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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

Blinking adaptation for synchronizing a mobile agent network

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Journal of Zhejiang University-Science C(Computers and Electronics) 2011年第8期12卷 658-666页

作者： huan SHI hua-ping dai You-xian SUN State Key Laboratory of Industrial Control Technology Zhejiang University Hangzhou 310027 China

We investigate the issue of synchronizing a blinking coupling mobile agent network through a blinking adaptation strategy,where each agent with blinking wave emission behavior not only adjusts its blinking period according to the local property of its neighbors,but also coordinates its blinking phase with those of neighboring *** leading the agents to blink orderly with a blinking period commensurate with the characteristic time of the dynamical oscillator,the presented blinking adaptation strategy works effectively in guaranteeing the synchronous motion of the considered network when the power density is *** addition,the influence of the controlling parameter and moving velocity on network evolution is studied by assessing the convergence time.

关键词： Mobile agents Blinking adaptation Coupled-oscillator networks Synchronization

On the emergence of gravitational dynamics from tensor networks

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Communications in Theoretical Physics 2023年第8期75卷 134-138页

作者： hua-Yu dai Jia-Rui Sun Yuan Sun School of Physics and Astronomy Sun Yat-Sen UniversityGuangzhou 510275China

Tensor networks are used to describe the ground state wavefunction of the quantum many-body ***,it has been shown that a tensor network can generate the anti-de Sitter(AdS)geometry by using the entanglement renormalization approach,which provides a new way to realize bulk reconstruction in the AdS/conformal field theory ***,whether the dynamical connections can be found between the tensor network and gravity is an important unsolved *** this paper,we give a novel proposal to integrate ideas from tensor networks,entanglement entropy,canonical quantization of quantum gravity and the holographic principle and argue that the gravitational dynamics can be generated from a tensor network if the wave function of the latter satisfies the Wheeler–DeWitt equation.

关键词： AdS/CFT correspondence tensor network emergent gravity

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

INFLUENCE OF FILLING WATER ON AIR CONCENTRATION

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Journal of Hydrodynamics 2011年第5期23卷 601-606页

作者： WU Jian-hua MA Fei dai Hui-chao College of Water Conservancy and Hydropower Engineering Hohai University Nanjing 210098 China

The filling water inside the cavity below an aerator occurs for the flow of low Froude number or the small bottom slope of a spillway. The aerator may cease to protect against cavitation damages, and may even act as a generator of cavitation if it is fully filled by water. The experiments were conducted to investigate the influences of the geometric parameters, and then the filling water on the air concentration. The results show that the filling water, or the net cavity length, is closely related to the plunging jet length for a given aerator, and the air concentration at some section is proportional to the ratio Ln/Lj at a fixed Lj for different geometric parameters of aerators. Secondly, at the same ratio of Ln / Lj, the aerator with a larger height or a larger angle of ramp, or a larger bottom slope, would have a larger plunging jet length, and then a larger net cavity length based on the ratio of Ln / Lj. As a result, the large space of cavity, or the high air concentration of the flow could be obtained although the filling water increases also based on the fact that Lf = Lj - Ln. It is the space of the cavity that is the dominant factor to affect the air concentration of the flow.

关键词： aerator air concentration filling water jet length net cavity length

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