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ON THE LEAST SQUARES PROBLEM OF A MATRIXEQUATION

第七届海内外青年设计与制造科学会议

作者： Hou Zhixiang, Wu Yihu and Yu Dan college of Automobile and Mechanical Engineering, changsha university of science and technology, china college of information science and engineering, Central South university, china college of traffic and transportation, changsha university of science and technology, china

＜正＞Air fuel ratio accurate control is a key index decreasing emission and fuel consumption of gasoline engine, and its accurate control is very difficulty, especial under transient conditions. The composite air fuel ratio control strategy based on neural networks is advocated in this paper, where feedback control is achieved by means of regular PI controller to ensure the system stability and anti-disturbance, and feedforward control is achieved by virtue of neural networks controller to enhance response ability of control system under transient conditions. Radius basis function neural network whose inputs are the engine rotation speed and the throttle degree which are the two chief factors affecting engine admission volume is adopted. Overall control output of the system is generated by neural networks through on line study the output of PI controller. The system can effectively avoid the present defects elicited by enormous calibration to accurate control air fuel ration under transient condition with fair self-adaptability. The simulation was finished using experiment data of HL495 gasoline engine, and the results show the effectiveness of this control method.

关键词： Gasoline engine Mean value model Transient condition Air fuel ratio control Neural networks

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Journal of Computational Mathematics 1999年第6期17卷 589-594页

作者： An-ping Liao(college of science, Hunan Normal university, changsha 410081, china) 湖南师范大学理学院湖南长沙 410081

Least squares solution of F=PG with respect to positive semidefinite symmetric P is considered,a new necessary and sufficient condition for solvablity is given,and the expression of solution is derived in the some special cases. Based on the expression, the least spuares solution of an inverse eigenvalue problem for positive semidefinite symmetric matrices is also given.

关键词： least squares solution matrix equation inverse eigenvalue problem positive semidefinite symmetric matrix

Survival probability and ruin probability of a risk model

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Applied Mathematics(A Journal of Chinese Universities) 2008年第3期23卷 256-264页

作者： LUO Jian-hua college of science,Central South university of Forestry and technology,changsha 410004,china Institute of Statistics,Central South university of Forestry and technology,changsha 410004,china. college of science Central South University of Forestry and Technology Changsha China Institute of Statistics Central South University of Forestry and Technology Changsha China

In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning process. The integral representations of the survival probability are gotten. The explicit formula of the survival probability on the infinite interval is obtained in the special casc cxponential *** Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory.

关键词： risk model thinning process survival probability martingale ruin probability integral representation

IMPULSIVE BOUNDARY VALUE PROBLEMS FOR STURM-LIOUVILLE TYPE DIFFERENTIAL INCLUSIONS

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Journal of Systems science & Complexity 2007年第3期20卷 370-380页

作者： Yicheng LIU Jun WU Zhixiang LI Department of Mathematics and Systems science College of Science National University of Defense Technology Changsha 410073 China. college of Mathematics and Computer science Changsha University of Science Technology Changsha 410076 China.

In this paper, the authors investigate the existence of solutions of impulsive boundary value problems for Sturm-Liouville type differential inclusions which admit non-convex-valued multifunctions on right hand side. Two results under weaker conditions are presented. The methods rely on a fixed point theorem for contraction multi-valued maps due to Covitz and Nadler and Schaefer＇s fixed point theorem combined with lower semi-continuous multi-valued operators with decomposable values.

关键词： Boundary value problems contraction multi-valued map impulsive differential inclusions,measurable selection.

Heteroclinic orbits and heteroclinic chains for a discrete Hamiltonian system

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science china Mathematics 2010年第6期53卷 1555-1564页

作者： ZHANG Hao & LI ZhiXiang Department of Mathematics and Systems science,college of science,National university of Defense technology,changsha 410073,china Department of Mathematics and Systems science College of Science National University of Defense Technology

In the present work we prove some existence results of heteroclinic orbits and heteroclinic chains for a second order discrete Hamiltonian system of the form Δ2q(t-1)+V(q(t))=0,t∈*** methods we use are variational in *** results show that under general conditions,for each maximum point β of V,the above system possesses multiple heteroclinic orbits joining β and some other maximum points of *** also prove that for any pair of distinct maximum points η and ξ of V,there exists at least one heteroclinic chain from η to ξ.

关键词： difference equation heteroclinic orbit heteroclinic chain variational method

A DISCRETE CHARACTERIZATION OF HERZ-TYPE TRIEBEL-LIZORKIN SPACES AND ITS APPLICATIONS

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Acta Mathematica Scientia 2004年第3期24卷 412-420页

作者： XuJingshi DepartmentofMathematics HunanUniversityChanysha410082China

In this paper, the author establishes a discrete characterization of the Herz-type Triebel-Lizorkin spaces which is used to prove the boundedness of pseudo-differential operators on these function spaces.

