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GENERALIZED CONJUGATE A-ORTHOGONAL RESIDUAL SQUARED METHOD FOR COMPLEX NON-HERMITIAN LINEAR SYSTEMS

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Journal of Computational Mathematics 2014年第3期32卷 248-265页

作者： Jianhua Zhang hua dai Department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing 210016 China Department of Mathematics Anhui Science and Technology University Fengyang 233100 China Department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing 210016 China

Recently numerous numerical experiments on realistic calculation have shown that the conjugate A-orthogonal residual squared （CORS） method is often competitive with other popular methods. However, the CORS method, like the CGS method, shows irreg- ular convergence, especially appears large intermediate residual norm, which may lead to worse approximate solutions and slower convergence rate. In this paper, we present a new product-type method for solving complex non-Hermitian linear systems based on the bicon- jugate A-orthogonal residual （BiCOR） method, where one of the polynomials is a BiCOR polynomial, and the other is a BiCOR polynomial with the same degree corresponding to different initial residual. Numerical examples are given to illustrate the effectiveness of the proposed method.

关键词： Krylov subspace BiCOR method CORS method Complex non-Hermitianlinear systems.

ON SMOOTH LU DECOMPOSITIONS WITH APPLICATIONS TO SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS

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Journal of Computational Mathematics 2010年第6期28卷 745-766页

作者： hua dai Zhong-Zhi Bai Department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing 210016 China LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

We study the smooth LU decomposition of a given analytic functional A-matrix A（A） and its block-analogue. Sufficient conditions for the existence of such matrix decompositions are given, some differentiability about certain elements arising from them are proved, and several explicit expressions for derivatives of the specified elements are provided. By using these smooth LU decompositions, we propose two numerical methods for computing multiple nonlinear eigenvalues of A（A）, and establish their locally quadratic convergence properties. Several numerical examples are provided to show the feasibility and effectiveness of these new methods.

关键词： Matrix-valued function Smooth LU decomposition Pivoting Nonlinear eigenvalue problem Multiple eigenvalue Newton method.

ON EIGENVALUE BOUNDS AND ITERATION METHODS FOR DISCRETE ALGEBRAIC RICCATI EQUATIONS

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Journal of Computational Mathematics 2011年第3期29卷 341-366页

We derive new and tight bounds about the eigenvalues and certain sums of the eigenvalues for the unique symmetric positive definite solutions of the discrete algebraic Riccati equations. These bounds considerably improve the existing ones and treat the cases that have been not discussed in the literature. Besides, they also result in completions for the available bounds about the extremal eigenvalues and the traces of the solutions of the discrete algebraic Riccati equations. We study the fixed-point iteration methods for com- puting the symmetric positive definite solutions of the discrete algebraic Riccati equations and establish their general convergence theory. By making use of the Schulz iteration to partially avoid computing the matrix inversions, we present effective variants of the fixed-point iterations, prove their monotone convergence and estimate their asymptotic convergence rates. Numerical results show that the modified fixed-point iteration methods are feasible and effective solvers for computing the symmetric positive definite solutions of the discrete algebraic Riccati equations.

关键词： Discrete algebraic Riccati equation Symmetric positive definite solution Eigenvalue bound Fixed-point iteration Convergence theory.

High-resolution Absorption Spectra of Acetylene in 142.8-152.3 nm

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Chinese Journal of Chemical Physics 2008年第5期21卷 415-420页

作者： Ya-hua Hu Chen Zhen Jing-hua dai Xiao-guo Zhou Shi-lin Liu Hefei National Laboratory for Physical Sciences at Microscale Department of Chemical Physics University of Science and Technology of China Hefei 230026 China

The absorption spectra of acetylene molecules was measured under jet-cooled conditions in the wavelength range of 142.8-152.3 nm, with a tunable and highly resolved vacuum ultraviolet （VUV） laser generated by two-photon resonant four wave difference frequency mixing processes. Due to the sufficient vibrational and rotational cooling effect of the molecular beam and the higher resolution VUV laser, the observed absorption spectra exhibit more distinct spectral features than the previous works measured at room temperature. The major three vibrational bands are assigned as a C-C symmetry stretching vibrational progress （v2=0.2） of the C^1Πu state of acetylene. The observed shoulder peak at 148,2 nm is assigned to the first overtone band of the trans-bending mode V4 of the C^1Πu state of acetylene. Additionally, the two components, 4^20（μ^1Π） and 4^20（k^1Πu）, are suggested to exhibit in the present absorption spectra, due to their Renner-Teller effect and transition selection rule. All band origins and bandwidths are obtained subsequently, and it is found that bandwidths are broadened and lifetimes decrease gradually with the excitation of vibration.

