分数阶尺度函数的分解与重构算法

引入分数阶多分辨分析与分数阶尺度函数的概念.运用时频分析方法与分数阶小波变换,研究了分数阶正交小波的构造方法,得到分数阶正交小波存在的充要条件.给出分数阶尺度函数与小波的分解与重构算法,算法比经典的尺度函数与小波的分解与重构算法更具有一般性.     

In situ PM‐IRRAS studies of organothiols and organosilane monolayers–ZnO interfaces at high water activities

In situ photoelastic‐modulated Fourier transform infrared reflection absorption spectroscopy has been applied for the investigation of interfacial stability of organothiol and organosilane monolayer films on nanocrystalline zinc oxide thin films. It has been shown that for octadecyltriethoxysilane films, exposure to high water activities results in physisorption of water in the cross‐linked film. This high water activity at the interface leads to a reversible wet de‐adhesion of the interfacial silanol groups from the ZnO surface. However, the organothiol seems to form a denser monolayer and a stable by S–Zn bond that is resistant to the competition with adsorbed water. The reversible attachment for cross‐linked organosilanol films has been demonstrated for the first time by means of an in situ spectroscopic method on model ZnO surfaces. Copyright © 2016 John Wiley & Sons, Ltd.     

Interrelationship between total volatile organic compounds emissions,structure and properties of natural rubber/polycaprolactone bio-blends cross-linked with peroxides

Natural rubber/polycaprolactone (NR/PCL) bio-based blends with different organic peroxides were prepared using an internal batch mixer and subsequently cross-linked at 170 °C. Two types of commonly used organic peroxides, dicumyl peroxide and di(tert-butylperoxyisopropyl)benzene peroxide, were applied as free-radical initiator. Cross-linking efficiency of NR/PCL blends were investigated using oscillating disc rheometer measurements, followed by infrared spectroscopy, thermogravimetric analysis, differential scanning calorimetry, dynamic mechanical analysis and tensile testing. Total volatile organic compounds (TVOCs) emissions were determined using headspace analysis integrated with gas chromatography with flame ionization detector. Determined TVOCs emissions varying in range 21.6–52.1 μg/g and generally value of this parameter decreased with increasing content of PCL phase in studied blends or with application of more efficient di(tert-butylperoxyisopropyl)benzene peroxide as cross-linking agent. It was found that increasing of TVOCs parameter indicated deterioration of mechanical properties of NR/PCL blends, which corresponded with the changes in chemical structure and thermal properties of cross-linked NR/PCL. This confirms that evaluation of TVOCs parameter is interesting alternative for “conventional methods” to characterization of the studied bio-based blends.     

基于虚拟相位平面的相位展开方法

在基于相位分析的三维测量系统中,为了准确地得到物体的高度,相位展开扮演着很重要的角色。传统的相位展开方法常常需要额外的投影图,而傅里叶变换轮廓术只需要采集一幅或两幅变形条纹图就可以实现对物体轮廓的测量,其方法速度快,易于实现。针对傅里叶变换轮廓术方法计算得到的截断相位分布,本文提出了一种利用截断相位与参考平面相位差值2π的整数倍数获得截断相位的正确级次,辅助相位展开的方法。当被测物体较复杂,或者相位截断次数较多时,该方法在已有参考平面相位的基础上虚拟新的相位平面,依次比较截断相位和虚拟相位,进行多次分级相位展开,结合多个展开相位结果,最终得到正确的展开相位。该方法展开速度快,展开错误不会蔓延传递。仿真和实物实验结果证明了该方法的可行性,说明该方法可用于傅里叶变换轮廓术中进行截断相位的快速展开。     

Contractivity results in ordered spaces. Applications to relative operator bounds and projections with norm one

This paper provides various “contractivity” results for linear operators of the form where C are positive contractions on real ordered Banach spaces X . If A generates a positive contraction semigroup in Lebesgue spaces , we show (M. Pierre's result) that is a “contraction on the positive cone ”, i.e. for all provided that .  We show also that this result is not true for 1 ⩽ . We give an extension of M. Pierre's result to general ordered Banach spaces X under a suitable uniform monotony assumption on the duality map on the positive cone . We deduce from this result that, in such spaces, is a contraction on for any positive projection C with norm 1. We give also a direct proof (by E. Ricard) of this last result if additionally the norm is smooth on the positive cone. For any positive contraction C on base‐norm spaces X (e.g. in real spaces or in preduals of hermitian part of von Neumann algebras), we show that for all where N is the canonical half‐norm in X . For any positive contraction C on order‐unit spaces X (e.g. on the hermitian part of a algebra), we show that is a contraction on . Applications to relative operator bounds, ergodic projections and conditional expectations are given.     

Pseudo‐differential operators in a Gelfand–Shilov setting

We introduce some general classes of pseudodifferential operators with symbols admitting exponential type growth at infinity and we prove mapping properties for these operators on Gelfand–Shilov spaces. Moreover, we deduce composition and certain invariance properties of these classes.     

Applications of ‐invariant distributions

In this sequel to the article 17 , a criterion for the regularity of fundamental solutions of differential operators with positive symbol is proved in analogy to Hörmander's criteria, see 9 , 12 . It implies that the temperate fundamental solution of the operator is not regular. Furthermore, a formula for the convolution of two ‐invariant distributions is presented, and, finally, L. Schwartz' question on the surjectivity of linear partial differential operators with constant coefficients on the space is completely answered in the case of ‐invariant differential operators.     

Strong Convergence Theorems for a Countable Family of Multi-Valued Bregman Quasi-Nonexpansive Mappings in Reflexive Banach Spaces

This article uses the shrinking projection method introduced by Takahashi, Kubota and Takeuchi to propose an iteration algorithm for a countable family of Bregman multi-valued quasi-nonexpansive mappings in order to have the strong convergence under a limit condition in the framework of reflexive Banach spaces. We apply our results to a zero point problem of maximal monotone mappings and equilibrium problems in reflexive Banach spaces. The results presented in the article improve and extend the corresponding results of that found in the literature.     

Minimal Projections onto Subspaces with Codimension 2

In this article, the relationship between absolute projection constants with dimension n and with codimension n is given. In particular, bounds from below are found for absolute projection constants with codimension 2. Also, exact formulas for minimal projections in this case are given. It is shown that these minimal projections are not unique.