一类方程系统的零点分解

关于MESFET晶体管的制作与设计的研究已有许多结果,在研究求解MESFET晶体管方程系统的基础上,运用Wu-Ritt零点分解方法,给出了这类MESFET晶体管方程系统的零点分解.基于这个分解,可以对这类晶体管的制作与设计给出一个快速稳定算法.

Double-Pole Solution and SolitonAntisoliton Pair Solution of MNLSE/DNLSE Based upon Hirota Method

Hirota method is applied to solve the modified nonlinear Schrodinger equation/the derivative nonlinear Schrodinger equation(MNLSE/DNLSE) under nonvanishing boundary conditions(NVBC) and lead to a single and double-pole soliton solution in an explicit form. The general procedures of Hirota method are presented, as well as the limit approach of constructing a soliton-antisoliton pair of equal amplitude with a particular chirp. The evolution figures of these soliton solutions are displayed and analyzed. The influence of the perturbation term and background oscillation strength upon the DPS is also discussed.

一种高性能迭代预处理方法及其在岩土工程中的应用

岩土工程建设的发展极大地促进了三维数值模拟的应用。大规模三维有限元计算需要求解一系列大型线性方程组,这些线性方程组的求解直接影响着整个有限元计算的效率。复杂岩土工程问题通常涉及多相和多体耦合相互作用,各相之间或不同固体材料之间性质差别显著,可能导致Krylov子空间迭代法收敛缓慢,甚至求解失败。为了提高Krylov子空间迭代法的求解效率和可靠性,提出一种新的高效预处理技术,通过算例验证了所提出的分区块迭代预处理方法的有效性。

IMPROVEMENT OF MATRIX REPRESENTATION METHOD IN NORMAL FORM THEORY

In this paper, based on the invariant subspace theory and adjoint operator concept of linear operator, a new matrix representation method is proposed to calculate the normal forms of n order general nonlinear dynamic systems. In the method, there is no need to determine the structure of the class of normal forms in advance. Because the subspace is not related to the dimensions of the system and the order of the normal forms directly, it is determined only by a given vector field. So the normal forms with high orders and dimensions can be calculated by the method without difficulties. In this paper, is used the method for selecting the minimal subspace and solving homological equations in the subspace, the examples show that the method is very effective.

Existence results for a class of parabolic evolution equations in Banach spaces

We discuss the existence results of the parabolic evolution equation d(x(t)+g(t,x(t)))/dt+A(t)x(t)=f(t,x(t)) in Banach spaces, where A(t) generates an evolution system and functions f,g are continuous. We get the theorem of existence of a mild solution, the theorem of existence and uniqueness of a mild solution and the theorem of existence and uniqueness of an S-classical (semi-classical) solution. We extend the cases when g(t)=0 or A(t)=A.

Conditional Similarity Reductions of Jimbo—Miwa Equation via the Classical Lie Group Approach

Recently, the Clarkson and Kruskal direct method has been modified to find new similarity reductions (conditional similarity reductions) of nonlinear systems and the results obtained by the modified direct method cannot be obtained by the current classical and/or non-classical Lie group approach. In this paper, we show that the conditional similarity reductions of the Jimbo-Miwa equation can be reobtained by adding an additional constraint equation to the original model to form a conditional equation system first and then solving the model system by means of the classical Lie group approach.

A Hierarchy of Integrable Nonlinear Lattice Equations and New Integrable Symplectic Map

A discrete spectral problem is discussed, and a hierarchy of integrable nonlinear lattice equations related to this spectral problem is devised. The new integrable symplectic map and finite-dimensional integrable systems are given by nonlinearization method. The binary Bargmann constraint gives rise to a B?cklund transformation for the resulting integrable lattice equations.

AN IMPROVED RECURSIVE DOUBLING ALGORITHM FOR THE PARALLEL SOLUTION OF LINEAR RECURRENCE R

An improved recursive doubling algorithm for solving linear recurrence R <n,1>is given,whose parallel time complexity is (τ++τ.) logn when n processors are available,achieving the lower bound in array processor type computation.

