为什么在太阳系中至今尚未找到一颗逆行行星

本文用圆型限制三体问题的Jacobi积分来建立一个测检函数,用于确定测试质点作类行星运动时能否长留于一个确定的区域(可称为稳定域).经用电子计算机检定,对于质点作准圆形轨道的情况下,质点作类逆行行星运动的稳定域远小于质点作类顺行行星运动的稳定域.这说明了逆行行星存在的可能性很小.     

生态系统的参数确定问题

通过不同观测数据研究捕食者—被捕食者生态系统参数确定问题.研究了四种情形1.观察数据无误差,并已知一个参数值.这种情况下,参数可由其相轨线和最小二乘法精确确定.2.观察数据无误差,但所有参数未知.此时仅靠相轨线的研究,无论给出多少组精确数据,都无法精确确定这些参数.通过原非线性模型的数值计算和网格搜索法,至少需要4组数据,同样得到了精度较高的参数值.3.当观测数据有误差时,根据解的周期性,引入标准周期的概念,在一个标准周期里讨论参数的确定问题,并利用标准周期内的捕食者与被捕食者的数量均值与系统的平衡点的关系对参数进行修正,然后使用网格法进行搜索,进一步提高了参数的精度.4.当观测时间也有误差时,先选取相对最优的随机正态数对观测时刻进行修正,然后再利用3.的方法估计参数.     

Enabling the Practice of Mathematics Teachers in Context: Toward a New Equity Research Agenda

In this article, I address the need for a more clearly articulated research agenda around equity issues by proposing a working definition of equity and a focal point for research. More specifically, I assert that rather than pitting them against each other, we must coordinate (a) efforts to get marginalized students to master what currently counts as "dominant" mathematics with (b) efforts to develop a critical perspective among all students about knowledge and society in ways that ultimately facilitate (c) a positive relationship between mathematics, people, and equity on the planet. I make this argument partly by reviewing the literature on (school) contexts that engage marginalized students in mathematics. Then, I argue that the place that holds the most promise for addressing equity is a research agenda that emphasizes enabling the practice of teachers and that draws more heavily on design-based and action research, thereby redefining what the practice of mathematics means along the way. Specific research questions are offered.     

Enabling the Practice of Mathematics Teachers in Context: Toward a New Equity Research Agenda

In this article, I address the need for a more clearly articulated research agenda around equity issues by proposing a working definition of equity and a focal point for research. More specifically, I assert that rather than pitting them against each other, we must coordinate (a) efforts to get marginalized students to master what currently counts as “dominant” mathematics with (b) efforts to develop a critical perspective among all students about knowledge and society in ways that ultimately facilitate (c) a positive relationship between mathematics, people, and equity on the planet. I make this argument partly by reviewing the literature on (school) contexts that engage marginalized students in mathematics. Then, I argue that the place that holds the most promise for addressing equity is a research agenda that emphasizes enabling the practice of teachers and that draws more heavily on design-based and action research, thereby redefining what the practice of mathematics means along the way. Specific research questions are offered.     

Approximating the larger eddies in fluid motion V: Kinetic energy balance of scale similarity models

We first review a classical scale-similarity model used to simulate the motion of large eddies in a turbulent flow. The kinetic energy balance of this model is very unclear in theory. Experiments with it often have reported that an additional Smagorinski type subgridscale term is needed. This term is not benign; it can alter significantly the predicted long term dynamics of the large eddies. However, we also show that the principal of scale-similarity (introduced in 1980 by Bardina, Ferziger and Reynolds) can also give rise to other scale similarity models which have the correct kinetic energy balance.     

为什么大行星可以同时有顺行和逆行卫星

本文用圆型限制三体问题的Jacobi积分来建立一个能确定卫星是否稳定的测检函数.凡是对其主行星所作的瞬时椭圆轨道要素已知的卫星都可检定其稳定性.对于作准圆形轨道运动的卫星,我们可用电子计算机来求出它的稳定域,这域的界面是一个近似的扁椭球面.这闭面所包围的空间比“引力作用球”和其相应的卫星区的“Hill曲面”要小得多.由于卫星对其主行星的相对动能表示式对顺行和逆行轨道两者形式相同,所以两者可以在卫星的稳定域中同时存在.     

