Topology and a lorentz-invariant pseudo-riemannian metric of the manifold of directions in the physical space

In the mathematical model of the special relativity theory, a two-dimensional Minkowski subspace is treated as a one-dimensional direction in the physical space. The manifold of such planes is naturally endowed with the structure of a pseudo-Riemannian manifold on which the group of isochronous Lorentz transformations acts transitively by isometries. In this paper, the topology and the metric geometry of this manifold are studied. Bibliography: 4 titles. Translated from Zapiski Nauchnykh Seminar POMI, Vol. 246, 1997, pp. 141–151. Translated by S. Yu. Pilyugin.     

Hot-wire visualization of breakdown to turbulence in complex flows

The nonlinear stage of breakdown to turbulence is a strongly three-dimensional process and represents a difficult task for experimental studies. Investigation of laminar-turbulent transition in aerospace applications additionally involves a complex base-flow with pressure gradients and secondary velocity components resulting in successive increase of necessary measurements. The developed hot-wire visualization technique offers a possibility for an advanced analysis whilst retaining the advantages of traditional visualization methods and is especially suitable for resolving such complex flows. Thanks are due to the Royal Swedish Academy of Sciences, the Swedish Energy Agency (Energimyndigheten). The work was financially supported by the President of the Russian Federation (Grant No. NSh-964.2003.1), the Russian Foundation for Basic Research (Grant No. 05-01-00034) and Ministry of Education and Sciences of the Russian Federation (Grant No. RNP.2.1.2.3370).     

(Z)-3,4,4,4-Tetrachlorobut-2-enoates of Certain Natural Alcohols, Phenols, and Oximes

Previously unknown (Z)-3,4,4,4-tetrachlorobut-2-enoates 1b-20b were prepared in 77-88% yields by reaction in the presence of pyridine of 3,3,4,4,4-pentachlorobutanoic acid chloride with cetyl alcohol (1a), terpenols and terpenone oximes (2a-13a), sterols (14a and 15a), diosgenin (16a), and plant phenols and their oximes (17a-20a).     

Structural instability in metals and alloys

An analysis of features of the electron structure required to produce the spectrum of structural states in alloys indicated a number of relationships inherent to such systems. The types of structural states that can occur under the conditions of instability of the system as a whole or of an individual structural phase component are considered theoretically and experimentally. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 16–25, August, 1998.     

Phosphorus-substituted carbothioamides

A facile procedure was developed for the synthesis of phosphorus-substituted carbothioamides by the reaction of the corresponding nitriles with O,O-diisopropyl dithiophosphate in the presence of methanol. The structural features and hydrogen bonding in crystals of structurally different P-thioamides are discussed.     

Synthesis of 12-hetaryl-9,9-dimethyl-7,8,9,10-tetrahydrobenzo[a]acridin-11(12H)-ones

Three-component condensation of naphthalen-2-amine with 5-arylfuran(thiophene, N-methylpyrrole)-2-carbaldehyde and 5,5-dimethylcyclohexane-1,3-dione, as well as condensation of N-[(5-arylfuran(thiophen)-2-ylmethylidene]naphthalen-2-amine with 5,5-dimethylcyclohexane-1,3-dione gave the corresponding 12-[5-arylfuran(thiophen, N-methylpyrrol)-2-yl]-7,8,9,10-tetradrobenzo[a]acridin-11(12H)-ones.     

How Absorbed Hydrogen Affects the Catalytic Activity of Transition Metals

Heterogeneous catalysis is commonly governed by surface active sites. Yet, areas just below the surface can also influence catalytic activity, for instance, when fragmentation products of catalytic feeds penetrate into catalysts. In particular, H absorbed below the surface is required for certain hydrogenation reactions on metals. Herein, we show that a sufficient concentration of subsurface hydrogen, H^sub, may either significantly increase or decrease the bond energy and the reactivity of the adsorbed hydrogen, H^ad, depending on the metal. We predict a representative reaction, ethyl hydrogenation, to speed up on Pd and Pt, but to slow down on Ni and Rh in the presence of H^sub, especially on metal nanoparticles. The identified effects of subsurface H on surface reactivity are indispensable for an atomistic understanding of hydrogenation processes on transition metals and interactions of hydrogen with metals in general.     

Oxidation of benzene with hydrogen peroxide catalyzed with ferrocene in the presence of pyrazine carboxylic acid

It is found that ferrocene in the presence of small amounts of pyrazine carboxylic acid (PCA) effectively catalyzes the oxidation of benzene to phenol with hydrogen peroxide. Two main differences upon the oxidation of two different substrates, i.e., cyclohexane and benzene, with the same H₂O₂-ferrocene-PCA catalytic system are revealed: the rates of benzene oxidation and hydrogen peroxide decomposition are several times lower than the rate of cyclohexane oxidation at close concentrations of both substrates, and the rate constant ratios for the reactions of oxidizing particles with benzene and acetonitrile are significantly lower than would be expected for reactions involving free hydroxyl radicals. The overall rate of hydrogen peroxide decomposition, including both the catalase and oxidase routes, is lower in the presence of benzene than in the presence of cyclohexane. It is suggested on the grounds of these data that a catalytically active particle different from the one generated in the absence of benzene is formed in the presence of benzene. This particle catalyzes hydrogen peroxide decomposition less efficiently than the initial complex and generates a dissimilar oxidizing particle that exhibits higher selectivity. It is shown that reactivity of the system at higher concentrations of benzene differs from that of an initial system not containing an aromatic component with the capability of π-coordination with metal ions.     

Effective Modular Assembling of Novel Ligands Starting from (Thio)Phosphorylated Anilines

Abstract

A series of novel oligodentate ligands has been designed by the modular assembly of ortho-(thio)phosphorylated anilines with a range of commercially available carbonyl compounds. The new ligands readily form complexes with a series of metal ions (Pd(II), Cu(II), Ni(II), and Re(I)) both in neutral and deprotonated forms, providing OO, SN, ONO, SNO, SNS, SNN, and ONN donor sets. The structure and composition of the resulting complexes depend on the nature and mutual disposition of the donating groups as well as on the reaction conditions.     

On G-Compactifications

The semilattice of G-compactifications of a G-Tikhonov space X is studied. The question of what sets containing X and contained in the maximal G-compactification β _G X must be contained also in all other G-compactifications of X is considered. Conditions for β _G X to be the completion of the G-space X with respect to a natural uniformity (proximity) on X are obtained. Sufficient conditions for the existence of a smallest (minimal, unique) G-compactification of X are given.