Minimization of the root of a quadratic functional under a system of affine equality constraints with application to portfolio management

We present an explicit closed form solution of the problem of minimizing the root of a quadratic functional subject to a system of affine constraints. The result generalizes Z. Landsman, Minimization of the root of a quadratic functional under an affine equality constraint, J. Comput. Appl. Math. 2007, to appear, see http://www.sciencedirect.com/science/journal/03770427, articles in press, where the optimization problem was solved under only one linear constraint. This is of interest for solving significant problems pertaining to financial economics as well as some classes of feasibility and optimization problems which frequently occur in tomography and other fields. The results are illustrated in the problem of optimal portfolio selection and the particular case when the expected return of finance portfolio is certain is discussed.     

一个非对称线性风险函数与证券组合投资分析

在分析Jia&D yer的风险-价值理论基础上,给出了一个基于预先给定的目标收益的非对称线性风险函数.该风险函数是低于参考点的离差和高于参考点的离差的加权和,它利用一阶"上偏矩"来修正一阶下偏矩,进一步建立了在此非对称风险函数下的线性规划证券投资组合模型;并证明了该模型与二阶随机占优准则的一致性;最后通过上海证券市场的实际数据验证了该模型的有效性和实用性.     

Waste marble dust-filled sustainable polymer composite selection using a multi-criteria decision-making technique

This research works with the optimal design of marble dust-filled polymer composites using a multi-criteria decision-making (MCDM) technique. Polylactic acid (PLA) and recycled polyethylene terephthalate (rPET)-based composites containing 0, 5, 10, and 20 wt% of marble dust were developed and evaluated for various physicomechanical and wear properties. The results showed that the incorporation of marble dust improved the modulus and hardness of both PLA and rPET. Moreover, a marginal improvement in flexural strength was noted while the tensile and impact strength of the matrices were deteriorating due to marble dust addition. The outcomes of wear analysis demonstrated an improvement in wear resistance up until 10 wt% filler reinforcement, after which the incidence of dust particles peeling off from the matrix was observed, thereby reducing its efficiency. The best tensile modulus of 3.23 GPa, flexural modulus of 4.39 GPa, and hardness of 83.95 Shore D were obtained for 20 wt% marble dust-filled PLA composites. The lowest density of 1.24 g/cc and the highest tensile strength of 57.94 MPa were recorded for neat PLA, while the highest impact strength of 30.94 kJ/m² was recorded for neat rPET. The lowest wear of 0.01 g was obtained for the rPET containing 5 wt% marble dust content. The experimental results revealed that for the examined criteria, the order of composite preference is not the same. Therefore, the optimal composite was identified by adopting a preference selection index-based MCDM technique. The findings demonstrated that the 10 wt% marble dust-filled PLA composite appears to be the best solution with favorable physical, mechanical, and wear properties.     

A simple topological factor determining the allowance of pericyclic reactions

The study is aimed at revealing the possible manifestation of the overlap topology of AOs at early stages of pericyclic reactions. To this end, formation of an evenmembered cycle of carbon atoms is considered as a unified model, wherein relatively strong (C?C) bonds alternate with weak ones. A direct perturbative method is applied to derive algebraic expressions for energy and bond order corrections due to cyclization. To represent the overlap topology of 2p_z AOs over the cycle, a new concept of the roundabout interaction is introduced. The relevant definition contains a product of resonance parameters (or overlap integrals) between orbitals of all neighboring pairs of C?C bonds and a certain N‐dependent parity factor, where N coincides with the total number of these bonds. The principal result of the study consists in demonstration of proportionality of both energy and bond order corrections to the roundabout interaction of the given cycle and thereby of a direct dependence between these corrections and the overlap topology of AOs. Moreover, the sign of the roundabout interaction is shown to determine the allowance of the given way of the process, viz. cycles described by positive (negative) roundabout interactions refer to allowed (forbidden) ways. Thus, an analog of the famous Woodward‐Hoffmann rule is obtained, wherein the overlap topology of AOs stands instead of symmetry of molecular orbitals. Along with stabilization of the cycle vs. the initial open chain, the allowed processes also are necessarily characterized by growing uniformity of all bond orders over the cycle, while the forbidden ones are accompanied by both destabilization and an increasing distinction between strong and weak bonds. The results obtained also yield a new definition of the concerted nature of pericyclic processes. The general conclusions of the study are illustrated by consideration of specific examples including the electrocyclic closure of polyene chains. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Modeling phase decomposition and patterning in binary alloy systems subjected to neutron irradiation

We study processes of phase decomposition and patterning in a model of a binary alloy system subjected to sustained irradiation. We exploit the reaction rate theory and generalize the Darken approach of vacancy diffusion to describe generation, recombination, annihilation and spatial interaction of point defects. It is shown that an increase in the defect production rate phase, decomposition processes are replaced by disordering and patterning with vacancy clusters' formation. At elevated damage rates, both phase separation and patterning are accompanied by pattern selection processes. In the framework of numerical simulations, dynamics of phase decomposition and vacancy clusters formation is studied in detail. A change in the morphology of vacancy clusters during irradiation and their statistical properties are discussed.     

全天时星敏感器光学系统参量选择与光学设计

以10km观测高度探测4.5等星为例,分析星点在600~1100nm谱段的辐射特性,使用Modtran软件计算同谱段的天空背景辐射亮度以及大气透过率,在信噪比阈值为5的情况下,选择一组典型的光学系统参量.采用一块平面反射镜和石英球面镜系统设计了轻、小型化的光学系统,该系统在600~1 100nm宽光谱范围内全视场光斑形状接近圆形、调制传递函数接近衍射极限,色差很小,具有良好的成像质量.计算了地面环境下星敏感器的昼夜探测信噪比,以信噪比阈值5对星敏感器的探测能力评估,结果表明在白昼地面环境下可以实现2.5等G型恒星的探测,在夜间地面环境下可以实现6等G型恒星的探测.     

基于精英单亲遗传算法的冷链物流VRP模型优化研究

针对冷链物流配送的特殊性,探索冷链物流车辆路径问题(VRP)优化方案.首先,在保证货物不超载的条件下,建立基于时间和品质因素的顾客满意度约束的多配送中心VRP(MDVRP)模型;其次,采用重心分区法和改进的精英单亲遗传算法,求解顾客在配送中心的分配,确定配送车辆数以及顾客服务次序;最后,用Matlab工具编程对模型进行求解分析.结果表明构建基于满意度的冷链物流MDVRP模型更适合冷链物流配送最优路径选择,并且改进单亲遗传算法能够有效求解这类问题.     

基于最大期望满意度与背景风险的模糊投资组合模型研究

模糊投资组合是不确定性理论研究的重要领域.然而,由于人的理性局限性,投资者在决策的过程中,可能不是追求理性的效用最大化,而是追求心理满意度的最大化;在金融市场中,投资者不仅面临市场风险,也需要承担由自身因素产生的背景风险.因此,提出了一个考虑背景风险等因素的最大期望满意度模型,该模型的目标是最大化投资组合收益与最小收益证券的差值;最后,以上海证券交易所180指数的十支证券构成的的投资组合为例,分析了此模型在分散投资风险与增加满意度方面的有效性.