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Time eigenvectors and Their Applications

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Chinese Physics Letters 1992年第2期9卷 57-60页

作者： FENG Kaiyin HUANG Xiangyou CCAST(World Laboratory)and Department of Physics Peking UniversityBeijing 100871

Time eigenvectors and time operator are constructed from energy eigenvectors of *** features of them are *** applications to harmonic oscillating system and to double wave description of system are discussed.

关键词： system eigenvector oscillating

Primary component analysis method and reduction of seismicity parameters

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Acta Seismologica Sinica(English Edition) 2005年第5期18卷 68-77,132页

作者：王炜马钦忠林命周吴耿锋吴绍春 Earthquake Administration of Shanghai Municipality Shanghai 200062 China School of Computer Engineering and Science Shanghai University Shanghai 200072 China

In the paper, the primary component analysis is made using 8 seismicity parameters of earthquake frequency N (ML≥3.0), b-value, η-value, A(b)-value, Mf-value, Ac-value, C-value and D-value that reflect the characteristics of magnitude, time and space distribution of seismicity from different respects. By using the primary component analysis method, the synthesis parameter W reflecting the anomalous features of earthquake magnitude, time and space distribution can be gained. Generally, there is some relativity among the 8 parameters, but their variations are different in different periods. The earthquake prediction based on these parameters is not very well. However, the synthesis parameter W showed obvious anomalies before 13 earthquakes (MS≥5.8) occurred in North China, which indicates that the synthesis parameter W can reflect the anomalous characteristics of magnitude, time and space distribution of seismicity better. Other problems related to the conclusions drawn by the primary component analysis method are also discussed.

关键词： primary component analysis method data mining eigenvector contribution rate

INEXACT TWO-GRID METHODS FOR EIGENVALUE PROBLEMS

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Journal of Computational Mathematics 2015年第6期33卷 557-575页

作者： Qun Gu Weiguo Gao MOE Key Laboratory of Computational Physical Sciences and School of Mathematical Sciences Fudan Univecsity Shanghai 200433 China

We discuss the inexact two-grid methods for solving eigenvalue problems, including both partial differential and integral equations. Instead of solving the linear system exactly in both traditional two-grid and accelerated two-grid method, we point out that it is enough to apply an inexact solver to the fine grid problems, which will cut down the computational cost. Different stopping criteria for both methods are developed for keeping the optimality of the resulting solution. Numerical examples are provided to verify our theoretical analyses.

关键词： Inexact Two-grid Eigenvalue eigenvector Finite element method Conver-gence rate.

Total Graphs Are Laplacian Integral

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Algebra Colloquium 2022年第3期29卷 427-436页

作者： David Dolžan Polona Oblak Department of Mathematics Faculty of Mathematics and Physics University of LjubljanaJadranska 21SI-1000 LjubljanaSlovenia Facultyof Computerand Information Science University of Ljubljana Vecna pot 113SI-1000 LjubljanaSlovenia

We prove that the Laplacian matrix of the total graph of a finite commutative ring with identity has integer eigenvalues and present a recursive formula for computing its eigenvalues and *** also prove that the total graph of a finite commutative local ring with identity is super integral and give an example showing that this is not true for arbitrary rings.

关键词： eigenvalue eigenvector Laplacian matrix total graph Laplacian integral

Completeness of system of root vectors of upper triangular infinitedimensional Hamiltonian operators appearing in elasticity theory

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Applied Mathematics and Mechanics(English Edition) 2012年第3期33卷 385-398页

作者：王华阿拉坦仓黄俊杰 School of Mathematical Sciences Inner Mongolia University College of Sciences Inner Mongolia University of Technology

This paper deals with a class of upper triangular infinite-dimensional Hamilto- nian operators appearing in the elasticity theory. The geometric multiplicity and algebraic index of the eigenvalue are investigated. Furthermore, the algebraic multiplicity of the eigenvalue is obtained. Based on these properties, the concrete completeness formulation of the system of eigenvectors or root vectors of the Hamiltonian operator is proposed. It is shown that the completeness is determined by the system of eigenvectors of the operator entries. Finally, the applications of the results to some problems in the elasticity theory are presented.

