Search

Formulas for the asymptotics of some class of integrals of rapidly oscillating functions that generalize the well-known stationary phase method, which were obtained in the previous paper of the author, are applied to integrals arising in the well-known tsunami hydrodynamic piston model in the case of a constant pool bottom. As a result, asymptotic formulas are obtained for the head part of the wave for large values of the time elapsed since the occurrence of the tsunami. These formulas contain some special reference integrals and have different forms depending on combinations of wave and time parameters.

Asymptotic formulas are obtained for a class of integrals that are Fourier transforms of rapidly oscillating functions. These formulas contain special functions and generalize the well-known method of stationary phase.

A linear problem for propagation of gravity waves in the basin having the bottom of a form of a smooth background with added rapid oscillations is considered. The formulas derived below are asymptotic ones; they are quite formal, and we do not discuss the problem concerning their uniformness with respect to these parameters.

The system of equations of gravity surface waves is considered in the case where the basin’s bottom is given by a rapidly oscillating function against a background of slow variations of the bottom. Under the assumption that the lengths of the waves under study are greater than the characteristic length of the basin bottom’s oscillations but can be much less than the characteristic dimensions of the domain where these waves propagate, the adiabatic approximation is used to pass to a reduced homogenized equation of wave equation type or to the linearized Boussinesq equation with dispersion that is “anomalous” in the theory of surface waves (equations of wave equation type with added fourth derivatives). The rapidly varying solutions of the reduced equation can be found (and they were also found in the authors’ works) by asymptotic methods, for example, by the WKB method, and in the case of focal points, by the Maslov canonical operator and its generalizations.

In this paper, we derive sufficient conditions for the existence of an eigenvalue for the Laplace and the Schrodinger operators with transversal potential for homogeneous Dirichlet boundary conditions in a tube, i.e., in a curved and twisted infinite cylinder. For tubes with small curvature and small internal torsion, we derive an asymptotic formula for the eigenvalue of the problem. We show that, under certain relations between the curvature and the internal torsion of the tube, the above operators possess no discrete spectrum.

Metal-catalyzed/-promoted trifluoromethylation reactions represent a powerful tool for the synthesis of a broad variety of organic compounds bearing a CF3 group on sp3-, sp2-, or sp-hybridized carbon atoms.

Reduction of OsO4 by molecular hydrogen in alkane (cycloalkane) or benzene media at 20–150 °C yields small osmium clusters of the Os1C0.34-0.48H0-0.6 composition with a specific surface area of 34–46 m2/g. The systems obtained are shown to be ligand deficient osmium clusters (LDC) of 7–16 A in diameter, stabilized by a small amount of carbonaceous ligands with Os-Os = 2.68-1.70 A and Os-C = 2.11-2.19 A. The characteristics of these chemically prepared Os-LDC are similar to those of Ni- and Co-LDC, prepared by a vapour phase synthesis. The novel Os-LDC effectively catalyze hydrogenolysis of alkanes and cycloalkanes at 100–150 ° C and initial H2 pressure of 5 MPa, hydrogenation of cyclopentadiene and arenes at 20 ° C, multiple H/D exchange between CH4 and D2 at 100–120 ° C and methanation of CO2 at 150–180 ° C.

We report a class of highly efficient electroluminescent materials based on fluorinated iridium compounds. Using aluminum as the cathode, a device, using fac-tris[5-fluoro-2(5-trifluoromethyl-2-pyridinyl)phenyl-C,N]iridium (Ir-2h) as the luminescent layer, displayed intense electroluminescence at 525 nm with an efficiency of 20 cd/A and a maximum radiance of 4800 cd/m2. Differing from the previously reported Ir(ppy)3, Ir-2h can be used in the undiluted form without the use of a charge-transporting host. This indicates that Ir-2h by itself has good enough charge-transporting properties. Photoluminescence studies at room temperature and 77 K revealed that electroluminescence originates from the metal-to-ligand charge transfer state with a quantum yield of 0.56 for Ir-2h and 0.5 for Ir(ppy)3 in toluene at room temperature. In the thin-film form, photoluminescence quantum yield of Ir-2h is a factor of 10 greater than that of Ir(ppy)3 due to the larger self-quenching effect of Ir(ppy)3.

Rapid and reversible η 2 -coordination of molecular hydrogen to the monohydrides IrHCl 2 L 2 , with LPPr i 3 ( I ) and P(c-C 6 H 11 ) 3 ( II ), has been established by 1 H and 2 H NMR. The complexes formed eliminate HCl to afford the dihydrides IrH 2 ClL 2 . The spectral data are reported and discussed in connection with the structure of the proposed intermediates.

The chlorohydrido complexes of ruthenium (Ph 3 P) 3 Ru(H)Cl and iridium (Pr 3 i P) 2 Ir(H)Cl 2 react smoothyl with H 2 (1 atm, 20°C) in a 50% NaOH/benzene two-phase system in the presence of triethylbenzylammonium chloride as a phase transfer catalyst to form polyhydride complexes (Ph 3 P) 3 Ru(H 2 )(H) 2 ( 1 ) and (Pr 3 i P) 2 IrH 5 ( 2 ), respectively, in quantitative yields.

This paper discusses the possibility of fabricating aspheric optical items with an automatic processing complex having a built-in monitoring system. Samples of interferograms of aspheric surfaces are presented, obtained in a holographic aspherometer, using synthesized holograms.

