Hopf–Galois Extensions with Central Invariants and Their Geometric Properties

We set up a general framework to study representation theory of certain algebras whichusually appear in the study of restricted Lie algebras or various quantum objects at roots of unity.The object of the study is a Hopf–Galois extension with central invariants. It turns out that theseextensions possess some geometric properties which are close to those of principal bundles andFrobenius manifolds. We define Hopf–Galois extensions of not necessarily affine schemes andprove that the classification problem of such extensions leads to a stack.     

Mössbauer Study of Thin Iron Film Beryllization

Beryllium coating of the iron foil is made by means of magnetron sputtering. Mössbauer studies are performed by means of two registration techniques: conversion electron Mössbauer spectroscopy (CEMS) and the γ-ray technique in absorption geometry. Performed investigations confirm the original thermodynamic approach to creation of thermally stable multi-layer materials.

     

The Synthesis of New Organoselenium Heterocyclic Compounds: 2‐aryl‐4‐phenyl‐5,6,7,8‐tetrahydro‐4H‐selenochromenes

We have explored the reactions of 2‐(3‐oxo‐1‐aryl‐3‐phenylpropyl)cyclohexanone ( 1–3 ) with hydrogen selenide in situ in conditions of acid catalysis, and synthesized new 2‐aryl‐4‐phenyl‐5,6,7,8‐tetrahydro‐4H‐selenochromenes ( 4–6 ).     

One-dimensional and two-dimensional analogs for three-dimensional viscous flows in the neighborhood of the plane of symmetry of a blunt body

An approximate method of determining the heat transfer and friction stress in three-dimensional flow problems using the two-dimensional and one-dimensional solutions is proposed. This method is applicable over a wide range of Reynolds numbers — from low to high. On the basis of a theoretical analysis of the approximate analytic solution of the equations of a three-dimensional viscous shock layer it is shown that the problem of determining the heat flux in the neighborhood of the plane of symmetry of bodies inclined to the flow at an angle of attack can be reduced, firstly, to the problem of determining that quantity for an axisymmetric body and, secondly, to the problem of determining the heat transfer to an axisymmetric stagnation point. On the basis of an analysis of the results of a numerical solution of the problem it is shown that corresponding analogs can also be used for the friction stress. The accuracy of the similarity relations established is estimated by solving the problem by a finite-difference method. A similarity relation of the same kind was previously obtained in [1] for a double-curvature stagnation point.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 117–122, January–February, 1990.     

Effect of thermal radiation exchange between boundaries on convection in a gas heated from below

Natural convection problems offer many examples of branching of the solutions [1]. Usually, such branching (from the standpoint of catastrophe theory) can be described by a Whitney fold or cusp. A characteristic feature of nontrivial branching is the presence of some small but finite disturbance of the convective equilibrium conditions. In this study the perturbation disturbing the convective equilibrium of a fluid heated from below is Stefan-law thermal radiation exchange between the boundaries of the enclosure. Natural convection with lateral heating and allowance for radiative heat transfer was previously investigated in [2].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 47–51, September–October, 1992.     

Synthesis, structure, and spectroscopic characterization of [H(8-n)Rh22(CO)35](n-) (n = 4, 5) and [H2Rh13(CO)24{Cu(MeCN)}2](-) clusters: assessment of CV and DPV as techniques to circumstantiate the presence of elusive hydride atoms

The previously ill-characterized [H(x)Rh(22)(CO)(35)](4-/5-) carbonyl cluster has been obtained as a byproduct of the synthesis of [H(3)Rh(13)(CO)(24)](2-) and effectively separated by metathesis of their sodium salts with [NEt(4)]Cl. Although the yields are modest and never exceed 10-15% (based on Rh), this procedure affords spectroscopically pure [H(3)Rh(22)(CO)(35)](5-) anion. Formation of the latter in mixture with other Rh clusters was also observed by electrospray ionization-mass spectrometry (ESI-MS) in the oxidation of [H(2)Rh(13)(CO)(24)](3-) with Cu(2+) salts. The recovery of further amounts of [H(3)Rh(22)(CO)(35)](5-) was hampered by too similar solubility of the salts composing the mixture. Conversely, the reaction in CH(3)CN of [H(2)Rh(13)(CO)(24)](3-) with [Cu(MeCN)(4)](+)[BF(4)](-) leads to the [H(2)Rh(13)(CO)(24){Cu(MeCN)}(2)](-) bimetallic cluster. The X-ray crystal structures of [H(4)Rh(22)(CO)(35)](4-), [H(3)Rh(22)(CO)(35)](5-), and [H(2)Rh(13)(CO)(24){Cu(MeCN)}(2)](-) are reported. From a formal point of view, the metal frame of the former two species can be derived by interpenetration along two orthogonal axes of two moieties displaying the structure of the latter. The availability of [H(8-n)Rh(22)(CO)(35)](n-) salts prompted their detailed chemical, spectroscopic, and electrochemical characterization. The presence of hydride atoms has been directly proved both by ESI-MS and (1)H NMR. Moreover, both [H(4)Rh(22)(CO)(35)](4-) and [H(3)Rh(22)(CO)(35)](5-) undergo distinctive electrochemically reversible redox changes. This allows to assess electrochemical studies as indisputable though circumstantial evidence of the presence of (1)H NMR-silent hydride atoms in isostructural anions of different charge.     

Comprehensive core-level study of the effects of isomerism, halogenation, and methylation on the tautomeric equilibrium of cytosine

Core-level X-ray photoemission and near-edge X-ray absorption fine structure spectra of 5-methylcytosine, 5-fluorocytosine, and isocytosine are presented and discussed with the aid of high-level ab initio calculations. The effects of the methylation, halogenation, and isomerization on the relative stabilities of cytosine tautomers are clearly identified spectroscopically. The hydroxy-oxo tautomeric forms of these molecules have been identified, and their quantitative populations at the experimental temperature are calculated and compared with the experimental results and with previous calculations. The calculated values of Gibbs free energy and Boltzmann population ratios are in good agreement with the experimental results characterizing tautomer equilibrium.