Use of dynamic trees in a network simplex algorithm for the maximum flow problem

Goldfarb and Hao (1990) have proposed a pivot rule for the primal network simplex algorithm that will solve a maximum flow problem on ann-vertex,m-arc network in at mostnm pivots and O(n ² m) time. In this paper we describe how to extend the dynamic tree data structure of Sleator and Tarjan (1983, 1985) to reduce the running time of this algorithm to O(nm logn). This bound is less than a logarithmic factor larger than those of the fastest known algorithms for the problem. Our extension of dynamic trees is interesting in its own right and may well have additional applications.Research partially supported by a Presidential Young Investigator Award from the National Science Foundation, Grant No. CCR-8858097, an IBM Faculty Development Award, and AT&T Bell Laboratories.Research partially supported by the Office of Naval Research, Contract No. N00014-87-K-0467.Research partially supported by the National Science Foundation, Grant No. DCR-8605961, and the Office of Naval Research, Contract No. N00014-87-K-0467.     

Convergence analysis of time-point relaxation iterates for linear systems of differential equations

We study convergence properties of time-point relaxation (TR) Runge-Kutta methods for linear systems of ordinary differential equations. TR methods are implemented by decoupling systems in Gauss-Jacobi, Gauss-Seidel and successive overrelaxation modes (continuous-time iterations) and then solving the resulting subsystems by means of continuous extensions of Runge-Kutta (CRK) methods (discretized iterations). By iterating to convergence, these methods tend to the same limit called diagonally split Runge-Kutta (DSRK) method. We prove that TR methods are equivalent to decouple in the same modes the linear algebraic system obtained by applying DSRK limit method. This issue allows us to study the convergence of TR methods by using standard principles of convergence of iterative methods for linear algebraic systems. For a particular problem regions of convergence are plotted.     

The Equivalence of Several Basic Theorems for Subdifferentials

Several different basic tools are used for studying subdifferentials. They are a nonlocal fuzzy sum rule in (Borwein et al., 1996; Zhu, 1996), a multidirectional mean value theorem in (Clarke and Ledyaev, 1994; Clarke et al., 1998), local fuzzy sum rules in (Ioffe, 1984, 1990) and an extremal principle in (Kruger and Mordukhovich, 1980; Mordukhovich, 1976, 1980, 1994). We show that all these basic results are equivalent and discuss some interesting consequences of this equivalence.     

Ionic nanocomposites based on XNBR-OMg filled with layered nanoclays

Ionic elastomers based on carboxylated nitrile rubber (XNBR) crosslinked with magnesium oxide (OMg) and filled with layered nanoclays have been prepared. Two types of nanofillers were employed: a commercial one (Cloisite 15 A) and the other prepared in our laboratory (BCA-ODA). The properties of raw and vulcanized compounds have been studied in order to elucidate the effect of layered nanoclays. X-ray diffraction analysis shows that during compounding and crosslinking the macromolecular chains of rubber were intercalated in a commercial nanofiller, whilst our nanoclay was exfoliated. However, this fact does not affect the properties of compounds homogeneously. Vulcanization parameters, Mooney viscosity and decay and rheological properties were affected depending on the filler type. Mechanical properties were not significantly varied, but glass transition temperature and ionic transition temperature were shifted in comparison with those of the unfilled compound.     

An Interval-Parameter Fuzzy Approach for Multiobjective Linear Programming Under Uncertainty

An interval-parameter fuzzy linear programming method (IFMOLP) is proposed in this study for multiple objective decision-making under uncertainty. As a hybrid of interval-parameter and fuzzy methodologies, the IFMOLP incorporates interval-parameter linear programming and fuzzy multiobjective programming approaches to form an integrated optimization system. The method inherits advantages of interval-parameter programming, and allows uncertainties and decision-makers’ aspirations to be effectively communicated into its programming processes and resulting solutions. Membership functions for both objectives and constraints are formulated to reflect uncertainties in different system components and their interrelationships. An interactive solution procedure has been developed based on solution approaches of the interval-parameter and fuzzy programming techniques, plus necessary measures for handling the multiobjective feature. A didactic example is provided in the paper to illustrate the detailed solution process. Possibilities of further improvements by seeking Pareto optimum and incorporating flexible preference within constraints are also discussed.     

关于(QU)型模糊拓扑群的直积

研究(QU)型模糊拓扑群族直积,证明了任意(QU)型模糊拓扑群族的直积仍是(QU)型模糊拓扑群;研究了(QU)型模糊拓扑群族直积的模糊单位元之重域基的结构,得到了(QU)型模糊拓扑群族直积的一些重要性质.     

重力输水管道优化设计方法研究

针对重力输水管道设计中存在的问题，文章以管道造价最小为目标，应用动态规划，提出了一种新的重力输水管道优化设计方法，对输水管的当量管径、流量分配、连接管设置与可靠性校核计算等问题作了探讨。该方法可用于沿线有节点流量流出的并联输水管道优化设计，能明显节省投资，有良好的实用性     

Interpreting Intuitionistic Propositional Logic in Terms of Intuitionistic Protothetics

An algebra of sentences of the quite intuitionistic protothetics, that is, an intuitionistic propositional logic with quantifiers augmented by the negation of the excluded middle, is a faithful model of intuitionistic propositional logic.     

基于专家动态权重的群组AHP交互式决策方法

为了能在群组决策中得到更为客观和准确的决策结果,在把专家权重划分为静态权重和动态权重的基础上,研究了在交互式决策中专家动态权重的确定方法,给出了共识度的一个定义.在此基础上,研究了群组AHP交互式决策方法中的一致性和相容性检验,给出了基于专家动态权重的群组AHP交互式决策方法流程,最后用一个示例说明了该方法的应用步骤.     

Guaranteed-accuracy approximation of reachable sets for a linear dynamic system subject to impulse actions

A method is proposed for approximating the reachable set of a dynamic system with a state space dimension no higher than six-eight considered on a finite time interval. The system is governed by linear differential equations with piecewise constant coefficients and impulse actions specified at prescribed times. The method is based on guaranteed-accuracy polyhedral approximations of reachable sets at researcher-specified times. Every approximation is constructed using the preceding one. A procedure is described for choosing parameters of the method that ensure the required accuracy with close-to-minimal time costs.