the end of transition to the fully developed state of turbulence, it was in the transient period, for which the similarity did not hold.

关键词： turbulence, similarity, compressibility effect, supersonic boundary layer, direct numerical simulation.

Estimates for eigenvalues of Laplacian operator with any order

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Science china mathematics 2007年第8期50卷 1078-1086页

作者： Fa-en WU~(1+) Lin-fen CAO~2.1 department of mathematics,Beijing Jiaotong University,Beijing 100044,{2. 2.department of mathematics,henan Normal University,Xinxiang 453007,{2. department of mathematics Beijing Jiaotong University Beijing 100044 China department of mathematics Henan Normal University Xinxiang 453007 China

Let D be a bounded domain in an n-dimensional Euclidean space ? n . Assume that $$0 < \lambda _1 \leqslant \lambda _2.\leqslant \cdots \leqslant \lambda _k \leqslant \cdots $$ are the eigenvalues of the Dirichlet Lapl... 详细信息

Let D be a bounded domain in an n-dimensional Euclidean space ? n . Assume that $$0 < \lambda _1 \leqslant \lambda _2 \leqslant \cdots \leqslant \lambda _k \leqslant \cdots $$ are the eigenvalues of the Dirichlet Laplacian operator with any order l: $$\left\{ \begin{gathered} ( - \vartriangle )^l u = \lambda u, in D \hfill \\ u = \frac{{\partial u}}{{\partial \vec n}} = \cdots = \frac{{\partial ^{l - 1} u}}{{\partial \vec n^{l - 1} }} = 0, on \partial D \hfill \\ \end{gathered} \right.$$ . Then we obtain an upper bound of the (k+1)-th eigenvalue λ k+1 in terms of the first k eigenvalues. $$\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )} \leqslant \frac{1}{n}[4l(n + 2l - 2)]^{\tfrac{1}{2}} \left\{ {\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{1}{2}} \lambda _i^{\tfrac{{l - 1}}{l}} \sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{1}{2}} \lambda _i^{\tfrac{1}{l}} } } } \right\}^{\tfrac{1}{2}} $$ . This ineguality is independent of the domain D. Furthermore, for any l ? 3 the above inequality is better than all the known results. Our rusults are the natural generalization of inequalities corresponding to the case l = 2 considered by Qing-Ming Cheng and Hong-Cang Yang. When l = 1, our inequalities imply a weaker form of Yang inequalities. We aslo reprove an implication claimed by Cheng and Yang.

关键词： Dirichlet problem eigenvalue estimate Laplacian operator 35P15 58G2.

A Note on the Multifractal Decomposition of Directed Graph Self Similar Sets

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Wuhan University Journal of Natural Sciences 2004年第3期9卷 269-272页

作者： Zheng Shui-cao 1,2., Hu Di-he 1 1. School of mathematics and Statistics, Wuhan University , Wuhan 430072. Hubei, china 2. The Basic Teaching {2., Jimei University, Xiamen 36102., Fujian, china Wuhan University School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***) Jimei University The Basic Teaching Department Xiamen Fujian China (GRID:grid.411902.f) (ISNI:***) Wuhan University School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***)

We investigated the directed graph self similar sets under some weak overlapping condition. We get the multifractal decomposition formulas for these sets, i. e., dimK u a =DimK u a =f(a), wheref is the multifractal spectral function of the directed graph self similar measure, Especially, the results improve that of Edgar and Mauldin to the case which allows certain overlapping. Key words Hausdorff dimension - Hausdorff measure - multifractal decomposition CLC number O 2.1. 6 Foundation item: Supported by the National Natural Science Foundation of china (10371092. and the Foundation of Wuhan UniversityBiography: Zheng Shui-cao (1973-), male, Ph. D candidate, research direction: stochastic processes and random fractals.

关键词： Hausdorff dimension Hausdorff measure multifractal decomposition

Quasirational dynamic system

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Chinese Science Bulletin 2000年第14期45卷 1277-1279页

作者： SUN Daochun & YANG Lo1. department of mathematics, South{2. Normal University, Guangzhou 510631,{2. 2. Institute of mathematics, Academy of mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080,{2. department of mathematics South China Normal University Guangzhou China Institute of mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

Using the iterations of quasirational mappings, the theorems on dynamic system are generalized to the quasirational dynamic system. Some different results are also obtained.

关键词： quasirational mapping dynamic system covering surface.

Uniform estimate for maximum of randomly weighted sums with applications to insurance risk theory

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Science china mathematics 2005年第10期48卷 1379-1394页

作者： WANG Dingcheng~1 SU Chun~2.& ZENG Yong~1 1. School of Management and School of Applied mathematics,University of Electronic Science and Technology of china,Chengdu 610054,{2. 2. department of Statistics and Finance,University of Science and Technology of china,Hefei 2.002.,{2. 1. School of Management and School of Applied mathematics University of Electronic Science and Technology of China 610054 Chengdu China 2. department of Statistics and Finance University of Science and Technology of China 230026 Hefei China

This paper obtains the uniform estimate for maximum of sums of independent and heavy-tailed random variables with nonnegative random weights, which can be arbitrarily dependent of each other. Then the applications to ... 详细信息

关键词： dependent stochastic return, discount factor, heavy-tails, discrete time insurance risk model, maxima of randomly weighted sums, ruin probability, tail probabilities, uniformly asymptotic estimate.

The proof of FFD(L)≤11/9OPT(L) +7/9

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Chinese Science Bulletin 1997年第15期42卷 1262-1265页

作者： LI Rongheng, YUE Minyi1. department of mathematics, Hunan Normal University, Changsha 410081,{2. 2. Institute of Applied mathematics, Chinese Academy of Sciences, Beijing 100080,{2. department of mathematics Hunan Normal University Changsha 410081 China Institute of Applied mathematics Chinese Academy of Sciences Beijing 100080 China

THE one-dimensional bin-packing problem is defined as follows: for a given list L={p1, p2.…, Pn}, where 0i≤1 denotes the item and its size as well, we are to pack all the items in-to bins, each of which has a capaci... 详细信息

THE one-dimensional bin-packing problem is defined as follows: for a given list L={p1, p2./sub>,…, Pn}, where 0i≤1 denotes the item and its size as well, we are to pack all the items in-to bins, each of which has a capacity 1, and the goal is to minimize the number of bins *** first-fit-decreasing （FFD） algorithm is a famous approximate algorithm for the bin-pack-ing problem. The FFD algorithm first sorts all the list into non-increasing order and then pro-cesses the pieces in that order by placing each item into the first bin into which it fits.

关键词： bin-packing minimal counter-example weigtht-function FFD-algorithm.