Stability criteria with less LMI variables for linear system with additive time-delays

In this technical note, equivalent stability criterion with minimal number of variables for three recently reported stability criteria is proposed for a class of linear systems with additive time-varying delays. The existing delay-dependent stability criteria for additive time-delay systems have more number of matrix variables in the LMI; and hence, they require more computational cost. The proposed equivalent criteria, unlike the original ones, encompass only the matrix variables that are associated in the Lyapunov-Krasovskii functional, making the criteria mathematically less complex and computationally more attractive. The complexity involved in the existing stability criteria is attributed to the fact the cross-terms that emanate from the time-derivative of the Lyapunov-Krasovskii functional are dealt with free-weighting matrices. Hence, apart from the matrix variables that are associated in the corresponding Lyapunov-Krasovskii functional, the existing criteria also have additional matrix variables in them. In this paper, we have devised techniques to eliminate the free-weighting matrices in the existing stability criteria without sacrificing the conservatism. The resulting equivalent stability criteria, therefore, have least possible number of variables in the LMI; and hence, have minimum computational burden. The effectiveness of the proposed equivalent criteria is validated on a numerical example.     

奖学金的评定与模糊优选数学模型

本文运用模糊数学思想 ,按照相对隶属度原则 ,通过制定各门课程之间的权重系数 ,建立了一种新的奖学金评定的模糊优选数学模型 .该模型解决了按总成绩排名评定法中所存在的一些问题 .使评定的结果更具科学性与合理性 ,同时模型可推广到其它评比当中     

Zero—one programming with multiple criteria

The study of multiple criteria problems is not new, but during the last seventeen years more and more study has been done in this area. The study of 0–1 multiple criteria problems started much later than the study of continuous multiple criteria problems. Some of the earliest works on 0–1 problems with multiple criteria was first presented in 1973. Quite a few solution methods have been developed since then, especially during the last seven years. In this paper most of these methods and some applications will be treated.     

Integer Programming Duality in Multiple Objective Programming

The weighted sums approach for linear and convex multiple criteria optimization is well studied. The weights determine a linear function of the criteria approximating a decision makers overall utility. Any efficient solution may be found in this way. This is not the case for multiple criteria integer programming. However, in this case one may apply the more general e-constraint approach, resulting in particular single-criteria integer programming problems to generate efficient solutions. We show how this approach implies a more general, composite utility function of the criteria yielding a unified treatment of multiple criteria optimization with and without integrality constraints. Moreover, any efficient solution can be found using appropriate composite functions. The functions may be generated by the classical solution methods such as cutting plane and branch and bound algorithms.     

随机泛函微分系统的渐近性分析

针对已有的随机泛函微分系统的渐近稳定性的结果,要求系统的系数满足线性增长条件,本文主要目的是去掉这一限制条件,给出了非线性随机泛函微分系统的渐近稳定性的新结果.新的稳定性判据不仅可以涵盖更多的非线性随机泛函微分系统,而且证明方法更加简单.     

关于Gauss-Seidel迭代收敛的新判据

本文给出了Gauss-seidel迭代收敛的两则判据及相应敛速估计,一是改进,包括了前人的结果,另一是新的工作。所给判据比目前常用的判据,应用范围广,敛速估计精。     

Intuitionistic fuzzy cognitive map approach for the evaluation of supply chain configuration criteria

Because of the growing global competence and effectiveness concepts, supply chain becomes more important for organizations. Therefore, managers object to find best supply chain configuration for their firms. This study proposes a comprehensive configuration for supply chain management process, and it enables to understand relationships among supply chain integration, supply chain strategies, supply chain risk factors, and performance criteria. By reviewing the literature and using experts' knowledge, supply chain configuration criteria are determined. Intuitionistic fuzzy cognitive map methodology is employed to consider the interrelations between criteria. Intuitionistic fuzzy cognitive map methodology is a suitable tool due to the presence of causalities and relationships among criteria and the difficulty of expressing the interrelations with crisp numbers. It also deals with uncertain and vague data and allows representing hesitation. The application is conducted in an automobile factory, which is one of the largest manufacturers in Turkey. The results show that selection of proper supplier is the most significant supply chain configuration criteria. Thus, the importance of supplier selection criteria is also analyzed as the second phase of the study.     

A survey of recent results on continuous-time Markov decision processes

This paper is a survey of recent results on continuous-time Markov decision processes (MDPs) withunbounded transition rates, and reward rates that may beunbounded from above and from below. These results pertain to discounted and average reward optimality criteria, which are the most commonly used criteria, and also to more selective concepts, such as bias optimality and sensitive discount criteria. For concreteness, we consider only MDPs with a countable state space, but we indicate how the results can be extended to more general MDPs or to Markov games. Research partially supported by grants NSFC, DRFP and NCET. Research partially supported by CONACyT (Mexico) Grant 45693-F.     

Error bounds for vector-valued functions: Necessary and sufficient conditions

In this paper, we attempt to extend the definition and existing local error bound criteria to vector-valued functions, or more generally, to functions taking values in a normed linear space. Some new derivative-like objects (slopes and subdifferentials) are introduced and a general classification scheme of error bound criteria is presented.     

Prospective and current secondary mathematics teachers’ criteria for evaluating mathematical cognitive technologies

As technology becomes more ubiquitous in the mathematics classroom, teachers are being asked to incorporate it into their lessons more than ever before. The amount of resources available online is staggering and teachers need to be able to analyse and identify resources that would be most appropriate and effective with their students. This study examines the criteria prospective and current secondary mathematics teachers use and value most when evaluating mathematical cognitive technologies (MCTs). Results indicate all groups of participants developed criteria focused on how well an MCT represents the mathematics, student interaction and engagement with the MCT, and whether the MCT was user-friendly. However, none of their criteria focused on how well an MCT would reflect students’ solution strategies or illuminate their thinking. In addition, there were some differences between the criteria created by participants with and without teaching experience, specifically the types of supports available in an MCT. Implications for mathematics teacher educators are discussed.     

