Discrete skew self-adjoint canonical system and the isotropic Heisenberg magnet model

A discrete analog of a skew self-adjoint canonical (Zakharov-Shabat or AKNS) system with a pseudo-exponential potential is introduced. For the corresponding Weyl function the direct and inverse problem are solved explicitly in terms of three parameter matrices. As an application explicit solutions are obtained for the discrete integrable nonlinear equation corresponding to the isotropic Heisenberg magnet model. State-space techniques from mathematical system theory play an important role in the proofs.     

MONOTONE APPROXIMATION TO A SYSTEM WITHOUT MONOTONE NONLINEARITY

1. IntroductionDue to the development of various studies in electromagnetism, biology and someother fields, nonlinear systems hajve been paid extellsive attention both analytically andnumerically, e.g., see [1--12]. As we kll')w, a reasonable numerical method should notonly have the approximation error of higher order, but also preserve the main feature ofthe original problem. In this case? the numerical results might fit the physical processbetter. Since the usual approximations simulate the …     

Recurrence Relations for Chebyshev-Type Methods

The convergence of new second-order iterative methods are analyzed in Banach spaces by introducing a system of recurrence relations. A system of a priori error bounds for that method is also provided. The methods are defined by using a constant bilinear operator A , instead of the second Fréchet derivative appearing in the defining formula of the Chebyshev method. Numerical evidence that the methods introduced here accelerate the classical Newton iteration for a suitable A is provided. Accepted 23 October 1998     

半导体瞬态问题特征变网格有限元法和分析

1 引 言考虑平面区域Ω　R2上的二维问题,其数学模型为[1]-△ψ=α（p-e+N（x））,（x,t）∈Ω×J,J（0,T],（1.1）     

Numerical computation of nonsimple turning points and cusps

Summary A method is developed for the numerical computation of a double turning point corresponding to a cusp catastrophe of a nonlinear operator equation depending on two parameters. An augmented system containing the original equation is introduced, for which the cusp point is an isolated solution. An efficient implementation of Newton's method in the finite-dimensional case is presented. Results are given for some chemical engineering problems and this direct method is compared with some other techniques to locate cusp points.     

Bifurcation of a Modified Leslie-Gower System with Discrete and Distributed Del

A modified Leslie-Gower predator-prey system with discrete and distributed delays is introduced. By analyzing the associated characteristic equation, stability and local Hopf bifurcation of the model are studied. It is found that the positive equilibrium is asymptotically stable when $\tau$ is less than a critical value and unstable when $\tau$ is greater than this critical value and the system can also undergo Hopf bifurcation at the positive equilibrium when $\tau$ crosses this critical value. Furthermore, using the normal form theory and center manifold theorem, the formulae for determining the direction of periodic solutions bifurcating from positive equilibrium are derived. Some numerical simulations are also carried out to illustrate our results.     

一般交叉规划与经济均衡模型

本文首先给出了有多个子规划的一般交叉规划模型,然后把它转化为抽象经济模型,并给出其均衡解存在的条件.最后利用一般交叉规划建立了一类非合作型寡头垄断市场的均衡模型.     

Mixed Method for Compressible Miscible Displacement with Dispersion in Porous Media

Compressible miscible displacement of one fluid by another in porous media is modelled by a nonlinear parabolic system. A finite element procedure is introduced to approximate the concentration of one fluid and the pressure of the mixture. The concentration is treated by a Galerkin method while the pressure is treated by a parabolic mixed finite element method. The effect of dispersion, which is neglected in [1], is considered. Optimal order estimates in L2 are derived for the errors in the approximate solutions.     

A N. Bourbaki type General Theory and the Properties of Contracting Symbols and Corresponding Contracted Forms

A system of contracting symbols is introduced for a N. Bourbaki type general mathematical theory corresponding to a general classical mathematical theory T.     

On a proposed model for heat conduction

^** Corresponding author. Email: jcsong{at}hanyang.ac.kr A system of partial differential equation for modelling theconduction of heat was proposed by Ghaleb & El-Deen Mohamedein(1989). According to their theory, the initial-value problemfor the temperature is ill-posed. In this paper, two well-posedproblems for the temperature are introduced and investigated.     

Linear Forward—Backward Stochastic Differential Equations

The problem of finding adapted solutions to systems of coupled linear forward—backward stochastic differential equations (FBSDEs, for short) is investigated. A necessary condition of solvability leads to a reduction of general linear FBSDEs to a special one. By some ideas from controllability in control theory, using some functional analysis, we obtain a necessary and sufficient condition for the solvability of a class of linear FBSDEs. Then a Riccati-type equation for matrix-valued (not necessarily square) functions is derived using the idea of the Four-Step Scheme (introduced in [11] for general FBSDEs). The solvability of such a Riccati-type equation is studied which leads to a representation of adapted solutions to linear FBSDEs. Accepted 29 April 1997     

Modified Legendre Rational Spectral Method for the Whole Line

A mutually orthogonal system of rationalSome approximation results are establishedfunctions on the whole line is introduced.As an example of applications, a modified Legendre rational spectral scheme is given for the Dirac equation. Its numerical solution keeps the same conservation as the genuine solution. This feature not only leads to reasonable numerical simulation of nonlinear waves, but also simplifies the analysis. The convergence of the proposed scheme is proved. Numerical results demonstrate the efficiency of this new approach and coincide with the analysis well.     

