钢管订购与运输问题一的数学模型与求解

本文针对 2 0 0 0年全国大学生数学建模竞赛 B题—钢管订购与运输问题的问题 ,建立了数学模型 ,并给出了该数学模型的精确求解     

探井布局问题的遗传算法

首先建立探井布局问题的数学模型 .其次基于所建立的数学模型 ,给出了求解探井布局问题的遗传算法 ,并就一个具体问题进行了计算 .计算结果表明 ,用遗传算法求解探井布局问题耗时少 ,适应性好 ,且对于处理大规模的探井布局问题十分有效 .     

钢管订购与运输问题三的数学模型与灵敏度分析

本文针对 2 0 0 0年全国大学生数学建模竞赛 B题——钢管订购与运输问题的问题 ( 3) ,建立了数学模型 ,给出了该数学模型的精确求解 .然后对问题 ( 1 )与问题 ( 3)给出了灵敏度分析 .     

构造数学模型解应用问题

本刊及兄弟刊物中有关文章多次提到了构造数学模型解决实际问题。但究竟哪些类应用题可以通过构造数学模型来解,又都构造出怎样的数学模型去解。本文试着把可以使用构造数学模型来解的系列应用题作一初步归类。     

数学解题 中的模型化思考

数学模型是联系客观世界与数学的桥梁 .数学模型是用数学语言来模拟空间形式和数量关系的模型 .广义地看 ,一切数学概念、公式、理论体系、算法系统都可称为数学模型 ,如 :算术是计算盈亏的模型 ,几何是物体外形的模型等 .狭义地看 ,只有反映特定问题的数学结构才称为数学模型 ,如一次函数是匀速直线运动的模型 ,不定方程是鸡兔同笼问题的模型等 .数学模型方法是针对要解决的问题来构造相应的数学模型、再通过对数学模型的研究去解决实际问题的一种数学方法 .数学模型方法在解题中的基本步骤是 :( 1 )从要解决的问题中恰当构建相应的数学模…     

对工科在校生应如何进行数学训练

随着计算机技术的日益发展,要求工程师解决的问题越来越复杂。本文讨论了在工科课程中引入这些内容的后果。并且强调了建立数学模型的日益重要性。提出了与建立数学模型教学有关的问题及把它们应用于工科课程的一些方法。     

公交转车的最短时间模型及求解

针对2007年全国大学生数学建模竞赛B题——"乘公交,看奥运"中的关于公交线路的选择问题,建立了最短时间的数学模型,并给出了该数学模型的精确求解.     

数据资料与拟合模型

1　建模中的数据资料组建数学模型的目的是想利用它来有效地分析和解决实际问题,而数据资料就是数学模型与实际问题相联系的重要途径和手段.这里所说的数据资料指的是人们从实际问题中所收集到的事实观察值和测量值.然而由于实际问题的复杂性,使得我们所得到的数据资料有可能是不精确的或者不完善的.但是与我们所组建的数学模型相比较,它更直接来自于现实世界,并带有大量与实际问题相关的信息,所以,数据资料应该是组建数学模型的重要依据和检验数学模型的重要标准.因此,在建模过程中如何处理好数据资料和数学模型的关系就显得非常重要.在建…     

构建数学模型 培养解题能力

把实际问题转化为一个数学问题,通常称为数学模型.提高中学数学教学质量,最重要的是学生学到有用的数学,构建数学模型也是中学数学教学改革的方向.自实施新课标以来,以物理、化学、生物、医学等学科知识为背景的跨学科综合题颇受关注.有些问题用常规方法难以解决,往往需要构建一个与之有关的数学模型.建立数学模型的过程称为数学建模.数学建模就是要把现实     

中考数学建模思想解读

所谓数学模型,就是用数学符号、式子、图形等把问题的本质属性进行简洁的刻画,用数学语言解释一些客观现象,揭示问题的发展与变化规律.数学中考常见数学模型有:三角函数模型、方程(组)模型、不等式(组)模型和函数模型等.数学建模的过程就是把生活实际中的问题转化为数学问题,运用数学模型     

电网安全调度中输电阻塞管理的演化策略

输电阻塞是电力系统运行中的常见问题 .本文建立了用于电网安全调度中输电阻塞管理的数学模型——带线性约束的多目标模糊优化问题模型 ,给出了求解该模型的演化策略 .实际的计算结果表明 ,演化策略解决输电阻塞问题是有效的 .     

On the Weak Solutions to Steady-State Mixed Navier—Stokes/Darcy Model

Acta Mathematica Sinica, English Series - In this paper, for the mixed Navier—Stokes/Darcy model with Beavers—Joseph—Saffman’s interface condition, we first establish an a...     

The use of fuzzy variables in pert

In this paper we present a method—called Fpert—for estimating a project completion time in the situation when activity duration times in the project network model are given in the form of fuzzy variables—fuzzy sets on time space. Theoretical foundations of the method as well as results of calculations derived from a simple example are included.     