混合时滞的随机微分方程的稳定性研究

本文研究了混合时滞的随机微分方程的稳定性,利用Lyapunov函数方法和半鞅收敛定理得到了p阶矩指数稳定和几乎必然指数稳定的判定定理.M矩阵技巧的使用使所得结果更便于应用.最后举例说明了结果的实用性.     

Management of multicriteria inventory classification

The most common method that materials managers use for classifying inventory items for planning and control purposes is the annual-dollar-usage ranking method (ABC classification). Recently, it has been suggested that multiple criteria ABC classification can provide a more comprehensive managerial approach, allowing consideration of other criteria such as lead time and criticality. This paper proposes the use of the Analytical Hierarchy Process (AHP) to reduce these multiple criteria to a univariate and consistent measure to consider multiple inventory management objectives.     

关于变系数线性方程的稳定性

本文给出了变系数线性方程有关稳定性的一些简洁的判据．对周期系数线性方程，给出了较为精确的渐近稳定性判据．从理论上解释了原先“冻结系数法”一般不能成立的原因．     

Solvability criteria for systems of fuzzy relation equations

By solving systems of fuzzy relation equations, qualitative process models can be obtained. To give more information on the solving procedure and to help constructing models, solvability criteria for-systems of fuzzy relation equations are necessary. In this article such criteria will be developed. Both methods are considered. In addition to some ideas on general , the is evaluated in detail. Criteria of practical use will be developed. These criteria will limit the variety of premise intersections to guarantee solvability. Nevertheless, they will still allow to model the significant behaviour of the processes.     

Relative importance of criteria in multiobjective programming: A cone-based approach

This article develops a convex polyhedral cone-based preference modeling framework for decision making with multiple criteria which extends the classical notion of Pareto optimality and accounts for relative importance of the criteria. The decision maker’s perception of the relative importance is quantified by an allowable tradeoffs between two objectives representing the maximum allowable amount of decay of a less important objective per one unit of improvement of a more important objective. Two cone-based models of relative importance are developed. In the first model, one criterion is designated as less important while all the others are more important. In the second model, more than one criterion may be classified as less important while all the others are considered more important. Complete algebraic characterization of the models is derived and the relationship between them and the classical Pareto preference is examined. Their relevance to decision making is discussed.     

关于共轭梯度法的下降性和收敛性

本文给出了重新开始的一个准则,其准则是为保证共轭梯度法的下降性,我们不仅得到了具有不同参数选择的一般共轭梯度法的收敛性,而且将Ｒｅｆ．１中的结论给予推广。     

Supervisor and Teacher Educator Perceived Relevance of Recommendations in the NCTM Curriculum Standards

Based on judgments of mathematics supervisors and teacher educators, the findings of this empirical study confirm that the Curriculum and Evaluation Standards (National Council of Teachers of Mathematics [NCTM], 1989) reflect content that is relevant to mathematics instruction. However, some concern did exist about the relevancy of teaching statistics and probability at the elementary level. Despite the general consensus about the Standards, total agreement was not evident. Respondents with asecondary-school focus rated many of the standards and criteria across grade levels significantly lower in importance than did other respondents; elementary- and middle-school respondents judged several K-8 standards and criteria to be more important than did some higher-education and secondary respondents, while secondary-and middle-school respondents judged the 9–12 standards and critera to be more important than did elementary and some higher education respondents. Respondents with 30 or more years of experience or who were less familiar with the standards rated the K-8 standards and criteria to be lower in importance than did other respondents.     

Sequential clinical scheduling with service criteria

This study investigates sequential appointment scheduling with service criteria. It uses a constraint-based approach with service criteria bounded in a constraint set in contrast to the more typical weighted linear objective function. Properties are derived and a sequential scheduling algorithm is developed. Fairness properties of generated schedules are considered in detail, where fairness is the uniformity of performance across patients. New unfairness measures are proposed and used to capture the inequity among patients assigned to different slots. Other criteria such as expectation and variance of patient waiting time, queue length, and overtime are also considered. The fairness/revenue tradeoff is investigated as is the flexibility of the constraint-based approach in handling unavailable time periods.     

Synthetic indicators of mutual funds’ environmental responsibility: An application of the Reference Point Method

Socially Responsible Investing (SRI) is broadly defined as an investment process that integrates not only financial but also social, environmental, and ethical (SEE) considerations into investment decision making. SRI has grown rapidly around the world in the last decades. In the last years, given the causes of the 2008 financial crisis, ethical, social, environmental and governance concerns have become even more relevant investment decision criteria. However, while a diverse set of models have been developed to support investment decision-making based on financial criteria, models including also social responsibility criteria are rather scarce.     

Corrected versions of cross-validation criteria for selecting multivariate regression and growth curve models

This paper is concerned with cross-validation (CV) criteria for choice of models, which can be regarded as approximately unbiased estimators for two types of risk functions. One is AIC type of risk or equivalently the expected Kullback-Leibler distance between the distributions of observations under a candidate model and the true model. The other is based on the expected mean squared error of prediction. In this paper we study asymptotic properties of CV criteria for selecting multivariate regression models and growth curve models under the assumption that a candidate model includes the true model. Based on the results, we propose their corrected versions which are more nearly unbiased for their risks. Through numerical experiments, some tendency of the CV criteria will be also pointed.