工科研究生"应用泛函分析"教学的几点思考

根据多年工科研究生"应用泛函分析"的教学实践,结合重点课程建设,就工科研究生"应用泛函分析"教学内容、教学方法与教学模式提出几点见解与思考,以期对促进工科研究生"应用泛函分析"的教学起到一定的作用.     

第三届全国研究生数学建模竞赛

经过2004和2005年成功的实践,全国研究生数学建模竞赛"为提高研究生的培养质量,推动研究生教学的改革,培养研究生的创新精神与团队合作精神"的宗旨已经为全国的研究生培养单位所接受;全国研究生数学建模竞赛在"增进研究生之间及研究生与外界的交流,拓宽研究生的知识面,激发研究生群体的活力和广大研究生的学习兴趣"等方面所起的作用更受到全国广大研究生的热烈欢迎;全国研究生数学建模竞赛作为提高研究生创新能力的有益探索,已逐渐成为广大研究生探索实际问题、开展学术交流、提高科研能力和培育团队意识的有效平台也得到教育部的认可和鼓励,2006年初教育部研究生司正式批准东南大学的申请,将全国研究生数学建模创新能力培养改革和举办全国研究生数学建模竞赛列入教育部研究生创新教育计划项目.全国研究生数学建模竞赛正在迅速成长.     

城市道路交通信号实时控制问题的评述

对2008年全国研究生数学建模竞赛B题"城市道路交通信号实时控制问题"的命题背景,问题要求,建模方法,模型算法,结果分析,模型应用、模型评价等相关问题进行了分析和评述.结果表明,该问题的选择具有重要理论和实际应用价值,对研究生创新能力的培养具有重要作用.     

第十五届中国研究生数学建模竞赛

<正>在竞赛的主办单位教育部学位与研究生教育发展中心的领导下和竞赛承办单位中国海洋大学积极而卓有成效的工作,2018年"华为杯"第十五届中国研究生数学建模竞赛,共有439个研究生培养单位、40389名研究生(其中国际、港澳地区研究生34名)参赛,在参赛的研究生人数和组成两方面都有可喜的变化,再创历史新高,充分说明该项赛事在培养研究生创新能力、解决实际问题能力和团队意识方面确有成效,深受广大研究生欢迎和研究生培养     

第四届全国研究生数学建模竞赛

全国研究生数学建模竞赛一贯努力遵循"为提高研究生的培养质量,推动研究生教学的改革,培养研究生的创新精神与团队合作精神"的宗旨在近几年取得了长足的进步.2007年第四届全国研究生数学建模竞赛承办单位北京航空航天大学对竞赛组织工作非常重视,努力认真地工作,使竞赛有了新的突破,迈上了新的台阶,进一步获得国务院学位办公室的大力支持和全国各研究生培养单位和广大研究生的积极参与.     

第五届全国研究生数学建模竞赛

全国研究生数学建模竞赛一贯以"提高研究生的培养质量,推动研究生教学的改革,培养研究生的创新精神与团队合作精神"为宗旨,五年来迅速发展.     

第十二届全国研究生数学建模竞赛

正在竞赛的主办单位教育部学位与研究生教育发展中心的领导下和竞赛承办单位-北京交通大学的精心组织下,2015年第十二届"中关村青联杯"全国研究生数学建模竞赛,共有30个省(市、自治区)的390所高校、研究所的6355队、近两万名研究生(其中包括1106名博士生)参赛,规模空前,完满落幕.与2014年相比,全国研究生数学建模竞赛规模扩大近30%.充分说明该项赛事在培养研究生创新能力、解决实际问题能力和团队意识方面确有成效,深受广大研究生欢迎和研究生培养单位的重视.     

第十届全国研究生数学建模竞赛

<正>2013年12月21日第十届"华为杯"全国研究生数学建模竞赛颁奖大会在长沙中南大学隆重举行,至此2013年全国研究生数学建模竞赛取得完满成功.2013年竞赛最重大的事件是教育部学位与研究生教育发展中心将全国研究生数学建模竞赛列入了教育部"全国研究生创新实践系列活动",作为该项活动的主题赛事,并由教育部学位与研究生教育发展中心担任竞赛组织委员会的主任委员单位主办该项赛事.2013年竞赛的另一个亮点是华为公司不仅继续冠名赞助研究生数学建模竞赛,而且根据公司的研发方面     

军事行动避空侦察的时机和路线选择的评述

建模竞赛D题"军事行动避空侦察的时机和路线选择"来源于国家反卫星侦察的军事背景,其核心是要找出卫星的运行规律并建立相关预测模型,体现了全国研究生数学建模竞赛的特色.阐述了命题背景,分析了本赛题的建模及求解思路.通过赛题的研究,使得研究生们更加关心国防建设,引导学生把数学建模应用到军事领域建模中来,解决实际问题.     

第十一届全国研究生数学建模竞赛

<正>2014年12月13日在天津大学隆重举行的第十一届"华为杯"全国研究生数学建模竞赛颁奖大会标志着2014年研究生数学建模竞赛成功地落下帷幕.在竞赛的主办单位教育部学位与研究生教育发展中心的领导下和竞赛承办单位一天津大学的精心组织下,2014年的竞赛,共有30个省(市、自治区)的371所高校、研究所的4900队、14700名研究生,(其中包括691名博士生)参赛,规模空前.十一年来全国研究生数学建模竞赛不断发展壮大的事实说明在培养研究生创新能力、解决实际问题能力和团队意识方面研究生数学建模活动确实发挥了积极的作用,深受广大研究生欢迎,成效是显著的.     

