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.     

复杂装备研制协调超网络均衡与实现路径

复杂装备研制主体间呈现社会关系、合作关系、协调关系等网络关系,并且相互影响相互作用,其影响复杂装备研制的重要参数。为有效描述在资源环境约束下制造商和供应商的关系,探讨复杂装备研制协调机理与实现路径,本文利用超网络方法,设计了相互影响、相互作用的社会关系网络、协调网络和合作网络的复杂装备研制协调超网络,并将社会关系水平、协调度和合作水平作为超网络的3个决策变量,建立基于关系价值最大、协调成本最低、协调风险最小、合作收益最大、合作风险最小和成本最小等不同偏好下的多目标最优决策模型,构建了复杂装备研制超网络均衡模型,并利用其探讨超网络均衡和实现路径。     

城市老旧居住小区交通环境评价指标与评价方法

定量的评判城市老旧居住小区整体交通环境质量并进而科学有效的提出老旧小区交通环境更新与改善措施,对城市老旧居住小区交通环境进行了调查,明确了老旧居住小区存在的突出交通问题,并提出了城市老旧居住小区交通环境评价的指标体系,包括行人跨路出行指数、无人行道路段长度占比、停车泊位供需比、路内非法停车占比、平均停车步行距离、泊位数量户数比、人均步行空间、无障碍通道、盲道设置比例、非机动车泊位供需比、地面停放车辆数小区面积比、外部穿行交通周转量小区面积比等。并给出了具体指标的计算方法与获得办法。以长沙市四个典型老旧居住小区为例,对评价方法进行了论证,并得到城市老旧居住小区存在的一般问题,包括人车混杂、人车交织现象严重,停车泊位短缺、车辆乱停乱放,交通设施、特别是弱势群体交通设施缺乏。给出的评价指标、评价方法与结论可为城市老旧小区改造更新,特别是其中很重要的交通环境更新提供决策依据。     

乡村绿色生态旅游适宜等级VIKOR评估方法

针对乡村绿色生态旅游特征,并考虑旅游者个体感受与群体效益,本文从乡村绿色生态旅游开发与适宜评级概念出发,提出乡村绿色生态旅游适宜等级VIKOR评估模型与方法。首先,从等级评估的概念与内涵出发,刻画乡村绿色生态旅游适宜评级问题,避免混淆旅游适宜评级和排序两个本质不同的问题。然后,构建乡村绿色生态旅游适宜等级评估指标及隶属函数,提出评估指标的熵权确定方法。其次,提出乡村绿色生态旅游适宜等级VIKOR评估模型与二元语义等级评估方法。最后,通过案例研究和比较分析,说明本文所提模型与方法的合理性、可行性与实用性。     

网络团购环境下基于电子中介的商品交易优化模型

在网络团购环境下,如何考虑顾客、商家和电子中介三方主体的利益并实现商品交易最优化,这是一个值得关注的研究问题。本文针对基于电子中介的网络团购商品交易问题,依据商家与电子中介事先商定的团购商品的交易数量区间、交易数量折扣以及顾客和商家分别提交的商品的报价和保留价,在考虑顾客、商家和电子中介三方利益最大化的前提下,构建了多目标商品交易优化模型;进一步地,将多目标优化模型转化为单目标优化模型,并给出了求解优化模型的遗传算法。最后,通过一个算例说明了本文构建的模型及其求解算法的可行性和有效性。     

道路维修施工路段交通分流信控优化模型

针对道路维修施工期间常采用的部分路面封闭施工且利用辅路进行分流的情形,探讨了交通分流信控优化模型。借助交通流波动理论,分析了施工路段及其前后车流拥挤排队及疏散特征和规律,分析了对车流进行控制需满足的约束,并分析了车流的延误计算公式。以总的车辆行驶时间最小化目标,原路径及分流路径的绿时分配及信号周期为优化参数,考虑交通分流控制的各种约束,建立了道路施工路段交通分流信控优化模型。分析了该模型属于非凸问题,因此提出了一种近似求解最优解的办法。通过一个示例对模型和求解算法进行了验证,并对一些规律性结果进行了分析。     

