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QR factorization for row or column symmetric matrix

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Science China Mathematics 2003年第1期46卷 83-90页

作者：邹红星戴琼海李衍达王殿军 Department of Automation Tsinghua University Department of Mathematical Sciences Tsinghua University

The problem of fast computing the QR factorization of row or column symmetric matrix isconsidered. We address two new algorithms based on a correspondence of Q and R matrices between the rowor column symmetric matrix and its mother matrix. Theoretical analysis and numerical evidence show that, fora class of row or column symmetric matrices, the QR factorization using the mother matrix rather than therow or column symmetric matrix per se can save dramatically the CPU time and memory without loss of anynumerical precision.

关键词： QR factorization, row or column symmetric matrix, fast computation.

The density matrix picture of laser coherent control current

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Science China(Physics,Mechanics & Astronomy) 2004年第2期47卷 231-243页

作者： SHOU Qian ZHANG Haichao LIU Luning LIN Weizhu State Key Laboratory of Optoelectronic Materials and Technologies Zhongshan (Sun Yat-Sen) UniversityGuangzhou 510275 China State Key Laboratory of Optoelectronic Materials and Technologies Zhongshan (Sun Yat-Sen) UniversityGuangzhou 510275 China State Key Laboratory of Optoelectronic Materials and Technologies Zhongshan (Sun Yat-Sen) UniversityGuangzhou 510275 China State Key Laboratory of Optoelectronic Materials and Technologies Zhongshan (Sun Yat-Sen) UniversityGuangzhou 510275 China

The physical substance of the coherent control current and the optical rectification have been analyzed based on density matrix perturbation theory. The analytical results demonstrate that they arise from the real and virtual manifestations of the same nonlinear process associated with diagonal and non-diagonal density matrix. And in terms of polarization, they respectively arise from the intraband and interband polarizations. Both the evolution of the coherent control current exited by ultrafast laser pulse and its dependence on frequency have been studied in time and frequency domains. In order to get an explicit knowledge of intraband polarization and the origination of the coherent control current, we have investigated the initial photo-carriers momentum distribution. The ultrafast decay of the polar momentum population in order of tens of femtosends is given to illustrate its instantaneous optical response.

关键词： density matrix, Feynman diagrams, coherent control current, intraband polarization.

Application of the Conditional Inverse matrix Theory for Estimation of Origin-Destination Trip Matrices from Link Traffic Flows

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Journal of Traffic and Transportation Engineering 2014年第1期2卷 19-35页

作者： Chung-Yung Wang Jia-Wun Zhang Department of Logistics Management Management College of National Defense University Taipei 11258 Taiwan Republic ofChina

This study focuses on estimating O-D （origin-destination） trip demand from link traffic flows. Equality relationship among link traffic flow, path flow, and O-D trip matrices are used to establish a linear equation system. Solution characteristics are analyzed based on the relationship between the rank of the link/path incidence matrix and column variables. And under the solution framework of conditional inverse matrices, a column exchange method and a path flow proportion method have been developed. Network testing results verify that the proposed methods yield good results.

关键词： O-D trip demand, conditional inverse matrix, column exchange method, path flow proportion method.

LEVERRIER-LAGUERRE ALGORITHM FOR THE matrix POLYNOMIAL OF DEGREE TWO

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Numerical Mathematics A Journal of Chinese Universities(English Series) 2002年第2期11卷 226-234页

作者：吴筑筑郑兵王国荣 Dept. of Comput. Dept. of comput. Institute of Math. Sci.

An algorithm for simultaneous computation of the adjoint G(s) and determinant d(s) of the matrix polynomial s2J-sA 1-A 2 is presented, where J is a singular matrix. Both G(s) and d(s) are expressed relative to a basis... 详细信息

关键词： adjoint, determinant, inverse matrix, orthogonal polynomial.

The limiting theorems of random quadratic forms and their application

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Science China Mathematics 2005年第4期48卷 493-502页

作者： PAN Guangming MIAO Baiqi TAN Changchun Department of Statistics and Finance University of Science and Technology of China Hefei230026 China Department of Statistics and Finance University of Science and Technology of China Hefei230026 China Department of Statistics and Finance University of Science and Technology of China Hefei230026 China

The strong convergence and convergence rate of the random quadratic formss1T(S1S1T)ms1 and s1T(SST)ms1 are set up. The application of these results in wireless communication is given. Simulation results are presented.

关键词： random quadratic forms, large dimensional matrix, martingale difference, strong convergence.

Nonlinear balance constraints in 3DVAR data assimilation

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Science China Earth Sciences 2006年第3期49卷 331-336页

作者： ZHU Jiang YAN Changxiang International Center for Climate and Environment Sciences Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China International Center for Climate and Environment Sciences Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China

In many applications of 3DVAR, the balance constraints can be considered via two main approaches: weak constraint method which adds penalty terms to the cost function; and proper defi- nition of the background error covariance matrix with non-zero cross-correlation sub-matrices. The weak constraint approach requires determining the weighting matrices of the penalty terms. The background error covariance approach does not require determining those additional weighting ma- trices. However, it is only applicable to those linear or linearized balance constraints. A novel ap- proach is proposed based on the background error covariance approach by generalizing the so-called Derber-Bouttier formulation. An assimilation experiment of estimating temperature and salinity from the sea surface dynamic height observation is given to illustrate the proposed treatments of nonlinear balance constraints.

