Asymptotic methods in the theory of nonlinear stochastic oscillations

We study applications of asymptotic methods of nonlinear mechanics and the method of Fokker-Planck-Kolmogorov equations to stochastic oscillations in quasilinear oscillating systems with random perturbations. __________ Translated from Neliniini Kolyvannya, Vol. 10, No. 4, pp. 510–518, October–December, 2007.     

The mean-value theorem for elliptic operators on stratified sets

In this paper, an analog of the mean-value theorem for harmonic functions is proved for an elliptic operator on the stratified set of “stratified” spheres whose radius is sufficiently small. In contrast to the classical case, the statement of the theorem has the form of a special differential relationship between the mean values over different parts of the sphere. The result is used to prove the strong maximum principle.     

Distributive lattices of numberings

We study into a semilattice of numberings generated by a given fixed numbering via operations of completion and taking least upper bounds. It is proved that, except for the trivial cases, this semilattice is an infinite distributive lattice every principal ideal in which is finite. The least upper and the greatest lower bounds in the semilattice are invariant under extensions in the semilattice of all numberings. Isomorphism types for the semilattices in question are in one-to-one correspondence with pairs of cardinals the first component of which is equal to the cardinality of a set of non-special elements, and the second — to the cardinality of a set of special elements, of the initial numbering. Supported by INTAS grant No. 00-429. __________ Translated from Algebra i Logika, Vol. 46, No. 1, pp. 83–102, January–February, 2007.     

On quasi-conformally flat weakly Ricci symmetric manifolds

The object of the present paper is to study quasi-conformally flat weakly Ricci symmetric manifolds.      

Experience Gained Using Second-Moment Closure Modeling for Transitional Flows Due to Boundary Layer Separation

This paper presents detailed information on the experience gained during the attempts to model a set of transitional flows due to boundary layer separation. These flows are developed on a flat plate with a semi-circular leading edge and they have been coded by the ERCOFTAC Special Interest Group on Transition, as T3L flows. Different freestream velocities and turbulence intensities configure these transitional flows and, by consequence, govern the transition mechanism, resulting in larger or smaller transitional regions. The modeling of the T3L flows has been performed by adopting a low-Reynolds number second-moment closure turbulence model. The results showed satisfactory agreement with the experimental measurements, although some difficulties regarding successful convergence have been faced. The final conclusion is that turbulence modeling can present quite accurate results for transitional flows without any additional use of ad-hoc modifications or additional equations based on various transition models and intermittency transport modeling.     

Lines Tangent to Four Triangles in Three-Dimensional Space

We investigate the lines tangent to four triangles in R³. By a construction, there can be as many as 62 tangents. We show that there are at most 162 connected components of tangents, and at most 156 if the triangles are disjoint. In addition, if the triangles are in (algebraic) general position, then the number of tangents is finite and it is always even.     

Achievements in the field of proton-conductive portion electrolyte membranes

The 2000–2006 achievements in the field of synthesis, property examination, and application of proton-exchange membranes are reviewed on the basis of more than 120 papers.     

Uniform non-amenability of free Burnside groups

The aim of this paper is to show that free Burnside groups of sufficiently large odd exponent are non-amenable in a certain strong sense. More precisely their left regular representations are isolated from the trivial representation uniformly on finite generating sets. It follows that free Burnside groups are of uniform exponential growth. This answers a question of de la Harpe. This work has been partially supported by the NSF grant DMS-0605093 and by the RFBR Grant # 05-01-00892. Received: 25 April 2006     

Discovery and frequency measurement of short-wavelength far-infrared laser emissions from optically pumped <Superscript>13</Superscript>CD<Subscript>3</Subscript>OH and CHD<Subscript>2</Subscript>OH

A three-laser heterodyne system was used to measure the frequencies of twelve previously observed far-infrared laser emissions from the partially deuterated methanol isotopologues ¹³CD₃OH and CHD₂OH. Two laser emissions, a 53.773 μm line from ¹³CD₃OH and a 74.939 μm line from CHD₂OH, have also been discovered and frequency measured. The CO₂ pump laser offset frequency was measured with respect to its center frequency for twenty-four FIR laser emissions from CH₃OH, ¹³CD₃OH and CHD₂OH. PACS 07.57.Hm; 42.55.Lt; 42.62.Eh