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fixed-point methods for a semiconductor quantum dot model

MATHEMATICAL AND COMPUTER MODELLING 2004年第5-6期40卷 519-533页

作者： Hwang, TM Lin, WW Liu, JL Wang, WC Natl Univ Kaohsiung Dept Appl Math Kaohsiung 811 Taiwan Natl Taiwan Normal Univ Dept Math Taipei 116 Taiwan Natl Tsing Hua Univ Dept Math Hsinchu 300 Taiwan Natl Chiao Tung Univ Dept Appl Math Hsinchu 300 Taiwan

This paper presents various fixed-point methods for computing the ground state energy and its associated wave function of a semiconductor quantum dot model. The discretization of the three-dimensional Schrodinger equation leads to a large-scale cubic matrix polynomial eigenvalue problem for which the desired eigenvalue is embedded in the interior of the spectrum. The cubic problem is reformulated in several forms so that the desired eigenpair becomes a fixed point of the new formulations. Several algorithms are then proposed for solving the fixed-point problem. Numerical results show that the simple fixed-point method with acceleration schemes can be very efficient and stable. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： cubic eigenvalue problem fixed-point method linear Jacobi-Davidson method linear successive iterations 3D Schrodinger equation

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Optimal investment and reinsurance to reach a bequest goal with random time solvency regulation

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INTERNATIONAL JOURNAL OF CONTROL 2025年第2期98卷 380-392页

作者： Xu, Lin Fan, Kun Wang, Minghan Yao, Dingjun Anhui Normal Univ Sch Math & Stat Wuhu Peoples R China East China Normal Univ Sch Stat Shanghai 200241 Peoples R China Nanjing Univ Finance & Econ Sch Finance Nanjing Peoples R China

This paper studies optimal investment and proportional reinsurance policies for an insurer with Markov regime-switching model and random time solvency regulation. The goal of the insurer is to maximise the probability that its wealth exceeds a predetermined level l before the regulatory time arrives. By constructing an auxiliary control problem without regime switching, together with the classical results on Hamilton-Jacobi-Bellman (HJB) equation and fixed-point method, we prove the regularity of the value function. When the current state of the Markov chain is given, we found that the optimal policies for an insurer in a multiple-regime market is the same as those in a single-regime market. Explicit optimal policies can be derived when the premium is calculated by the expectation principle. For more general cases, numerical schemes for value functions and feedback optimal policies are given by the Markov chain approximating method.

关键词： Investment reinsurance fixed-point method bequest goal random audit time

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An elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor

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Applied Mathematics and Mechanics(English Edition) 2021年第5期42卷 747-754页

作者： Tianbo WANG Dinglin YANG Chen LI Diwei SHI Department of Engineering Mechanics School of Aerospace EngineeringTsinghua UniversityBeijing 100084China

Based on the Cayley-Hamilton theorem and fixed-point method,we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional(3D)inner-product space,which avoids introducing the generating function and Taylor series *** proof is also extended to any finite-dimensional inner-product space.

关键词： representation theorem analytic tensor function fixed-point method

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Lossy transmision lines terminated by R-loads with exponential V-I characteristics

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NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS 2007年第2期8卷 579-589页

作者： Angelov, V. G. Univ Min & Geol St I Rilski Dept Math Sofia 1700 Bulgaria

It is known that in many cases the losses in the transmission lines cannot be disregarded. Here we consider the mixed problem for a system describing a lossy transmission line terminated by a nonlinear R-load. Most often, the V-I characteristics of the nonlinear loads are approximated by polynomials. But analysis and design of integrated electronic circuits sometimes require an approximation by exponential functions. This leads to neutral functional differential equations with exponential nonlinearities. We show of how to solve such equations by means of the fixed-point method and obtain conditions for the existence of periodic regimes of lossy transmission lines. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： Lossy transmission lines exponential V-I characteristics neutral equations fixed-point method

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Convergence of fixed-point Continuation Algorithms for Matrix Rank Minimization

