Area functions on affine planes

Oriented area functions are functions defined on the set of ordered triangles of an affine plane which are antisymmetric under odd permutations of the vertices and which behave additively when triangles are cut into two. We compare several elementary properties which such an area function may have (roughly speaking shear invariance, equality of area of the two triangles obtained by cutting a parallelogram along a diagonal, and equality of area of the two triangles obtained by cutting a triangle along a median). It turns out purely by arguments of elementary affine geometry (if cleverly arranged) that these properties are grosso modo equivalent, although one has to be careful about “pathological” situations. Furthermore, all oriented area functions satisfying these properties are explicitly determined. Finally they are compared with so-called geometric valuations.     

Analysis of repeated hashing

A performance analysis of an overflow handling method for hash files, here called repeated hashing, is reported. The basic idea of repeated hashing is to rehash the overflow records into a smaller separate storage area; the overflow records from this area are in turn hashed into a still smaller separate storage area, etc. The expected retrieval performance and the storage requirements are analysed, both for initial loading and steady state. The problem of optimally partitioning the total storage area is considered and the optimal solution is given. It is concluded, however, that the usefulness of repeated hashing is in doubt because there are methods having the same performance but requiring less maintenance.     

The discrete forward–reserve problem – Allocating space,selecting products,and area sizing in forward order picking

To reduce labor-intensive and costly order picking activities, many distribution centers are subdivided into a forward area and a reserve (or bulk) area. The former is a small area where most popular stock keeping units (SKUs) can conveniently be picked, and the latter is applied for replenishing the forward area and storing SKUs that are not assigned to the forward area at all. Clearly, reducing SKUs stored in forward area enables a more compact forward area (with reduced picking effort) but requires a more frequent replenishment. To tackle this basic trade-off, different versions of forward–reserve problems determine the SKUs to be stored in forward area, the space allocated to each SKU, and the overall size of the forward area. As previous research mainly focuses on simplified problem versions (denoted as fluid models), where the forward area can continuously be subdivided, we investigate discrete forward–reserve problems. Important subproblems are defined and computation complexity is investigated. Furthermore, we experimentally analyze the model gaps between the different fluid models and their discrete counterparts.     

统计分析方法在市场调研前期的应用

本文基于聚类分析和判别分析 ,对在众多的区域市场中如何选取一个或几个有代表性的区域市场进行了一些探索性的研究。并利用这种方法进行了一个关于在新产品上市的营销策划中如何进行营销试点市场的选取的实证分析     

An algorithm to solve a quantile optimization problem with loss function having a separable structure,and its application to an aerospace problem

A quantile minimization problem with loss function having separable structure is considered. The distribution of the random parameters is assumed to be normal. To solve the problem, the confidence method and the sample average approximation method are used. Thus, the problem is reduced to a combinatorial one, which is solved by using the variable neighborhood search. The suggested algorithm is applied to optimization of runway area. Parameters of the runway are selected to minimize the area taking into account random wind speed.     

基于哈密顿体系的平面无限解析元

在有限元法中,无限域的问题不便于处理求解。但无限域往往可以由规则的无限外域再加上有限的局部域组成。将无限域问题中的有限局部域用有限元法处理,在规则的无限外域中建立极坐标系,将规则无限域问题导向哈密顿体系,利用本征向量展开的方法,推导出一种新的半解析无限解析元,其刚度阵是精确的。该单元可用常规方法作为一个超级有限单元与有限的局部域连接。数值计算结果表明,该单元具有精度高,应用方便,数据处理非常简单的特点。对无限域问题的数值求解有重要意义。该方法可推广到三维无限域问题中。     

Determination of a Constitutive Friction Law Using an Elastic-Plastic Half-Space Model

Friction influences metal forming processes both in economic and technical terms. A precise understanding of friction is inevitable as friction restricts the potential of the product design. Friction depends on the occurring contact loads which is especially true for sheet-bulk metal forming (SBMF) as the incorporated contact loads appear in a very broad range. Numerical simulations, which are verified experimentally, are carried out to analyse contact interactions which typically appear in SBMF. On the one hand the multi-scale character of rough surfaces requires a very fine resolution of the contact area, on the other hand a large contact area is necessary to be representative. A half-space model is chosen for the contact analysis, because it only depends on the two-dimensional surface boundary which consumes less computing capacity than the finite element method (FEM) with its three-dimensional volume approach for the same surface resolution and area. The outcome is a constitutive friction law (CFL) consisting of two equations. The law is implemented into the framework of FEM to see the impact in a typical SBMF-process which aims to form metal sheet into cups with integrated gearing teeth. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

有保护区的海洋渔业资源离散动力学模型分析

假设海洋渔业资源分属于保护区和非保护区两个区域,本文建立一个渔业资源储量-捕捞力度模型,用聚合方法得到一个简化的离散动力系统,从而分析正不动点的存在性、稳定性以及关于保护区面积比例的局部分叉,运用中心流形定理分析平衡点的局部稳定性,并用数值模拟验证不动点的局部分叉.最后,用全局分析方法分析保护区面积比例变化对可行吸引域的结构和大小的影响,从而揭示保护区对渔业资源可持续利用的影响.     