拟弱几乎周期点的等价定义与系统的混沌性

1992年, 周作领引进了弱几乎周期点这一概念. 1995年, 周和何伟弘又引进了拟弱几乎周期点这个概念, 并利用它们深刻地刻画了一个动力系统的本质所在. 为了更好地看出这两者的区别,首先从回复时间集的角度给出拟弱几乎周期点的等价定义,然后研究了一个存在真的拟弱几乎周期点的系统的混沌情况,得到了这样的系统是Takens-Ruelle混沌的.     

求解非线性规划问题的两个微分方程系统

本文给出Evtushenko与Zhadan（1974）提出的求解数学规划问题微分方程系统的两个校正形式,它们可用于求解具有等式和不等式约束的非线性规化问题。第一个校正系统拓宽了Evtushenko与Zhadan微分方程方法;第二个校正系统通过引入新的方程系统导出乘子函数得到,它无需使用Evtushenko与Zhadan所用的那样强的约束规范。我们建立了这两个微分方程方法及其离散迭代方法的收敛性定理,给出了基于第二个微分方程离散格式的数值算法及其某些数值结果。     

Modelling of high-pressure gas transmission lines

Gas flow in a transmission line is described by a set of three coupled partial differential equations (PDE) expressing conservation of mass, momentum and energy; the gas properties are described by a non-ideal equation of state. A technique is introduced which reduces the energy equation into a single parameter in the mass equation without the assumption of isothermal or isentropic flow.The remaining set of PDEs is solved by two different techniques. An accurate but time-consuming technique consists of applying the method of characteristics, for which an improved representation of the friction term is presented. The second way consists of a finite-difference implementation with a second-order truncation error on an analogue computer. Both the physical assumptions and the numerical approximations are checked against data obtained from experiments in the main transport system of Gasunie.Guidelines on the analogue modelling of pipeline systems and the interpretation of simulation results conclude the paper.     

Semi-Biplanes and Antiregular Generalied Quadrangles

A natural method to construct semi-biplanes from antiregular generalized quadrangles is introduced. Properties of the semi-biplanes constructed are discussed. In the finite case and in the topological case the semi-biplanes that arise bear a strong resemblance to semi-biplanes that arise in the natural way from projective planes admitting an involutory homology.     

Dynamic approach to a stochastic domination: The FKG and Brascamp-Lieb inequalities

A coupling based on a pair of stochastic differential equations is introduced to show a stochastic domination for a system with continuous spins, from which the FKG and Brascamp-Lieb like inequalities follow.

     

A SHIFT-SPLITTING PRECONDITIONER FOR NON-HERMITIAN POSITIVE DEFINITE MATRICES

A shift splitting concept is introduced and, correspondingly, a shift-splitting iteration scheme and a shift-splitting preconditioner are presented, for solving the large sparse system of linear equations of which the coefficient matrix is an ill-conditioned non-Hermitian positive definite matrix. The convergence property of the shift-splitting iteration method and the eigenvalue distribution of the shift-splitting preconditioned matrix are discussed in depth, and the best possible choice of the shift is investigated in detail. Numerical computations show that the shift-splitting preconditioner can induce accurate, robust and effective preconditioned Krylov subspace iteration methods for solving the large sparse non-Hermitian positive definite systems of linear equations.     

微分代数系统的渐近性

从动力系统的角度研究微分代数系统,利用单调流理论中的结果和方法讨论微分代数系统渐近性态.首先,我们把所考察的系统嵌入到一族相关的系统,引进使得系统族中的每个系统生成单调流的相应偏序和条件.然后给出了若干关于解收敛于平衡点的一般性结果,并对一类微分代数系统的渐近性作了较为精细的讨论.我们的结果是Hirch等关于常微分方程的相关结果的推广和改进.     

Height-analysis ofk-dimensional leaf and node height-balanced trees: A new approach

A new general approach is proposed for the height-analysis ofk-dimensional leaf and node height-balanced trees which is expected to be useful for such analysis of other neighbor-supported balanced multidimensional trees as well. The approach leads to upper bounds which are the same as the known upper bounds for the corresponding 1-dimensional trees, to within an additive term.This research is partially supported by a grant from the College of Business Administration, Georgia State University, Atlanta, Georgia.Actually a variant calledalmost 2-dimensional leaf AVL-trees is introduced in order to facilitate the derivation of an upper bound for the height of these trees which is within an additive term to the bound for such 1-dimensional trees.