关键词： Acetylene Vacuum ultraviolet Absorption spectrum

Riddled Basin of Laser Cooled-Ions in a Paul Trap

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Chinese Physics Letters 1996年第2期13卷 81-84页

作者： SHEN Jing-ling YIN hua-wei dai Jian-hua ZHANG Hong-jun Optical Physics Laboratory Institute of PhysicsAcademia SinicaBeijing 100080

Recently it has been found that the entire basin of a given attractor is riddled with"lioles^leading to another *** we present the first physical system-the laser cooled ions in a Paul trap that exhibits riddled basin... 详细信息

关键词： attractor. Paul laser

Hand-assisted laparoscopic surgery of abdominal large visceral organs

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World Journal of Gastroenterology 2006年第29期12卷 4736-4740页

作者： Li-hua dai Bo Xu Guang-Hui Zhu Department of Surgery The First Hospital of Guangzhou Guangzhou 510180 Guangdong Province China

AIM： To design a hand-assisted laparoscopic approach in an attempt to provide an option for laparoscopic resection of abdominal large viscera. METHODS： A 5-6 cm incision （for HandPort） and 2 trocars were employed. The main vessel of the target organ was taken as a ＂core＂, and all tissues around the core were taken as peripheral structures. The peripheral structures were dissected first, and the core vessels were treated last. Twenty-six patients underwent laparoscopic deroofing of the hepatic huge cysts, resection of the segments lying at the outer edge of the liver （segments 2 to 6）, splenectomy, hemicolectomy, ileocecectomy and subtotal gastrectomy with HandPort device, harmonic scalpel, or Ligasure. RESULTS： The duration of the procedure was within 2 hours. Blood loss amounted to 8-120 mL. The conversion rate was 3.8% （1/26）. All patients had uneventful postoperative courses with less pain, earlier oral intake, and faster recovery, compared with conventional surgery. CONCLUSION： This method combines the advantages of both open and laparoscopic techniques, achieving better hemostasis effect, shortening the operative time, and is beneficial to the patients.

关键词： Minimally invasive surgery, Hand-assistedlaparoscopic surgery Hepatic segmentectomy,Hemicolectomy Subtotal gastrectomy

Comparisons of EVD and DVD

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The Journal of China Universities of Posts and Telecommunications 2006年第2期13卷 74-78页

作者： YAN Ming dai Jian-hua HU Guo-rong GxSOC Research Institute Communication University of China Beijing 100024 P.R. China

The goal of the Enhanced Versatile Disc （EVD） standard is to define an advanced high definition disc competing with Digital Versatile Disc （DVD）. The EVD standard consists of the physical specification, the file system .specification, and the specification for audio/video data and Enhanced （ x ） Audio Coding （ExAC） technology. EVD is an integrated .system similar to DVD. Comprehensive comparisons of EVD and DVD are given in this paper. Their key differences include disc formats, file system structures, data structures, audio/video coding, and other issues. Among them, we emphasize on the logic structure of EVD data and its enhanced audio coding method ExAC. We can draw conclusions through these comparisons that EVD is more the advantageous.

关键词： EVD DVD logic structure ExAC MPEG-2

Attribute reduction in interval-valued information systems based on information entropies

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Frontiers of Information Technology & Electronic Engineering 2016年第9期17卷 919-928页

作者： Jian-hua dai Hu HU Guo-jie ZHENG Qing-hua HU Hui-feng HAN Hong SHI School of Computer Science and Technology Tianjin University College of Computer Science and Technology Zhejiang University

Interval-valued data appear as a way to represent the uncertainty affecting the observed values. Dealing with interval-valued information systems is helpful to generalize the applications of rough set theory. Attribute reduction is a key issue in analysis of interval-valued data. Existing attribute reduction methods for single-valued data are unsuitable for interval-valued data. So far, there have been few studies on attribute reduction methods for interval-valued data. In this paper, we propose a framework for attribute reduction in interval-valued data from the viewpoint of information theory. Some information theory concepts, including entropy, conditional entropy, and joint entropy, are given in interval-valued information systems. Based on these concepts, we provide an information theory view for attribute reduction in interval-valued information systems. Consequently, attribute reduction algorithms are proposed. Experiments show that the proposed framework is effective for attribute reduction in interval-valued information systems.

关键词： Rough set theory Interval-valued data Attribute reduction Entropy

Abstracts of Main Papers

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会计研究 2015年第7期 96-96,F0003页

作者： Zhou hua dai Deming