Transition to turbulence, small disturbances, and sensitivity analysis I: A motivating problem

For over 100 years, researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized Navier-Stokes equations. However, for many simple flows this approach fails to match experimental results. Recently, new scenarios for transition have been proposed that are based on the interaction of the linearized equations of motion with small disturbances to the flow system. These new “mostly linear” theories have increased our understanding of the transition process, but the role of nonlinearity has not been explored in detail. This paper is the first of a two part work in which sensitivity analysis is used to study the effects of small disturbances on transition to turbulence. In this part, we study a highly sensitive one-dimensional Burgers' equation as a motivating problem. Sensitivity analysis is used to predict the large changes in solutions in the presence of a small disturbance. Also, sensitivity analysis is shown to provide more information about the disturbed nonlinear problem than a purely linear analysis of the problem. In the second part of this work, this analysis will be extended to the three-dimensional Navier-Stokes equations to show that small disturbances have great potential to trigger transition to turbulence.     

出租车司机社会贡献评价方法研究

出租车司机的社会贡献对于促进城市经济发展和社会进步具有重要的作用,评价出租车司机的社会贡献是激励出租车司机多做社会贡献的重要手段。为了评价出租车司机的社会贡献,本文提出了一种基于实际出租车运营数据的评价方法。本文设计了运营特性、重点区域、恶劣天气、大事件四个体现司机社会贡献的指标,以此构建了出租车司机社会贡献评价指标体系,进而选用了主观赋权法G1法和客观赋权法拉开档次法相结合的赋权方式对指标赋权,并选择四种评价信息集结方法建立了出租车司机社会贡献评价模型。最后,通过实际的出租车运营数据验证了本方法的可行性。本文为评价出租车司机社会贡献提供了一种研究思路和方法,并对政府政策的制定和企业策略的实施具有一定的启示。     

快递企业航空货运网络的构建

快递业竞争激烈,构建高效合理的航空货运网络是快递企业提高竞争力的重要手段。“枢纽—辐射”式航空货运网络是整合航空快递资源、提高航空快递资源利用效率、提高快递企业竞争力的有效模式。本文以降低航空快递网络成本、加快航空快递处理时间为目标,从航空快递网络枢纽的选取、指派关系的确定、枢纽个数的选择三个方面研究了航空快递网络模型建立问题,选用遗传算法求解不同枢纽个数下航空快递网络的运输成本,并据此进行枢纽的选取,运用重力模型法进行指派关系的确定,在此基础上运用超效率DEA模型确定枢纽个数。接着,以包含17个节点的顺丰航空快递网络的规划为例,对本文所提出的模型和算法进行了验证,验证结果证实了模型的合理性。本文的研究为快递企业构建航空货运网络提供了科学实用的方法,该方法的使用可以降低航空货运成本,提高效率,从而提高快递企业的竞争力。     

Factorisation of Littlewood-Richardson coefficients

The hive model is used to show that the saturation of any essential Horn inequality leads to the factorisation of Littlewood-Richardson coefficients. The proof is based on the use of combinatorial objects known as puzzles. These are shown not only to account for the origin of Horn inequalities, but also to determine the constraints on hives that lead to factorisation. Defining a primitive Littlewood-Richardson coefficient to be one for which all essential Horn inequalities are strict, it is shown that every Littlewood-Richardson coefficient can be expressed as a product of primitive coefficients. Precisely the same result is shown to apply to the polynomials defined by stretched Littlewood-Richardson coefficients.     

煤层注水非线性渗流方程的解析解及应用

本文运用流体力学,多孔介质流体动力学,渗流理论等理论知识,结合实验室和现场试验,从理论上对煤层注水预湿煤体机理进行了研究.分析了煤层注水过程,建立起了煤层注水的数学模型;对煤层注水的边界条件进行了描述.由于描述煤层注水的方程组为非线性的,为简化它们,利用了因次分析理论,引入了注水压力,渗透速度,煤水份增加量等无因次量.之后讨论了其解析和近似解.另外:结合实际煤层注水的科研项目,说明了该理论指导煤层注水及设计的作用和重要性.     

Effects of imprecise weighting in hierarchical preference programming

Preference programming is a general term for multi-criteria decision analytical approaches allowing incomplete preference information. In the PAIRS method, interval judgments are assigned to weight ratios between attributes to model imprecision in multi-attribute value trees. This paper studies the effects of a hierarchical model structure on the overall imprecision, as the form of the hierarchy also affects the form of imprecision that can be assigned to the model. The aim is to find out good procedural practices for reducing overall imprecision descending inherently from the model structure. The study provides simulation results about the ability of various weighting schemes to identify dominated alternatives, which are discussed with respect to other issues related to the weighting process. According to the results, a hierarchical model is structurally somewhat more unable to identify dominances than a corresponding nonhierarchical model, but its cognitive advantages often cancel out this. The results also suggest paying reasonable attention to the precision of the lower level judgments and to identifying possible correlations between the criteria.     

