The reduction method,II

In part I of this paper focusing on a further development of the well-known algorithms for deriving theorems of the method of Lyapunov vector functions, we suggested the reduction method as a logical technique for formulating hypotheses. This part illustrates its implementation in qualitative analysis of the various properties of dynamical systems represented as systems of motions, differential equations, and automata models with different depths of delays.     

Free-boundary regularity on the focusing problem for the Gauss Curvature Flow with flat sides

We consider the motion of a compact weakly convex two-dimensional surface of revolution under the Gauss Curvature Flow. We assume that the initial surface has a flat side and as a consequence the parabolic equation describing the motion of the hypersurface becomes degenerate at points where the curvature is zero. Expressing the strictly convex part of the surface near the interface as the graph of a function , we show that if at ti me vanishes linearly at the flat side, then will become smooth up to the interface for $t >0$ and it will remain smooth up to the focusing time T of the flat side. We also show that at the focusing time of the flat side, the function g is of class for all and no better than . This implies that at the focusing time the surface is of class for all $\beta < $ and no better than . In the case of the evolution Monge-Ampère equation, we find the exact self-similar profile of the function g at its focusing time. Received July 1, 1999; in final form February 11, 2000 / Published online April 12, 2001     

OPTIMAL CONTROL OF MULTIPLE-USE PRODUCTS: THE CASE OF TIMBER,FORAGE AND WATER PRODUCTION

ABSTRACT. A thorough analysis of the optimal control of multiple-use forest management at the stand level reveals that the results of earlier studies, which seem to contradict each other, are in fact part of a common solution space. We provide an explanation for this result by showing that it is caused by the growth function and the interaction between the timber and forage production functions. We discuss the sensibility of the results using this new knowledge. Most optimal control models focusing on multiple-use forest management have applied production functions that are quadratic in the state variable. This makes explicit solutions easy because the first order derivative is linear. However, in reality, production is often better described by more complex nonlinear functions, but, unfortunately, such functions are difficult to handle in an optimal control framework. We illustrate how the convenience of the quadratic production function can be combined with better approximations to nonlinear production functions.     

Interactive High-Dimensional Data Visualization

Abstract

We propose a rudimentary taxonomy of interactive data visualization based on a triad of data analytic tasks: finding Gestalt, posing queries, and making comparisons. These tasks are supported by three classes of interactive view manipulations: focusing, linking, and arranging views. This discussion extends earlier work on the principles of focusing and linking and sets them on a firmer base. Next, we give a high-level introduction to a particular system for multivariate data visualization—XGobi. This introduction is not comprehensive but emphasizes XGobi tools that are examples of focusing, linking, and arranging views; namely, high-dimensional projections, linked scatterplot brushing, and matrices of conditional plots. Finally, in a series of case studies in data visualization, we show the powers and limitations of particular focusing, linking, and arranging tools. The discussion is dominated by high-dimensional projections that form an extremely well-developed part of XGobi. Of particular interest are the illustration of asymptotic normality of high-dimensional projections (a theorem of Diaconis and Freedman), the use of high-dimensional cubes for visualizing factorial experiments, and a method for interactively generating matrices of conditional plots with high-dimensional projections. Although there is a unifying theme to this article, each section—in particular the case studies—can be read separately.     

Steady state scheduling of a flexible manufacturing system with periodic releasing and flow time constraints

This paper deals with the dynamic behaviour of an FMS when parts are released periodically. The minimal release period is induced by the most critical machine or fixture pallet type. Moreover, with a fixed period, the limited number of available pallets induces a maximal flow time for every part type. Thus, the objective of this paper is to determine a part release strategy and an activity schedule on every machine which allows to control every part flow time for steady state. An analysis method for this objective is presented in this paper. Its purpose is to obtain releasing and scheduling conditions ensuring a workshop steady state compatible with the considered constraints, especially part flow times. This method is based on the resolution of conflicts between activities processed on a common machine. This resolution uses limit times associated with each activity and it can modify these limit times. These modifications in turn can induce modifications for other activity limit times due to part routing, steady-state periodicity, and part flow time constraints. Thus, an iterative procedure has been defined. It refines steady-state feasibility conditions through limit times and sequencing conditions of activities processed on a common machine. The method is illustrated with two examples.     

Mathematical tables in Ptolemy's Almagest

This paper is a discussion of Ptolemy's use of mathematical tables in the Almagest. By focusing on Ptolemy's mathematical practice and terminology, I argue that Ptolemy used tables as part of an organized group of units of text, which I call the table nexus. In the context of this deductive structure, tables function in the Almagest in much the same way as theorems in a canonical work, such as the Elements, both as means of presenting acquired knowledge and as tools for producing further knowledge.     

