Regular variation of order 1 nonlinear AR-ARCH models

We prove both geometric ergodicity and regular variation of the stationary distribution for a class of nonlinear stochastic recursions that includes nonlinear AR-ARCH models of order 1. The Lyapounov exponent for the model, the index of regular variation and the spectral measure for the regular variation all are characterized by a simple two-state Markov chain.     

Enantioselective synthesis of hydroxy-substituted α-methyl-α-amino acids using Al and Mn derivatives of cyclo-(L-Ala-L-AIa) bis-Iactim ethers

Aluminum and manganese derivatives of lithiated bis-lactim ethers of cyclo-(L-Ala-L-Ala) were used for the enantioselective synthesis of 84w2x3j22hh/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-hydroxy and polyhydroxy 84w2x3j22hh/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-amino acids of the 2-methyIserine series. A new variant of the synthesis of these acids via 3-acyl-2, 5-dialkoxy-3, 6-dimethyl-3, 6-dihydropyrazines is proposed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 590–595, March, 1993.     

Can the presence of chemically inert species modify the face selectivity in asymmetric induction by cyclodextrins?

Reduction of84r111834221113/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-cyclodextrin (84r111834221113/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-CD) aromatic ketone (acetophenone and acetonaphthones) inclusion compounds were carried out in the presence of a large number of chemically inert species as potential co-guests. In several cases, it was observed that stoichiometric molar ratios of these compounds to ketone significantly modify the chiral induction yielding the inverted alcohol enantiomer and increasing the face selectivity. The results were found to depend strongly on the respective structure and shape of both the ketone and the additive, and on the molar ratio of84r111834221113/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-CD:ketone:third compound. These observations suggest the formation of a three-component inclusion complex in which the geometry of binding of the substrate and its mobility are changed with respect to the binary system.     

Crystal structure of copper(II) bis-hexafluoroacetylacetonate

An X-ray diffraction investigation has performed for copper(II) bis-hexafluoroacetylacetonate (Bruker AXS P4 automatic diffractometer, MoK _{84u4555pg0g4286/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">} radiation, t = –25°C). Crystal data for C₁₀H₂CuF₁₂O₄: a = 5.530(1) Å, b = 6.038(1) Å, c = 11.266(2) Å, 84u4555pg0g4286/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0"> = 95.948(3)°, 84u4555pg0g4286/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0"> = 101.743(3)°, 84u4555pg0g4286/xxlarge947.gif" alt="gamma" align="MIDDLE" BORDER="0"> = 92.298(3)°, space group; P1, V = 365.6(1) ų, Z = 1, d _calc = 2.169 g/cm³. The square-planar environment of the copper atom (Cu-O_av 1.912 Å, 84u4555pg0g4286/xxlarge8736.gif" alt="ang" align="BASELINE" BORDER="0">O-Cu-O_av 93°) is completed to bipyramidal by two fluorine atoms of the neighboring molecules, Cu...F 2.71 Å and 2.75 Å.Original Russian Text Copyright © 2004 by S. A. Gromilov, I. A. Baidina, P. A. Stabnikov, and G. V. RomanenkoTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 3, pp. 502–507, May–June 2004.     

Atom-surface elastic scattering in the presence of laser radiation

A qualitative discussion on atom-surface elastic scattering taking place in the presence of laser radiation is given. It is suggested that appreciable effects of laser radiation on diffraction patterns may be expected if the laser radiation is capable of inducing electronic transitions in atoms with a large probability.Research sponsored by the Air Force Office of Scientific Research (AFSC), United States Air Force, under Contract No. F49620-78-C-0005, and the National Science Foundation under Grant No. CHE77-27826. The United States Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation hereon.Alfred P. Sloan Research Fellow, 1976–1980; Camille and Henry Dreyfus Teacher-Scholar, 1975–1980.     

Mobility of small molecules in membrane materials based on copolyimide P84

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高中化学“次氯酸盐的性质”的项目式教学*——84消毒液的使用指南

以“84消毒液的使用指南”为主题,开展高中化学“次氯酸盐的性质”的教学。学生通过完成“一张图说清消毒剂”“探究84消毒液的漂白效果与酸碱性的关系”“探究84消毒液的漂白效果与光照的关系”“探究84消毒液的漂白效果与温度的关系”“84消毒液与酒精混合会有氯气吗”等5个项目任务,理解了次氯酸盐的性质及漂白原理,培养了学生的文献检索能力、实验探究能力以及发展了学生的高阶思维能力。将文献查阅与学生实验相结合,让学生在真实问题的解决中,完成次氯酸盐的性质等相关知识的内化,是顺利完成本项目教学的关键。     

Nonlinear wave propagation along periodic-loaded transmission line

A high frequency transmission line periodically loaded with varactor diodes is presented to study nonlinear wave propagation. The nonlinearity and dispersion characteristics are experimentally and theoretically analysed. Experimental results on shock wave formation and harmonic frequency generation are found to be in good agreement with theoretical predictions. The influence of dispersion on second-harmonic frequency generation is particularly discussed yielding large values of the efficiency.     

Low-frequency scattering by rectangular dielectric particles

The field scattered by a homogeneous isotropic dielectric particle illuminated by a low-frequency plane electromagnetic wave is expressed in terms of a single polarizability tensor which is a function of only the geometry of the particle and a material parameter τ representing either the relative permittivity or permeability of the dielectric. The mathematical formulation is specialized to the case of a rectangular parallelepiped and numerical techniques are developed for computing the tensor elements. Specific data are presented for the tensor elements of rectangular parallelepipeds having square cross sections and are compared to the results obtained for spheroids and right circular cylinders of similar dimensions.     

Guided-wave methods for optical configurations

Guided-wave methods used in the past to treat electromagnetic problems and applications in the microwave area have recently been extended to cover work in fiber and integrated optics. The basic principles of these methods are reviewed briefly and, in particular, the “open” properties of optical configurations are contrasted to the “closed” characteristics that describe most microwave applications. These aspects are illustrated in the context of beam couplers of uniform and periodic varieties, which are shown to lend themselves to rigorous treatment by microwave guided-wave methods that include both theoretical and experimental facets.