管道订购与运输问题

本文在详细分析的基础上 ,通过合理假设并引入等价转换原则 ,将管道订购与运输问题转化为单一的公路运输问题 .运用组合优化的思想和方法 ,给出了数学模型——产量未定的运输模型 .针对此模型 ,我们设计了“改进的最小元素法”和“改进的伏格尔法”,先求得了一个初始解 ,再通过“试探法”和“迭代法”进行调整优化 ,最后得出结果 :对第一问 ,最小总费用为 1 2 790 1 9万元 ;对第三问 ,最小总费用为 1 4 0 7383万元     

Performability Analysis of Fork-join Queueing Systems

Fork-join queueing systems offer a natural modelling paradigm for parallel processing systems and for assembly operations in automated manufacturing. The analysis of fork-join queueing systems has been an important subject of research in recent years. Existing analysis methodologies—both exact and approximate—assume that the servers are failure-free. In this study, we consider fork-join queueing systems in the presence of server failures and compute the cumulative distribution of performability with respect to the response time of such systems. For this, we employ a computational methodology that uses a recent technique based on randomization. We compare the performability of three different fork-join queueing models proposed in the literature: the distributed model, the centralized splitting model, and the split-merge model. The numerical results show that the centralized splitting model offers the highest levels of performability, followed by the distributed splitting and split-merge models.     

Development and calibration of a currency trading strategy using global optimization

We have developed a new financial indicator—called the Interest Rate Differentials Adjusted for Volatility (IRDAV) measure—to assist investors in currency markets. On a monthly basis, we rank currency pairs according to this measure and then select a basket of pairs with the highest IRDAV values. Under positive market conditions, an IRDAV based investment strategy (buying a currency with high interest rate and simultaneously selling a currency with low interest rate, after adjusting for volatility of the currency pairs in question) can generate significant returns. However, when the markets turn for the worse and crisis situations evolve, investors exit such money-making strategies suddenly, and—as a result—significant losses can occur. In an effort to minimize these potential losses, we also propose an aggregated Risk Metric that estimates the total risk by looking at various financial indicators across different markets. These risk indicators are used to get timely signals of evolving crises and to flip the strategy from long to short in a timely fashion, to prevent losses and make further gains even during crisis periods. Since our proprietary model is implemented in Excel as a highly nonlinear “black box” computational procedure, we use suitable global optimization methodology and software—the Lipschitz Global Optimizer solver suite linked to Excel—to maximize the performance of the currency basket, based on our selection of key decision variables. After the introduction of the new currency trading model and its implementation, we present numerical results based on actual market data. Our results clearly show the advantages of using global optimization based parameter settings, compared to the typically used “expert estimates” of the key model parameters.     

ENVIRONMENTAL POLLUTION AND UNILATERAL CONTROL IN AN OPEN ECONOMY

In this paper we study two questions in environmental economics. First, within the context of a simple 2 × 2 × 2 static general equilibrium model, we seek to determine the conditions under which environmental policy, pursued unilaterally by a large country will make that country worse off. The empirical dimension of this question is stressed, and the key parameters which are germane to any policy discussion regarding this issue are identified. Second, we study—once again from the perspective of a large country—the possibility of using the domestic tax structure optimally to attain environmental policy objectives. Keeping the empirical dimension of the question in mind, we show how to compute optimal externality correcting taxes. We then briefly focus on the links between our stylized analytical model and the applied general equilibrium models currently being developed to study the effects of environmental policy quantitatively.     

Exploring Images of Parental Participation in Mathematics Education: Challenges and Possibilities

In this article, we draw on research within a large project on parental involvement in mathematics education in working-class Latino communities. Our research is situated within a sociocultural framework and, in particular, the concept of funds of knowledge. We also draw on research on parental involvement in education, particularly that which critically examines issues of power and perceptions of parents. We build on the concept of dialogic learning and on the characterization of parents as intellectual resources and present a model for parental involvement in mathematics in which parents engage as (a) parents, (b) learners, (c) facilitators, and (d) leaders. In particular, in this article, we focus on the third component—parents as facilitators of mathematics workshops for the community at large—centering on some of the challenges as parents and teachers engage in this type of collaboration. We also look at the possibilities afforded by a model for parental involvement that views parents as intellectual resources. By looking at examples of interactions among parents and teachers, and among parents and children, in mathematics workshops, we challenge conventional notions about parental involvement—in particular, as they apply to working-class, language/ethnic "minority" parents.     

多主体参与下我国光伏设备合作研制演化博弈模型

针对我国光伏设备合作研制的问题,建立了以光伏企业、设备制造商和地方政府为博弈主体的三方演化博弈模型。通过演化稳定策略分析可知,实现更多的创新价值增值是各方主体趋于合作的基础,确定合理的利益分配比例是光伏设备合作研制成为可能的关键;与此同时,应构建惩罚机制以抑制各方主体的背叛行为,并通过政府的有效激励以降低合作研制成本。     

Singularity formation in thin jets with surface tension

We derive and study asymptotic models for the dynamics of a thin jet of fluid that is separated from an outer immiscible fluid by fluid interfaces with surface tension. Both fluids are assumed to be incompressible, inviscid, irrotational, and density-matched. One such thin jet model is a coupled system of PDEs with nonlocal terms—Hilbert transforms—that result from expansion of a Biot-Savart integral. In order to make the asymptotic model well-posed, the Hilbert transforms act upon time derivatives of the jet thickness, making the system implicit. Within this thin jet model, we demonstrate numerically the formation of finite-time pinching singularities, where the width of the jet collapses to zero at a point. These singularities are driven by the surface tension and are very similar to those observed previously by Hou, Lowengrub, and Shelley in large-scale simulations of the Kelvin-Helmholtz instability with surface tension and in other related studies. Dropping the nonlocal terms, we also study a much simpler local model. For this local model we can preclude analytically the formation of certain types of singularities, though not those of pinching type. Surprisingly, we find that this local model forms pinching singularities of a very similar type to those of the nonlocal thin jet model. © 1998 John Wiley & Sons, Inc.