关键词： Herz-type space Triebel-Lizorkin space discrete characterization pseudo-differential operator maximal operator

A New Clustering Algorithm for Categorical Attributes

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International Journal of Minerals,Metallurgy and Materials 2000年第4期14卷 318-322页

作者： Songfeng Lu, Zhengding Lu (college of Computer science and technology, Huazhong university of science and technology, Wuhan 430074, china) college of Computer science and technology Huazhong University of Science and Technology Wuhan 430074 China

In traditional data clustering, similarity of a cluster of objects is measured by distance between objects. Such measures are not appropriate for categorical data. A new clustering criterion to determine the similarity between points with categorical attributes is pre- sented. Furthermore, a new clustering algorithm for categorical attributes is addressed. A single scan of the dataset yields a good clus- tering, and more additional passes can be used to improve the quality further.

关键词： data mining clustering similarity Information

Fluorometric enzyme immunosensing system based on natural product resveratrol for horseradish peroxidase and Ag/SiO_2 nanoparticles

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science china Chemistry 2008年第3期51卷 233-240页

作者： GONG FuChun, CAO Zhong, TAN ShuZhen, TAN YaFei & HE XiaoChun college of Chemistry and Environmental Engineering, changsha university of science and technology, changsha 410076, china college of Chemistry and Environmental Engineering Changsha University of Science and Technology Changsha China

The properties of resveratrol (3′, 4′, 5-trihydroxystlbene, RST) were for the first time evaluated as a potential substrate for horseradish peroxidase (HRP)-catalyzed fluorogenic reaction. The properties of RST for use as fluorogenic substrates for HRP and its application in immunoassays were compared with commercially available substrates such as p-hydroxyphenylpropionic acid (pHPPA), chavicol and Amplex red by a fluoroimmunosensing method in the use of Schistosomia japonicum antibody (SjAb) as a model analyte. The fluoroimmunosensing device was constructed by dispersing Schistosomia japonicum antigen (SjAg), nano-Ag/SiO2 particles and sol-gel at low temperature. In pH 5.8 Britton-Robinson buffer (B-R), HRP-SjAb conjugates can catalyze the polymerization reaction of RST by H2O2 forming fluorescent dimmers. The increase of the fluorescence intensity of the dimmers product at emission of 462 nm (excitation: 315 nm) is proportional to the concentration of HRP-SjAb binding to the SjAg entrapped in the nano-Ag/SiO2 particles-sol-gel matrix. A competitive binding assay has been used to determine SjAb in rabbit serum with the aid of SjAb labeled with HRP. Substrate RST showed comparable ability for HRP detection and its enzyme-linked immunosensing reaction system, in a linear detection ranging of 1.5×10-6-7.3×10-4 g/L and with a detection limit of 1.5×10-6 g/L. The immobilized biocomposites surface could be regenerated by simply polishing with an alumina paper, with an excellent reproducibility (RSD = 4.7%). The proposed method has been successfully used for analysis of the rabbit serum sample with satisfactory results.

关键词： resveratrol HRP fluorogenic substrate Ag/SiO2 nanoparticles enzyme-linked immunosensing Schistosomia japonicum

New interpretation of laser gyro drifts

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science china(Technological sciences) 2010年第5期53卷 1168-1175页

作者： GAO BoLong,ZHANG Mei & ZHANG Wen college of Opto-electric science and Engineering,National university of Defense technology,changsha 410073,china college of Opto-electric science and Engineering National University of Defense Technology

Discuss and develop some contents which are relevant to the IEEE Std 647TM-2006 in this paper. The IEEE Std only involves Allan variance, and decomposes it into five primary noise terms, in which, however, the noise nature of the so called "rate random walk noise" and the "rate ramp" is doubted by the IEEE Std editors. Here we use a mathematical identity to entirely affirm the first query and partially the second query as mentioned above. Besides, we argue that only the classical variance can be used in navigation, not the Allan variance. In order to seek the true nature of all drift terms in the variance, we adopt our original work that represents the noises as damped oscillations, to obtain the power spectral density (PSD) of the noises which is then transformed back into time domain. When the damped time constant is much longer than the sampling interval, the re-sulting slow variation term may be expanded into three terms: ordinary bias instability, rate random walk, and rate ramp. Therefore, these "noise terms" are not independent, and they are more of deterministic errors than random noises, and can be explained quantitatively. The resulting fast variation drift may be expanded into two terms. The first term is the same as angle random noise, while the second term adds to the true quantization noise term to form a new combined term called "quantiza-tion noise term". As the result of our research, not only the IEEE Std editors’ suspicions above are answered completely, but a new theory to analyze the laser gyro drifts is also presented, with several supporting examples to explain and verify the theory.

关键词： allan variance classical variance drift laser gyro