关键词： upper triangular infinite-dimensional Hamiltonian operator eigenvector root vector multiplicity completeness

Principal component analysis using neural network

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Journal of Zhejiang University Science 2002年第3期3卷 298-304页

作者：杨建刚孙斌强 DepartmentofComputerScience&Engineering ZhejiangUniversityHangzhou310027China

The authors present their analysis of the differential equation d X(t)/ d t = AX(t)-X T (t)BX(t)X(t) , where A is an unsymmetrical real matrix, B is a positive definite symmetric real matrix, X ∈R n; showing that the equation characterizes a class of continuous type full feedback artificial neural network; We give the analytic expression of the solution; discuss its asymptotic behavior; and finally present the result showing that, in almost all cases, one and only one of following cases is true. 1. For any initial value X 0∈R n, the solution approximates asymptotically to zero vector. In this case, the real part of each eigenvalue of A is non positive. 2. For any initial value X 0 outside a proper subspace of R n, the solution approximates asymptotically to a nontrivial constant vector (X 0) . In this case, the eigenvalue of A with maximal real part is the positive number λ=‖(X 0)‖ 2 B and (X 0) is the corresponding eigenvector. 3. For any initial value X 0 outside a proper subspace of R n, the solution approximates asymptotically to a non constant periodic function (X 0,t) . Then the eigenvalues of A with maximal real part is a pair of conjugate complex numbers which can be computed.

关键词： PCA Unsymmetrical real matrix Eigenvalue eigenvector Neural network

Least H-eigenvalue of adjacency tensor of hypergraphs with cut vertices

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Frontiers of Mathematics in China 2020年第3期15卷 451-465页

作者： Yizheng FAN Zhu ZHU Yi WANG School of Mathematical Sciences Anhui UniversityHefei 230601China

Let G be a connected hypergraph with even uniformity,which contains cut *** G is the coalescence of two nontrivial connected sub-hypergraphs(called branches)at a cut *** A(G)be the adjacency tensor of *** least H-eigenvalue of A(G)refers to the least real eigenvalue of A(G)associated with a real *** this paper,we obtain a perturbation result on the least H-eigenvalue of A(G)when a branch of G attached at one vertex is relocated to another vertex,and characterize the unique hypergraph whose least H-eigenvalue attains the minimum among all hypergraphs in a certain class of hypergraphs which contain a fixed connected hypergraph.

关键词： Hypergraph adjacency tensor least H-eigenvalue eigenvector perturbation

Ozone Profile Retrieval from Satellite Observation Using High Spectral Resolution Infrared Sounding Instrument

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Advances in Atmospheric Sciences 2001年第5期18卷 959-971页

作者： Yanni Qu, Mitchell D. Goldberg and Murty Divakarla Research and Data System Corporation, 7833 Walker Dr Greenbelt. MD 20770 National Eivironment Satellite Data and Information Service, Office of Research and Application, World Weather Building. 5200 Auth Research and Data System Corporation Greenbelt USA National Environment Satellite Data and Information Service Office of Research and Application Camp Springs USA

This paper presents a preliminary result on the retrieval of atmospheric ozone profiles using an im- proved regression technique and utilizing the data from the Atmospheric InfraRed Sounder (AIRS), a hyper-spectral Instrument expected to be flown on the EOS-AQUA platform in 20D2. Simulated AIRS spectra were used to study the sensitivity of AIRS radiance on the tropospheric and stratospheric ozone changes, and to study the impact of various channel combinations on the ozone profile retrieval. Sensitivity study results indicate that the AIRS high resolution spectral channels between the wavenumber 650- 800 cm-1 provide very useful information to accurately retrieve tropospheric and stratospheric ozone pro- files eigenvector decomposition of AIRS spectra indicate that no more than 100 eigenvectors are needed to retrieve very accurate ozone profiles. The accuracy of the retrieved atmospheric ozone profile from the pres- ent technique and utilizing the AIRS data was compared with the accuracy obtained from current Advanced TIROS Operational Vertical Sounder (ATOVS) data aboard National Oceanic and Atmospheric Admini- stration (NOAA) satellites As expected, a comparison of retrieval results confirms that the ozone profile re- trieved with the AIRS data is superior to that of ATOVS

关键词： AIRS ATOVS Regression eigenvector Principal component

The Least Eigenvalue of Unicyclic Graphs with Application to Spectral Spread

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Algebra Colloquium 2022年第2期29卷 265-272页

作者： Jiming Guo Gege Zhang Zhiwen Wang Panpan Tong School of Mathematics East China University of Science and Technology Shanghai 200237China

Let U^(g)_(n)be the set of connected unicyclic graphs of order n and girth *** C(T_(1),T_(2),…,T_(g))∈U^(g)_(n)be obtained from a cycle v_(1)v_(2)…v_(g)v_(1)(in an anticlockwise direction)by identifying v_(i)with the root of a rooted tree T_(i)of order n_(i)for each i=1,2,…,g,where n_(i)≥1 and∑^(g)_(i=1)n_(i)=*** this note,the graph with the minimal least eigenvalue(and the graph with maximal spread)in C(T_(1),T_(2),…,T_(g))is determined.

关键词： adjacency matrix least eigenvalue eigenvector unicyclic graph