TWO-DIMENSIONAL RIEMANN PROBLEMS： FROM SCALAR CONSERVATION LAWS TO COMPRESSIBLE EULER EQUATIONS

In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections： 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.     

CONVERGENCE RATE OFDISTRIBUTIONS OF TRIMMED SUMS

1.IntroductionLet{Xn,n2l}beasequenceofi.i.d.randomvariableswithnondegeneratedistributionF.Fornonnegativeintegersk.andrn,k. rn相似文献   

PHANTOM MAPS AND SPACES OF THE SAME n-TYPE FOR ALL n

1.IntroductionLetXbeaconnectedCWcomplexandX.denoteitsn-skeleton.Amapf:X-YiscalledaphantommapifitsrestrictiontoeachskeletonXuisnullhomotopic.ItiseasytoknowthateveryphantommapfromafiniteCWcomplexortoaspacewithonlyfinitenootrivialhomotopygroupsisnecessarilytrivialuptohomotopy.HenceessentialphantommapcanoccuronlywhenthedomainXisaninfinitedimensionalspaceorthetargetisaspacewithinfinitenontrivialhomotopygroups.Suchmapsappeartobenullhomotopicfromanumberofdifferentpoilltsofview;e.g.,theyinducethe…     

CONTINUOUS L-DOMAINS

61.IntroductionConiinuousDCPOisoneofthemostimportantstructuresin-domaintheory.Unfor-tunatelythecategoryofcolltinuousDCPOandtheScottcontinuousfunctionsfailstobeCartesianclosed,soitisaverysignificantproblemtofinditsmakimalCartesianclosedfullsubcategories.ThecategoryofL-domain'swasdiscoveredbyA.JungwhilesolvingtheproblemoffindingmtalmalCartesianclosedcategoriesofalgebraicDCPO's[1l,andrecentworksbyA.JungandG.Gund.r[2]showsthatthecategoryofL-domain'sisaninterestingcategoryOntheotherhand,i…     

POLES OF ZETA FUNCTIONS OF COMPLETE INTERSECTIONS

51.IntroductionLetF.beafinitefieldofqele~swithcharederisticp.LetXbeanThdilnensionalalgebraicsetdeadedoverF..ThezetafunctionofX/F.isdennedbywhereXOdenotesthesetofclosedpointsOfX/F.and#X(F.d)denotesthenUInberof.F.d-rationalpointsonX.ItiseasytoseethatZ(X,T)isapowerserieswithintegercoefficients.Dwork'srationalltytheoremIg]showsthatthezetafunctionZ(X,T)isrationalinT.ThuS,therearealgebraicintegerspll'.3Pr,pl,'3basuchthatThereisagoodreasonthatwemoantheabovezetafunctionbythepower(--1)"-…     

仿酉对称矩阵的构造及对称正交多小波滤波带的参数化

仿酉矩阵在小波、多小波、框架的构造中发挥了重要的作用.本文给出仿酉对称矩阵(简记为p.s.m.)的显式构造算法,其中仿酉对称矩阵是元素为对称或反对称多项式的仿酉矩阵.基于已构造的p.s.m.和已知的正交对称多小波(简记为o.s.m.),给出o.s.m.的参数化.恰当地选择一些参数,可得到具有一些优良性质的o.s.m.,例如Armlet.最后作这一个算例,构造出一类对称的Chui-Lian Armlet滤波带.     

Improvement of convergence to steady state solutions of Euler equations with weighted compact nonlinear schemes

The convergence to steady state solutions of the Euler equations for weighted compact nonlinear schemes (WCNS) [Deng X. and Zhang H. (2000), J. Comput. Phys. 165, 22-44 and Zhang S., Jiang S. and Shu C.-W. (2008), J. Comput. Phys. 227, 7294-7321] is studied through numerical tests. Like most other shock capturing schemes, WCNS also suffers from the problem that the residue can not settle down to machine zero for the computation of the steady state solution which contains shock waves but hangs at the truncation error level. In this paper, the techniques studied in [Zhang S. and Shu. C.-W. (2007), J. Sci. Comput. 31, 273-305 and Zhang S., Jiang S and Shu. C.-W. (2011), J. Sci. Comput. 47, 216-238], to improve the convergence to steady state solutions for WENO schemes, are generalized to the WCNS. Detailed numerical studies in one and two dimensional cases are performed. Numerical tests demonstrate the effectiveness of these techniques when applied to WCNS. The residue of various order WCNS can settle down to machine zero for typical cases while the small post-shock oscillations can be removed.     

名人名著谈统计学

W.E.Denting(1940),Discussion of Professor Hottelling's Paper "The Teaching of Statistics"(Ann.Math.Stat.Vol.11,457-470): Above all,a statistician must be a scientist. 最重要的是,统计学家应该是科学家.     

D.C.隶属函数模糊集及其应用(I)--D.C.隶属函数模糊集基本概念与性质

本文是D.C.隶属函数模糊集及其应用系列研究的第一部分.建立了D.C.隶属函数模糊集的基本概念.探讨了D.C.隶属函数模糊集的基本性质和D.C.隶属函数模糊集对一些常见的重要t模、余模和伪补的封闭性.并以此建立了丰富的模糊数学应用模型.     

FINITENESS CONDITIONS FOR GENERALIZED EXPONENTS OF DIGRAPHS

1.IntroductionR.A.BrualdiandBolianLiuintroducedin199011]theconceptofgeneralizedexponentsforprimitivedigraphs.Thisconceptisageneralizationofthetraditionalconceptoftheexponentsforprimitivedigraphsandhasbackgroundsinmemorylesscommunicationsystemsassociatedwithdigraphs.Inthispaperweshowthatgeneralizedexponentscanalsobedefinedfordigraphswhicharenotnecessarilyprimitive.WewillgivenecessaryandsufficientconditionsforthefinitenessofthegeneralizedexponentsexpD(k),f(D,k)andF(D,k).Theseideasandresultss…     

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.     

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。     

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.     

不确定环境下再制造生产调度研究

针对再制造过程中存在的再制造件质量状况和加工时间不确定性调度问题,分别采用随机数和三角模糊数表示质量状况和加工时间的不确定性。在满足工序顺序、机器等限制下,将各自带有权重系数的最大完工时间和总成本之和最小值当做目标函数,构造不确定环境下再制造生产调度模糊模型且转换成确定的单目标非线性规划模型。应用多层编码遗传算法求解某个再制造子系统算例得到,决策者对于最大完工时间和总成本的重视程度不同,调度方案不同,其需要根据自身关注的重点做出决策,选择合适的调度方案。并且调度结果会受到决策者消极或积极态度的影响,态度越积极,结果越好,反之,态度越消极,结果越差,从而检验了再制造生产调度模型的正确性。希望为再制造实现产业化,规模化提供相关参考意见。     

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.     

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。     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

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。     

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。     

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。