Computations of critical groups and applications to asymptotically linear wave equation and beam equation

In this paper, by using the Morse index theory for strongly indefinite functionals developed in [Nonlinear Anal. TMA, in press], we compute precisely the critical groups at the origin and at infinity, respectively. The abstract theorems are used to study the existence (multiplicity) of nontrivial periodical solutions for asymptotically wave equation and beam equation with resonance both at infinity and at zero.     

Photoluminescence characteristics of ZnTiO3: Bi nanocrystals

The photoluminescence properties of the Bi³⁺ in sol-gel derived ZnTiO₃ nanocrystals have been investigated. An ultra-violet emission at 360 nm and a visible emission band at 506 nm have been observed, originating from two kinds of emission centers. The former is ascribed to the ³P₁-¹S₀ transition of Bi³⁺ and the latter to the recombination of the electrons with the photo-generated holes trapped in the zinc vacancies. In all cases the latter contribution is predominant.     

NOESY技术在地胆草倍半萜内酯化合物结构鉴定中的应用（I）

明确从地胆草中分离得到的两对牦牛儿内酯型的立体异构体即地胆草种内酯（scabertopin）、异地胆草种内酯（isoscabertopin）、异去氧地胆草内酯（isodeoxyelephantopin）和去氧地胆草内酯（deoxyelephantopin）的C-2相对构型；方法 NOESY技术，并结合这4个化合物的¹H NMR，¹³C NMR，HMQC谱；结果 两对立体异构体的NOESY谱有明显差异；结论 通过分析NOESY谱，找寻H-1相关信息，若发现H-1与H-8，H-9β和14-CH₃有NOE相关，可以判断化合物的C-2为α构型，若H-1与H-5，H-7，H-3α及H-9α之间有NOE相关，则化合物的C-2为β构型.     

用横波推导简谐波的能量

本文提出用横波推导简谐波能量的方法，并就此进行了具体时推导。     

Ionic conductivity of epitactic MBE-grown BaF2 films

We studied parallel conductivities of pure BaF₂ films with thicknesses ranging from 35 to 300 nm, epitaxially grown on Al₂O₃(0 1 2) substrates by molecular beam epitaxy technique. The overall conductivities of the films are found to increase with decreasing thickness. The detailed investigation of the overall conductance as a function of the thickness permits the deconvolution of bulk and boundary effects, the latter being attributed to distinct space charge effects in the interface between BaF₂ film and Al₂O₃ substrate. The (extrinsic) Debye length (λ) is estimated to be about 8 nm at T=593 K, which corresponds to an impurity content of 10¹⁸/cm³ (singly ionized dopant assumed). This is consistent with the fact that we observed a constant boundary contribution for all investigated films (film thickness >4λ). It is also consistent with the Debye length observed in a previous report on CaF₂/BaF₂ heterolayers fabricated by the same technique, in which the low temperature enhancement was also attributed to space charges in BaF₂ [Nature 408 (2000) 946]. Only at low temperatures (below 370 °C), the conductance seems to be influenced by strain effect.     

Essentially normal Hilbert modules and Khomology Ⅲ: Homogenous quotient modules of Hardy modules on the bidisk

In this paper, we study the homogenous quotient modules of the Hardy module on the bidisk. The essential normality of the homogenous quotient modules is completely characterized. We also describe the essential spectrum for a general quotient module. The paper also considers K-homology invariant defined in the case of the homogenous quotient modules on the bidisk. This work is partially supported by the National Natural Science Foundation of China (Grant No. 10525106), the Young Teacher Fund, the National Key Basic Research Project of China (Grant No. 2006CB805905) and the Specialized Research for the Doctoral Program     

Solid codes and the uniform density of fd-domains

By means of further investigation of solid codes,the problem“Is every fd-domain uni- formly dense”proposed by Yuqi Guo,C.M.Reis and G.Thierrin in 1988 is solved in this paper.     

关于《一类奇异边值问题的正解》的注记

文[4]通过构造反例断言文[1]中定理的必要性证明有误,本文首先指出文[4] 的这个断言不正确,然后对文[4]中定理2.1作了本质性的改进.     

基于目标信息系统学习的多准则决策方法

给出目标信息系统学习的多准则决策方法，建立多准则决策的规则学习模型，讨论该模型的性质。该模型优于Z．Pawlak方法，将规则提取与信息融合为一体。也优于AHP等模型，具有简洁性．通过实例计算，取得了满意结果。     

On semi cover-avoiding subgroups of finite groups

A subgroup H of a finite group G is said to have the semi cover-avoiding property in G if there is a normal series of G such that H covers or avoids every normal factor of the series. In this paper, some new results are obtained based on the assumption that some subgroups have the semi cover-avoiding property in the group.