Hemivariational inequality approach to constrained problems for star-shaped admissible sets

The hemivariational inequality approach is applied to establish the existence of solutions to a large class of nonconvex constrained problems in a reflexive Banach space. The admissible sets are supposed to be star-shaped with respect to a ball. Due to a discontinuity property of the Clarke directional differential related to the corresponding distance functions, the proposed method permits one to attain the solution without passing to zero with the penalization parameter. Some applications to nonconvex constrained variational problems illustrate the theory.     

Filtering germs: Groupoids associated to inverse semigroups

We investigate various groupoids associated to an arbitrary inverse semigroup with zero. We show that the groupoid of filters with respect to the natural partial order is isomorphic to the groupoid of germs arising from the standard action of the inverse semigroup on the space of idempotent filters. We also investigate the restriction of this isomorphism to the groupoid of tight filters and to the groupoid of ultrafilters.     

Mathematical programming modeling of the Response Time Variability Problem

The Response Time Variability Problem (RTVP) is a scheduling problem that has recently been defined in the literature. The RTVP has a broad range of real-life applications from manufacturing to services and information technology. A previous study developed a position exchange heuristic to apply to initial sequences for the RTVP, and a MILP (Mixed Integer Linear Programming) to obtain optimal solutions with a practical limit of 25 units to be scheduled. This paper aims to improve the best mathematical programming model developed thus far in order to solve larger instances up to 40 units to optimality. The contribution of this paper is 4-fold: (i) larger instances can be solved to optimality by the off the shelf standard software; (ii) the new optimal solutions of the RTVP can be used to compare the results of heuristic procedures; (iii) the importance of modeling is demonstrated, as well as the huge impact that reformulation, redundant constraints and the elimination of symmetries have on the efficiency of MILPs is clearly established; finally (iv) a challenge to develop a customized optimization algorithm to rival the MILP solution efficiency for the RTVP is put forward.     

一类广义指派问题的有效解法

提出一类广义指派问题,这类问题研究的是m个人执行n项任务,每个人执行的任务数、执行每项任务的人数以及总的指派人项数均有限制,要求最优指派.对这类广义指派问题建立了数学模型,并找到一种转换方法,将这类问题转换为平衡指派问题,从而用传统方法,如匈牙利法求解.最后用一个箅例来说明这种转换方法的简便和有效性.     

Asymptotic behavior of continuous stochastic games

Summary The aim of this paper is to analyze the asymptotic behavior of the value functions of a continuous stochastic game as the number of stages grows to infinity or the discount factor approaches 1. After the setup of the problem we prove that, in both cases, the extrema of the value functions converge to the same limits. The convergence of the value functions is then obtained from the unicity of the solution of a functional problem and it is thus possible to design hypotheses that assure the convergence to a constant. This allows to assign a value to an undiscounted infinite-stage stochastic game in several senses and to show that optimal strategies are available for both players. Furthermore the boundedness of the remainders of the value function after removing the principal terms is analyzed, with appropriate hypotheses, and related to the existence of solutions of a Howard's type functional equation. This allows to show that for an infinite-stage undiscounted stochastic game optimal stationary strategies exist at least if this functional equation has some solution.     

Pareto optimal solutions of a cost–time trade-off bulk transportation problem

A cost–time trade-off bulk transportation problem with the objectives to minimize the total cost and duration of bulk transportation without according priorities to them is considered. The entire requirement of each destination is to be met from one source only; however a source can supply to any number of destinations subject to the availability of the commodity at it. Two new algorithms are provided to obtain the set of Pareto optimal solutions of this problem. This work extends and generalizes the work related to single-objective and prioritized two-objective bulk transportation problems done in the past while providing flexibility in decision making.     

PAC-Bayesian bounds for randomized empirical risk minimizers

The aim of this paper is to generalize the PAC-Bayesian theorems proved by Catoni [6, 8] in the classification setting to more general problems of statistical inference. We show how to control the deviations of the risk of randomized estimators. A particular attention is paid to randomized estimators drawn in a small neighborhood of classical estimators, whose study leads to control of the risk of the latter. These results allow us to bound the risk of very general estimation procedures, as well as to perform model selection.      

Scheduling of corrugated paper production

Corrugated paper is produced by gluing three types of papers of the same breadth. Given a set of orders, we first assign each order to one of the standard breadths, and then sequence those assigned to each standard breadth so that they are continuously manufactured from the three rolls of the specified standard breadth equipped in the machine called corrugator. Here we are asked to achieve multi-goals of minimizing total length of roll papers, total loss of papers caused by the differences between standard breadths and real breadths of the orders, and the number of machine stops needed during production. We use integer programming to assign orders to standard breadths, and then develop a special purpose algorithm to sequence the orders assigned to each standard breadth. This is a first attempt to handle scheduling problems of the corrugator machine.     

