Stability Concepts in Topological Dynamics by Nonstandard Methods

It is known that it is not possible to introduce C⁰ -structural stability for whole systems in topological dynamics. Using the methods of Nonstandard Analysis, we suggest four different purely topological stability concepts for dynamical systems on compact subsets of Rⁿ. Classically these amount to considering the space of all systems on a given subset of Rⁿ as the fundamental entity when deforming a continuous system (instead of the space of all continuous systems as is normally done in topological dynamics). For two of the introduced stability concepts, we will show that all minimal flows are stable in this sense. Besides this, we will show that one of our stability concepts is related to what is called the pseudo orbit tracing property in a recently published book by Aoki and Hiraide and compare some of our results to the theory of dynamical systems as presented there.     

Aggregation structure and mechanical properties of functionally graded polyurethane elastomers

Functionally graded polyurethane elastomers (FGPUEs) were prepared with two molds fixed at different temperatures (30 and 150 °C). The effects of the molar ratio of the curing agent (60/40, 75/25, or 97/3 1,4‐butane diol/1,1,1‐trimethylol propane) and the molecular weight of the polymer glycol (number‐average molecular weight = 2000 or 3000) on the molecular aggregation state and mechanical properties of the FGPUEs were investigated with differential scanning calorimetry, polarized optical microscopy, dynamic viscoelastic measurements, and tensile tests. The aggregation state of the FGPUEs was changed continuously from the one side (lower temperature side) to the other side (higher temperature side); for example, the glass‐transition temperature gradually increased in this direction. Also, the number of spherulites formed in the FGPUEs increased in the same manner. In the mechanical tests, the tensile strength and elongation at break of the lower temperature side were higher than those of the higher temperature side. This was correlated with the strong phase separation of the lower temperature side. The poly(oxytetramethylene glycol)‐based FGPUE with a chain extender of 75 wt % showed the largest degree of the temperature gradient. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2355–2363, 2003     

The Volterra Property of Some Problems with the Bitsadze-Samarskii-Type Conditions for a Mixed Parabolic-Hyperbolic Equation

We consider problems with the Bitsadze-Samarskii-type conditions for a mixed parabolic-hyperbolic equation with noncharacteristic type change curve. We prove theorems on the unique existence of regular and strong solutions and the Volterra property for the problems under consideration.Original Russian Text Copyright © 2005 Berdyshev A. S.__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 500–510, May–June, 2005.     

Polyisophthalamides with heteroaromatic pendent rings: Synthesis,physical properties,and water uptake

A set of novel aromatic polyamides containing pyridine pendent groups was prepared from aromatic diamines and new monomers that are 5‐substituted derivatives of isophthalic acid bearing nicotinamide, isonicotinamide, or picolinamide groups. The polymers were obtained in high yield and high molecular weight by the phosphorylation method of polycondensation. They were characterized by spectroscopic and chromatographic methods and several of their properties were investigated. All of the polymers were soluble in polar aprotic solvents and gave films of good mechanical properties. Glass transition temperatures were higher than that of the reference polymer, poly(m‐phenyleneisophthalamide) (IP‐MPD), while the thermal resistance, defined by the initial decomposition temperature observed by thermogravimetry, was in the range 370–420 °C, lower by 30–70 °C than that of IP‐MPD. The presence of a pendent pyridine group and an additional amide side group per repeat unit made the polymers essentially amorphous and greatly improved their abilities to absorb water in comparison with nonsubstituted polyamides. Water uptake values up to 15% were observed at 65% relative humidity. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5300–5311, 2005     

性质(u)在序列空间ces_p(E_n)中的提升

主要研究了性质(u)从Banach空间En到序列空间cesp(En)的提升问题.     

Isomer‐dependent properties of poly(vinyl pyridine)‐based films grown on copper surfaces

The effect of poly(2‐vinyl pyridine) (P2VP) and poly(4‐vinyl pyridine) (P4VP) isomers on the growth of surface films on copper substrates was studied by electrochemical, spectroscopic, thermogravimentric, and microscopic methods. In acid environment (3% v/v acetic acid) and in the presence of KSCN, electrochemically generated copper cations reacted rapidly with SCN^? and P2VP or P4VP, yielding coordination compounds, which deposited onto copper surfaces as films. The characteristics of such polymer–metal complexes (films) were markedly isomer‐dependent. Cu(I)/P2VP/SCN^? complexes with monovalent cations and sulfur‐coordinated thiocyanate were obtained in the presence of P2VP, whereas the formation of Cu(II)/P4VP/SCN^? complexes with divalent cations and nitrogen‐coordinated thiocyanate was observed in the presence of P4VP. Interestingly, similar physical–chemical properties (electronic structure, stoichiometry, and thermal behavior) were observed for materials synthesized by electrochemical and chemical methods. These results suggest, therefore, that control over the surface properties of copper substrates can be achieved using electrosynthesized films based on different PVP isomers. Besides acting as effective protective barriers against aggressive media and thus reducing the metal dissolution (corrosion) kinetics, these materials are potentially attractive for other applications in which surface properties are paramount, such as in catalysis. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 215–225, 2009     

The class of co-Namioka compact spaces is stable under product

In an earlier paper we have established that the cartesian product of a family of co-Namioka compact spaces is co-Namioka if and only if all finite cartesian products of this family are co-Namioka. The purpose of this note is to show that the product of two co-Namioka compact spaces is always co-Namioka. The class of co-Namioka compact spaces is consequently stable under arbitrary products.

     

掺锌LiNbO3晶体的生长及其光学性能

在LiNbO₃中掺进3mol%、5mol%、7mol%ZnO生长Zn:LiNbO₃晶体.测试Zn:LiNbO₃晶体的吸收光谱,研究Zn:LiNbO₃晶体吸收边紫移的机制.测试Zn:LiNbO₃晶体的红外光谱,研究Zn(7mol%):LiNbO₃晶体OH 吸收峰由3484cm^-1移到3530cm^-1的机制.测试Zn:LiNbO₃晶体倍频转换效率和相位匹配温度,研究Zn:LiNbO₃晶体倍频转换效率增强的机制.     

Twist points of the von Koch snowflake

It is known that the set of twist points in the boundary of the von Koch snowflake domain has full harmonic measure. We provide a new, simple proof, based on the doubling property of the harmonic measure, and on the existence of an equivalent measure, invariant and ergodic with respect to the shift.