Local spatial transformations and local observables

Traditionally spatial transformations such as translations and rotations are formulated in terms of transformations of the entire spatial space. In other words, transformations are taken automatically to be of a global nature. This paper investigates a local approach to spatial transformations; local transformations lead naturally to local observables in quantum mechanics.     

The variational Lyapunov function and strict stability theory for differential systems

In this paper, we investigate strict stability of differential systems by variational Lyapunov function. We obtain some sufficient conditions and comparison theorems.     

积分方程的ε复杂性

本文考虑积分方程的ε复杂性问题.问题的ε复杂性是在误差不超过ε的前提下解决问题所需的最小成本.对某些具各向异性核与自由项的第二类Fredholm方程,求得了ε复杂性的精确阶.同时,找到了解决该问题具最小成本的算法.     

ASYMPTOTIC APPROXIMATION METHOD AND ITS CONVERGENCE ON SEMI-INFINITE PROGRAMMING

The aim of this article is to discuss an asymptotic approximation model and its convergence for the minimax semi-infinite programming problem. An asymptotic surrogate constraints method for the minimax semi-infinite programming problem is presented by making use of two general discrete approximation methods. Simultaneously, the consistence and the epi-convergence of the asymptotic approximation problem are discussed.     

Synthesis of poly(ethylene oxide) with pending 2,2,6,6‐tetramethylpiperidine‐1‐oxyl groups and its further initiation of the grafting polymerization of styrene

A new stratagem for the synthesis of amphiphilic graft copolymers of hydrophilic poly(ethylene oxide) as the main chain and hydrophobic polystyrene as the side chains is suggested. A poly(ethylene oxide) with pending 2,2,6,6‐tetramethylpiperidine‐1‐oxyls [poly(4‐glycidyloxy‐2,2,6,6‐tetramethylpiperidine‐1‐oxyl‐co‐ethylene oxide)] was first prepared by the anionic ring‐opening copolymerization of ethylene oxide and 4‐glycidyloxy‐2,2,6,6‐tetramethylpiperidine‐1‐oxyl, and then the graft copolymerization of styrene was completed with benzoyl peroxide as the initiator in the presence of poly(4‐glycidyloxy‐2,2,6,6‐tetramethylpiperidine‐1‐oxyl‐co‐ethylene oxide). The polymerization of styrene was under control, and comblike, amphiphilic poly(ethylene oxide)‐g‐polystyrene was obtained. The copolymer and its intermediates were characterized with size exclusion chromatography, ¹H NMR, and electron spin resonance in detail. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3836–3842, 2006     

Investigation of sulfonated poly(ether ether ketone sulfone)/heteropolyacid composite membranes for high temperature fuel cell applications

The sulfonated poly(ether ether ketone sulfone) (SPEEKS)/heteropolyacid (HPA) composite membranes with different HPA content in SPEEKS copolymers matrix with different degree of sulfonation (DS) were investigated for high temperature proton exchange membrane fuel cells. Composite membranes were characterized by Fourier transfer infrared spectroscopy (FTIR) and scanning electron microscopy (SEM). FTIR band shifts suggested that the sulfonic acid groups on the copolymer backbone strongly interact with HPA particles. SEM pictures showed that the HPA particles were uniformly distributed throughout the SPEEKS membranes matrix and particle sizes decreased with the increment of copolymers' DS. The holes were not found in SPEEKS‐4/HPA30 (consisting of 70% SPEEKS copolymers with DS = 0.8 and 30% HPA) composite membrane after composite membranes were treated with boiling water for 24 h. Thermal stabilities of the composite membranes were better than those of pure sulfonated copolymers membranes. Although the composite membranes possessed lower water uptake, it exhibited higher proton conductivity for SPEEKS‐4/HPA30 especially at high temperature (above 100 °C). Its proton conductivity linearly increased from 0.068 S/cm at 25 °C to 0.095 S/cm at 120 °C, which was higher than 0.06 S/cm of Nafion 117. In contrast, proton conductivity of pure SPEEKS‐4 membrane only increased from 0.062 S/cm at 25 °C to 0.078 S/cm at 80 °C. At 120 °C, proton conductivity decreased to poor 0.073 S/cm. The result indicated that composite membranes exhibited high proton conductivity at high temperature. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1967–1978, 2006     

Preparation and characterization of rigid poly(vinyl chloride)/MMT nanocomposites. II. XRD,morphological and mechanical characteristics

A Haake torque rheometer equipped with an internal mixer is used to study the influence of the amount of sodium montmorillonite (Na⁺‐MMT) and organically modified MMT (O‐MMT) on X‐ray diffraction (XRD), morphology, and mechanical characteristics of rigid poly (vinyl chloride) (PVC)/Na⁺‐MMT and PVC/O‐MMT nanocomposites, respectively. Results of XRD and transmission electron microscopy (TEM) indicate that MMT is partially encapsulated and intercalated in the rigid PVC/Na⁺‐MMT nanocomposites. However, results of XRD and TEM show MMT is partially intercalated and exfoliated in the rigid PVC/O‐MMT nanocomposites. Tensile strength, yield strength, and elongation at break of the rigid PVC/MMT nanocomposites were improved simultaneously with adding 1–3 wt % Na⁺‐MMT or O‐MMT with respect to that of pristine PVC. However, the addition of Na⁺‐MMT or O‐MMT should be kept as not more than 3 wt % to optimize the mechanical properties and the processing stability of the rigid PVC/MMT nanocomposites. SEM micrographs of the fractured surfaces of the rigid PVC/Na⁺‐MMT and PVC/O‐MMT nanocomposites both before and after tensile tests were also illustrated and compared. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2145–2154, 2006     

Nondegeneracy and uniqueness of positive solutions for Robin problem of second order ordinary differential equations and its applications

This article studies positive solutions of Robin problem for semi-linear second order ordinary differential equations. Nondegeneracy and uniqueness results are proven for homogeneous differential equations. Necessary and sufficient conditions for the existence of one or two positive solutions for inhomogeneous differential equations or differential equations with concave-convex nonlinearities are obtained by making use of the nondegeneracy and uniqueness results for positive solutions of homogeneous differential equations.     

Catalytic enantioselective Mukaiyama aldol reaction via a chiral indium(III)-pybox complex

A chiral indium(III) complex prepared from indium triflate and a pybox ligand has been developed to give good yields and enantioselectivities (up to 92% ee) in the addition of (1-methoxy-2-methyl-propenyloxy)-trimethylsilane to various aromatic and aliphatic aldehydes via the Mukaiyama aldol reaction.