Natural convection from a cylinder in a narrow gap and in a porous medium

The problem of natural convection from a horizontal cylinder in a narrow gap and in a porous medium is solved both theoretically and experimentally. An integral method for calculating heat transfer from the cylinder for constant flux on its surface was suggested. Numerical analysis clarified the role of regime and geometrical factors. It is shown that natural convection from a cylinder in a porous medium can be modeled by a Hele Shaw cell. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 140–150. January–February, 1999.     

Film absorption on a plane surface imbedded in a granulated medium

Institute of Thermophysics, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 36, No. 3, pp. 98–115, May–June, 1995.     

The Möbius function on Abelian semigroups

Let X be an Abelian semigroup such that the following conditions hold: (i) if x × y = II (II is the identity element), then x = y = II; (ii) the set {{x, y}: x × y = a} is finite for any a ∈ X. Let Λ be any field, and let ℰ be the algebra of all Λ-valued functions on X. The convolution of u, υ ∈ ℰ is defined by

Spherically symmetric random permutations

We consider random permutations which are spherically symmetric with respect to a metric on the symmetric group S_n and are consistent as n varies. The extreme infinitely spherically symmetric permutation‐valued processes are identified for the Hamming, Kendall‐tau and Cayley metrics. The proofs in all three cases are based on a unified approach through stochastic monotonicity.     

Some remarks in connection with a certain problem of B. P. Paneyakh on equivalent norms in spaces of analytic functions

Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 44, pp. 23–32, 1985.     

On a condition on the radical of a Banach algebra ensuring strong decomposability

The main result is the following theorem. Let be a commutative Banach algebra with radical R, where the factor algebra is isomorphic to the algebra of all continuous functions on a totally disconnected compact space. If rⁿ¹ /n 0 as n uniformly for r R, rl, then the algebra is strongly decomposable, i.e., there exists a closed subalgebra B isomorphic to such that =BR.This is a strengthening of the theorem of A. Ya. Khelemskii, who assumed . There are 4 references.Translated from Matematicheskie Zametki, Vol. 2, No. 6, pp. 589–592, December, 1967.     

Effects of simultaneous 13C?1H and 13C?11B decoupling on the carbon-13 n.m.r. spectra of some organoboron compounds

¹³C FT n.m.r. spectra were obtained from borates of methyl α-D -glucopyranoside, triethylboron, sodium tetraphenylboron and 1-butaneboronic acid employing a simultaneous ¹H and ¹¹B decoupling network. The effectiveness of the system was evident using the three latter organoboron compounds. Since no diminution in line broadening of signals occurred in the spectrum of the sugar borate, the absence of ¹³C? O? ¹¹B coupling was indicated. This finding was confirmed by comparing the effects of varying the temperatures of sugar borates and triethylboron on their conventional ¹³C n.m.r. spectra.