Hierarchical classification of mathematical structures

The application area of the methods of cluster analysis has largely developed during the last fifteen years. Nevertheless, the applications of cluster analysis were always made on concrete data resulting from experiments, observations, or more simply, from simulations. This paper presents an application of hierarchical clustering to exact mathematical structures. On the one hand the set of formal series of defined on a field, on the other hand the set of integers fit with the p-adic distance. In addition to a purely technical aspect, the aim of this work is also to show how, and in what way, cluster analysis enables us to understand the structure of a strictly organized data set.     

A new multi-criteria approach dealing with dependent and heterogeneous criteria for end-of-life product strategy

Strict regulations, technological growth and environmental impacts are influent factors in the choice of the best strategy for end-of-life (EOL) product. In fact, EOL is one stage of the life cycle having gained the attention of the market.This study proposes an integrated methodology that relies on multi-criteria analysis and takes into account both quantitative and qualitative criteria while respecting mutual interactions between them. This has been performed by introducing, on the one hand, the 2-tuple linguistic representation model dealing with non-homogeneous information data, and on the other hand, the Choquet integral interaction modeling between criteria into the PROMETHEE method. Although it has been developed for EOL selection problems, the proposed method fits to all kinds of decision-making problems with heterogeneous information. As this work demonstrates, this multi-criteria analysis approach can offer a technical-scientific decision making support tool in the EOL product sector. We also perform a sensitivity to reveal the effect of the subjective parameter variations on the originally resulted ranking.     

On sensitivity of central solutions in semidefinite programming

In this paper we study the properties of the analytic central path of a semidefinite programming problem under perturbation of the right hand side of the constraints, including the limiting behavior when the central optimal solution, namely the analytic center of the optimal set, is approached. Our analysis assumes the primal-dual Slater condition and the strict complementarity condition. Our findings are as follows. First, on the negative side, if we view the central optimal solution as a function of the right hand side of the constraints, then this function is not continuous in general, whereas in the linear programming case this function is known to be Lipschitz continuous. On the positive side, compared with the previous conclusion we obtain a (seemingly) paradoxical result: on the central path any directional derivative with respect to the right hand side of the constraints is bounded, and even converges as the central optimal solution is approached. This phenomenon is possible due to the lack of a uniform bound on the derivatives with respect to the right hand side parameters. All these results are based on the strict complementarity assumption. Concerning this last property we give an example. In that example the set of right hand side parameters for which the strict complementarity condition holds is neither open nor closed. This is remarkable since a similar set for which the primal-dual Slater condition holds is always open. Received: April 2, 1998 / Accepted: January 16, 2001?Published online March 22, 2001     

基于协变量缺失的Horvitz-Thompson加权分位回归估计方法

含有协变量缺失的数据缺失问题是现代统计分析中的热点之一.当缺失数据中同时存在厚尾,偏斜和异方差问题时则更加难以处理.为此,本文提出一种逆概率加权分位回归估计来研究响应和协变量之间的关系.与经典估计方法相比具有明显优势,一方面,该估计量使用了所有可用的数据,并且允许缺失的协变量与响应高度相关;另一方面,该估计量在所有分位数水平上满足一致性和渐近正态性.通过模拟验证了该方法的在有限样本下的有效性,进一步将该方法推广到线性多元回归模型和非参数回归模型.     

Measurement and the verificationist theory/observation distinction

In the following article, we propose to show that following the general verificationist epistemic programme (its demand that the truth of our judgments be verifiable), the analysis of measurement on the one hand, and the classical positivist analysis of common-sense observation on the other, do not lead to same conclusions. This is especially important, because the differences in conclusions concern the positivist theory/observation distinction. In particular, the analysis of measurement does not fully support this distinction. This fact might have important consequences for the problem of scientific realism and related ontological and epistemological problems in the philosophy of science.     

