一类没有单调性假设的渐近线性波方程的多解

本文借助文[1]除去零空间的技巧,利用L—S度数理论讨论了一类浙近线性波方程。在对非线性项不做单调性假设的前提下,给出了一个新的多解定理。     

钐(Ⅱ)类卡宾CH_3SmCH_2X(X=Cl、Br和Ⅰ)促进乙烯环丙烷化反应途径的理论研究(英文)

用密度泛函B3LYP方法研究了过渡金属钐类卡宾与乙烯的环丙烷化反应的机理。对三种不同的钐的SS试剂CH_3SmCH_2X(其中X=Cl、Br和Ⅰ)分别和CH_2CH_2反应的各反应物、中间体、过渡态和产物构型的全部结构几何参数进行了优化,用内禀反应坐标(IRC)计算和频率分析方法,对过渡态进行了验证。结果表明：CH_3SmCH_2X(其中X=Cl、Br和Ⅰ)与CH_2CH_2环丙烷化反应按亚甲基转移通道(通道A)和卡宾金属化通道(通道B)都可以进行,与锂类卡宾的反应机理相同,只是按亚甲基转移通道(通道A)进行反应较容易一些,而且此反应在较低的温度下就可以发生。     

A CLASS OF r-POINT (r+1)ST-ORDER A-STABLE ONE-BLOCK METHODS WITH DAMPING AT THE INFINITE POINT

1　ＩｎｔｒｏｄｕｃｔｉｏｎＦｏｒｓｏｌｖｉｎｇｓｔｉｆｆｉｎｉｔｉａｌｖａｌｕｅｐｒｏｂｌｅｍｓｆｏｒｓｙｓｔｅｍｓｏｆＯＤＥｓｙ′=ｆ(ｙ) ,ｙ(ｔ0 ) =ｙ0 ,ｔ0 <ｔ≤Ｔ ,ｙ0 ,ｙ∈Ｒｍ,ｆ :Ω Ｒｍ →Ｒｍ (1 .1 )ｍａｎｙｐａｒｔｉｃｕｌａｒｏｎｅ ｂｌｏｃｋｍｅｔｈｏｄｓｏｆｔｈｅｆｏｒｍＹｎ+1= ＡＹｎ+ｈ( Ｂ0 Ｆ(Ｙｎ) + Ｂ1Ｆ(Ｙｎ+1) ) , Ａ =Ａ Ｉｍ, Ｂｉ=Ｂｉ Ｉｍ,Ａ ,Ｂｉ∈Ｒｒ×ｒ,Ｙｎ =(ＹＴｎｒ,… ,ｙＴ(ｎ+1)ｒ- 1) Ｔ,Ｆ(Ｙｎ) =(ｆＴ(ｙｎｒ) ,… ,ｆＴ(ｙ(ｎ+1)ｒ- 1) ) Ｔ,ｙｊ≈ ｙ(ｔｊ) ,…     

外加电场下激光诱导Al等离子体特性的实验研究

由Q-Nd:YAG脉冲激光(波长1.06μm,脉宽10 ns)烧蚀Al靶产生等离子体.观测了在低气压和直流电场条件下的Al等离子体发射光谱.研究了激光功率密度和直流电场对各谱线强度的影响,分析了谱线半高全宽与外加电压,等离子体电子温度与激光能量的变化规律.结果表明,直流电场对铝原子谱线强度有显著的增强,铝原子谱线的半高全宽与直流电场的外加电压基本上呈线性关系.     

