Universal spaces for asymptotic dimension

We construct a universal space for the class of proper metric spaces of bounded geometry and of given asymptotic dimension. As a consequence of this result, we establish coincidence of asymptotic dimension with asymptotic inductive dimension.     

Topological Simplicity of a Certain LF-Algebra

We show that the LF-algebra considered by Akkar and Nacir in [1] is topologically simple.     

Series solution to the laser-ion interaction in a Raman-type configuration

The Raman interaction of a ultracold ion trapped with two travelling wave lasers is studied analytically with series solutions, in the absence of the rotating wave approximation (RWA) and without restrictions of both the Lamb-Dicke limit and the weak excitation regime. The comparison is made between our solutions and those obtained under the RWA in order to demonstrate the validity region of the RWA. As a practical example, the preparation of Schr?dinger-cat states is proposed beyond the weak excitation regime, using our calculations. Received 12 March 2001 and Received in final form 16 October 2001     

Electrostatic calculation of the substituent effect: an efficient test on isolated molecules

The energy of a disubstituted molecule has often been approximated by simple electrostatic formulas that represent the substituents as poles or dipoles. Herein, we test this approach on a new model system that is more direct and more efficient than testing on acid-base properties. The energies of 27 1,4-derivatives of bicyclo[2.2.2]octane were calculated within the framework of the density functional theory at the B3LYP/6-311+G(d,p) level; interaction of the two substituents was evaluated in terms of isodesmic homodesmotic reactions. This interaction energy, checked previously on some experimental gas-phase acidities, was considered to be accurate and served as reference to test the electrostatic approximation. This approximation works well in the qualitative sense as far as the sign and the order of magnitude are concerned: beginning with the strongest interaction between two poles, a weaker interaction between pole and dipole, and the weakest between two dipoles. However, all the electrostatic calculations yield energies that are too small, particularly for weak interaction, and this fundamental defect is not remedied by some possible improvements. In particular, variation of the effective permittivity would require a physically impossible value less than unity. The explanation must lie in a more complex distribution of electron density than anticipated in the electrostatic model. It also follows that possible conclusions about the transmission of substituent effects "through space" have little validity.     

分子诱导效应指数与链烷烃的沸点

利用基团的诱导效应指数，首次提出了分子的诱导效应指数的概念，并定义了 链烷烃的有效碳链长度NC＝（MIs,N/MIb,N)·N，式中MIs,N,MIb,N分别为直链和支 链异构体的分子诱导效应指数。研究结果表明，链烷烃的沸点Tb(℃）与NC关系是 ：1n(806.5-Tb)=6.9824-0.11431NC^2/3     

Basicity and structure of 5-hydroxybenzimidazoles in nitromethane

Examination of the acid-base properties of 5-hydroxybenzimidazoles has shown them to exist in nitromethane as the 5-hydroxy-tautomers. Substituents in the 2-position have a predominantly inductive effect on the basicity of the 3-nitrogen, rationalized as in other nitrogen heterocycles by the proximity of the substituents to the reaction center.N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, 117977 Moscow. The Research Institute for Intermediates and Dyes, 103787 Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 2, pp. 421–425, February, 1992.     

Operator Semigroup Compactifications

A weakly continuous, equicontinuous representation of a semitopological semigroup on a locally convex topological vector space gives rise to a family of operator semigroup compactifications of , one for each invariant subspace of . We consider those invariant subspaces which are maximal with respect to the associated compactification possessing a given property of semigroup compactifications and show that under suitable hypotheses this maximality is preserved under the formation of projective limits, strict inductive limits and tensor products.

     

诱导效应指数与脂肪族胺、醇和醚的气相碱性

用烷基诱导效应指数I和RX分子中质子亲合原子X所带电荷qx及元素电负性XN与 脂肪胺，醇、醚的气相质子亲合PA进行关联，结果表明，脂肪胺，醇、醚的气相碱 性可以用下式定量描述：PA(kJ.mol^-1)-2732.0333-2457.1510∑I-1492.2351qx- 732.6277XN利用上式对64种化合物的气相碱性进行预测，平均相对误差为0．34％ ，预测值和实验值的偏差均在实验误差范围内。     

Correlation analysis of quantum chemical data and the polarizability effect in H-complexes

The study is concerned with analysis of the energies of formation (E), frequency shifts (Δν) in IR spectra, ionization potentials (IP) of H-complexes, hydrogen bond lengths (r), and spin densities (sd) in H-complexes involving radical cations, obtained from quantum chemical calculations for 20 series of H-complexes. It was for the first time established that the E, IP, r, and sd values and the changes in enthalpy (δH) depend not only on the inductive and resonance effects but also on the polarizability effect of the substituents bound to the donor and acceptor centers in the H-complexes. Interrelations between the polarizability effect and the molecular structure of H-complexes are considered. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 602–608, April, 2006.