An efficient method for nonlinearly constrained networks

Many nonlinear network flow problems (in addition to the balance constraints in the nodes and capacity constraints on the arc flows) have nonlinear side constraints, which specify a flow relationship between several of the arcs in the network flow model. The short-term hydrothermal coordination of electric power generation is an example of this type. In this work we solve this kind of problem using an approach in which the efficiency of the well-known techniques for network flow can be preserved. It lies in relaxing the side constraints in an augmented Lagrangian function, and minimizing a sequence of these functions subject only to the network constraints for different estimates of the Lagrange multipliers of the side constraints. This method gives rise to an algorithm, which combines first- and superlinear-order multiplier methods to estimate these multipliers. When the number of free variables is very high we can obtain a superlinear-order estimate by means of the limited memory BFGS method fitted to our problem. An extensive computational comparison with other methods has been performed. The numerical results reported indicate that the algorithm described may be employed advantageously to solve large-scale network flow problems with nonlinear side constraints.     

基于随机活动工期的多模式现金流均衡项目调度优化

承包商在项目执行过程中的现金流均衡是保证项目成功的关键因素。本文研究基于随机活动工期的多模式现金流均衡项目调度问题,旨是在项目工期及鲁棒性阈值约束下合理安排活动执行模式与开始时间,实现承包商现金流均衡。本文通过构建整数规划优化模型对研究问题进行刻画,随后设计模拟退火算法进行求解,最后进行案例分析。结果表明:鲁棒性阈值虽然可以保证基准进度的稳定性,但是提高鲁棒性阈值水平反而不利于承包商的现金流均衡,该值过高时甚至得不到可行解。本文研究可为随机活动工期背景下承包商的现金流控制提供定量化决策支持。     

CFD application for coal/air balancing in power plants

Unbalanced coal/air flow in the pipe systems of coal-fired power plants will lead to non-uniform combustion in the furnace, and hence a overall lower efficiency of the boiler. A common solution to this problem is to put orifices in the pipe systems to balance the flow. It is well known that if the orifices are sized to balance clean air flow to individual burners connected to a pulverizer, the coal/air flow would still be unbalanced and vice versa. However, the current power industry practice throughout the world is to size orifices for balancing the clean air flow and accept the resulting imbalance in coal/air flow. Field tests are mostly conducted to verify a balanced clean air flow.     

Data and queueing analysis of a Japanese air-traffic flow

Congestion is a major cause of inefficiency in air transportation. A question is whether delays during the arrival phase of a flight can be absorbed more fuel-efficiently in the future. In this context, we analyze Japan’s flow strategy empirically and use queueing techniques in order to gain insight into the generation of the observed delays. Based on this, we derive a rule to balance congestion delays more efficiently between ground and en-route. Whether fuel efficiency can be further improved or not will depend on the willingness to review the concept of runway pressure.     

Hopf bifurcation in a conceptual climate model with ice–albedo and precipitation–temperature feedbacks

In this paper we analyse a dynamical system based on the so-called KCG (Källén, Crafoord, Ghil) conceptual climate model. This model describes an evolution of the globally averaged temperature and the average extent of the ice sheets. In the nondimensional form the equations can be simplified facilitating the subsequent analysis. We consider the limiting case of a stationary snow line for which the phase plane can be completely analysed and the type of each critical point can be determined. One of them can exhibit the Hopf bifurcation and we find sufficient conditions for its existence. Those, in turn, have a straightforward physical meaning and indicate that the model predicts internal oscillations of the climate. Using the typical real-world values of appearing parameters we conclude that the obtained results are in the same ballpark as the conditions on our planet during the quaternary ice ages. Our analysis is a rigorous justification of a generalization of some previous results by KCG and other authors.     