财政支农专项转移支付制度制定:矫正工商资本下乡异化行为

制定怎样的财政支农专项转移支付制度才能正确引导与矫正工商资本下乡行为？为了探索出能够有效矫正工商资本下乡异化行为的财政制度,文章采用动态博弈的方法剖析工商资本下乡企业的行为。经深入研究发现,国家财政支付制度的实施成效取决于分配制度(“勉励”还是“嘉奖”)及工商资本下乡企业的发展阶段。随着企业的逐渐壮大,在政策机制中融入“嘉奖”制度较事后的“勉励”制度,对于发展农业提升企业利益与反哺农民改善民生的两种行为,可更好的引导工商资本下乡正确与合理的分配资金。     

Teachers’ conceptions of tangent line

In order to study the conceptions, and their evolutions, of the tangent line to a curve an updating workshop which took place in México was designed for upper secondary school teachers. This workshop was planned using the methodology of cooperative learning, scientific debate and auto reflection (ACODESA) and the conception-knowing-concept model (cK¢) developed mainly by Balacheff. In order to initiate the conceptions reorganization, an initial activity was made in the graphic frame; it seems optimal to start the debates without leading participants to failure. The mathematical core of the workshop was formed by an algebraic method to find tangents to algebraic curves which is close to Descartes’ method. The ACODESA methodology allowed some intense debates mainly concerning the local character of a tangent, generating the teachers’ cognitive unbalance which is a starting point for the refinement or transformation of their conceptions. On the other hand, the cK¢ model allows to understand the conceptions of participants and to analyze the evolution of their knowings.     

Modeling customer impatience in a newsboy problem with time-sensitive shortages

Customers across all stages of the supply chain often respond negatively to inventory shortages. One approach to modeling customer responses to shortages in the inventory control literature is time-dependent partial backlogging. Partial backlogging refers to the case in which a customer will backorder shortages with some probability, or will otherwise solicit the supplier’s competitors to fulfill outstanding shortages. If the backorder rate (i.e., the probability that a customer elects to backorder shortages) is assumed to be dependent on the supplier’s backorder replenishment lead-time, then shortages are said to be represented as time-dependent partial backlogging. This paper explores various backorder rate functions in a single period stochastic inventory problem in an effort to characterize a diversity of customer responses to shortages. We use concepts from utility theory to formally classify customers in terms of their willingness to wait for the supplier to replenish shortages. Under mild assumptions, we verify the existence of a unique optimal solution that corresponds to each customer type. Sensitivity analysis experiments are conducted in order to compare the optimal actions associated with each customer type under a variety of conditions. Additionally, we introduce the notion of expected value of customer patience information (EVCPI), and then conduct additional sensitivity analyses to determine the most and least opportune conditions for distinguishing between customer behaviors.     

Auxiliary tool allocation in flexible manufacturing systems

This paper analyses a new approach to the machine loading problem arising in flexible manufacturing systems (FMSs). This approach allows the operations to be assigned to machines assuming that machines have access to all the tools required for their operations. This exploits the flexibility of the FMS completely. Next an allocation of tools to machines is determined which satisfies the tool requirements for each machine and minimizes the total number of tools. Thus this approach minimizes the unnecessary tool duplications in the system and maximizes the tool utilization. The problem is modeled as an integer linear program (ILP). We notice that the main problem has a block diagonal structure which is decomposable by relaxing a set of linking constraints. Each separated sub-problem represents a problem of allocation of a single type of tools. We develop a branch-and-bound based exact solution procedure and three heuristic procedures to solve the sub-problems. Our lower bounding approach uses Lanrangean relaxation. The solutions to the Lagrangean relaxation are further used to determine the branching sequences and to develop heuristic approaches. Since finding even a feasible solution to the main problem is NP-hard, we develop only enumerative procedures to solve the main problem. Finally, these solution procedures are tested on randomly generated test problems.     

考虑充电设施重入的电动汽车旅行商问题研究

出于减少环境危害和响应相关法规的考虑,物流企业开始逐步将运输车辆转变为电动汽车;而由于电动汽车的续航里程有限,对电动汽车的路径优化也将涉及充电设施。充电设施的“重入”是指电动汽车返回之前已经通过的充电设施进行充能的现象,它的存在需要改变经典旅行商问题模型中的“子回路约束”。本文聚焦于充电设施的“重入”,构建了一个无需预估充电设施重入次数上限的电动汽车旅行商问题模型,并通过引入路径可行性判别方法和增加充电设施选择与重复策略,设计了一种改进蚁群算法对问题进行求解。结果表明:与未考虑重入的模型相比,本文提出的考虑充电设施重入的模型能在电动汽车电池容量较低的情况下求出最优解,同时也能够使充电设施承担多次充电任务,从而在较少充电设施情况下依然能够得到可行的最优路径。