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A Method for Solving boundary value problems for Nonlinear Control Systems in the Class of Discrete Controls

DIFFERENTIAL EQUATIONS 2008年第11期44卷 1559-1570页

作者： Kvitko, A. N. St Petersburg State Univ St Petersburg Russia

We suggest an algorithm for constructing discrete control functions, This algorithm is sufficiently convenient for numerical implementation mid. for a wide class of nonlinear systems of ordinary differential equations. provides the passage from the initial state into an arbitrary given or arbitrarily small neighborhood of a given terminal state. We obtain constructive criterion for the choice. of terminal states and discretization Steps for which the passage is possible with regard of the constraints imposed Oil the control and the phase. coordinates. We consider an interorbital flight problem, for which we carry out. numerical simulation.

关键词： boundary value problems -- numerical solutions NONLINEAR control theory DIFFERENTIAL equations ALGORITHMS COMPUTER simulation MATHEMATICAL physics

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On the nonuniqueness of the solution of a mixed boundary value problem for the Laplace equation

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DIFFERENTIAL EQUATIONS 2008年第5期44卷 734-736页

作者： Moiseev, T. E. Moscow MV Lomonosov State Univ Moscow Russia

We study the solvability of the mixed boundary value problem for the Laplace equation with three distinct boundary conditions, two of which include two directional derivatives with distinct tilt angles and the remaining one is the first boundary condition. An example of a nontrivial solution of the homogeneous problem is given, and conditions under which the problem has a unique solution are established. The solvability of the problem with a nonhomogeneous first boundary condition is studied.

关键词： boundary value problems -- numerical solutions HARMONIC functions (Mathematics) DIRECTIONAL derivatives DIFFERENTIAL equations -- numerical solutions INITIAL value problems

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On an Adjoint Initial-boundary value Problem

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DIFFERENTIAL EQUATIONS 2008年第12期44卷 1730-1736页

作者： Andreev, V. K. Siberian Fed Univ Russian Acad Sci Siberian Branch Inst Comp Modeling Krasnoyarsk Russia

We study an adjoint initial-boundary value problem for linear parabolic equations;which arises when modeling the unidirectional motion of two viscous fluids with a common interface under the action of a pressure gradient. Under some conditions on the pressure gradient, we obtain a priori estimates and show that the solution enters a stationary mode. For semi-bounded layers, we find the solution in closed form and indicate the case of a self-similar solution. We determine the volume flow rates in the layers.

关键词： ADJOINT differential equations boundary value problems -- numerical solutions PARABOLIC differential equations -- numerical solutions NAVIER-Stokes equations -- numerical solutions FLUID dynamics RESEARCH

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On the Basis Property of Root Elements of Ordinary Differential Operators in the Space L_2,n(a, b)

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DIFFERENTIAL EQUATIONS 2008年第12期44卷 1651-1658页

作者： Vagabov, A. I. Dagestan State Univ Makhachkala Russia

We study a spectral problem for a system of linear ordinary differential operators in the vector function space L-2,L-n(a, b) with parameter-dependent boundary conditions. We prove a theorem stating that the system of root functions of the problem is a basis with parentheses in L-2,L-n (a, b). Corollaries of the theorem are considered.

关键词： DIFFERENTIAL equations -- numerical solutions boundary value problems -- numerical solutions MATRICES DIFFERENTIAL equations -- Asymptotic theory EIGENvalueS

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Positive solutions for Multiparameter Semipositone Discrete boundary value problems via Variational Method

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ADVANCES IN DIFFERENCE EQUATIONS 2008年第1期2008卷 840458-840458页

作者： Yu, Jianshe Zhu, Benshi Guo, Zhiming Hunan Univ Coll Math & Econometr Changsha 410082 Peoples R China Guangzhou Univ Coll Math & Informat Sci Guangzhou 510006 Guangdong Peoples R China

We study the existence, multiplicity, and nonexistence of positive solutions for multiparameter semipositone discrete boundary value problems by using nonsmooth critical point theory and subsuper solutions method. Copyright (c) 2008 Jianshe Yu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

关键词： boundary value problems -- numerical solutions NONSMOOTH optimization CRITICAL point theory (Mathematical analysis) EXISTENCE theorems MULTIPLICITY (Mathematics)

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RANDOM MATRIX THEORY AND ITS APPLICATION TO THE DECAY OUT OF A SUPERDEFORMED BAND

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INTERNATIONAL JOURNAL OF MODERN PHYSICS E 2008年第Dec2008期17卷 292-303页

作者： Gu, Jianzhong China Inst Atom Energy Beijing 102413 Peoples R China Natl Lab Heavy Ion Accelerator Lanzhou Ctr Theoret Nucl Phys Lanzhou 73000 Peoples R China

Originally, random matrix theory (RMT) was designed by Wigner to deal with the statistics of eigenvalues and eigenfunctions of complex many-body quantum systems in 1950s. During the last two decades, the RMT underwent an unexpected and rapid development: The RMT has been successfully applied to an ever increasing variety of physical problems, and it has become an important tool to attack many-body problems. In this contribution I briefly outline the development of the RMT and introduce its basics. Its application to the decay out of a Superdeformed band and a comparison of the approach used in Ref. 34 with that proposed by Vigezzi et al. are presented. Current theoretical activities on the decay out problem are reviewed, and the influence of the degree of chaoticity of the normally deformed states on the decay out intensity is examined systematically.