Emergy-based urban ecosystem health assessment: A case study of Baotou,China

Ecosystem health has been a hot topic of ecosystem management research for years. Considering the urban area as a complex ecosystem consisted of natural, societal and economic entities, urban ecosystem health assessment is necessary to be conducted for the scientific management and proper ecological restoration. Combining with the ecosystem service function of the urban ecosystem, theoretical framework and methodology of the urban ecosystem health assessment based on emergy are proposed and the temporal variation of the health level of the city are also outlined in this paper. Following the principle of ecosystem health assessment, four major factors, including vigor (V), organizational structure (O), resilience (R) and function maintenance (F), are integrated to construct a novel emergy-based urban ecosystem health index (EUEHI). Based on the EUEHI and comparing with those of five other typical Chinese cities, the case study of Baotou city shows that its urban ecosystem health level is steadily arising despite the year 2001 as a turning point. Due to the emphasis on the resource structure adjustment and utilization efficiency, Baotou has obtained a better organizational structure and service function for the total urban ecosystem.     

Creating Advanced Bases For Large Scale Linear Programs Exploiting Embedded Network Structure

In this paper, we investigate how an embedded pure network structure arising in many linear programming (LP) problems can be exploited to create improved sparse simplex solution algorithms. The original coefficient matrix is partitioned into network and non-network parts. For this partitioning, a decomposition technique can be applied. The embedded network flow problem can be solved to optimality using a fast network flow algorithm. We investigate two alternative decompositions namely, Lagrangean and Benders. In the Lagrangean approach, the optimal solution of a network flow problem and in Benders the combined solution of the master and the subproblem are used to compute good (near optimal and near feasible) solutions for a given LP problem. In both cases, we terminate the decomposition algorithms after a preset number of passes and active variables identified by this procedure are then used to create an advanced basis for the original LP problem. We present comparisons with unit basis and a well established crash procedure. We find that the computational results of applying these techniques to a selection of Netlib models are promising enough to encourage further research in this area.     

Discrete storage processes and their Poisson flow and fluid flow approximations

Consider discrete storage processes that are modulated by environmental processes. Environmental processes cause interruptions in the input and/or output processes of the discrete storage processes. Due to the difficulties encountered in the exact analysis of such discrete storage systems, often Poisson flow and/or fluid flow models with the same modulating environmental processes are proposed as approximations for these systems. The analysis of Poisson flow and fluid flow models is much easier than that of the discrete storage processes. In this paper we give sufficient conditions under which the content of the discrete storage processes can be bounded by the Poisson flow and the fluid flow models. For example, we show that Poisson flow models and the fluid flow models developed by Kosten (and by Anick, Mitra and Sondhi) can be used to bound the performance of infinite (finite) source packetized voice/data communication systems. We also show that a Poisson flow model and the fluid flow model developed by Mitra can be used to bound the buffer content of a two stage automatic transfer line. The potential use of the bounding techniques presented in this paper, of course, transcends well beyond these examples.Supported in part by NSF grant DMS-9308149.     

A conic quadratic formulation for a class of convex congestion functions in network flow problems

In this paper we consider a multicommodity network flow problem with flow routing and discrete capacity expansion decisions. The problem involves trading off congestion and capacity assignment (or expansion) costs. In particular, we consider congestion costs involving convex, increasing power functions of flows on the arcs. We first observe that under certain conditions the congestion cost can be formulated as a convex function of the capacity level and the flow. Then, we show that the problem can be efficiently formulated by using conic quadratic inequalities. As most of the research on this problem is devoted to heuristic approaches, this study differs in showing that the problem can be solved to optimum by branch-and-bound solvers implementing the second-order cone programming (SOCP) algorithms. Computational experiments on the test problems from the literature show that the continuous relaxation of the formulation gives a tight lower bound and leads to optimal or near optimal integer solutions within reasonable CPU times.     

