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.     

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.     

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.     

Indefinite Least Squares Problem with Quadratic Constraint and Its Condition Numbers

In this paper,we consider the indefinite least squares problem with quadratic constraint and its condition numbers.The conditions under which the problem has the unique solution are first presented.Then,the normwise,mixed,and componentwise condition numbers for solution and residual of this problem are derived.Numerical example is also provided to illustrate these results.     

ON THE BOUNDEDNESS CONDITIONS FOR SOLUTIONS OF A AUTONOMOUS DIFFERENTIAL SYSTEM

ＯＮＴＨＥＢＯＵＮＤＥＤＮＥＳＳＣＯＮＤＩＴＩＯＮＳＦＯＲＳＯＬＵＴＩＯＮＳＯＦＡＡＵＴＯＮＯＭＯＵＳＤＩＦＦＥＲＥＮＴＩＡＬＳＹＳＴＥＭ￥ＨｕａｎｇＬｉｈｏｎｇ（黄立宏）；ＷａｎｇＺｈｉｃｈｅｎｇ（王志成）（ＨｕｎａｎＵｎｉｖｅｒｓｉｔｙ，湖南大学...     

一类广义Liénard系统解的有界性

研究了一类广义 Liénard系统dxdt=p(y) -F(x) ,　 dydt=-g(x) (E)解的有界性 .首先获得了系统 (E)存在无界解的两个新的充分条件 ,然后获得系统 (E)所有解正向有界的若干充分条件和充要条件 ,所获结果改进和扩展了文 [1 -2 ]中的相应结果 .     

非线性泛函微分方程解的性态

本文给出了一类非线性泛函微分方程解的性态的若干充要条件,推广了[1]的某些结论.     

Necessary and Sufficient Constraint Qualification for Surrogate Duality

In mathematical programming, constraint qualifications are essential elements for duality theory. Recently, necessary and sufficient constraint qualifications for Lagrange duality results have been investigated. Also, surrogate duality enables one to replace the problem by a simpler one in which the constraint function is a scalar one. However, as far as we know, a necessary and sufficient constraint qualification for surrogate duality has not been proposed yet. In this paper, we propose necessary and sufficient constraint qualifications for surrogate duality and surrogate min–max duality, which are closely related with ones for Lagrange duality.     

Stability Criteria for Solutions of Systems of Linear Deterministic or Stochastic Delay Difference Equations with Continuous Time

We give spectral and algebraic coefficient criteria (necessary and sufficient conditions) as well as sufficient algebraic coefficient conditions for the Lyapunov asymptotic stability of solutions to systems of linear deterministic or stochastic delay difference equations with continuous time under white noise coefficient perturbations for the case in which all delay ratios are rational. For stochastic systems, mean-square asymptotic stability is studied. The Lyapunov function method is used. Our criteria on algebraic coefficients and our sufficient conditions are stated in terms of matrix Lyapunov equations (for deterministic systems) and matrix Sylvester equations (for stochastic systems).     

Nondominated decisions and cone convexity in dynamic multicriteria decision problems

The concepts of domination structures and non-dominated decisions are extended to dynamic decision problems. Previously derived results are utilized in conjunction with optimal control theory to deduce necessary as well as sufficient conditions for nondominated controls. Cone convexity for dynamic problems is discussed, and sufficient conditions are given for a class of linear systems.     

两类模糊系统作为通用逼近器的充分条件的比较与分析

对现有的Mamdani模糊系统和T-S模糊系统作为通用逼近器的充分条件作比较分析,提出了通过三种不同算法获得的单输入单输出Mamdani模糊系统作为通用逼近器的充分条件的保守性比较定理。     

Positive definite solutions of some matrix equations

In this paper we investigate some existence questions of positive semi-definite solutions for certain classes of matrix equations known as the generalized Lyapunov equations. We present sufficient and necessary conditions for certain equations and only sufficient for others.     

Leakage delays in BAM

A well known bidirectional associative memory (BAM) model is generalized with the introduction of discrete time delays in the leakage (or forgetting) terms. By using a model transformation, the system is converted to one of a neutral delay system. Two sets of delay dependent sufficient conditions are derived for the existence of a unique equilibrium as well as its asymptotic and exponential stability. The methods of degenerate Lyapunov-Kravsovskii functionals and inequalities together with some properties of M-matrices are used in the derivation of sufficient conditions. In the absence of leakage delays, the sufficient conditions lead to some known sufficient conditions.     

Global observer design for nonlinear systems

This paper is a geometric study of the global observer design for nonlinear systems. Using the theory of foliations, we derive necessary and sufficient conditions for global exponential observers for nonlinear systems under some assumptions. Our proof for these necessary and sufficient conditions for global exponential observers if via defining two equivalence relations known as horizontal and vertical equivalence relations, and constructing two foliations known as horizontal and vertical foliations from these equivalence relations. Finally, as a corollary of our global theorem, we derive necessary and sufficient conditions for local exponential observers of critically Lyapunov stable nonlinear systems.