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FOUNDATIONS OF COMPUTATIONAL MATHEMATICS 2011年第2期11卷 183-210页

作者： Goldfarb, Donald Ma, Shiqian Columbia Univ Dept Ind Engn & Operat Res New York NY 10027 USA

The matrix rank minimization problem has applications in many fields, such as system identification, optimal control, low-dimensional embedding, etc. As this problem is NP-hard in general, its convex relaxation, the nuclear norm minimization problem, is often solved instead. Recently, Ma, Goldfarb and Chen proposed a fixed-point continuation algorithm for solving the nuclear norm minimization problem (Math. Program., doi:10.1007/s10107-009-0306-5, 2009). By incorporating an approximate singular value decomposition technique in this algorithm, the solution to the matrix rank minimization problem is usually obtained. In this paper, we study the convergence/recoverability properties of the fixed-point continuation algorithm and its variants for matrix rank minimization. Heuristics for determining the rank of the matrix when its true rank is not known are also proposed. Some of these algorithms are closely related to greedy algorithms in compressed sensing. Numerical results for these algorithms for solving affinely constrained matrix rank minimization problems are reported.

关键词： Matrix rank minimization Matrix completion Greedy algorithm fixed-point method Restricted isometry property Singular value decomposition

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Optimal parameters of viscoelastic tuned-mass dampers

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JOURNAL OF SOUND AND VIBRATION 2019年 445卷 17-28页

作者： Batou, A. Adhikari, S. Univ Liverpool Sch Engn Liverpool Merseyside England Swansea Univ Coll Engn Bay Campus Swansea SA1 8EN W Glam Wales

A vibration absorber, also known as a tuned mass damper (TMD), is a passive vibration control device. This is achieved by attaching a secondary oscillator to a primary oscillator. In general, the aim is to reduce the vibration of the primary oscillator by suitably choosing the parameters of the secondary oscillator. The effectiveness of a TMD depends on (a) optimised the value of the tuned parameters, and (b) the nature of ambient damping of the absorber. They theory of TMD when the secondary and the primary oscillators are undamped or viscously damped is well developed. This paper presents an analytical approach to obtain optimal parameters of a TMD when the vibration absorber is viscoelastically damped. Classical results on viscously damped vibration absorbers can be obtained as a special case of the general results reduced in the paper. It is shown that by using a viscoelastically damped TMD, it is possible to obtain superior vibration absorption compared to an equivalent viscously damped TMD. Crown Copyright (C) 2019 Published by Elsevier Ltd. All rights reserved.

关键词： Tuned mass damper Vibration absorber fixed-point method Viscoelastic Optimisation

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A fixed-point approach for nonlinear discrete boundary value problems

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 1998年第10-12期36卷 115-121页

作者： Agarwal, RP O'Regan, D Natl Univ Singapore Dept Math Singapore 117548 Singapore Univ Coll Galway Dept Math Galway Ireland

关键词： discrete boundary value problems fixed-point method

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Adams-Bashforth and Adams-Moulton methods for solving differential Riccati equations

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2010年第11期60卷 3032-3045页

作者： Peinado, J. Ibanez, J. Arias, E. Hernandez, V. Univ Politecn Valencia Dept Sistemas Informat & Computac Valencia 46022 Spain Univ Castilla La Mancha Dept Sistemas Informat Albacete 02071 Spain

Differential Riccati equations play a fundamental role in control theory, for example, optimal control, filtering and estimation, decoupling and order reduction, etc. In this paper several algorithms for solving differential Riccati equations based on Adams-Bashforth and Adams-Moulton methods are described. The Adams-Bashforth methods allow us explicitly to compute the approximate solution at an instant time from the solutions in previous instants. In each step of Adams-Moulton methods an algebraic matrix Riccati equation (AMRE) is obtained, which is solved by means of Newton's method. Nine algorithms are considered for solving the AMRE: a Sylvester algorithm, an iterative generalized minimum residual (GMRES) algorithm, a fixed-point algorithm and six combined algorithms. Since the above algorithms have a similar structure, it is possible to design a general and efficient algorithm that uses one algorithm or another depending on the considered differential matrix Riccati equation. MATLAB versions of the above algorithms are developed, comparing precision and computational costs, after numerous tests on five case studies. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： differential matrix Riccati equation (DMRE) algebraic matrix Riccati equation (AMRE) algebraic matrix Sylvester equation (AMSE) Adams-Bashforth methods Adams-Moulton methods GMRES methods fixed-point method

