On a Problem of Judicious k‐Partitions of Graphs

For positive integers and m , let be the smallest integer such that for each graph G with m edges there exists a k‐partition in which each contains at most edges. Bollobás and Scott showed that . Ma and Yu posed the following problem: is it true that the limsup of tends to infinity as m tends to infinity? They showed it holds when k is even, establishing a conjecture of Bollobás and Scott. In this article, we solve the problem completely. We also present a result by showing that every graph with a large k‐cut has a k‐partition in which each vertex class contains relatively few edges, which partly improves a result given by Bollobás and Scott.     

Solving continuous min max problem for single period portfolio selection with discrete constraints by DCA

In this article, we consider the application of a continuous min–max model with cardinality constraints to worst-case portfolio selection with multiple scenarios of risk, where the return forecast of each asset belongs to an interval. The problem can be formulated as minimizing a convex function under mixed integer variables with additional complementarity constraints. We first prove that the complementarity constraints can be eliminated and then use Difference of Convex functions (DC) programming and DC Algorithm (DCA), an innovative approach in non-convex programming frameworks, to solve the resulting problem. We reformulate it as a DC program and then show how to apply DCA to solve it. Numerical experiments on several test problems are reported that demonstrate the accuracy of the proposed algorithm.     

细颈倾角对挠性接头力学性能影响分析

为确定某单平衡环挠性接头的最佳细颈倾角,对挠性接头进行了力学性能分析。首先给出了挠性接头的离散动力学模型,然后利用ANSYS仿真分析软件对不同细颈倾角结构的挠性接头进行了抗冲击能力和等刚度的力学性能分析,得出了细颈倾角在30°～60°范围内的冲击响应和等刚度性能。最后结合两种力学性能分析可知:当细颈倾角为44°时,该挠性接头在加速度幅值为40g、脉宽为11ms冲击条件下的轴向最大响应应力为448MPa,径向最大响应应力为584MPa;在该倾角情况下挠性接头由不等刚度造成的g2项误差优于0.06(°)/h。综合两方面的性能指标可最终确定挠性接头的最佳细颈倾角为44°。     

Constrained inverse min–max spanning tree problems under the weighted Hamming distance

In this paper, we consider the constrained inverse min–max spanning tree problems under the weighted Hamming distance. Three models are studied: the problem under the bottleneck-type weighted Hamming distance and two mixed types of problems. We present their respective combinatorial algorithms that all run in strongly polynomial times. This research is supported by the National Natural Science Foundation of China (Grant No. 10601051).     

基于最大等增益圆的矢量调制器增益控制方法

矢量调制器因其自身结构小、功耗低等特点已广泛应用于雷达、导航、仪器仪表及卫星通信等领域。基于矢量调制器的最大等增益圆理论,深入分析了增益圆点、半径与调制器增益输出的关系,设计出一种可全频段扫描、一键自动测试的通用矢量调制器增益控制方案,实现了对矢量调制器增益输出以及其平坦度的精确控制,并可灵活设置矢量调制器的精度和平坦度指标,提高了矢量调制器的性能以及校准效率。验证对象为Hittite Microwave公司的HMC1097LP4E矢量调制芯片,单点验证时间不超过1min,增益控制精度可达0.1dB,平坦度可达0.5dB。     

A duality recipe for non-convex variational problems

The aim of this paper is to present a general convexification recipe that can be useful for studying non-convex variational problems. In particular, this allows us to treat such problems by using a powerful primal–dual scheme. Possible further developments and open issues are given.     

Dynamic Robust Output Min–Max Control for Discrete Uncertain Systems

Min–max control is a robust control, which guarantees stability in the presence of matched uncertainties. The basic min–max control is a static state feedback law. Recently, the applicability conditions of discrete static min–max control through the output have been derived. In this paper, the results for output static min–max control are further extended to a class of output dynamic min–max controllers, and a general parametrization of all such controllers is derived. The dynamic output min–max control is shown to exist in many circumstances under which the output static min–max control does not exist, and usually allows for broader bounds on uncertainties. Another family of robust output min–max controllers, constructed from an asymptotic observer which is insensitive to uncertainties and a state min–max control, is derived. The latter is shown to be a particular case of the dynamic min–max control when the nominal system has no zeros at the origin. In the case where the insensitive observer exists, it is shown that the observer-controller has the same stability properties as those of the full state feedback min–max control.     

A deep cut ellipsoid algorithm for convex programming: Theory and applications

This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent some of the numerical instabilities and theoretical drawbacks usually associated with the algorithm are also provided. Moreover, for a large class of convex programs a simple proof of its rate of convergence is given and the relation with previously known results is discussed. Finally some computational results of the deep and central cut version of the algorithm applied to a min—max stochastic queue location problem are reported.Author on leave from D.E.I.O. (Universidade de Lisboa, Portugal). This research was supported by J.N.I.C.T. (Portugal) under contract number BD/631/90-RM.     

多入口多出口串行生产线的最优节奏控制

本文用极大代数方法讨论了多入口多出口情况下带存储器有阻塞串行生产线的最优节奏控制问题,给出了串行生产线的状态方程,批量生产的生产周期公式及其函数形式,最后应用陈文德(1997)提出的算法对生产线实现了最优节奏控制。