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.     

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.     

Synthesis,properties, and mass-spectrometric behavior of 6-substituted imidazo[1,2-f]xanthines

Alkylation at the N₍₆₎ atom of 6H-1-ethyl ethyl(methyl-2-phenylimidazo[1,2-f]xanthenes was realized with -halogenoacetic esters. The alkylation of these compounds with glycidyl alcohol in the presence of organic bases also leads to 6-(dihydroxypropyl) derivatives.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1105–1109, August, 1987.     

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.     

On One Sufficient Condition for the Validity of the Strong Law of Large Numbers for Martingales

We prove a theorem on the strong law of large numbers for martingales. The existence of higher moments is not assumed. From the theorem proved, we deduce numerous well-known results on the strong law of large numbers both for martingales and for sequences of sums of independent random variables.