Fluctuations in cavities in a supersonic gas flow

Numerical calculations are carried out within the framework of the ideal compressible gas model for the unsteady flows in rectangular cavities exposed to a supersonic external stream. The Euler equations are integrated by means of Godunov's finite-difference method [6]. On the basis of an analysis of the calculation results an expression is proposed for determining the possible frequencies of the flow rate oscillations in the cavity as a function of the free-stream Mach number M and the geometry of the cavity. The results obtained are compared with the experimental data and calculations of other authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 121–127, March–April, 1990.     

Effects of adsorbed bismuth on Si(001) surface electronic states

It is shown that depositing Bi on an Si(001) surface fills the free broken-bond surface states, whose concentration decreases linearly as the bismuth coating 8 increases up to _st, = 0.6 monolayer. The bismuth desorption activation energy is constant < _st, (E_d = 2.77 ± 0.1 eV) and decreases for > _st.Taras Shevachenko Kiev National University, ul. Vladimirskaya 64, 252601 Kiev-17, Ukraine. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 32, No. 3, pp. 168–171, May–June, 1996. Original article submitted September 19, 1995.     

Crystal and Molecular Structure of (4′<Emphasis Type="Italic">R</Emphasis>,5′<Emphasis Type="Italic">R</Emphasis>,22<Emphasis Type="Italic">R</Emphasis>)-22-Hydroxy-22-(3′,4′-dimethylisoxazolin-5′-yl)-6β-methoxy-3α,5-cyclo-23,24-dinorcholane

The crystal and molecular structure of (4′R,5′R,22R)-22-hydroxy-22-(3′, 4′-dimethylisoxazolin-5′-yl)-6β-methoxy-3α,5-cyclo-23,24-dinorcholane was studied by single crystal X-ray diffraction. The compound crystallizes in the monoclinic system, space group C2; a 19.649(7), b 7.680(2), c 17.254(6) Å; β 101.05(3)°. The only diastereomer formed by the 1,3-dipolar cycloaddition of acetonitriole oxide has the 4′R,5′R stereochemistry of the arising chiral centers. The conformation of the side chain of the molecule is additionally stabilized by an intramolecular hydrogen bond.     

Synthesis of modified vitamin D precursors

Modified vitamin D precursors with oxygen-containing substituents at various positions in the side-chain were obtained using previously synthesized 20-isoxazolin-3-yl-and 20-isoxazolin-5-ylsteroids.Institute of Bioorganic Chemistry, National Academy of Sciences of Belarus, 220141 Minsk, Belarus;Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 230–235, February, 2000.     

Conformational study of chiral heterocyclic enamino ketones

An assumption regarding the existence of a homoconjugation effect involving enaminoketo and phenyl groups as a result of the drawing together in space of their orbitals was made on the basis of circular dichroism (CD) data and an examination of the preferred conformations of two-ring enamino ketones with -phenylethyl and -benzylethyl substituents. A study of enamino ketones with a chiral alkyl substituent attached to the nitrogen atom made it possible to confirm this assumption.Communication XLIX from the series Stereochemical Studies. See [1] for communication XLVIII.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1230–1233, September, 1978.     

On the Strong Law of Large Numbers for Multivariate Martingales with Continuous Time

We prove the strong law of large numbers for vector martingales with arbitrary operator normalizations. From the theorem proved, we deduce several known results on the strong law of large numbers for martingales with continuous time.     

Strong Law of Large Numbers with Operator Normalizations for Martingales and Sums of Orthogonal Random Vectors

We establish the strong law of large numbers with operator normalizations for vector martingales and sums of orthogonal random vectors. We describe its applications to the investigation of the strong consistency of least-squares estimators in a linear regression and the asymptotic behavior of multidimensional autoregression processes.     

Energy distributions and emission coefficients of secondary ions ejected from AIIIBV group semiconductors

The energy distributions of Ga⁺ and Ga₂ ⁺ secondary ions sputtered from the surface of single crystals of GaAs and GaP by Ar⁺ (E = 18 keV, j = 1·10^–6 A/cm²) ions were studied. Integral emission coefficients for secondary ions from four semiconductors (GaAs, GaP, InAs, and A1_0.35Ga_0.65As) bombarded by Ar⁺ ions (E = 2 keV, j₀ = 1·10^–6 A/cm²) were also measured. It is shown that the energy distribution of the Ga⁺ secondary ions are broad and qualitatively similar to distributions of secondary ions sputtered from metal oxide surfaces. Very high integral emission coefficients (up to 20–30%) for secondary ions are also observed, exceeding analogous coefficients for clean metal surfaces. These facts (the significant number of low energy secondary electrons and high secondary ion emission coefficients) are due to the lower density of free electrons in comparison with metals, which ensures a high degree of survival of sputtered ions, and the partially ionic character of the bonds in the semiconductors under study.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 88–92, November, 1990.