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.     

Navier-Stokes方程与Euler方程的稳定性比较

比较了Navier-Stokes 方程和Euler方程的稳定性;并以它们的典型初值问题为例,分析了Navier-Stokes方程和Euler方程稳定性不同的原因．     

Gauge-invariant description of several (2+1)-dimensional integrable nonlinear evolution equations

We obtain new gauge-invariant forms of two-dimensional integrable systems of nonlinear equations: the Sawada-Kotera and Kaup-Kuperschmidt system, the generalized system of dispersive long waves, and the Nizhnik-Veselov-Novikov system. We show how these forms imply both new and well-known twodimensional integrable nonlinear equations: the Sawada-Kotera equation, Kaup-Kuperschmidt equation, dispersive long-wave system, Nizhnik-Veselov-Novikov equation, and modified Nizhnik-Veselov-Novikov equation. We consider Miura-type transformations between nonlinear equations in different gauges. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 160, No. 1, pp. 35–48, July, 2009.     

VISCOSITY METHOD OF A NON－HOMOGENEOUS BURGERS EQUATION

Abstract In [1], Ding et al. studied the nonhomogeneous Burgers equation ut uux = μuxx 4x.(1.1) This paper will prove that when μ → 0 the solution of (1.1) will approach the generalized solution of ut uux = 4x.(1.2) The authors notice that the equation (1.2) is beyond the scope of investigations by Oleinik O. in [2]. The solutions here are unbounded in general. The paper also studies the δ-wave phenomenon when (1.2) is jointed with some other equation.     

REMARK ON UNIQUE CONTINUATION OF SOLUTIONS TO THE STOKES AND THE NAVIER-STOKES EQUATIONS

1IntroductionUnique continuation of solutions to the linear partial di?erential equations with analyticcoe?cients is well known.There are more general results in elliptic,parabolic and hyperbolicequations(cf.[8-10,12-13]and references therein).The continu…     

New Bounds for the Inhomogenous Burgers and the Kuramoto-Sivashinsky Equations

We give a substantially simplified proof of the near-optimal estimate on the Kuramoto-Sivashinsky equation from a previous paper of the third author, at the same time slightly improving the result. That result relied on two ingredients: a regularity estimate for capillary Burgers and an a novel priori estimate for the inhomogeneous inviscid Burgers equation, which works out that in many ways the conservative transport nonlinearity acts as a coercive term. It is the proof of the second ingredient that we substantially simplify by proving a modified Kármán-Howarth-Monin identity for solutions of the inhomogeneous inviscid Burgers equation. We show that this provides a new interpretation of recent results obtained by Golse and Perthame.     

“Pexiderized” homogeneity almost everywhere

In the paper we examine Pexiderized ?-homogeneity equation almost everywhere. Assume that G and H are groups with zero, (X,G) and (Y,H) are a G- and an H-space, respectively. We prove, under some assumption on (Y,H), that if functions and satisfy Pexiderized ?-homogeneity equation

F₁(αx)=?(α)F₂(x)     

Validity of the KdV equation for the modulation of periodic traveling waves in the NLS equation

Bethuel et al.  and  and Chiron and Rousset [3] gave very nice proofs of the fact that slow modulations in time and space of periodic wave trains of the NLS equation can approximately be described via solutions of the KdV equation associated with the wave train. Here we give a much shorter proof of a slightly weaker result avoiding the very detailed and fine analysis of ,  and . Our error estimates are based on a suitable choice of polar coordinates, a Cauchy–Kowalevskaya-like method, and energy estimates.     

Oscillation and Nonoscillation Criteria for a Second Order Linear Equation

New oscillation and nonoscillation criteria are established for the equation

几种广义非线性发展方程的新解

本文研究了构造了广义Kd V方程和广义KP-Burgers方程等几种广义非线性发展方程的新解的问题.利用三种辅助方程及其新解,获得了广义Kd V方程和广义KP-Burgers方程等几种广义非线性发展方程的新解.这些解由双曲余割函数、双曲正切函数、双曲正割函数、双曲余切函数和余割函数组成.