I-模糊拓扑空间中的紧度

In this paper, the concept of degree of compactness is introduced in the general framework of I-fuzzy topological spaces, and its property is discussed. All good compactness are generalized to I-fuzzy topological spaces accordingly.     

Synthesis and characterization of polycyanurate/montmorillonite nanocomposites

The advantages of cyanate esters (CEs) versus competitor systems such as epoxies and polyimides, as well as the great reinforcing potential of organoclays properly dispersed into a polymeric matrix, have been examined in a series of polycyanurate (PCN)/montmorillonite (MMT) nanocomposites prepared under appropriate polymerization conditions. The curing schedule applied resulted in gradual propagation of polymerization. Through this procedure, the intragallery curing rate becomes comparable to the extragallery one, allowing intercalation before gelation. Systems with clay loadings from 1 to 3% per weight were synthesized, and their morphology and mechanical properties were studied by means of scanning electron microscopy (SEM), atomic force microscopy (AFM), wide angle X‐ray scattering (WAXS), dynamic mechanical analysis (DMA), and tensile tests. Microscopy investigations revealed better dispersion for the 3 wt % system compared to smaller concentrations, in which aggregation and, in some cases, agglomeration were the conspicuous features. Roughness and area analyses revealed more homogeneous dispersion for this nanocomposite. Topology and 3D‐phase images further suggested considerable reduction of the average particle diameters. WAXS analysis showed that the interlayer spacing of nanocomposites was increased compared to pristine MMT, indicating the formation of intercalated structures. On the other hand, tensile strength and elongation at break values displayed abrupt diminution with MMT addition, while Young's modulus exhibited a slight but systematic increment with MMT content. The decreasing glass transition tendency observed for small clay loadings was reversed in the case of 3 wt %, while secondary transitions were practically unaffected by the presence of MMT. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1036–1049, 2008     

Densely continuous forms, pointwise topology and cardinal functions

We consider the space D(X, Y) of densely continuous forms introduced by Hammer and McCoy [5] and investigated also by Holá [6]. We show some additional properties of D(X, Y) and investigate the subspace D*(X) of locally bounded real-valued densely continuous forms equipped with the topology of pointwise convergence τ- _p . The largest part of the paper is devoted to the study of various cardinal functions for (D*(X), τ _p ), in particular: character, pseudocharacter, weight, density, cellularity, diagonal degree, π-weight, π-character, netweight etc. This work was supported by Science and Technology Assistance Agency under the contract No. APVT-51-006904. The authors would like to thank Ľubica Holá for suggestions and comments.     

Fell topology on the hyperspace of a non-Hausdorff space

Fell topology is very widely used today, even in metric spaces; but J. Fell introduced it in a non-Hausdorff context in the connection with the theory of C ^*-algebras. In spite of this, it has been studied only on the hyperspace of a Hausdorff space, except for the first results due to Fell himself. The present paper aims to fill this gap, in particular extending some results of H. Poppe and of G. Beer to the general case. Project 10251002 supported by National Natural Science Foundation of China.     

$I$-模糊拓扑空间中的模糊紧度

本文借助不等式给出了$I$-模糊拓扑空间中模糊紧度的概念, 并研究了相关的性质.     

Monotonicity properties of operations on generalized topologies

Summary In the paper [5], several operations on generalized topologies are considered. They are not monotone in general, but an old result on monotonicity may be sharpened.     

The effect of air exposure on palladium–copper composite membranes

It was found that when electrolessly deposited thin Pd and Pd–Cu membranes were exposed to air at temperatures above 350 °C, their H₂ flux increased substantially immediately after the air exposure, then decreased to a new steady-state value. While this was a quasi-reversible change for the H₂ flux, the flux of insoluble species, such as N₂, irreversibly increased with every air exposure but by a much smaller extent. The extent of these changes was found to be dependent on the exposure time and the temperature of the tests. Thus, we decided to investigate the effect of gas exposures on the properties of these materials.

Palladium and palladium–copper films, prepared by electroless deposition on ceramic supports, and commercial foils were exposed to air, hydrogen and helium at 500 and 900 °C for times varying from 1 h to 1 week with the objective of determining the effect of the different exposure conditions on the surface morphology, the flux of different penetrants and the crystalline structure of the materials. Atomic force microscopy (AFM) and X-ray diffraction (XRD) were used to study the changes occurring in the films under those conditions.

It was observed that the exposure of both the electroless films and the foils to hydrogen and air markedly modified their surface morphology. The hydrogen exposure tended to smooth the surface features whereas the oxygen exposure created new surface features such holes and large peaks. Additionally it was found that the air exposure produced some oxidation of the film to create PdO.

These results suggested that a common hypothesis stating that air oxidation just cleans the surface of the membrane might not be sufficient to explain all of those changes. A contributing effect of air exposure may be the increase in surface area due to the formation of palladium oxide. However, the extent of the surface area increase was insufficient to explain the increase in steady-state H₂ flux.     

A Zariski Topology for Bicomodules and Corings

In this paper we introduce and investigate top (bi)comodules of corings, that can be considered as dual to top (bi)modules of rings. The fully coprime spectra of such (bi)comodules attains a Zariski topology, defined in a way dual to that of defining the Zariski topology on the prime spectra of (commutative) rings. We restrict our attention in this paper to duo (bi)comodules (satisfying suitable conditions) and study the interplay between the coalgebraic properties of such (bi)comodules and the introduced Zariski topology. In particular, we apply our results to introduce a Zariski topology on the fully coprime spectrum of a given non-zero coring considered canonically as duo object in its category of bicomodules. Supported by King Fahd University of Petroleum & Minerals, Research Project # INT/296.     

Global properties of integrable Hamiltonian systems

This paper deals with Lagrangian bundles which are symplectic torus bundles that occur in integrable Hamiltonian systems. We review the theory of obstructions to triviality, in particular monodromy, as well as the ensuing classification problems which involve the Chern and Lagrange class. Our approach, which uses simple ideas from differential geometry and algebraic topology, reveals the fundamental role of the integer affine structure on the base space of these bundles. We provide a geometric proof of the classification of Lagrangian bundles with fixed integer affine structure by their Lagrange class.      

与一拓扑紧性反例相关的结果

有反例表明一个紧致拓扑空间不一定是序列紧致的拓扑空间 .我们给出了一个与此反例密切相关的分析结果 ,表明由任一非常值的单边连续周期函数 ,都可构造一个这样的反例 .