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Seismic protection of SDOF systems with a negative stiffness amplifying damper

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ENGINEERING STRUCTURES 2019年 190卷 128-141页

作者： Wang, Meng Sun, Fei-fei Yang, Jia-qi Nagarajaiah, Satish Tongji Univ Coll Civil Engn 1239 Siping Rd Shanghai 200092 Peoples R China Tongji Univ State Key Lab Disaster Reduct Civil Engn 1239 Siping Rd Shanghai 200092 Peoples R China Rice Univ Dept Civil & Environm Engn 6100 Main St Houston TX 77005 USA

A new passive device named negative stiffness amplifying damper (NSAD) is proposed in this paper by introducing a negative stiffness (NS) spring into to the flexibly-supported-viscous-damper systems (represented by classical Maxwell damping element, MDE).. The NS spring is combined with the dashpot of the MDE, amplifying the stroke of the dashpot;therefore, lead to significant damping magnification effect. The proposed NSAD not only achieves significant damping magnification effect, but also preserves the property of negative stiffness. This feature is attractive for reducing both displacement and structural acceleration when subjected to earthquakes. The closed-form expressions of optimal parameters for an undamped SDOF system with a NSAD is also proposed by modifying the 'fixed point' method of tuned mass damper. Then, the performance of NSAD is investigated and evaluated under stochastic excitations, pulse excitations, and real earthquakes. Result shows that the optimal NSAD can substantially reduce displacement and acceleration responses simultaneously. For instance, even using the same small additional damping ratio (i.e., 2.8%), the optimal NSAD reduces the resonance response of MDE by 76.9%. Also with that small additional damping, the NSAD improves the energy dissipation capability by 5-16 times, causing 40-60% of seismic response reduction for most structural period range. Moreover, the NSAD is also effective for both far-field and near-fault earthquakes. Especially for near-fault pulse-like earthquakes which may potentially cause larger seismic responses for long-period structures, the NSAD provides an extra improvement of 15-20% in energy dissipation capability for long-period structures.

关键词： Negative stiffness amplifying damper fixed-point method Passive structural control Stochastic response analysis Pulse-like excitation Near-fault pulse-like earthquake

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Solving long haul airline disruption problem caused by groundings using a distributed fixed-point computational approach to integer programming

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NEUROCOMPUTING 2017年 269卷 232-255页

作者： Wu, Zhengtian Li, Benchi Dang, Chuangyin Hu, Fuyuan Zhu, Qixin Fu, Baochuan Suzhou Univ Sci & Technol Suzhou Jiangsu Peoples R China City Univ Hong Kong Hong Kong Hong Kong Peoples R China

Disruptions are prevalent phenomenons that prevent airline from operating as original scheduled. This paper adopts the iterative fixed-point method for integer programming proposed by Dang and Ye [1] to generate feasible flight routes that are used to construct an aircraft reassignment in response to the grounding of one aircraft. Two division methods are proposed with which the solution space can be divided into several independent segments and implemented a distributed computation. The second division method is emphasized in this paper for the good performance of partial feasible flight routes which are generated by this division approach. Comparison with CPLEX CP Optimizer [2] shows that less partial feasible flight routes which are generated by Dang's algorithm [1] are required to find an aircraft reassignment when disruptions happen, and this division method is more promising when dealing with long haul airline disruption problem. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Airline disruption management Irregular operation fixed-point method Integer programming Distributed computation Lexicographical order MPI

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