New olefinic functionalized disilanes. Synthesis and NMR spectroscopical investigations

The new olefinic substituted aminodisilanes, which are obtained from the reaction of organometallic reagents with aminochlorodisilanes, are converted into the chlorodisilanes by equilibration reactions or treatment with HCI. The resulting olefinic functionalized disilanes are identified by means of ²⁹Si, ¹³C, ¹H NMR and GC MS measurements.     

Filled Julia Sets with Empty Interior Are Computable

We show that if a polynomial filled Julia set has empty interior, then it is computable.     

On the index of composition of integers from various sets

Given an integer n ≥ 2, let λ(n) := (log n)/(log γ(n)), where γ(n) = Π _p|n p, stand for the index of composition of n, with λ(1) = 1. We study the distribution function of (λ(n) – 1) log n as n runs through particular sets of integers, such as the shifted primes, the values of a given irreducible cubic polynomial and the shifted powerful numbers. Research supported in part by a grant from NSERC. Research supported by the Applied Number Theory Research Group of the Hungarian Academy of Science and by a grant from OTKA. Professor M.V. Subbarao passed away on February 15, 2006. Received: 3 March 2006 Revised: 28 October 2006     

Exciton-polaritons in microcavities: present and future

An overview is given of the current research trends in the physics of exciton-polaritons in microcavities. Potential applications of the Bose–Einstein condensation and superfluidity of exciton-polaritons are discussed. The perspectives for the realization of polariton lasers, polariton spin transistors and polarization modulators are presented. PACS 78.67.-n; 71.36.+c; 42.55.Sa; 42.25.Kb     

Temperature dependent structure of spider silk by X-ray diffraction

We have investigated the structure of spider dragline silk by X-ray diffraction over a broad temperature range from room temperature up to thermal denaturation conditions. The dominating signal from the β-sheet crystallites is analyzed. Pronounced changes of scattering intensity starting at temperatures around 150 °C are observed. These changes are discussed in view of the respective lattice constants, crystal size, size distribution, crystallite number density and amino acid composition. PACS 87.68.+z; 87.15.-v; 87.64.Bx     

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.     

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.