关键词： RANDOM matrices EIGENvalueS boundary value problems -- numerical solutions QUANTUM theory MATRICES

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Twisted-order parameter applied to dimerized ladders

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JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 2008年第48期41卷 485301-485301页

作者： Almeida, J. Martin-Delgado, M. A. Sierra, G. Univ Complutense Dept Fis Teor 1 E-28040 Madrid Spain CSIC UAM Inst Fis Teor Madrid Spain

We apply the twisted-order parameter (TOP) for dimerized quantum spin ladders to locate the critical points that separate gapped phases representing quantum spin liquids of various types. Using the density matrix renormalization group (DMRG), method, we find that the TOP is a good order parameter for these systems regardless of the number of legs. As a check, we reproduce with the DMRG and periodic boundary conditions the computations previously done with quantum Monte Carlo for one-dimensional S = 1/2, S = 1, S = 3/2 and S = 2 Heisenberg chains with alternating bonds.

关键词： MATHEMATICAL analysis CRITICAL point DOMAIN structure RENORMALIZATION group QUANTUM theory boundary value problems -- numerical solutions MONTE Carlo method

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Correction factors in series solutions for one- and two-dimensional boundary value problems

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JOURNAL OF ENGINEERING MECHANICS 2007年第11期133卷 1151-1161页

作者： GangaRao, Hota V. S. Prachasaree, Woraphot Constructed Facil Ctr Morgantown WV 26506 USA Prince Songkla Univ Fac Engn Dept Civil Engn Hat Yai 90010 Songkla Thailand W Virginia Univ Coll Engn & Mineral Resources Dept Civil & Environm Engn Morgantown WV 26506 USA

A Fourier cum polynomial series solution with correction factors is presented herein for differential equations with variable coefficients. The differential equations correspond to a wide range of boundary value problems. The correction factors included herein are: (1) modified Lanczos correction;(2) Bessel J;and (3) loading correction factor. These correction factors are introduced in terms of Fourier and polynomial series. The main purpose of using correction factors through a set of series is to improve convergence of the proposed solution, using the first two terms of the series. For the loading correction factor, a Fourier series expansion coupled with orthogonality conditions leads to evaluating undetermined Fourier coefficients of arbitrarily applied loads using concepts of summation equations. Representative boundary value problems are provided to demonstrate the efficiency and accuracy of the first two terms of the proposed solution with correction factors.

关键词： MECHANICAL engineering -- Research boundary value problems -- numerical solutions FINITE element method GIRDERS PLATES (Engineering) FOURIER series

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Car-Parrinello simulation of an O-H stretching envelope and potential of mean force of an intramolecular hydrogen bonded system: Application to a Mannich base in solid state and in vacuum

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JOURNAL OF CHEMICAL PHYSICS 2007年第20期126卷 205101.1-205101.9页

作者： Jezierska, Aneta Panek, Jaroslaw J. Koll, Aleksander Mavri, Janez Natl Inst Chem SI-1001 Ljubljana Slovenia Univ Wroclaw Fac Chem PL-50383 Wroclaw Poland

Car-Parrinello molecular dynamics (CPMD) study was performed for an anharmonic system - an intramolecularly hydrogen bonded Mannich-base-type compound, 4,5-dimethyl-2(N,N-dimethylaminemethyl)phenol, to investigate the vibrational spectrum associated with the O-H stretching. Calculations were carried out for the solid state and for an isolated molecule. The classical CPMD simulation was performed and then the proton potential snapshots were extracted from the trajectory. The vibrational Schrodinger equation for the snapshots was solved numerically, and the (O-H) envelope was calculated as a superposition of the 0 -> 1 transitions. The potential of mean force for the proton stretching mode was calculated from the proton vibrational eigenfunctions and eigenvalues incorporating statistical sampling, nuclear quantum effects, and effects of the environment. Perspectives for application of the presented methodology in the computational support of biocatalysis are given in the study. (C) 2007 American Institute of Physics.

关键词： MANNICH bases MOLECULAR dynamics SOLID state physics AMINO compounds CARBONYL compounds VIBRATIONAL spectra boundary value problems -- numerical solutions

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FEM/BEM for simulation of LSAW devices

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IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL 2007年第10期54卷 2060-2069页

作者： Taziev, R. A. Russian Acad Sci Inst Semicond Phys Siberian Branch Novosibirsk 630090 Russia

This paper presents a modeling of the propagation of surface acoustic, leaky acoustic, and surface skimming bulk waves in piezoelectrics with a finite array of metallic electrodes over their surface. A combined method of matrix Green's function and the finite element method for computation of all acoustic wave fields is an effective tool for simulation of the propagation of acoustic waves in such structures. The proposed method is optimized in the speed of computation of all matrix Green's function components originally obtained. The Fourier transformations of Green's function from k-space domain to real space domain are performed by combined trapezoidal and Filon's integration methods for rapidly oscillating functions. The trapezoidal integration method is used on a distance from a point source from zero to a few wavelengths long, but the other has the advantage for a distance from some wavelength to infinity. That allows one, by selectively condensing computation grids around branch and singular points of the sharp behavior of Green's function, to maximize speed and accuracy of computation of integrals. FEM is used, modified originally to achieve acceleration without loss accuracy. Because of the simple geometry of the electrodes, unknown elastic fields are presented as a series of known eigenfunctions with unknown coefficients over the whole region of electrodes. All unknown coefficients are determined by applying the Galerkin method. There is good agreement between numerical and experimental conductances of acoustic wave transducers on materials such as lithium niobate and lithium tantalate.

关键词： RADIO wave propagation ACOUSTIC surface wave devices boundary value problems -- numerical solutions ELECTRODES VIBRATION transducers

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