一些组合地图新算法的实现

本文主要讨论组合地图列举问题.刘的一部专著中提出了一个判定两个地图是否同构的算法.该算法的时间复杂度为O(m2),其中m为下图的规模.在此基础上,本文给出一个用于地图列举以及进而计算任意连通下图的地图亏格分布的通用算法.本文所得结果比之前文献中所给结果更优.     

Propagation of traveling wave solutions for nonlinear evolution equation through the implementation of the extended modi ed direct algebraic method

In this work,di erent kinds of traveling wave solutions and uncategorized soliton wave solutions are obtained in a three dimensional(3-D)nonlinear evolution equations(NEEs)through the implementation of the modi ed extended direct algebraic method.Bright-singular and dark-singular combo solitons,Jacobi's elliptic functions,Weierstrass elliptic functions,constant wave solutions and so on are attained beside their existing conditions.Physical interpretation of the solutions to the 3-D modi ed KdV-Zakharov-Kuznetsov equation are also given.     

Sign-based Test for Mean Vector in High-dimensional and Sparse Settings

In this article, we introduce a robust sparse test statistic which is based on the maximum type statistic. Both the limiting null distribution of the test statistic and the power of the test are analysed. It is shown that the test is particularly powerful against sparse alternatives. Numerical studies are carried out to examine the numerical performance of the test and to compare it with other tests available in the literature. The numerical results show that the test proposed significantly outperforms those tests in a range of settings, especially for sparse alternatives.     

Multiple Positive Solutions for One Dimensional Third Order p-Laplacian Equations with Integral Boundary Conditions

In this paper,we consider the one dimensional third order p-Laplacian equation■u^′′(0)=0.By using kernel functions and the Avery-Peterson fixed point theorem,we establish the existence of at least three positive solutions.     

中国数学会举行第十次全国代表大会

中国数学会第十次全国代表大会暨2007学术年会11月2日在北京航空航天大学开幕,这是中国数学会历史上规模最大的一次全国代表大会.教育部副部长吴启迪、中国科协书记处书记冯长根、北京航空航天大学校长李未及中科院、科技部等单位的相关领导、嘉宾出席开幕式.     

Bayesian Approach for Recovering Piecewise Constant Viscoelasticity from MRE Data

This paper deals with an inverse problem for recovering the piecewise constant viscoelasticity of a living body from MRE(Magnetic Resonance Elastography)data.Based on a scalar partial differential equation whose solution can approximately simulate MRE data,our inverse coefficient problem is considered as a statistical inverse problem of reconstructing the posterior distribution of unknown viscoelastic modulus.For sampling this distribution,one usually can use the Metropolis-Hastings Markov chain Monte Carlo(MHMCMC)algorithm.However,without an appropriate"proposal"distribution given artificially,the MH-MCMC algorithm is hard to draw samples efficiently.To avoid this,a so-called slice sampling algorithm is introduced in this paper and applied for solving our problem.The performance of these statistical inversion algorithms is numerically tested basing on simulated data.     

Solitary Wave Solutions of Delayed Coupled Higgs Field Equation

This paper is devoted to the study of the solitary wave solutions for the delayed coupled Higgs field equation{vtt-uxx-αu+βf*u|u|²-2uv-τu(|u|²)x=0 vtt+vxx-β(|u|^x)xx=0.We first establish the existence of solitary wave solutions for the corresponding equation without delay and perturbation by using the Hamiltonian system method.Then we consider the persistence of solitary wave solutions of the delayed coupled Higgs field equation by using the method of dynamical system,especially the geometric singular perturbation theory,invariant manifold theory and Fredholm theory.According to the relationship between solitary wave and homoclinic orbit,the coupled Higgs field equation is transformed into the ordinary differential equations with fast variables by using the variable substitution.It is proved that the equations with perturbation also possess homoclinic orbit,and thus we obtain the existence of solitary wave solutions of the delayed coupled Higgs field equation.     

RIEMANN-HILBERT PROBLEMS AND SOLITON SOLUTIONS OF NONLOCAL REVERSE-TIME NLS HIERARCHIES

The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations.A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix,corresponding to the reflectionless inverse scattering transforms,is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reversetime NLS hierarchies.     

RIEMANN-HILBERT PROBLEMS AND SOLITON SOLUTIONS OF NONLOCAL REVERSE-TIME NLS HIERARCHIES

The paper aims at establishing Riemann-Hilbert problems and presenting soliton solutions for nonlocal reverse-time nonlinear Schrodinger(NLS) hierarchies associated with higher-order matrix spectral problems.The Sokhotski-Plemelj formula is used to transform the Riemann-Hilbert problems into Gelfand-Levitan-Marchenko type integral equations.A new formulation of solutions to special Riemann-Hilbert problems with the identity jump matrix,corresponding to the reflectionless inverse scattering transforms,is proposed and applied to construction of soliton solutions to each system in the considered nonlocal reversetime NLS hierarchies.     