Reaction of [(C 5 Me 5 IrCl) 2 (μ-H) 2 ] (1) with PPh 3 in benzene/60 % aqueous KOH/[PhCH 2 NEt 3 ] + Cl - leads to the elimination of 2 equiv of HCl from 1, oxidative addition of C-P and C-H bonds to iridium, and formation of the dinuclear complex [Ir 2 (C 5 Me 5 ) 2 (μ-H)(μ-PPh 2 )(μ-C 6 H 4 )] (2); the X-ray structure of 2 showed that it has bridging hydrido, diphenylphosphido, and o-phenylene ligands

Reduction of OsO4 by molecular hydrogen in alkane (cycloalkane) or benzene (toluene) solution produces small-ligand clusters of osmium of composition Os1.5–2.5. CH0–2 with a particle size 10–40 A and a specific surface area of 34–46 m2/g. Hydrogenation of dry catalyst produces methane. The small-ligand osmium clusters obtained effectively catalyze hydrogenolysis of alkanes and cycloalkanes at 100–150°C and\(P_{H_2 } \)=5 MPa and hydrogenation of benzene at 20°C and\(P_{H_2 } \)=0.1 MPa.

metallic chemistry laboratory of the Moscow State University [I, 2], a new phenyl-9-o-carboranyliodonium salt was synthesized [3]. This compounds is an example of a new type of iodonium compound, with heteroorganic groups, characteristic of which is the linking iodine atom bonded to a boron atom. An x-ray structural study of phenyl-9-o-carboranyliodonium iodide was undertaken to elucidate the crystallographic and molecular structure of the compound.

Clinical symptomatology of acute poisoning by drugs with central cholinolytic action is little known to practitioners. Drug dependence due to systematic intake of drugs is accompanied by tolerance to them and loss of control over intake, the consequence of which is often acute poisoning.

An x-ray structural investigation (/lambda/ MoK/alpha/, 2591 reflections, R 0.080) was carried out on bis-9-M-carboranylbromonium borofluoride. The presence of bulky carboranyl groups leads to an increase in the B/sub carb/BrB/sub carb/ bond angle, unprecedented for bromine salts, to 111.6(3)/degree/; unlike the halogen derivatives investigated earlier (including bromides) the Br atom in the cation we have investigated does not participate in additional interion interactions. Steric obstacles, occurring when the nucleophile approaches the Br atom also occur in solution and are apparently the cause of the low reactivity of the bromine center in the cation of the salt.

Trans -[Ph 3 P) 2 Pt(H)Cl] reacts with PhCCPh, trans -PhCHCHPh, CH 2 CHCOOCH 3 , PPh 3 , CO, PhI, Ph 2 Hg under Phase Transfer conditions (benzene—60% KOH—18-crown-6) to give [(Ph 3 P) 2 Pt(Ph 2 C 2 )], [(Ph 3 P) 2 Pt(PhCHCHPh)], [(Ph 3 P) 2 Pt(CH 2 CHCOOCH 3 )], [(Ph 3 P) 3 Pt], [(Ph 3 P) 2 Pt(CO) 2 ], [(Ph 3 P) 2 Pt(I)Ph], [(Ph 3 P) 2 PtPh 2 ] respectively, in 71–96% yield. The availability and stability of the initial Pt-hydride as well as the simplicity of the reaction procedure and the isolation of the desired products, allow these reactions to be used for the preparative synthesis of platinum complexes. The reaction with CH 3 I carried out under similar conditions results in a mixture of [(Ph 3 P) 2 Pt(I)CH 3 ) (3–5%) and [(Ph 3 P) 2 Pt(H)I] (95–97%). The latter compound is also formed in quantitatively yield by the reaction of [(Ph 3 P) 2 Pt(H)Cl] with KI. The [(Ph 3 P) 2 Pt(H)Cl]—benzen—60% KOH—18-crown-6 system is active in the symmetrization of PhHgCl but showed low activity in the hydrogenation and isomerisation of octene-1. The decomposition of [(Ph 3 P) 2 Pt(H)Cl] in the benzene—aqueous alkali—phase transfer catalyst system in absence of substrate results in tris(triphenylphosphine)platinum as the main product and a mixture of unidentified compounds. Data obtained are interpreted in terms of several alternative mechanisms, on of which involves the formation, and further conversions of, bis(triphenylphosphine)platinum.

At the end of August of this year the Central Committee (TsK) of the Communist Party of the Soviet Union (KPSS) approved the initiative of the Yaroslavskii Combine “Avtodizel” and the Kremenchugskii Automobile Works in extending the active struggle to raise the quality, reliability, and life of domestic motors and automobiles.

The present paper is a survey of some results concerning higher-order elliptic differential operators which degenerate on the boundary of a domain. The principal aspect in the study of such operators is that of investigating the corresponding ordinary equations with parameters which degenerate at a single point. The parametrix for such operators is a degenerating pseudo-differential operator. We investigate the properties of the kernels of these pseudo-differential operators.

A considerable increase in the quadrupole coupling constants (e2Qqzz) and significant decrease in the asymmetry parameterη is found in carborane-containing CBICl2 and PhCBIX compounds in comparison with the corresponding phenyl and diphenyl derivatives.