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.     

集值映射空间上的自然映射(英文)

In this paper,we discuss the continuities of some natural mappings on pointcompact continuous set-valued mapping spaces with compact-open topology and obtain the properties of set-valued injective mappings,set-valued diagonal mappings,induced mappings,set-valued evaluation mappings,set-valued topological sum mappings and set-valued topological product mappings.     

集值优化全局真有效解的最优性条件

本文引进集值映射的全局真有效次微分的概念,并用它得到了约束集值优化问题全局真有效解在集值映射的支撑函数和Lagrange乘子形式下的最优性必要条件.     

Stampacchia variational inequality with weak convex mappings

ABSTRACT

In this paper, the concept of weak convex set-valued mapping is introduced and various conditions for a set-valued mapping to be weak convex are given. Then, existence theorems for the Stampacchia variational inequality problem are established, when the involved mapping is weak convex.     

集值变分不等式问题的例外簇

本文首先在Banach空间中证明了零调集值映射的一个Leray-Schauder型不动点定理,然后在Hilbert空间中定义了零调集值映射的变分不等式的例外簇,利用本文给出的不动点定理给出了无界集上的变分不等式问题存在解的一个充分条件．此条件弱于许多已知的关于变分不等式问题的解的存在性条件,并由此得到Hilbert空间中几个变分不等式约解的存在性定理．     

THEOREMS OF THE ALTERNATIVE FOR CONE-CONVEX SET-VALUED MAPPING

Let S be a nonempty convex subset in Rn, Aj be a nonempty convex cone in Rjm , the set-valued mapping fj: S Rjm be Aj convex and dom(fj) riS , ( j = 1,2,3,4); g, S Rt be linear and dom (fj) riS . In this paper, we discuss the theorems of the alternative for the systems:Gordan type and some other type alternative theorems for cone-convex set-valued mapping are derived also by using above results.     

集值映射最优化问题超有效解集的连通性

本文在局部凸空间中对集值映射最优化问题引入超有效解的概念．首先研究了超 有效点的一些重要特性．其后证明了当目标函数为锥类凸的集值映射时，其目标空间里 的超有效点集是连通的；若目标函数为锥凸的集值映射时，其超有效解集也是连通的．     

Poincare''s recurrence theorems for set-valued dynamical systems

In this paper, we introduce a new concept called ‘a pair of coincident invariant measures’ and establish the existence of coincident invariant measures for set-valued dynamical systems. As applications, we first give the existence of minimal invariant measures (see definition below) for a set-valued mapping, and then set-valued versions of Poincare's recurrence theorems are also derived.     

粘结引理对于集值映射的推广

粘结引理是分析中的一个基本定理,在诸多领域都有重要应用.将单值映射情形下的粘结引理,推广至集值映射情形,它在集值分析中具有进一步的应用.     

Existence of Solutions of New Generalized Mixed Vector Variational-Like Inequalities in Reflexive Banach Spaces

In this paper, we extend the concept of monotonicity for a vector set-valued mapping to semimonotonicity for a vector set-valued mapping. Then, we prove solvability results for a class of new generalized mixed vector variational-like inequalities by applying the Fan-KKM theorem and Nadler’s result. On the other hand, we introduce the concepts of complete semicontinuity and strong semicontinuity for vector multivalued mappings. Moreover, by using the Brouwer fixed point theorem, we prove the solvability for the class of generalized vector variational-like inequalities without monotonicity assumption. Using this result, we obtain a theorem and corollary that improve and extend some known results.     

On Set-Valued Differentiation and Integration

Both the notion of differential of a set-valued mapping and the concept of a set-valued integral are introduced in such a way that, on the one hand, the class of differentiable mappings is rather extensive, while on the other hand, the concept of integral includes as special cases Dinghas' approach and Pontryagin's alternated integral. At the same time, the differential of an integral with respect to the upper limit of integration equals in some sense the integrant. Thus the differentiation of a set-valued mapping can be interpreted as an operation inverse to set-valued integration. Both the differential and the integral are defined via approximation by quasi-affine mappings introduced below. The class of quasi-affine mappings is compared with the classes of affine, semi-affine, eclipsing and multi-affine mappings.