Fixed point theorems on fuzzy normed linear spaces

In this paper, definitions of strongly fuzzy convergent sequence, l-fuzzy weakly convergent sequence and l-fuzzy weakly compact set are given in a fuzzy normed linear space. The concepts of fuzzy normal structure, fuzzy non-expansive mapping, uniformly convex fuzzy normed linear space are introduced and fixed point theorems for fuzzy non-expansive mappings are proved.     

Oxidation of some aliphatic polyols on anodically deposited MnO2

Galvanostatic steady state current potential measurements were carried out for oxidation of a series of aliphatic alcohols having varying number of hydroxyl groups. The anodically deposited layer of MnO₂ on platinum was used as the electrode material. The deposit was characterised by scanning electron microscopy (SEM), energy dispersive X-ray analysis (EDAX) and electrode potential measurements. The catalytic role of MnO₂ in the electro-oxidation of alcohols was indicated by the chronopotentiograms and the cyclic voltammograms. An analysis of the electrochemical data indicated a catalytic EC mechanism in which Mn (V) is generated electrochemically and consumed chemically in succession. Based on this and the hydrogen bonding interaction between alcoholic hydroxyl groups and MnO₂ layer, a mechanism was proposed which accounts for the variation in the observed electrochemical reaction orders. Tafel behaviour was found to be followed only approximately. Current efficiency of the electrochemical oxidation of polyols was studied. Replacement of platinum by carbon as current collector was found to leave the electrocatalytic activity of the MnO₂ deposit practically unaltered.     

A globally convergent algorithm for transportation continuous network design problem

The continuous network design problem (CNDP) is characterized by a bilevel programming model, in which the upper level problem is generally to minimize the total system cost under limited expenditure, while at the lower level the network users make choices with regard to route conditions following the user equilibrium principle. In this paper, the bilevel programming model for CNDP is transformed into a single level convex programming problem by virtue of an optimal-value function tool and the relationship between System Optimum (SO) and User Equilibrium (UE). By exploring the inherent nature of the CNDP, the optimal-value function for the lower level user equilibrium problem is proved to be continuously differentiable and its derivative in link capacity enhancement can be obtained efficiently by implementing user equilibrium assignment subroutine. However, the reaction (or response) function between the upper and lower level problem is implicit and its gradient is difficult to obtain. Although, here we approximately express the gradient with the difference concept at each iteration, based on the method of successive averages (MSA), we propose a globally convergent algorithm to solve the single level convex programming problem. Comparing with widely used heuristic algorithms, such as sensitivity analysis based (SAB) method, the proposed algorithm needs not strong hypothesis conditions and complex computation for the inverse matrix. Finally, a numerical example is presented to compare the proposed method with some existing algorithms.     

基于可拓学模型的大批量定制实施方法分析

简要阐述了当前企业环境的特点，分析了大批量定制及其可拓学模型；然后，从可拓学中的可拓工程出发，以“系列化”、“变型结构设计”和“变型工艺设计”为例，说明了可拓学在实施大批量定制中的应用，为企业寻找新的、有效的大批量定制实施方法提供料新的思路和工具。     

三参量速度分析的迭代算法

采用预求倾角法进行三参量速度分析时，首先要确定地下界面的倾向和倾角。若没有准确速度，就求不准倾向和倾角，因此无法一次求得准确的结果。若采用迭代算法，则可以使三参量逐渐向精确值逼近。在地层倾角小于４５＾０的情况下，迭代是收敛的。在有噪音的情况下，噪音会使叠加道集上同相轴的时间发生变化，从而影响倾向的确定，因此在迭代的每一步，都必须估算倾向。理论实际资料的试算表明，采用迭代方法求取地下界面参数是切实可     

Lyapunov analysis of the approximate motion equations of flexible structures

In this paper, the effectiveness of the approximate motion equations of a flexible structure, obtained by the RitzKantorovich method, is analysed by using Lyapunov functions. The analysis, which is restricted to the case of a single flexible beam for the sake of simplicity, is carried out under the assumption that a partial dissipation is present, affecting only the first degrees of freedom of the system. By means of suitable Lyapunov functions, an overbounding estimate of the quadratic approximation error is determined as a decreasing function of the approximation order. The analysis is completed by considering the two ‘extreme’ cases: the theoretical absence of dissipation and the presence of structural dissipation, affecting all the infinite degrees of freedom.     

Explosive Random‐Coefficient AR(1) Processes and Related Asymptotics for Least‐Squares Estimation

Abstract. Large sample properties of the least‐squares and weighted least‐squares estimates of the autoregressive parameter of the explosive random‐coefficient AR(1) process are discussed. It is shown that, contrary to the standard AR(1) case, the least‐squares estimator is inconsistent whereas the weighted least‐squares estimator is consistent and asymptotically normal even when the error process is not necessarily Gaussian. Conditional asymptotics on the event that a certain limiting random variable is non‐zero is also discussed.     

THE ANALYSIS OF THE SEPARATED LAYERS ALGORITHM BY DOMAIN DECOMPOSITION METHOD

From the principle of of the Domain Decomposition Method (DDM), we analyse the 2nd-order linear elliptic partial differential problems and link the Separated-Layers Algorithm (SLA) with DDM. The mathematical properties of SLA and numerical example are presented to obtain satisfactory computation results. For general linear differential ones, also are the structure of SLA and its characteristics discussed.     

共轭高分子三阶非线性光学材料

概述了ｎ－共轭高分子材料的三阶非线性光学性质，着重讨论了化学结构对其光学非线性的影响，说明了ｎ－共轭聚合物的三阶非线性极化率主要取决于共轭主链的结构，侧链取代基的变化对其非线性影响不大，文中展望了共轭高分子材料在集成光学中的应用前景。