Using commonality as backup safety stock

It is well known that replacing several parts by a single common part can reduce required safety stock levels due to the benefits of risk pooling. It is not clear, however, if this reduces cost when the common part is more expensive than the parts it would replace. Recent analysis has shown that even when the common part is more expensive, it is often still worthwhile to employ in the single-period case. However, this is usually not true in the multiple-period case. This paper will consider the possibility of using both cheaper unique parts and a more expensive common part. Initial demand is met with the unique parts. The common part is used only as backup, when one or more of the unique parts stocks out. A multiple-period (or infinite-horizon) model is developed that considers purchasing, holding, and shortage costs. Results will show that the strategy of using commonality as backup (CAB) dominates the strategies of no commonality (NC) or pure commonality (PC), and may still be worthwhile even if the common part is significantly more expensive than the unique parts.     

Modeling Dependencies in Operational Risk with Hybrid Bayesian Networks

This paper addresses the problem of quantifying and modeling financial institutions’ operational risk in accordance with the Advanced Measurement Approach put forth in the Basel II Accord. We argue that standard approaches focusing on modeling stochastic dependencies are not sufficient to adequately assess operational risk. In addition to stochastic dependencies, causal topological dependencies between the risk classes are typically encountered. These dependencies arise when risk units have common information- and/or work-flows and when failure of upstream processes imply risk for downstream processes. In this paper, we present a modeling strategy that explicitly captures both topological and stochastic dependencies between risk classes. We represent the operational-risk taxonomy in the framework of a hybrid Bayesian network (BN) and provide an intuitively compelling approach for handling causal relationships and external influences. We demonstrate the use of hybrid BNs as a tool for mapping causal dependencies between frequencies and severities of risk events and for modeling common shocks. Monte-Carlo simulations illustrate that the impact of topological dependencies on triggering overall system breakdowns can be substantial.     

Cultural and linguistic problems in the use of authentic textbooks when teaching mathematics in a foreign language

This paper is a part of a longitudinal study focusing on qualitative aspects of learning in a foreign language in the development of cognitive processes in mathematics. The aim of the paper is to present a more complex analysis of textbook-based obstacles to communication. These obstacles originate in the process of vocabulary and grammar acquisition within a particular multicultural and sociocultural context. The study was carried out using mathematics textbooks from English-speaking countries which are used when teaching mathematics in English to Czech students.     

国内外两本微积分教材的比较与启示

通过中美两国有代表性的两本微积分教材在理论内容、知识应用、习题、现代化教学手段等方面进行比较,分析国外国内两本教材的特点,提出了一些值得思考的问题,给我国高等数学教材改革及教学提供一些启示.     

Problem-structuring methods and project management: an example of stakeholder involvement using Hierarchical Process Modelling methodology

Project Management has gained in importance over the last few decades and it isincreasingly common in many types of organisations. Today there is a concernover the relevance of the more conventional project management approaches toproblems that are increasingly complex and constrained and involve large numbersof interested parties or stakeholders. This paper examines the relevance ofproblem-structuring methods to project management, focusing on the front-end ofmanaging complex projects and discusses stakeholder involvement usingHierarchical Process Modelling methodology.     

Adaptation of the plant location model for regional environmental facilities and cost allocation strategy

This paper is divided into two parts. In the first part of the paper, the plant location model is adapted for the special case of siting wastewater treatment facilities when the wastewater sources and treatment facilities are arranged in a chain or linear configuration. In this problem, flows or shipments may be merged in common pipes that provide economies of scale in transport. In order to apply the plant location model, an appropriate definition of the additional cost incurred when a waste source joins a regional facility is required. In addition, sequential priority constraints are developed in the siting model in order to make possible proper accounting of transport costs. The new siting model can be conveniently solved by linear programming.In the second part of the paper, a dual of the plant location model is explored as a cost allocation method for the fixed charge facility siting problem. The constraint sets of the dual model can be shown to imply the core conditions of the related cost game; hence, a set of the dual variables from the dual problem can be regarded as rational cost allocations. The analysis places both facility siting and cost allocation in a common framework.     