Numerical simulation of stirred liquid-liquid systems

The numerical simulation of drop size distributions in stirred liquid-liquid systems requires, on one hand, the simulation of the flow field in the stirred tank and, on the other hand, the calculation of the population dynamical processes. These processes, in the considered application coalescence and breakage, describe how the number and the sizes of the drops in the dispersed phase change with time. In the presented approach, the (Reynolds-averaged) Navier-Stokes equations (with k -ε turbulence model), describing the turbulent flow in the stirred tank, are solved with a CFD code and the population balance equation, accounting for coalescence and breakage of the drops, is simulated with a population balance solver. The coupling of the two solvers is realized as a oneway coupling, i. e. the results of the CFD simulation are used for the calculation of the population dynamical processes. We will explain how the coupling can be realized, motivate why this type of coupling was chosen, and present simulation results. However, we will also discuss arising problems and risks of simulator coupling. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

等效均衡函数的性质及均衡函数的构造

从均衡函数的等效性出发研究均衡函数的性质,证明了等效的均衡函数之和、积以及数乘仍为均衡函数,并且得到的新均衡函数与原均衡函数等效,这些性质表明等效的均衡函数关于加法和乘法运算均具有半群的代数结构。另外,进一步讨论了构造均衡函数的方法,给出了两个构造均衡函数的定理,该方法具有一般性,现有文献中的均衡函数几乎都能由其构造得到。     

How do things go from bad to worse?

Humans are constantly making evaluations about the direction of movement in time of systems perceived as relevant, in terms of whether things are moving to the better or to the worse. The relevant system may be very small or as large as the whole planet earth; evaluations seldom go beyond the solar system. We evaluate things like health, wealth, security, justice, etc. and we have a strange capacity for putting many diverse variables together into a single rough evaluation. Accountants evaluate the state of a balance sheet or position statement quantitatively in terms of dollars; economists evaluate aggregates like the GNP. But almost everyone goes beyond quantification into rough, qualitative evaluations of the total state of a system. The evaluation of overall systems runs into the difficulty that different persons evaluate the same perceived change differently. Nevertheless, there are many processes in society by which differing evaluations are coordinated, even if they are not reconciled. The market is one, politics is another, and the moral order is a third. In large systems we are unlikely to come out with a single answer to even the question of whether things are getting better or worse. But we can identify certain instances where there is wide agreement that a movement is for the worse: the cliffs-disasters, premature deaths, losses of liberty, etc. We can furthermore specify certain dynamic systems likely to produce these dramatic worsenings, and perhaps do something about them.     

A unsplitting finite volume method for models with stiff relaxation source terms

We developed an unsplitting finite volume scheme to account the delicate nonlinear balance between numerical approximations of the hyperbolic flux function and the source linked to balance laws. The method is Riemann-solver-free and no upwinding technique is used. By means of this new approach, we conducted an analysis for two new models of balance laws linked to compositional and thermal flow in porous media problems, under and without a thermodynamic equilibrium hypothesis. For concreteness, we adopt the nitrogen and steam injection models in a porous media. To this model we found an interesting behavior linked to the relaxation term, which is the existence of a non-monotonic traveling wave. We applied this numerical technique to others well-known differential models with relaxation terms available in the literature. Qualitatively we were able to reproduce the expected results.     

Covariance in linearized elasticity

In this paper we covariantly obtain all the governing equations of linearized elasticity. Our motivation is to see if one can make a connection between invariance (covariance) properties of the (global) balance of energy in nonlinear elasticity and those of its counterpart in linear elasticity. We start by proving a Green-Naghdi-Rivilin theorem for linearized elasticity. We do this by first linearizing energy balance about a given reference motion and then by postulating its invariance under isometries of the Euclidean ambient space. We also investigate the possibility of covariantly deriving a linearized elasticity theory, without any reference to the local governing equations, e.g. local balance of linear momentum. In particular, we study the consequences of linearizing covariant energy balance and covariance of linearized energy balance. We show that in both cases, covariance gives all the field equations of linearized elasticity.