Laplace方程有孔椭圆区域边值问题的解析解

本文利用相似流动替换方法 ,解决了中心有圆孔的椭园形区域上 Laplace方程第一类边值问题 ;采用分区域解法 ,给出了中心有椭园孔的椭园形区域上 Laplace方程第一类边值问题的解析通解 .这一结果在许多工程领域有重要应用 ,本文给出了油藏工程实例     

用元素法把二重积分直接化为单积分

根据积分区域和被积函数情况,用曲线（或直线,射线）分割积分区域,构建区域元素一元微分,把二重积分直接化为单积分．此种方法可简化二重积分的计算,有必要编写入微积分教材中．     

An analytical contour integration method for handling body forces in elasticity

In the boundary element and superposition methods for two-dimensional elasticity problems, the presence of body forces requires the integration of the basic point load solution against the body force field over a specified area. For polynomial body forces, x^myⁿ, these area integrals may be transformed into contour integrals which have closed form analytic representations when the area is a polygon. This paper shows that commonly used numerical integration techniques developed for area integrals are unsuitable for handling body forces using the above named methods. Not only are these techniques inaccurate but expensive in terms of execution time in comparison to the analytical algorithm developed here. A computer program and four example problems are included.     

On the double curves of least area tori

The double curves of least area immersions of the torus into closed, orientable, irreducible 3-manifolds are simple in the torus. A related result for other least area surfaces is given.

     

Modeling forest core area with integer programming

Abundant and continuous old forest tend to be fragmented into isolated and small patches because of human harvest activities. Dispersive and isolated old forest patches cannot provide abundant interior habitat to wildlife, which is a fatal threat for specific plant communities and wildlife species. In this paper, an Integer Programming model for forest planning is designed to maximize the economical benefit of the forest and to guarantee a minimum area of interior old forest for wildlife habitat, the so-called core area satisfying minimum mature age requirements. The minimum core area constraints, to some degree, can help mitigate the negative impact of harvest activities to divide forest habitat into many small patches. The model is implemented in a commercial Integer Programming solver and it is applied to several hypothetical landscapes. The results show the possibility of incorporating a core area requirement into a forest planning model, and the possibility to obtain solutions within a reasonable computational time. Instances with up to 1600 management units have been solved in seconds to an optimality gap of 1% (0.1% in some cases).     

连续铸钢问题的有限元解法及参数优化

本文介绍连续铸钢二冷区钢坯温度分布的计算以及喷水量的优化，钢铁工艺对二冷区钢坯温度有一定要求，将其量化为求代价泛函最小问题，对状态方程用有限元模拟遗传算法求问题的最小解，确定最佳喷水方案。     

基于关键资源优先的三级装卸搬运分区协调策略

研究基于关键资源优先的单元化“装卸、搬运、装卸”三级作业链调度问题。已知关键资源调度方案,将两非关键作业级的调度问题分别转化为最小单位流问题求解。在数学模型基础之上提出三级装卸搬运的分区协调策略。对关键装卸级作业区进行合理分区和设备分配,从而合理设置已知参数;提出非关键级装卸作业区的分区协调策略,以扩大计算规模。以码头三级装卸搬运作业链为例,参照宁波港码头数据,设计面向集装箱码头的仿真算例,通过较大规模算例验证分区策略对于计算大规模非关键装卸级调度问题的可行性和快捷性。     

Exchange rate uncertainty and employment: an algorithm describing ‘play’

The paper deals with the impacts of exchange rate uncertainty on the relationship between macroeconomic labour market variables. Under uncertainty, areas of weak reactions—so‐called ‘play’ areas—have to be considered at the macrolevel. The width of the play area is a positive function of the degree of uncertainty. When changes go beyond the play‐area suddenly strong reactions (‘spurts’) occur. These non‐linear dynamics are captured in a simplified linearized way. An algorithm describing linear play hysteresis is developed and implemented into a regression framework. As an empirical application, the exchange rate impacts on German employment are analysed considering play effects. Copyright © 2001 John Wiley & Sons, Ltd.     

Generating Boundary Conditions for the Calculation of Tsunami Propagation on Nested Grids

Some boundary conditions used to numerically simulate tsunami generation and propagation are studied. Special attention is given to generating boundary conditions thatmake it possible to simulate tsunami waves with desired characteristics (amplitude, time period and, in general, waveform). Since the water flow velocity in a propagating tsunami wave is uniquely defined by its height and ocean depth, one can simulate a wave propagating from the boundary into the simulation area. This can be done by specifying the wave height and water flow velocity on the boundary. This method is used to numerically simulate the propagation of a tsunami from the source to the coast on a sequence of refined grids. In this numerical experiment the wave parameters are transferred from the larger area to the subarea via boundary conditions. This method can also generate a wave that has certain characteristics on a specified line.     

系统周界的观控模型在淤地坝坝控流域侵蚀研究中的应用

基于系统周界的观控模型及其可观控性定理,把淤地坝坝控流域概化为一个系统进行研究,通过对其输入、输出与内部状态及其之间的关系进行分析,得出了系统周界的观控模型可以对某一输入使其按评价水平的要求进行观控的结论.通过对陕西省榆林市子洲县南部的小河沟流域的石畔峁坝坝控流域进行观控分析,发现该模型在有效的评价水平的指引下,能够对输入该流域的人类活动影响做出分析、判断与调控,从而达到减小流域侵蚀的目的,实现了流域系统的协调稳定发展,开阔了淤地坝研究的思路.     

An efficient algorithm for computing traffic equilibria using TRANSYT model

Computing traffic equilibria with signal settings using TRANSYT model for an area traffic control road system is considered in this paper. Following Wardrop’s first principle, this problem can be formulated as a variational inequality problem. In this paper, we propose a novel algorithm to efficiently solve this equilibrium traffic assignment with global convergence. Numerical calculations are conducted on a grid-size road network. As it shows, the proposed method achieved greater savings in computational overheads than did those conventional methods for solving traffic equilibria when signal settings are particularly taken into account.     

On packing squares into a rectangle

We prove that every set of squares with total area 1 can be packed into a rectangle of area at most 2867/2048=1.399… . This improves on the previous best bound of 1.53. Also, our proof yields a linear time algorithm for finding such a packing.