Similarity of L-fuzzy Relations Based on L-topologies Induced by L-fuzzy Rough Approximation Operators

This paper proposes similarity of L-fuzzy relations based on L-topologies induced by L-fuzzy rough approximation operators. First, the notion L-fuzzy rough set is generalized and the relationship between generalized L-fuzzy rough sets and L-topologies on an arbitrary universe is investigated. It shows that Alexandrov L-topologies can be induced by L-fuzzy relations without any preconditions. Second, the concept of similarity of L-fuzzy relations is introduced and variations of an L-fuzzy relation are investigated. Third, algebraic structures on similarity of L-fuzzy relations are obtained. Finally, we prove that the subset of the transitive L-fuzzy relations similar to a fixed L-fuzzy relation is a complete distributive lattice.     

A comprehensive experimental study of the rheological behaviour of HDPE.

Extensional properties of four high density polyethylenes with different molecular weights and molecular weight distributions are presented. The samples have already been well characterized in shear and non-isothermal extensional flow. The data were collected at 180 °C for elongational rates between 3 · 10^–1 and 10^–4s^–1. Some qualitative and quantitative generalizations of the results are given.     

A tool for rapid quenching of elongated polymer melts

In this article, we present a device for rapid quenching of elongated polymer melts. The tool is an accessory to the uniaxial elongational rheometer RME of Meissner and Hostettler. It is intended to be used for microscopic and other investigations of stretched polymers. The device allows us to solidify a polymer melt by pouring liquid nitrogen on it and to cut it at the nearly same instant of time. Then the sample can be easily removed from the stretching apparatus. Solving the heat diffusion equation for a polymer melt, which is cooled by liquid nitrogen, we theoretically estimate the quenching time of this method. To demonstrate that this quenching procedure indeed rapidly cools a polymer melt, the stress birefringence of elongated and subsequently quenched polystyrene melts is measured and the stress-optical coefficient C is determined. The experimental value of the stress-optical coefficient is |C|= 4.65×10⁻⁹ Pa⁻¹, which agrees well with the data in literature. Using this tool for elongation experiments with the RME, polymer melts can be solidified in between approximately 0.2 and 2.0 s, depending on the thickness of the sample.     

Shape and topology optimization for elliptic boundary value problems using a piecewise constant level set method

The aim of this paper is to propose a variational piecewise constant level set method for solving elliptic shape and topology optimization problems. The original model is approximated by a two-phase optimal shape design problem by the ersatz material approach. Under the piecewise constant level set framework, we first reformulate the two-phase design problem to be a new constrained optimization problem with respect to the piecewise constant level set function. Then we solve it by the projection Lagrangian method. A gradient-type iterative algorithm is presented. Comparisons between our numerical results and those obtained by level set approaches show the effectiveness, accuracy and efficiency of our algorithm.     

Topology vs generalized rough sets

This paper investigates the relationship between topology and generalized rough sets induced by binary relations. Some known results regarding the relation based rough sets are reviewed, and some new results are given. Particularly, the relationship between different topologies corresponding to the same rough set model is examined. These generalized rough sets are induced by inverse serial relations, reflexive relations and pre-order relations, respectively. We point that inverse serial relations are weakest relations which can induce topological spaces, and that different relation based generalized rough set models will induce different topological spaces. We proved that two known topologies corresponding to reflexive relation based rough set model given recently are different, and gave a condition under which the both are the same topology.     

一类基于分层量化的Domain上的广义Alexander拓扑

文献[8]提出了一类基于分层量化的偏序集结构(以下简称R-偏序集).此结构是sfe[5]的非对称推广,也是拟度量空间(quasi-metric spaces,qms)[3]和广义超度量空间(generalized ultrametric spaces,gums)[4]的一种特殊情形.本文定义了其上的广义Alexande...     

空间F^＊上一类积分方程解的存在和唯一性

本文在引文［１—４］的基础出上，首次在空间~Ｆ＊上构造性的建立了一类积分方程。并获得了这类积分方程解的存在和唯一性定理。     

Critical Points and Error Rank in Best H 2 Matrix Rational Approximation of Fixed McMillan Degree

This paper deals with best rational approximation of prescribed McMillan degree to matrix-valued functions in the real Hardy space of the complement of the unit disk endowed with the Frobenius L ₂ -norm. We describe the topological structure of the set of approximants in terms of inner-unstable factorizations. This allows us to establish a two-sided tangential interpolation equation for the critical points of the criterion, and to prove that the rank of the error F-H is at most k-n when F is rational of degree k , and H is critical of degree n . In the particular case where k=n , it follows that H=F is the unique critical point, and this entails a local uniqueness result when approximating near-rational functions. January 23, 1996. Date revised: September 16, 1996.     

关于模糊数空间的Skorokhod拓扑的注记

首先考察模糊数空间中Skorokhod度量与紧承下方图度量之间的关系,然后说明了文献[4]中的关于Skorokhod拓扑紧致性的例子是错误的并给出了正确的例子.     

Structural analysis of the c(4 × 2) reconstruction in Si(0 0 1) and Ge(0 0 1) surfaces by low-energy electron diffraction

The c(4 × 2) structures in (0 0 1) surfaces of Si and Ge have been studied by low-energy electron diffraction (LEED). Using a proper cleaning method for the Si surface, we were able to observe clear c(4 × 2) LEED patterns up to incident energy of ∼400 eV as well as the Ge surface. Extensive experimental intensity-voltage curves allowed us to optimize the asymmetric dimer model up to the eighth layer (including the dimer layer) in depth in the dynamical LEED calculation. Optimized structural parameters are almost the same for the Si and Ge except for the height of the buckled-up atom of the asymmetric dimer. For the Ge surface, the structural parameters are in excellent agreement with those obtained by a previous theoretical calculation. The tilt angle and bond length of the dimer are 18 ± 1 (19 ± 1)° and 2.4 ± 0.1 (2.5 ± 0.1) Å for the Si(0 0 1) (Ge(0 0 1)), respectively.