Stabilization of nonlinear switched systems using control Lyapunov functions

In this paper, we study the stabilization of general nonlinear switched systems by using control Lyapunov functions. The concept of control Lyapunov function for nonlinear control systems is generalized to switched control systems. The first part of our contribution provides a necessary and sufficient condition of stabilization. The main idea is to use a common control Lyapunov function; this is achieved with the converse Lyapunov theorem dedicated to switched systems. In the second part, an explicit construction of a common control Lyapunov function is addressed with respect to a finite family of switched systems. The approach uses a family of control Lyapunov functions attached to the subsystems.     

Computational Reduction for Parametrized PDEs: Strategies and Applications

In this paper we present a compact review on the mostly used techniques for computational reduction in numerical approximation of partial differential equations. We highlight the common features of these techniques and provide a detailed presentation of the reduced basis method, focusing on greedy algorithms for the construction of the reduced spaces. An alternative family of reduction techniques based on surrogate response surface models is briefly recalled too. Then, a simple example dealing with inviscid flows is presented, showing the reliability of the reduced basis method and a comparison between this technique and some surrogate models.     

Decomposition of conflict as a distribution on hypotheses in the framework on belief functions

In this paper, we address the problem of identifying the potential sources of conflict between information sources in the framework of belief function theory. To this aim, we propose a decomposition of the global measure of conflict as a function defined over the power set of the discernment frame. This decomposition, which associates a part of the conflict to some hypotheses, allows identifying the origin of conflict, which is hence considered as “local” to some hypotheses. This is more informative than usual global measures of conflict or disagreement between sources. Having shown the unicity of this decomposition, we illustrate its use on two examples. The first one is a toy example where the fact that conflict is mainly brought by one hypothesis allows identifying its origin. The second example is a real application, namely robot localization, where we show that focusing the conflict measure on the “favored” hypothesis (the one that would be decided) helps us to robustify the fusion process.     

风险的变异序在保险中的应用

利用风险的变异序,对保险中两类问题——保费计算和破产概率进行了研究.首先通过建立一种变异序原理,从精算数学的角度给出常用的三种保费计算法的合理性,其次研究了破产风险与变异序的关系,得出结论:较变异的风险将导致高风险的破产.     

Completeness Theorems for a Non-Standard Two-Parameter Eigenvalue Problem

We consider two simultaneous Sturm-Liouville systems coupled by two spectral parameters. However, unlike the standard multiparameter problem, we now suppose that the principal part of each of the differential operators is multiplied by a different parameter. In a recent paper, Faierman and Mennicken derived various results concerning the eigenvalues and eigenfunctions, and in particular, they established the oscillation theory for this system. Here we continue this investigation focusing on the completeness of the set of eigenfunctions in a suitable function space. If either one of the potentials is identically zero, the completeness of the eigenfunctions is established, whereas, if this condition fails, then we show the existence of an essential spectrum having non-zero points. The completeness problem for this latter case will be left for a later work. M?ller and Watson supported in part by the John Knopfmacher Centre for Applicable Analysis and Number Theory.     

Schwarz引理的推广及其应用

引入Schwarz引理的一个最常见的推广定理,并且作出了详细的证明.同时以引理形式介绍了一个实用的复数性质,并且利用这两个引理,给出了开圆盘内解析函数的的实部,虚部以及模的估计式.     

Boundary critique and its implications for conflict prevention

This paper reviews developments in the theory of boundary critique, which has been used in a number of OR projects to support conflict resolution. The authors argue that this theory (and associated models) is also useful for conflict prevention. It indicates the need to support people in discussing their differences before conflict arises. Potential conflicts can be reframed through dialogue focusing on values, and participative governance can institutionalise fair processes for making decisions in the absence of consensus. Some of the boundary critique models also support people in recognising and countering the systemic conditions that enable stereotyping, stigmatisation and the victimisation of minorities. The paper ends by presenting a new model that was originally developed to inform mediation practice, but also has implications for conflict prevention. This helps explain how different interpretations of a common concern arise, and suggests ways to improve mutual understanding between people and/or reframe the common concern in order to defuse a potential conflict.     

A DEA methodology to evaluate the impact of information asymmetry on the efficiency of not-for-profit organizations with an application to higher education in Brazil

This paper presents a conceptual framework and an analytical DEA model for evaluating the impact of information asymmetry on organizational efficiency. The framework uses concepts from agency theory to estimate the extent of moral hazard by comparing the objectives of the principal to those of the agent. The framework and model are useful in the analysis of both for-profit and not-for-profit organizations because DEA is applicable whether or not inputs and/or outputs are subject to pricing mechanisms. An illustration focusing on the Brazilian not-for-profit federal university system finds that the agency problem indeed exists for a subset of those institutions, indicating the desirability of improved incentive and control mechanisms on the part of the principal.