Refined discrete regular variation and its applications

We introduce a new class of the so‐called regularly varying sequences with respect to τ and state its properties. This class, on one hand, generalizes regularly varying sequences. On the other hand, it refines them and makes it possible to do a more sophisticated analysis in applications. We show a close connection with regular variation on time scales; thanks to this relation, we can use the existing theory on time scales to develop discrete regular variation with respect to τ. We reveal also a connection with generalized regularly varying functions. As an application, we study asymptotic behavior of solutions to linear difference equations; we obtain generalization and extension of known results. The theory also yields, in some way, a new view on the tests for convergence and divergence of series; we establish the statement that generalizes Raabe test and Bertrand test.     

Classical versus vector geometry in problem solving. An empirical research among Greek secondary pupils

An analysis of written solutions to geometry exercises in the last year of Greek Lyceum (15–18 years old) showed relatively low performance on vector methods, which is justified on the one hand by pupils' false preconceptions with regards to the concept of vector, and on the other hand by the strong influence of classical geometry teaching in the previous years.     

Final-offer arbitration in major league baseball: A nonparametric analysis

This study extends the non-parametric methodology for empirical efficiency analysis to allow for a double frontier based on perspective and applies the model to final-offer arbitration in major league baseball. Arbitration eligible players perceive their worth relative to other players who earn more with no better performance. Owners, on the other hand, perceive a player's value relative to other players performing as well with lower salaries. The two different perspectives give rise to different perceived frontiers. The purpose of this paper is to analyze arbitration using this approach.     

Threshold start-up control policy for polling systems

A threshold start-up policy is appealing for manufacturing (service) facilities that incur a cost for keeping the machine (server) on, as well as for each restart of the server from its dormant state. Analysis of single product (customer) systems operating under such a policy, also known as the N-policy, has been available for some time. This article develops mathematical analysis for multiproduct systems operating under a cyclic exhaustive or globally gated service regime and a threshold start-up rule. It pays particular attention to modeling switchover (setup) times. The analysis extends/unifies existing literature on polling models by obtaining as special cases, the continuously roving server and patient server polling models on the one hand, and the standard M/G/1 queue with N-policy, on the other hand. We provide a computationally efficient algorithm for finding aggregate performance measures, such as the mean waiting time for each customer type and the mean unfinished work in system. We show that the search for the optimal threshold level can be restricted to a finite set of possibilities. This revised version was published online in June 2006 with corrections to the Cover Date.     

Optimized frames and multi-dimensional challenges in time-frequency analysis

The aim of this introductory communication is to present some challenges of the emerging research topics related to uncertainties, optimizations and multi-dimensional settings in the framework of time-frequency analysis. On one hand we study problems related to multivariate high-D Gabor frame constructions and on the other hand we corelate them with the optimal window constructions.     

Evaluating views of lecturers on the consistency of teaching content with teaching approach: traditional versus reform calculus

This study aims to evaluate the consistency of teaching content with teaching approaches in calculus on the basis of lecturers' views. In this sense, the structures of the examples given in two commonly used calculus textbooks, both in traditional and reform classrooms, are compared. The content analysis findings show that the examples in both textbooks are presented in a rather formal language and generally highlight procedural knowledge. And, even though the examples in the reform book chosen are structured using multiple representations, only a small number of them incorporated the usage of instructional technology. The lecturers' views which were gathered indicated that, although, on the one hand, the example structures of the traditional textbook largely overlapped with the characteristics of the traditional approach, the example structures of the reform textbook, on the other hand, were found to be inconsistent with the characteristics of the reform approach, especially with regard to its environment and knowledge components. At the end of the paper, some suggestions for further studies are provided for book authors and researchers.     

Metric regularity of epigraphical multivalued mappings and applications to vector optimization

In this work we combine in a meaningful way two techniques of variational analysis and nonsmooth optimization. On one hand, we use the error bound approach to study the metric regularity of some special types of multifunctions and, on the other hand, we exploit the incompatibility between the metric regularity and the Pareto minimality. This method allows us to present some $\varepsilon $ -Fermat rules for set-valued optimization problem in the setting of general Banach spaces. Our results are comparable to several recent results in literature.     