A Generalized F-expansion Method and Its Application in High-Dimensional Nonlinear Evolution Equation

A generalized F-expansion method is introduced and applied to (3+ 1)-dimensional Kadomstev-Petviashvili(KP) equation. As a result, some new Jacobi elliptic function solutions of the equation are found, from which the trigonometric function solutions and the solitary wave solutions can be obtained. The method can also be extended to other types of nonlinear evolution equations in mathematical physics.

Solutions to a Novel Casimir Equation for the Ito System

We discuss two classes of solutions to a novel Casimir equation associated with the Ito system,a couplednonlinear wave equation.Both travelling wave solutions and separable self-similar solutions are discussed.In a numberof cases,explicit exact solutions are found.Such results,particularly the exact solutions,are useful in that they provideus a baseline of comparison to any numerical simulations.Besides,such solutions provide us a glimpse of the behaviorof the Ito system,and hence the behavior of a type of nonlinear wave equation,for certain parameter regimes.

On a Matrix Equation AX+XB=C over a Skew Field

In this paper we study a matrix equation AX+BX=C(I)over an arbitrary skew field,and give a consistency criterion of(I)and an explicit expression of general solutions of(I).A convenient,simple and practical method of solving(I)is also given.As a particular case,we also give a simple method of finding a system of fundamental solutions of a homogeneous system of right linear equations over a skew field.

Infinite Sequence Soliton-Like Exact Solutions of (2 + 1)-Dimensional Breaking Soliton Equation

To seek new infinite sequence soliton-like exact solutions to nonlinear evolution equations （NEE（s））, by developing two characteristics of construction and mechanization on auxiliary equation method, the second kind of elliptie equation is highly studied and new type solutions and Backlund transformation are obtained. Then （2＋ l ）-dimensional breaking soliton equation is chosen as an example and its infinite sequence soliton-like exact solutions are constructed with the help of symbolic computation system Mathematica, which include infinite sequence smooth soliton-like solutions of Jacobi elliptic type, infinite sequence compact soliton solutions of Jacobi elliptic type and infinite sequence peak soliton solutions of exponential function type and triangular function type.

Exact Excitation and Abundant Localized Coherent Soliton Structures of （2＋1）—Dimensional Perturbed AKNS System

A simple and direct method is applied to solving the (2+1)-dimensional perturbed Ablowitz–Kaup–Newell–Segur system (PAKNS). Starting from a special B?cklund transformation and the variable separation approach, we convert the PAKNS system into the simple forms, which are four variable separation equations, then obtain a quite general solution. Some special localized coherent structures like fractal dromions and fractal lumps of this model are constructed by selecting some types of lower-dimensional fractal patterns.

Simple Procedure for Entanglement Transformation of Bipartite Pure States

An explicit procedure for transforming one bipartite entangled state into another via local operations and classical communication （LOCC） is presented. Our procedure is much simper than the previous ones in the sense that, it only involves two steps and the explicit expression of local general measurement used in the procedure can be obtained by solving a set of linear equations. Furthermore, this procedure is still applicable in high dimensional case.

Development of dynamic-mathematical model of hydraulic excavator

This work deals with analysis of dynamic behaviour of hydraulic excavator on the basis of developed dynamic-mathematical model.The mathematical model with maximum five degrees of freedom is extended by new generalized coordinate which represents rotation around transversal main central axis of inertia of undercarriage.The excavator is described by a system of six nonlinear,nonhomogenous differential equations of the second kind.Numerical analysis of the differential equations has been done for BTH-600 hydraulic excavator with moving mechanism with pneumatic wheels.

