Light scattering by groups of spherical particles

Light scattering by groups of spherical particles is considered. It is shown that the structure of the groups and their orientational distribution can be judged from the spectrum and polarization of the scattered light. Syktyvkar State University, 55, Oktyabr'skii Ave., Syktyvkar, 167001, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 2, pp. 228–231, March–April, 1997.     

Hilbert-Space Representations of a Cross-Product Algebra Related to the 3D-Calculus on O(SU q (1,1))

Hilbert-space representations of the right cross-product *-algebra of the quantum SU(1,1) with a *-algebra related to Woronowicz's 3D-calculus on the quantum SU(1,1) are studied and classified.     

Infrared Observation of the Effects of Aqueous Oxidizing Agents on the Functional Groups on Carbon Surfaces

FTIR photothermal beam deflection spectroscopy (PBDS) was used to record infrared spectra of medium-temperature carbons before and after they had been subjected to treatments with aqueous HNO₃ or H₂O₂ solution. Changes in the functional groups present on the carbon surfaces can be clearly observed.     

有限群的弱S-拟正规嵌入子群

群G的子群H称为在G中S-拟正规嵌入的,如果对于任意的素数p||H|,H的Sylow p-子群也是G的某个S-拟正规子群的Sylow p-子群.称群G的子群H在G中弱S-拟正规嵌入,如果存在群G的正规子群T,使得HT■G且H∩T在G中是S-拟正规嵌入的.研究了弱S-拟正规嵌入子群的性质,给出了某些群类的新的特征,并推广了一些已知的结论.     

Irradiation of detonation nanodiamonds with γ-rays does not produce long living spin radicals

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Mechanism of Copper(I)‐Catalyzed Allylic Alkylation of Phosphorothioate Esters: Influence of the Leaving Group on α Regioselectivity

The mechanism of Cu^I‐catalyzed allylic alkylation and the influence of the leaving groups (OPiv, SPiv, Cl, SPO(OiPr)₂; Piv: pivavloyl) on the regioselectivity of the reaction have been explored by using density functional theory (DFT). A comprehensive comparison of many possible reaction pathways shows that [(iPr)₂Cu]^? prefers to bind first oxidatively to the double bond of the allylic substrate at the anti position with respect to the leaving group, and this is followed by dissociation of the leaving group. If the leaving group is not taken into account, the reaction then undergoes an isomerization and a reductive elimination process to give the α‐ or γ‐selective product. If OPiv, SPiv, Cl, or SPO(OiPr)₂ groups are present, the optimal route for the formation of both α‐ and γ‐substituted products changes from the stepwise elimination to the direct process, in which the leaving group plays a stabilizing role for the reactant and destabilizes the transition state. The differences to the energy barrier for the α‐ and γ‐substituted products are 2.75 kcal mol^?1 with SPO(OiPr)₂, 2.44 kcal mol^?1 with SPiv, 2.33 kcal mol^?1 with OPiv, and 1.98 kcal mol^?1 with Cl, respectively; these values show that α regioselectivity in the allylic alkylation follows a SPO(OiPr)₂>SPiv>OPiv>Cl trend, which is in satisfactory agreement with the experimental findings. This trend mainly originates in the differences between the attractive electrostatic forces and the repelling steric interactions of the SPO(OiPr)₂, SPiv, OPiv, and Cl groups on the Cu group.     

Association behavior of linear ω-functionalized polybutadienes in cyclohexane

The dilute solution properties of linear polybutadienes with dimethylamine and zwitterionic end groups were studied by membrane osmometry (MO), low-angle laser light scattering (LALLS), viscometry, and dynamic light scattering (DLS) in cyclohexane. The polymers were prepared by anionic polymerization, under high vacuum conditions using [3-(dimethylamino)propyl]lithium as initiator. The dimethylamine groups were converted to zwitterions by reaction with cyclopropane sultone. No evidence of association was found for the amine-capped polymers, whereas the zwitterionic samples exhibited strong association in cyclohexane. The degrees of association increase by decreasing molecular weight of the base polymer due to the excluded volume repulsions. These aggregation numbers are of the same order as those found for ω-functionalized polyisoprenes, with the same polar groups in the same solvent. The hydrodynamic properties, measured by viscometry and dynamic light scattering, supported the conclusions drawn by LALLS and provide strong evidence that the aggregates behave hydrodynamically as star polymers. Comparison with theoretical models shows that the association behavior is best described by the linear head packing model. © 1996 John Wiley & Sons, Inc.     

Smooth equivalence of differential equations and linear automorphisms

For systems of ordinary differential equations admitting linear automorphisms, we consider the problems of smooth equivalence and linearization preserving these automorphisms. Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 567–578, October, 1999.