多产品公司创建平台邀请竞争对手进行联合销售的策略研究

由于资金分配或生产规模的限制,多产品公司的某类产品与专门销售此类产品的专业产品公司相比,会有一定的不足.以两个产品公司为对象,研究了两个竞争性公司的联合销售模式,即多产品公司投资建设平台,邀请销售单一产品的专业公司在平台上共同销售某类产品.运用主从博弈建立联合销售的基础模型,探讨不同销售模式下的相关投资,并利用数值计算进行决策分析.研究表明,通过创建平台进行联合销售,一方面,消除了消费者的额外购物成本;另一方面,在平台进行联合销售使得两个公司由单纯的竞争关系转化为相互补充,不仅能够吸引更多有不同产品需求的客户,而且能够在一定程度上提高两个产品公司的利润.     

AN AUTOMATED METHOD FOR EXTENDING SENSITIVITY ANALYSIS TO MODEL FUNCTIONS

Abstract Parameter sensitivity analysis is a relatively well‐developed field compared with function sensitivity analysis. How sensitive are model conclusions to the choice of functions used in the right‐hand side of difference or differential equation models? Most work in this area has been scenario based where alternative functions are tested. This requires knowledge of plausible alternatives and is usually restricted to well‐known functions. In this work, a method is proposed for function sensitivity analysis, which it is hoped will provide a starting point for discussion and stimulating further research on this important but neglected topic. The method provides information on the sensitivity of a model's results to changes in the shape of the functions. This is done in an automated way without the need to specify alternative functional forms. The proposed method is illustrated on a small ecosystem model.     

Assessing mutual funds’ corporate social responsibility: a multistakeholder-AHP based methodology

Currently, stochastic optimization on the one hand and multi-objective optimization on the other hand are rich and well-established special fields of Operations Research. Much less developed, however, is their intersection: the analysis of decision problems involving multiple objectives and stochastically represented uncertainty simultaneously. This is amazing, since in economic and managerial applications, the features of multiple decision criteria and uncertainty are very frequently co-occurring. Part of the existing quantitative approaches to deal with problems of this class apply scalarization techniques in order to reduce a given stochastic multi-objective problem to a stochastic single-objective one. The present article gives an overview over a second strand of the recent literature, namely methods that preserve the multi-objective nature of the problem during the computational analysis. We survey publications assuming a risk-neutral decision maker, but also articles addressing the situation where the decision maker is risk-averse. In the second case, modern risk measures play a prominent role, and generalizations of stochastic orders from the univariate to the multivariate case have recently turned out as a promising methodological tool. Modeling questions as well as issues of computational solution are discussed.     

Literacy, Matheracy, and Technocracy: A Trivium for Today

This article focuses on the relations between mathematics and mathematics education on the one hand and human behavior, societal models, and power on the other. Based on a critical analysis of school systems and of mathematical thinking, its history and its sociopolitical implications, anew concept of curriculum is suggested, organized in 3 strands: literacy, matheracy, and technoracy. This new concept sees education and scholarship as pursuing a major, comprehensive goal of building up a new civilization that rejects arrogance, inequity, and bigotry. Because the development of mathematics has been intertwined with all forms of human behavior in the history of human- kind, it is relevant to discuss mathematics and mathematics education with this major goal in mind.     

轴对称问题的对角线化—致质量矩阵和弹塑性撞击的动力有限元分析

本文找到了轴对称问题的三角圆环有限元的对角线化一致质量矩阵,从而克服了集总质量法的粗略随意性所引起的不安,以及一致质量法的非对角线项对计算工作带来的麻烦.本文也对弹塑性轴对称撞击问题提供了动力有限元分析计算的基础.     

Combining different theoretical perspectives for analyzing students’ difficulties in vector spaces theory

This paper originates from our doctorate research project, in which we investigated graduate and undergraduate students’ errors and difficulties in vector space theory (VST). After a brief account of the whole study, we will focus on the analyses carried out through the lenses of two different theoretical frameworks: Fischbein’s Theory of Tacit Models and Sfard’s process/object duality theory. We also propose a retrospective reflection concerning the reasons why we chose to carry out our analysis according to more than one theoretical framework and why we chose those specific theoretical frameworks as well. Hence this contribution has a double focus: on the one hand it reports on the results drawn from our study on students’ difficulties in VST; on the other hand it presents a personal retrospective reflection on the use of theoretical frames within that study.