Instability of the boundary layer on a curved surface

The excitation of instability of the boundary layer on a curved surface in the limit R (R is the Reynolds number) is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 176–179, January–February, 1990.I am grateful to O. S. Ryzhov for his interest in the work.     

Behavior on the real line of entire functions represented by Dirichlet series with complex exponents

It is shown, in particular, that if _{n k} when n k, Re _n > 0, and , then an entire function F that is bounded on the real line and represented by a Dirichlet series d_n exp (_nz) that is uniformly and absolutely convergent on each compactum in is identically zero.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 882–888, July, 1990.     

A certain functional algebra

We study the algebra of functions on the set of natural numbers with respect to the generalized convolution, generated by the generalized translation operator T_nf(k)=f(max (n, k)), n, k. With the help of the generalized Fourier transform, connected with this convolution, we establish numerous identities and recurrence relations, connecting, in particular, sums of powers of natural numbers.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 372–377, March, 1990.     

Impulse systems with fixed moments of shocks of general position: The structure of the set of moments of the shocks

Ordinary differential equations with impulse action are considered at fixed moments of time when finite limits points are admitted to the set of moments of the shocks. The topological structure of this set is clarified: it must be resolvable, in particular nowhere dense in R.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 378–383, March, 1990.     

Water 1H spin-lattice relaxation as a fingerprint of porous media

The 1H spin-lattice relaxation curves of water in samples of natural porous media can be thought of as "fingerprints" of the porous samples. Also the whole of traditional petrophysical properties (permeability, irreducible water saturation, etc.) can be thought of as "fingerprints" of the porous samples. The characteristics of the pore space determine on one hand the relaxation curve shape, and on the other the petrophysical properties. The understanding of this correspondence can contribute to a better definition of the concept of the architecture of a porous medium. At this purpose we have obtained 1H spin-lattice relaxation curves from a collection of standard sandstone cores of known petrophysical properties and characterized by the same surface properties. The results corroborate the idea that the structure of relaxation curves contains information on the distance scale and on the architecture of the pore space, even if it is difficult to extract it without ambiguities. Different methods of curve fitting were performed and compared with the aim of getting the maximum information from the relaxation curves. Several aspects of this kind of investigation indicate the analogies between 1H response of water confined in porous media and in biological tissues.     

Two-temperature channel model of a direct current arc

A relatively simple method is proposed for computing the gas and electron temperatures in an arc plasmotron channel within the framework of the self-consistent two-temperature channel model of an arc discharge. This method affords the possibility of obtaining the gas and electron temperature distribution with good enough accuracy for given discharge parameters (current intensity in the discharge, power inserted in the discharge, etc.) as a function of the radial coordinate in both nonequilibrium (T_e T_ai) and quasi-equilibrium (T_e = T_ai within the current conducting channel) cases. The results obtained can be utilized in model computations to estimate the gas and electron temperatures as well, possibly, as in a number of engineering computations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 80–86, July, 1990.The author is grateful to L. A. Rachevskii for useful discussion of results of the research.     

Relativistically covariant chronological ordering of interaction lagrangians

A general form of chronological ordering is proposed, based on introduction of relativistically invariant multipoint step functions (x₁, ..., x_n). A system of recursive relations is established for these functions, which guarantees that the scattering matrix is unitary, covariant, and causal. The explicit form of the first four -functions is found. A comparative analysis of the known methods of chronological ordering is given.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 70–73, May, 1990.     

Excitation spectrum of anisotropic non-dissipative elastic-plastic medium

The simplest gauge theory of an elastic-plastic medium is considered in this paper that takes account of just translational plasticity. The equations of motion for such a model turn out to be linear and permit the normal modes spectrum of a medium to be obtained. Taking account of plasticity results in a cardinal transformation of the elastic branches of the spectrum and the appearance of a group of plasma oscillations of a dislocation gas.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 64–68, June, 1990.     

Upper-Branch Instability of Flow in Pipes of Large Aspect Ratio with Three-Dimensional Nonlinear Viscous Critical Layers

We consider the upper-branch neutral stability of flow in pipesof large aspect ratio, basically extending the work of F. T.Smith to the nonlinear regime. The inclusion of weak nonlinearityleads to an eigenproblem whose solution depends on the propertiesof three-dimensional nonlinear critical layers. Two specialcases are considered. The first is for very small amplitude perturbations, where R is a Reynolds numberbased on the height of the tube and which is assumed large.Then a fully analytical solution of the three-dimensional criticallayers is possible, from which the linear results of Smith maybe deduced. The second case studied is that of flow in a rectangularpipe, where a solution of the nonlinear critical layer problemcan be obtained. Further analysis of neutral modes in this lattercase suggests the possible existence, inter alia, of neutralmodes for finite aspect ratio tubes. These modes depend on thescaled amplitude and have O(1) wavespeeds.     

Crystal structures of dimethylsuccinate and dimethyloxalate: Carbonyl group orientation for C13 chemical shielding tensor studies

The crystal structures of dimethylsuccinate (DMS) and dimethyloxalate (DMO) have been determined to facilitate the determination of the C-13 chemical shielding tensors of the carbonyl carbon in esters. Crystals of DMS are monoclinic, space groupC2/c,Z=4,a=13.154(4),b=6.156(1),c=9.363(4)Å,=98.53(3)°. The structure was solved by direct methods and refined by leastsquares procedures to giveR=0.071 for 932 observed data. Crystals of DMO are monoclinic space group,P2₁/n,Z=2, witha=3.891(1),b=11.879(2),c=6.213(2) Å,=103.32(2)°. The structure is the same (within experimental error) as that reported by Dougill and Jeffrey (1953) and refined to giveR=0.074 for 395 observed data.