关键词： 3DVAR, linear balance constraint, nonlinear balance constraint, background error covariance matrix, sea surface dynamic height.

A new method for spatio-temporal prediction of rainfall-induced landslide

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Science China Earth Sciences 2006年第4期49卷 421-430页

作者： DING Jixin1,2, YANG Zhifa2, SHANG Yanjun2, ZHOU Shenghua1 & YIN Juntao3 1. China Non-ferrous Metals Resource Geological Survey, Beijing 100012, China 2. Institute of Geology and Geophysics, Chinese Academy of Sciences, Key Laboratory of Engineering Geomechanics, Beijing 100029, China 3. School of Geoscience & Environmental Engineering, Central South University, Changsha 410083, China China Non-ferrous Metals Resource Geological Survey Beijing China Institute of Geology and Geophysics Chinese Academy of Sciences Key Laboratory of Engineering Geomechanics Beijing China School of Geoscience & Environmental Engineering Central South University Changsha China

Geological condition and rainfall are two most principal conditions inducing landslides in the Chongqing region. By analyzing the forming conditions of rainfall-induced landslides, a new method for spatio-temporal prediction of rainfall-induced landslide is brought forward on the basis of grading and overlapping geological condition and rainfall factor in this paper. At first, semi-quantitative assessment and grading for the geological condition of a certain area or slope can be carried out with the multi-factor interactive matrix. Then the severity of rainfall in that area is grading according to the maximum daily rainfall and the total rainfall in a rainfall course. Finally, the “landslide probability judgement factor” can be worked out through grading and overlapping “geological condition influenc- ing factor” and “rainfall influencing factor”, by which the landslide can be graded into 4 grades, they are landslide extremely easily happening, landslide easily happening, landslide difficultly happening and landslide hardly ever happening respectively. More accurate spatio-temporal prediction of rain- fall-induced landslides can come true on the ground of detailed geological survey of some dangerous slopes in an area and more precise weather forecast. Finally, the reliability and feasibility of carrying out the spatio-temporal prediction of rainfall-induced landslides with the method of “two factors” grading and overlapping are validated by the example of Jipazi landslide.

关键词： rainfall-induced landslide, geological condition, rainfall, two factors, grading and overlapping, interactive matrix, spatio-temporal prediction.

Geometry of 2×2 hermitian matrices

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Science China Mathematics 2002年第8期45卷 1025-1037页

作者：黄礼平万哲先 Institute of Mathematics Xiangtan Polytechnic University Xiangtan China Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China Center for Combinatorics Nankai University Tianjin China

LetD be a division ring which possesses an involution a → α . Assume that $F = \{ a \in D|a = \overline a \} $ is a proper subfield ofD and is contained in the center ofD. It is pointed out that ifD is of characteristic not two, D is either a separable quadratic extension of F or a division ring of generalized quaternions over F and that if D is of characteristic two,D is a separable quadratic extension ofF. Thus the trace map Tr:D → F, a → a + a is always surjective, which is formerly posed as an assumption in the fundamental theorem of n×n hermitian matrices overD when n ≥ 3 and now can be deleted. WhenD is a field, the fundamental theorem of 2 × 2 hermitian matrices overD has already been proved. This paper proves the fundamental theorem of 2×2 hermitian matrices over any division ring of generalized quaternions of characteristic not two

关键词： division ring, involution, generalized quaternion, hermitian matrix, adjacency.

Retrievals of underlying surface roughness and moisture from polarimetric pulse echoes in the specular direction through inhomogeneous vegetation canopy

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Science China(Technological Sciences) 2003年第1期46卷 71-81页

作者：金亚秋陈扉常梅 Center for Wave Scattering and Remote Sensing and School of Information Science and Engineering Fudan Univer-sity Shanghai 200433 China

The time-dependent Mueller matrix solution of vector radiative transfer for inhomoge-neous random media of non-spherical scatterers is presented. Co-polarized and cross-polarized bistatic scatterings for a polarized pulse incidence are numerically simulated. Numerical results well demonstrate volumetric and surface scattering mechanism and depict the inhomogeneous fraction profile of random scatterers. The peak tails in polarized echoes due to wave reflections from the underlying surface can be identified. Its co-polarized peaks in the specular direction are applied to simultaneous retrievals of the underlying surface roughness and moisture in the pres-ence of inhomogeneous vegetation canopy.

关键词： retrieval of roughness and moisture, vegetation canopy, polarimetric scattering, temporal Mueller matrix, pulse incidence.