针对一维空间分数阶扩散方程的一个新的最大模近似公式

Based on the maximum principle,the difference formula defined on a non-integral node is given to approximate the fractional Riemann-Liouville derivative and the finite difference scheme for solving one-dimensional space fractional diffusion equations(FDEs) with variable coefficients is presented.Furthermore,using the maximum principle the scheme is proved unconditionally stable and secondorder accuracy in spatial grid size.Several numerical examples are given to verify the efficiency of the scheme.     

波动方程系数反问题的求解方法

讨论了一维波动方程系数反演的一种求解方法,将解进行一阶渐进展开,得到相应的反问题,将其转化为第二类Volttera型积分方程组,证明了反问题解的存在唯一性.     

Uniqueness For An Inverse Boundary Value Problem For Dirac Operators

The uniqueness of both the inverse boundary value problem and inverse scattering problem for Dirac equation with a magnetic potential and an electrical potential are proved. Also, a relation between the Dirichlet to Dirichlet map for the inverse boundary value problem and the scattering amplitude for the inverse scattering problem is given     

Solvability and stability of the inverse Sturm–Liouville problem with analytical functions in the boundary condition

The paper deals with the Sturm–Liouville eigenvalue problem with the Dirichlet boundary condition at one end of the interval and with the boundary condition containing entire functions of the spectral parameter at the other end. We study the inverse problem, which consists in recovering the potential from a part of the spectrum. This inverse problem generalizes partial inverse problems on finite intervals and on graphs and also the inverse transmission eigenvalue problem. We obtain sufficient conditions for global solvability of the studied inverse problem, which prove its local solvability and stability. In addition, application of our main results to the partial inverse Sturm–Liouville problem on the star-shaped graph is provided.     

强部分逆网络流问题

Abstract. In this paper,a new model for inverse network flow problems,robust partial inverseproblem is presented. For a given partial solution,the robust partial inverse problem is to modify the coefficients optimally such that all full solutions containing the partial solution becomeoptimal under new coefficients. It has been shown that the robust partial inverse spanning treeproblem can be formulated as a combinatorial linear program,while the robust partial inverseminimum cut problem and the robust partial inverse assignment problem can be solved by combinatorial strongly polynomial algorithms.     

Recovery of differential equations with nonlinear dependence on the spectral parameter

The inverse spectral problem of recovering pencils of second-order differential operators on the half-line is studied. We give a formulation of the inverse problem, prove the uniqueness theorem and provided a procedure for constructing the solution of the inverse problem. We also establishe connections with inverse problems for partial differential equations.     

Inverse sorting problem by minimizing the total weighted number of changes and partial inverse sorting problems

In this paper, we consider two types of inverse sorting problems. The first type is an inverse sorting problem by minimizing the total weighted number of changes with bound constraints. We present an O(n ²) time algorithm to solve the problem. The second type is a partial inverse sorting problem and a variant of the partial inverse sorting problem. We show that both the partial inverse sorting problem and the variant can be solved by a combination of a sorting problem and an inverse sorting problem. Supported by the Hong Kong Universities Grant Council (CERG CITYU 103105) and the National Key Research and Development Program of China (2002CB312004) and the National Natural Science Foundation of China (700221001, 70425004).     

Inverse coefficient problem for a quasilinear hyperbolic equation with final overdetermination

The inverse problem of recovering a solution-dependent coefficient multiplying the lowest derivative in a hyperbolic equation is investigated. As overdetermination is required in the inverse problem, an additional condition is imposed on the solution to the equation with a fixed value of the timelike variable. Global uniqueness and local existence theorems are proved for the solution to the inverse problem. An iterative method is proposed for solving the inverse problem.     

一类双曲反问题的逼近算法及收敛性

该文考虑地球物理勘探中出现的间断特性阻抗的反演问题．利用样条插值理论，把无穷维空间上的反问题用有限维空间上的反问题来近似．利用半群理论，证明了近似反问题之解收敛于原反问题之解．据此可得到求解反问题的一种稳定的近似算法．     

Quasi-one-dimensional method for the two-dimensional inverse problem of magnetotelluric sounding

The article presents a quasi-one-dimensional method for solving the inverse problem of electromagnetic sounding. The quasi-one-dimensional method is an iteration process that in each iteration solves a parametric one-dimensional inverse problem and a two-dimensional direct problem. The solution results of these problems are applied to update the input values for the parametric one-dimensional inverse problem in the next iteration. The method has been implemented for a two-dimensional inverse problem of magnetotelluric sounding in a quasi-layered medium.     

具有未知源的某些非线性伪抛物型方程的反问题

考 虑具有未 知源项的 某些非 线性伪 抛物 型方程 的反演 问题． 首先 将伪抛 物型 方程初 边值问 题化为非线 性发展方 程 Ｃｏｕｃｈ ｙ 问题,然 后,利用半 群理论,论 证发展 方程反问 题解的存 在唯一 性,最后, 利用不 动点方法得到 伪抛物型方程反 问题的可解性