On the use of history of mathematics: an introduction to Galileo's study of free fall motion

In this paper, we report on an experimental activity for discussing the concepts of speed, instantaneous speed and acceleration, generally introduced in first year university courses of calculus or physics. Rather than developing the ideas of calculus and using them to explain these basic concepts for the study of motion, we led 82 first year university students through Galileo's experiments designed to investigate the motion of falling bodies, and his geometrical explanation of his results, via simple dynamic geometric applets designed with GeoGebra. Our goal was to enhance the students’ development of mathematical thinking. Through a scholarship of teaching and learning study design, we captured data from students before, during and after the activity. Findings suggest that the historical development presented to the students helped to show the growth and evolution of the ideas and made visible authentic ways of thinking mathematically. Importantly, the activity prompted students to question and rethink what they knew about speed and acceleration, and also to appreciate the novel concepts of instantaneous speed and acceleration at which Galileo arrived.     

Interpreting linear systems of equalities and inequalities. Application to the water supply problem

This paper shows how the mathematical and the engineering points of view are complementary and help to model real problems that can be stated as systems of linear equations and inequalities. The paper is devoted to point out these relations and making them explicit for the readers to realize about the new possibilities that arise when contemplating the compatibility conditions or the set of general solutions from the dual perspective. After reviewing an orthogonally based powerful algorithm to analyse the compatibility of linear systems of equations and solving them, a water supply problem is used to illustrate its mathematical and engineering multiple aspects, including the optimal statement of the problem in terms of an adequate selection and numbering of equations and unknowns, an analysis of the compatibility conditions and a physical interpretation of the general solution, together with that of each individual generators of the affine space. The possibilities of removing unknowns without altering the compatibility of the problem is also analysed. Next, the Γ‐algorithm to analyse the compatibility of linear systems of inequalities and solving them is described and then, the water supply problem is revisited adding some constraints, such as capacity limits for the pipes and retention valves, and discussed as to how they affect the resulting general solution and other aspects. Finally, some conclusions are derived. Copyright © 2005 John Wiley & Sons, Ltd.     

利益相关者视角下公路货运超限超载的对策研究——基于演化博弈模型和仿真分析

为有效遏制公路货运超限超载现象,深化交通执法领域的“放管服”改革,本研究针对运输者、稽查人员和交管部门等利益相关者,建立三方演化博弈模型,研究超限超载运输中各利益主体的决策演化过程,并对稳定策略的演化路径进行仿真分析,比较不同参数组合下不同政策力度的治理效果。研究发现,提高超限超载运输的处罚系数可以明显规范运输者的行为;管理成本越低,监管部门的策略越可能向积极监管的方向演化;三方博弈系统存在两种可能的演化稳定策略,加重对稽查人员消极执法行为的处罚、加大资金设备投入能够提高系统向最优状态演化的概率。     

Creep of polymer concrete in the nonlinear region

Two polyester-based polymer concretes with various volume content of diabase as an extender and aggregate are tested in creep under compression at different stress levels. The phenomenological and structural approaches are both used to analyze the experimental data. Common features of changes in the instantaneous and creep compliances are clarified, and a phenomenological creep model which accounts for the changes in the instantaneous compliance and in the retardation spectrum depending on the stress level is developed. It is shown that the model can be used to describe the experimental results of stress relaxation and creep under repeated loading. Modeling of the composite structure and subsequent solution of the optimization problem confirm the possibility of the existence of an interphase layer more compliant than the binder. A direct correlation between the interphase volume content and the instantaneous compliance of the composite is revealed. It is found that the distinction in nonlinearity of the viscoelastic behavior of the two polymer concretes under investigation can be due to the difference in their porosity. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000.) Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 147–164, 2000.     

激光辐照下圆薄板的动态屈曲研究

对强激光辐照下薄板（铜片）的动态热失稳过程进行了分析，得出了简支圆薄板在热冲击下发生的屈曲及后屈曲过程，并给出了临界激光功率密度与薄板厚径比的关系曲线，方法计入了温度分布、惯性项和缺陷大小对于失稳过程的影响。这一工作有利于人们对强激光引起的硬目标破坏机理的认识。