Maximal Lyapunov exponent and rotation numbers for two coupled oscillators driven by real noise

Asymptotic expansions for the exponential growth rate, known as the Lyapunov exponent, and rotation numbers for two coupled oscillators driven by real noise are constructed. Such systems arise naturally in the investigation of the stability of steady-state motions of nonlinear dynamical systems and in parametrically excited linear mechanical systems. Almost-sure stability or instability of dynamical systems depends on the sign of the maximal Lyapunov exponent. Stability conditions are obtained under various assumptions on the infinitesimal generator associated with real noise provided that the natural frequencies are noncommensurable. The results presented here for the case of the infinitesimal generator having a simple zero eigenvalue agree with recent results obtained by stochastic averaging, where approximate ItÔ equations in amplitudes and phases are obtained in the sense of weak convergence.Dedicated to Thomas K. Caughey on the occasion of his 65th birthday.     

SO(n,1) Wigner rotation as an SL(2,R) problem

We show that the composition of not only two SO(3,1) boosts, but also that of two SO(n,1) boosts for anyn 2, is basically an SO(2,1) problem and hence can be analysed completely using SL(2,R) matrices. By computing the expression for the Thomas/Wigner angle directly using SL(2,R) matrices we show that this approach results in considerable economy of algebra.     

应用分子图形学、分子力学、量子化学及静电势研究农药分子结构与性能关系(X)──磺酰脲分子内旋转通道的分子力学研究

磺酞豚分子是一类极其重要的低毒超高效除草剂，有着十分重要的用途．研究分子的空间结构对于了解分子的构效关系十分重要．最近，我们测定的一系列分子的晶体结构［‘－’1表明，分子1、2、3晶体结构的空间群分别为PZ；儿、Pz、Pz，说明晶体中分别有对称元素（对称面或者对称中心），分子以对映体的形式存在于晶体中．由于磺酸豚分子本身不存在手性原子，由此推断磺酷服分子在晶体中存在的对映异构体是由内旋转阻碍产生的，因而应是构象异构体．本项研究工作的目的是应用分子力学方法，计算阻碍内旋转的能垒，从而找出分子内旋转时的最低…     

分子内环加成的甾体全合成

近年来,分子内环加成反应已广泛用于甾体化合物全合成,其主要一步是由取代的苯并环丁烯热裂而成的5,6-二亚甲基-1,3-环己二烯发生区域专一和立体选择性的环加成反应,构成甾体骨架。现在用此法已合成了一系列消旋和光学活性的甾体化合物。     

The effect of side substituents on rotation hindrance in polyheteroarylenes

Hindered rotation was considered in calculations of the conformational parameters of a series of polyheteroarylenes with bulky side substituents by the Monte-Carlo method. Within the range of experimental errors, the results of calculations for several polyarylates coincide with the values of conformational rigidity, determined from hydrodynamic experimental data. The proposed procedure was used to estimate the rigidities of a number of polymers with bulky side substuents for which experimental determination is difficult. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1287–1296, July, 1998.     

Dependence of the rate constants on the treatment of internal rotation modes: the reaction OH + CH3SH --> CH3S + H2O as an example

The title reaction has been used as an example to test the importance of using a hindered rotor treatment instead of a harmonic oscillator model for calculating vibrational partition functions corresponding to low-frequency internal rotation modes. First, a normal-mode analysis according to the Ayala and Schlegel's algorithm has been used to identify the internal rotation modes of methanethiol and the transition state structure. Then, after calculation of the energy barrier for each internal rotation, the corresponding hindered rotor partition functions have been calculated following the CW scheme of Chuang and Truhlar. The results show that the anharmonic treatment produces a rather modest improvement of the rate constants at room temperature or below.     

2，4，6－三苯基氧鎓盐分子内旋转受阻对其发光行为的影响

研究了４－位苯基取代基旋转受阻和旋转自由的２，４，６－三苯基氧盐的光物理性质。实验结果表明，当４－位苯基取代基旋转受阻时，氧盐化合物在激发态时引起的分子内极化程度比４－位取代基旋转自由的氧盐化合物大，即在激发态时旋转受阻氧盐化合物发生的分子内电荷转移能力较强；４－位取代基旋转自由的化合物的荧光量子产率随溶剂粘度的增大而有所增大，但旋转受阻化合物在相同的条件下则出现相反的结果。实验结果还表明，４－位取代苯基旋转受阻对化合物的荧光发射不利。     

5,6—二亚甲基双环[2.2.1]庚—2—醇及其衍生物的旋光与构型

从（－）－（１Ｓ，２Ｒ，４Ｓ）－５，６－二亚甲基双环［２．２．１］庚－２－醇（Ｉ）和（－）－（１Ｓ，２Ｓ，４Ｓ）－５，６－二亚甲基双环［２．２．１］庚－２－醇（Ⅱ）出发，合成了它们的醚类和取代苯甲酸酯类光学纯的衍生物。通过［α］Ｄ测定和构型分析，发现它们是含有３个手性碳（Ｃ１，Ｃ２和Ｃ４）的桥环化合物，其旋光性与构型的关系均符合可极化度多级圆球不对称性模型。     

Drift tube investigations on the reactions of O 2 + with CH4 and of CO 2 + with NO in various buffer gases

The influence of internal excitation on the reactions of O ₂ ⁺ + CH₄ and of CO ₂ ⁺ + NO has been investigated using a slow flow drift tube. The rate coefficients for these reactions obtained as a function of relative kinetic energy in various buffer gases like He, Ne, Ar, and Kr showed higher values under conditions where the internal excitation of the reactant ions was enhanced. For both reactions the lowest reactivity at all kinetic energies was observed to occur in He, indicating that He is the least effective buffer for collisionally inducing internal excitation of molecular ions.     

Rotational isomerism involving an acetylenic carbon. Part 5: Restricted rotation about acetylenic axis in sterically crowded bis(1-phenyl-9-anthryl)ethynes

The title sterically crowded di-9-anthrylethyne derivative with 3,5-ⁱPr₂-phenyl groups at 1-position showed a barrier to rotation about the acetylenic axis of 18.0 kcal mol⁻¹ based on a dynamic NMR study, which is an extremely high value for acyclic diarylethynes. The mechanism of the dynamic stereochemistry and the substituent effect on the rotational barrier are discussed.