Mesopore size dependence of the ionic diffusivity in alumina based composite lithium ionic conductors

Ordered-mesoporous Al₂O₃ was synthesized by a sol–gel method using neutral copolymer surfactants as structure-directing agents. The pore size was controlled over the 3–15 nm range by the use of various surfactants. Composites composed of the synthesized mesoporous Al₂O₃ and a lithium ion conductor (LiI) were prepared. The maximum dc electrical conductivity, 2.6 × 10^− 4 S cm^− 1 at 298 K, was observed for 50 LiI·50 Al₂O₃ composite with 4.2 nm average mesopore size, which was considerably higher than the previously reported LiI-alumina composites. A systematic dependence of conductivity upon pore size was observed, in which conductivity increased with decreasing pore size, except for samples with a pore size of 2.8 nm. The lithium ion diffusion coefficient determined by the ⁷Li pulsed field gradient nuclear magnetic resonance (PFG-NMR) showed excellent agreement with the measured conductivity calculated by the Nernst-Einstein equation. On the other hand, lithium migration activation energies obtained by quasielastic neutron scattering (QENS) and ⁷Li NMR spin-lattice relaxation time (T₁) were considerably smaller than those obtained from electrical conductivity and PFG-NMR. This could be explained by the ion migration mechanism in heterogeneous composites and a possible enhancement of conductivity in mesoscopically confined spaces.     

Sums of Two Exact Powers

An asymptotic formula is obtained for the number of representations of an element of a finite field as a weighted sum of two prescribed powers of primitive elements. This generalises previous work on sums of primitive elements, including that relating to some conjectures of Golomb.     

Characterization of exciton self-trapping in amorphous silica

Triplet electron–hole excitations were introduced into amorphous silica to study self-trapping (localization) and damage formation using density functional theory. Multiple self-trapped exciton (STE) states are found that can be differentiated based on the luminescence energy, the localization and distribution of the excess spin density of the triplet state, and relevant structural data, including the presence or absence of broken bonds. The trapping is shown to be affected by the relaxation response of the silica network, and by comparing results of quartz and amorphous silica systems the effects of the inherent disordered structures on exciton self-trapping are revealed. A key result is that the process of exciton trapping can lead directly to the formation of point defects, without thermal activation. The proposed mechanism includes a non-radiative decay from the excited to the ground state followed by structure relaxation to a defect configuration in the ground state.     

New Synthetic Method for Industrial Manufacture of Glutaric Dialdehyde

A new synthetic method for the manufacture of glutaric dialdehyde is investigated. Glutaric dialdehyde was prepared by the addition-hydrolysis reaction of benzimidazolium salt with saturated dihalide as the di-Grignard reagent. The yield of glutaric dialdehyde by this method can reach 73%. Both infrared spectra and melting point of the compound were consistent with those reported earlier. Translated from Journal of Northwest University (Natural Science Edition), 2005, 35(2) (in Chinese)     

Analysis of some combination-overtone infrared bands of SO3

Several new infrared absorption bands for ³²S¹⁶O₃ have been measured and analyzed. The principal bands observed were ν₁+ν₂ (at 1561 cm⁻¹), ν₁+ν₄ (at 1594 cm⁻¹), ν₃+ν₄ (at 1918 cm⁻¹), and 3ν₃ (at 4136 cm⁻¹). Except for 3ν₃, these bands are very complicated because of (a) the Coriolis coupling between ν₂ and ν₄, (b) the Fermi resonance between ν₁ and 2ν₄, (c) the Fermi resonance between ν₁ and 2ν₂, (d) ordinary l-type resonance that couples levels that differ by 2 in both the k and l quantum numbers, and (e) the vibrational l-type resonance between the A₁^′ and A₂^′ levels of ν₃+ν₄. The unraveling of the complex pattern of these bands was facilitated by a systematic approach to the understanding of the various interactions. Fortunately, previous work on the fundamentals permitted good estimates of many constants necessary to begin the assignments and the fit of the measurements. In addition, the use of hot band transitions accompanying the ν₃ band was an essential aid in fitting the ν₃+ν₄ transitions since these could be directly observed for only one of four interacting states. From the hot band analysis we find that the A₁^′ vibrational level is 3.50 cm⁻¹ above the A₂^′ level, i.e., r₃₄=1.75236(7) cm⁻¹. In the case of the 3ν₃ band, the spectral analysis is straightforward and a weak Δk=±2, Δl₃=±2 interaction between the l₃=1 and l₃=3 substates locates the latter A₁^′ and A₂^′ “ghost” states 22.55(4) cm⁻¹ higher than the infrared accessible l₃=1 E^′ state.