β─凸集的内核、边界的分解定理

本文引进了β─凸集的β─代数内核等概念，并在讨论了β─凸集的基本性态基础上，得到了β─凸集的内核Ａ（或ｉｎｔＡ）和边界（Ａ）的分解定理。     

极小子群数为2的群

本文给出了ｎ（Ｇ）＝２的有限群的所有类型。     

Towards a socio-oecotechnology

The paper will attempt to demonstrate that within the broad ambit of the socio-technical model there is scope for development and for a degree of innovation. Two aspects of the model will be progressed and to some extent integrated. Firstly, I will argue that the joint optimisation (JtO) concept has not been elaborated and emphasised as much as it deserves and it needs to be sharply differentiated from the widely used notion of maximisation. Secondly, using JtO, I will extend the two system socio-technical model to a troika model by including the impact of technology on the oecological environment.¹ To obtain the best overall results, JtO has to be achieved between three systems: the social, the technical and the oecological. In this way, the extended model will engage with the public’s rapidly growing awareness of environmental hazards for which it frequently blames technologies. This extension also raises the socio-technical model from the micro- to the meso- and macro-level which was always the intention of the early pioneers. These theoretical developments will be treated heuristically and briefly illustrated by two case examples from recent research.     

凸约束下一种改进的非线性优化问题的非单调信赖域算法

在凸的可行域上求解非线性优化问题提出了一种新的信赖域方法 ,算法不强调逐次迭代点处目标函数值的严格单调性 对任意初始点 ,证明了算法收敛到问题的临界点     

Lord's MAD Paradox and Jensen's Inequality

Lord (1983) showed that the mean absolute deviation (MAD) measure of dispersion does not always increase when an additional independent source of random variation is added. Jensen's inequality is used to find necessary and sufficient conditions for this paradoxical behavior. The conditions are unlikely to occur in practice.     

Convex Ordering for Bivariate Distributions

An attempt is made to extend well-known univariate notion of convex ordering to bivariate case. A convex ordered family for bivariate distributions is then introduced and its properties are examined.     

A Unified Approach to Ordering Comparison of GPS Distributions with their Mixtures

Recently, several authors have been concerned with ordering comparison of known distributions of the family of generalized power series (GPS) distributions with their mixtures in various senses. In this article, we shall employ a unified approach and obtain similar results, more generally, for all members of the class of the GPS distributions. Some of the previous findings of Misra et al. (2003 Misra , N. , Singh , H. , Harner , E. J. ( 2003 ). Stochastic comparisons of Poisson and binomial random variables with their mixtures . Statist. Probab. Lett. 65 : 279 – 290 .[Crossref], [Web of Science ®] , [Google Scholar]), Alamatsaz and Abbasi (2008 Alamatsaz , M. H. , Abbasi , S. ( 2008 ). Ordering comparison of negative binomial random variables with their mixtures . Statist. Probab. Lett. 78 : 2234 – 2239 . [Google Scholar]), and Aghababaei Jazi and Alamatsaz (2010 Aghababaei Jazi , M. , Alamatsaz , M. H. ( 2010 ). Ordering comparison of logarithmic series random variables with their mixtures . Commun. Statist. Theor. Meth. 39 : 3252 – 3263 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) in this connection, then, follow as corollaries. Further, we have derived some more ordering comparison results.     

Tests for Stochastic Orders and Mean Order Statistics

The aim of this article is to emphasize the fact, not observed previously in the literature, that many discrepancy measures used in tests related to different stochastic orders can be expressed as expectations of order statistics. In this way, we provide a new meaning to the corresponding test statistics which allows us to understand better, and potentially improve, the testing procedures. As illustration, we consider tests to detect overdispersion with respect to a specific probability model. In this setting, a test for the Weibull distribution is discussed in detail.     

Portfolio rebalancing with an investment horizon and transaction costs

In this paper we consider the problem of rebalancing an existing financial portfolio, where transaction costs have to be paid if we change the amount held of any asset. These transaction costs can be fixed (so paid irrespective of the amount traded provided a trade occurs) and/or variable (related to the amount traded). We indicate the importance of the investment horizon when rebalancing such a portfolio and illustrate the nature of the efficient frontier that results when we have transaction costs. We model the problem as a mixed-integer quadratic programme with an explicit constraint on the amount that can be paid in transaction cost. Our model incorporates the interplay between optimal portfolio allocation, transaction costs and investment horizon. We indicate how to extend our model to include cardinality constraints and present a number of enhancements to the model to improve computational performance. Results are presented for the solution of publicly available test problems involving up to 1317 assets.     

A joint optimal pricing and order quantity model under parameter uncertainty and its practical implementation

We consider a robust optimization model of determining a joint optimal bundle of price and order quantity for a retailer in a two-stage supply chain under uncertainty of parameters in demand and purchase cost functions. Demand is modeled as a decreasing power function of product price, and unit purchase cost is modeled as a decreasing power function of order quantity and demand. While the general form of the power functions are given, it is assumed that parameters defining the two power functions involve a certain degree of uncertainty and their possible values can be characterized by ellipsoids. We show that the robust optimization problem can be transformed into an equivalent convex optimization which can be solved efficiently and effectively using interior-point methods. In addition, we propose a practical implementation of the model, where the stochastic characteristics of parameters are obtained from regression analysis on past sales and production data, and ellipsoidal representations of the parameter uncertainties are obtained based on a combined use of genetic algorithm and Monte Carlo simulation. An illustrative example is provided to demonstrate the model and its implementation.