Records in the Fα-scheme. II. Limit laws

Limit theorems for the number of records in a sequence of independent nonidentically distributed random variables are obtained. A generalization of the so-called F^α-scheme is given. Bibliography: 4 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 216, 1994, pp. 42–51. Translated by A. Sudakov.     

Synthesis of 4H-pyrans by O-cyclization of 1,5-diketones

Substituted 4H-pyrans were obtained in high preparative yields by the reaction of 1,5-diketones with acetic anhydride and boron trifluoride etherate in diethyl ether. It is assumed that the heterocyclization of 1,5-diketones includes a step involving the formation and transformations of an acyloxy carbonium ion.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 320–322, March, 1992.     

Large-scale computer simulation of fully developed turbulent channel flow with heat transfer

Recently, with the advent of supercomputers, there has been considerable interest in the use of direct numerical simulation to obtain information about turbulent shear flow at low Reynolds number. This paper presents a pseudospectral technique to solve the full three-dimensional time-dependent Navier-Stokes and advection-diffusion equations without the use of subgrid-scale modelling. The technique has not been previously used for fully developed turbulent channel flow simulation and is based on methods applied in other contexts. The emphasis of this paper is to provide a reasonably detailed account of how the simulation is done rather than to present new calculations of turbulence. The details of an algorithm for turbulent channel flow simulation and the grid and time step sizes needed to integrate through transient behaviour to steady state turbulence have not been published before and are presented here. Results from a Cray-2 simulation of fully developed turbulent flow in a channel with heat transfer are presented along with a critical comparison between experiment and computation. The first- and second-order moments agree well with experimental measurements; the agreement is poor for higher-order moments such as the skewness and flatness near the walls of the channel. Detailed information given about the effects of spatial grid resolution on a computed results is important for estimating the size of the computation required to study various aspects of a turbulent flow.     

Nitroazines. 20. Simple syntheses of nitropyrazolopyridines from aliphatic nitrosynthons and aminopyrazoles

Two variants of a synthesis for nitropyrazolopyridines from aminopyrazoles and two- or three-carbon nitrosynthons are examined.For Communication 19 see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1560–1564, November, 1992.