Symbolic Computations and Exact and Explicit Solutions of Some Nonlinear Evolution Equations in Mathematical Physics

With the aid of symbolic computation system Mathematica, several explicit solutions for Fisher＇s equation and CKdV equation are constructed by utilizing an auxiliary equation method, the so called G′/G-expansion method, where the new and more general forms of solutions are also constructed. When the parameters are taken as special values, the previously known solutions are recovered.

Modified Lindstedt-Poincaré Method for Obtaining Resonance Periodic Solutions of Nonlinear Non-autonomous Oscillators

A modified Lindstedt-Poincar＆#233; （LP） method for obtaining the resonance periodic solutions of nonlinear non-autonomous vibration systems is proposed in this paper. In the modified method, nonlinear non-autonomous equa-tions are converted into a group of linear ordinary differential equations by introducing a set of simple transformations. An approximate resonance solution for the original equation can then be obtained. The periodic solutions of primary, super-harmonic, sub-harmonic, zero-frequency and combination resonances can be solved effectively using the modi-fied method. Some examples, such as damped cubic nonlinear systems under single and double frequency excitation, and damped quadratic nonlinear systems under double frequency excitation, are given to illustrate its convenience and effectiveness. Using the modified LP method, the first-order approximate solutions for each equation are obtained. By comparison, the modified method proposed in this paper produces the same results as the method of multiple scales.

Application of a Derivative-Free Method with Projection Skill to Solve an Optimization Problem

Improving numerical forecasting skill in the atmospheric and oceanic sciences by solving optimization problems is an important issue. One such method is to compute the conditional nonlinear optimal perturbation(CNOP), which has been applied widely in predictability studies. In this study, the Differential Evolution(DE) algorithm, which is a derivative-free algorithm and has been applied to obtain CNOPs for exploring the uncertainty of terrestrial ecosystem processes, was employed to obtain the CNOPs for finite-dimensional optimization problems with ball constraint conditions using Burgers' equation. The aim was first to test if the CNOP calculated by the DE algorithm is similar to that computed by traditional optimization algorithms, such as the Spectral Projected Gradient(SPG2) algorithm. The second motive was to supply a possible route through which the CNOP approach can be applied in predictability studies in the atmospheric and oceanic sciences without obtaining a model adjoint system, or for optimization problems with non-differentiable cost functions. A projection skill was first explanted to the DE algorithm to calculate the CNOPs. To validate the algorithm, the SPG2 algorithm was also applied to obtain the CNOPs for the same optimization problems. The results showed that the CNOPs obtained by the DE algorithm were nearly the same as those obtained by the SPG2 algorithm in terms of their spatial distributions and nonlinear evolutions. The implication is that the DE algorithm could be employed to calculate the optimal values of optimization problems, especially for non-differentiable and nonlinear optimization problems associated with the atmospheric and oceanic sciences.

Symmetry Reduction of Two-Dimensional Damped Kuramoto-Sivashinsky Equation

In this paper, the problem of determining the largest possible set of symmetries for an important nonlinear dynamical system： the two-dimensional damped Kuramoto-Sivashinsky （（21）） DKS ） equation is studied. By applying the basic Lie symmetry method for the （217）） DKS equation, the classical Lie point symmetry operators are obtained. Also, the optimal system of one-dimensional subalgebras of the equation is constructed. The Lie invariants as well as similarity reduced equations corresponding to infinitesimal symmetries are obtained. The nonclassicaJ symmetries of the （2D） DKS equation are also investigated.

Chirped Bright and Dark Solitons for NLSE with Localized Dissipation

We report the existence of chirped bright and dark solitons for higher order nonlinear Schrodinger equation in the presence of localized dissipation. The parameter domains are delineated in which these solitons exist. It is found that the chirp associated with each of the soliton pulses is directly proportional to intensity and gets saturated at some finite value as the retarded time approaches its asymptotic value. We further show that the higher order nonlinearities in the system such as self-steepening and self-frequency shift do not influence the amplitude of the soliton pulses significantly but primarily control the strength of the localized dissipation.