A Representation and Economic Interpretation of a Two-Level Programming Problem

This paper first presents a formulation for a class of hierarchial problems that show a two-stage decision making process; this formulation is termed multilevel programming and could be defined, in general, as a mathematical programming problem (master) containing other multilevel programs in the constraints (subproblems). A two-level problem is analyzed in detail, and we develop a solution procedure that replaces the subproblem by its Kuhn-Tucker conditions and then further transforms it into a mixed integer quadratic programming problem by exploiting the disjunctive nature of the complementary slackness conditions.An example problem is solved and the economic implications of the formulation and its solution are reviewed.     

The convergence of diagonal Padé approximants and the Padé Conjecture

Questions related to the convergence problem of diagonal Padé approximants are discussed. A central place is taken by the Padé Conjecture (also known as the Baker-Gammel-Wills Conjecture). Partial results concerning this conjecture are reviewed and weaker and more special versions of the conjecture are formulated and their plausibility is investigated. Great emphasis is given to the role of spurious poles of the approximants. A conjecture by Nuttall (1970) about the number and distribution of such poles is stated and its importance for the Padé Conjecture is analyzed.     

Remote monitoring of environmental particulate pollution: a problem in inversion of first-kind integral equations

The possibility of remotely sensing the optical properties of scattering particulates from the variations in either the angular or the spectral characteristics, or both, of the radiation they transmit or scatter, is a problem of fundamental importance in the monitoring of environmental particulate pollution. It is shown that the corresponding problem is (or can be brought to) one of inverting first kind Fredholm integral equations. The solution to this problem would also enable one to follow the dynamical evolution of the polluted environment if it can be obtained in a time scale that is comparable to, or shorter than, the time constant of the physical measurements.The direct problem of how given physical parameters of such particles affect the transmission and scattering of incident radiation is first analyzed on the basis of the corresponding radiative transfer problem, including single and multiple scattering, and polarization induced on scattering. The various available methods for reconstructing the size distribution from the observed directly transmitted or scattered light are reviewed, particularly with regard to their main advantages and shortcomings. For direct light transmission, these include: library, iterative, and least-squares methods; the trial-and-error method; the matrix inversion method with smoothing constraint (MIM); the resolution accuracy trade-off method; and the analytical method. A minimization search method with smoothing constraint, an essential modification to the MIM, is also proposed. The corresponding methods for singly and multiply scattered light are likewise reviewed. The proposed forward-scattering method is shown to provide excellent reconstructions from either angular or spectral light measurements under proper experimental conditions. It can also be coupled with a minimization search in order to provide simultaneously the complex refractive index of the particles. The potentialities of other methods for the complete multiple scattering problem—the minimization search method, quasilinearization method, and small-angle Gaussian approximation method—are also studied.     

现代优化计算方法在蛋白质结构预测中的应用

现代优化计算方法在蛋白质结构预测中占有重要地位.简要地介绍了模拟退火算法,遗传算法,人工神经网络和图论算法在蛋白质结构预测中的应用.对国内外近年来应用这些算法,特别是在蛋白质构象搜索问题中,解决蛋白质结构预测的研究作了回顾,并分析、比较了这几种算法的效果和特点.     

Combinatorial analysis (matrix problems,order theory)

The survey is devoted to certain current problems in general combinatorial mathematics. The contemporary state-of-the-art of the theory of permanents, questions on the existence and the enumeration of matrices with nonnegative elements, and a number of problems connected with latin rectangles (enumeration, problem of completing a latin square, equidistant arrays) are examined. The main directions in combinatorial theory in connection with selection problems also are analyzed: matroid theory, transversals, extremal problems (coverings, depth of a matrix, Sperner families). Principal attention is paid to the papers reviewed in Referativnyi Zhurnal “Matematika” during 1975–1979.     

最优化方法任分子识别中的应用

分子识别是指两个或多个分子靠非共价键专一地结合在一起．分子识别在物质的形成,细胞信号的传递,基因信息的表达和药物的设计等方面起重要的作用．我们首先对数学和计算方法在分子识别上的应用作了回顾,并从量子力学,经典分子力学和热力学上解释分子识别可转换成一类最优化问题．其次,我们指出了解决这类最优化问题的困难．最后,我们报告了在预报配体与蛋白质识别上所获得的一类新的选择方法．这类方法可将预报的成功率从63％提高到90％．     

邮政运输网络中的邮路规划和邮车调度问题评注

对2007年全国研究生数学建模竞赛D题的命题背景和问题内容进行了分析,并对问题所涉及到的系统分析思路和数学建模及优化求解方法进行了评述.     

A Convergence Proof for Constrained Finite Element Solutions

A convergence proof is given for the finite-element solutionof the infinite dimensional quadratic programming problem ofminimizing a quadratic functional subject to linear constraints.The proof for the unconstrained problem is briefly reviewed,and then extended to the constrained case. Only the first partof the proof is given, in which necessary conditions for convergenceare derived for the specific problem and its finite-elementapproximation. The final step of proving that any problem doesobey these conditions will depend on the specific problem, butit is shown that if the finite element formulation is pointwiseconvergent and the unconstrained problem is convergent, thenso too will be the constrained problem.     

On Solving the Transportation Problem

The Hitchcock transportation problem is perhaps one of the ‘most solved’ linear programming problems in existence. We shall propose yet another computation for the problem....¹The current computational status of the transportation problem is reviewed, and the claims of three papers that recently appeared in this journal are put into perspective.     

一维非齐次BBM方程初边值问题的整体吸引子

研究了一维非齐次BBM方程ut-uxxt-(x^2n 1)x=f(u) γuxx g(x),ux(0,t)=0,u(1,5)=0,u(x,0)=u0(x).的初值边界问题，利用Sobolev插值不等式，对解做关于时间t的一致性先验估计，证明了该问题的整体吸引子的存在性．