有限群极大子群的θ-子群偶

N.P.Mukherjee和 P.Bhattacharya在“On theta pairs for a maximal sub-group”(Proc.Amer.Math.Soc,Vl09N3(1990))一文中定义了有限群的极大子群的θ-子群偶概念,研究了极大子群的极大θ-子群偶对群结构的影响,得到了一系列结果.本文在进一步探究θ-子群偶性质的基础上,对该文中一系列主要结果作出了本质性的改进,并给出了可解性、幂零性的一些新刻划.     

二阶积分微分方程周期边值问题的解的存在性

通过对比结果,用单调迭代方法证明了Banach空间中二阶积分微分方程的周期边值问题的最大最小解的存在性定理。     

Products of Photo- and Thermochemical Rearrangement of 19-Membered di-tert-Butyl-Azoxybenzocrown

The preparation and characterization of products of the photochemical and thermochemical rearrangements of 19-membered azoxybenzocrowns with two, bulky, tert-butyl substituents in benzene rings in the para positions to oligooxyethylene fragments (meta positions to azoxy group, i.e., t-Bu-19-Azo-O have been presented. In photochemical rearrangement, two colored typical products were expected, i.e., 19-membered o-hydroxy-m,m′-di-tert-butyl-azobenzocrown (t-Bu-19-o-OH) and 19-membered p-hydroxy-m,m′-di-tert-butyl-azobenzocrown (t-Bu-19-p-OH). In experiments, two colored atypical macrocyclic derivatives, one 6-membered and one 5-membered ring, bearing an aldehyde group (t-Bu-19-al) or intramolecular ester group (t-Bu-20-ester), were obtained. Photochemical rearrangement led to one more macrocyclic product being isolated and identified: a 17-membered colorless compound, without an azo moiety, t-Bu-17-p-OH. The yield of the individual compounds was significantly influenced by the reaction conditions. Thermochemical rearrangement led to t-Bu-20-ester as the main product. The structures of the four crystalline products of the rearrangement—t-Bu-19-o-OH, t-Bu-19-p-OH, t-Bu-20-ester and t-Bu-17-p-OH—were determined by the X-ray method. Structures in solution of atypical derivatives (t-Bu-19-al and t-Bu-20-ester) and t-Bu-19-p-OH were defined using NMR spectroscopy. For the newly obtained hydroxyazobenzocrowns, the azo–phenol⇄quinone–hydrazone tautomeric equilibrium was investigated using spectroscopic methods. Complexation studies of alkali and alkaline earth metal cations were studied using UV-Vis absorption spectroscopy. ¹H NMR spectroscopy was additionally used to study the cation recognition of metal cations. Cation binding studies in acetonitrile have shown high selectivity towards calcium over magnesium for t-Bu-19-o-OH.     

激光主动探测中回波信号的小波去噪方法

在分析激光主动探测中回波信号的噪声特性和小波变换去噪原理的基础上，提出了一种基于最大信噪比准则的小渡阈值去噪方法。首先用最大信噪比准则对小波变换系数进行阈值选取，然后采用软阂值方法对小波系数进行量化处理后再重构。仿真结果表明最大信噪比准则小波去噪方法改善信噪比效果十分显著，检测下限达到-16．2dB。证明了该方法在激光主动探测系统回波信号检测中的有效性。     

Sobolev-Lorentz范数约束下的次临界型Adams不等式

本文在Sobolev-Lorentz空间W2L2,q(R4)的范数约束下得到了一个最佳的二阶次临界型Adams不等式.进一步,当次临界指标逼近最佳常数时,得到了Adams泛函的上、下界的估计.本文主要采用了Lam和Lu[A new approach to sharp Moser-Trudinger and Adams ...     

A weighted estimate for the commutator of the Bochner-Riesz operator

A weighted estimate with power weights is established for the maximal operator associated with the commutator of the Bochner-Riesz operator. An application of this weighted estimate is also given.

     

弱Lp空间的Marcienkiewicz型内插定理及其应用

在弱$L_p$空间之间建立一类Marcienkiewicz型内插定理并且给出它在现代调和分析理论中的某些应用.     

光子晶体光纤在熔接夹具中的受力分析

运用接触力学和圆环压溃强度理论对由V型槽固定的光子晶体光纤进行了受力分析。分别考虑了两种极限情况,以推导光纤中的应力分布。第一种情况假设光纤是完全由纯石英材料制成的内部均匀的实芯圆柱体;第二种情况是把光纤假设成一个空芯圆柱体。根据这两种极限情况推导出了光子晶体光纤受力后光纤内部的最大应力点位于平行于接触面的外层空气孔的附近。采用有限元方法验证了此结论,计算出了光子晶体光纤可能承受的最大压力,并给出了光子晶体光纤在V型槽中的应力分布和变形情况。     

Influence of radiation damage on lattice vibration parameters in crystalline and vitreous SiO2

The influence of radiation damage on a number of lattice vibration parameters in two SiO₂ modifications was investigated using IR reflectance spectroscopy. The radiation kinetics of changes in spectral characteristics of SiO₂ fundamental vibrations in crystalline and glassy states were determined. The reflectivity coefficient and the frequency of degenerate vibrations as functions of dose showed minima, the locations of which were governed by the type of sample. At high neutron irradiation doses (10²¹ cm⁻²), certain characteristics of the bands had the same values for both modified materials. Features of the radiation kinetics of sample dynamic parameters were determined. It was deduced that the specific character of the observed radiation-induced changes in spectral and dynamic parameters of vibrations near degenerate modes was due to both the accumulation of radiation damage and a change in the force field surrounding bridging bonds, which is related to a change in the SiO₂ structure. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 3, pp. 354–358, May–June, 2008.     

Alkene Carboarylation through Catalyst-Free,Visible Light-Mediated Smiles Rearrangement

A light-mediated Truce–Smiles arylative rearrangement is described that proceeds in the absence of any photocatalyst. The protocol creates two C−C bonds from simple starting materials, with the installation of an aryl ring and a difluoroacetate moiety across unactivated alkenes. The reaction proceeds via a radical mechanism, utilizing a light-mediated reduction of ethyl bromodifluoroacetate by N,N,N′,N′-tetramethylethylenediamine (TMEDA) to set up intermolecular addition to an unactivated alkene, followed by Truce–Smiles rearrangement.