There are infinitely many limit points of the fractional parts of powers

Suppose that α > 1 is an algebraic number and ξ > 0 is a real number. We prove that the sequence of fractional partsξα ⁿ , n = 1, 2, 3, …, has infinitely many limit points except when α is a PV-number and ξ ∈ ℚ(α). For ξ = 1 and α being a rational non-integer number, this result was proved by Vijayaraghavan.     

Quadratic transformations of the sixth Painlevé equation with application to algebraic solutions

In 1991, one of the authors showed the existence of quadratic transformations between the Painlevé VI equations with local monodromy differences (1/2, a, b, ±1/2) and (a, a, b, b). In the present paper we give concise forms of these transformations. They are related to the quadratic transformations obtained by Manin and Ramani–Grammaticos–Tamizhmani via Okamoto transformations. To avoid cumbersome expressions with differentiation, we use contiguous relations instead of the Okamoto transformations. The 1991 transformation is particularly important as it can be realized as a quadratic‐pull back transformation of isomonodromic Fuchsian equations. The new formulas are illustrated by derivation of explicit expressions for several complicated algebraic Painlevé VI functions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Quantitative characterization of chaotic instabilities in semiconductors

A method for quantitative characterization of chaotic dynamical systems is discussed. An electronic instrument for determining the number of independent variablesk ^*, involved in the motion, is described. It allows one to obtain these in real time from a single observable. The suggested technique has been applied to quantification of strange attractors underlying chaotic instabilities in semi-insulating GaAsCr, and n-Ge, irradiated with high energy electrons. In n-Ge, for instance, the measured numbersk ^* range from 2 to 4 depending on control parameters. These measurements reveal the highly deterministic nature of the observed chaotic oscillations. The physical mechanisms responsible for the current instabilities and chaotic behaviour are discussed.     

Recyclization of 1,4-dihydropyridine derivatives in acidic medium

The recyclization of 1,4-dihydropyridines in aqueous-alcoholic hydrochloric acid medium proceeds with cleavage of a C-N bond and pyridine ring opening. Cyclohexenone derivatives are formed as a result of the subsequent intramolecular crotonic condensation of the acyclic intermediate. The leaving carbonyl substituents depart simultaneously with recyclization, depending on the acidity of the reaction medium. Dedicated to Prof. Dr. E. Lukevics on the occasion of his 70th birthday. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 49–58, January, 2007.     

Catalytic,asymmetric Mannich-type reactions of alpha-imino esters bearing readily removable substituents on nitrogen

[reaction: see text] Catalytic, enantioselective Mannich-type reactions of alpha-imino esters bearing readily removable substituents on nitrogen are described. Several N-carbamate-protected alpha-imino esters, which are readily prepared from 2-bromoglycine esters using a polymer-supported amine, reacted with silicon enolates to afford the desired adducts in high yields with high enantioselectivity using a copper(II)-diamine complex. Easy deprotection of the product amine and transformation to free alpha-amino acid derivatives have also been demonstrated.     

Transition metal salts-catalyzed aza-Michael reactions of enones with carbamates

Several transition metal salts were found to catalyze aza-Michael reactions of enones with carbamates efficiently. The catalytic activity was strongly dependent on the nature of the metal salts. While conventional Lewis acids such as BF(3).OEt(2), AlCl(3), or TiCl(4) showed lower activity, group 7-11 transition metal salts in higher oxidation states such as ReCl(5), Fe(ClO(4))(3).9H(2)O, RuCl(3).nH(2)O, OsCl(3).3H(2)O, RhCl(3).nH(2)O, PtCl(4).5H(2)O, or AuCl(3).H(2)O exhibited higher catalytic activity. [reaction: see text]     

Exciton absorption spectra of optically excited linear molecular aggregates

Exciton absorption spectrum of optically excited linear molecular aggregate is theoretically investigated. The sum rules for the integral intensity of the absorption spectrum are derived. The dipole moments of the optical transitions from the one-exciton states to the two-exciton states are presented. The results obtained indicate an energy increase of the exciton transition after a single excitation of the aggregate. It accounts for the observed short-wavelength shift of the J-band of the pseudoisocyanine (PIC) J-aggregates after their optical excitation. The comparison of the experimental energy of the shift with its theoretical evaluation allows to estimate the number of monomers forming a typical PIC J-aggregate in the solutionN ?20–30.     

Pulse plating effect on microstructure and corrosion properties of Zn–Ni alloy coatings

The influence of pulse plating parameters on the surface morphology, grain size, lattice imperfection and corrosion properties of Zn–Ni alloy has been studied. The coatings were electrodeposited in an alkaline cyanide-free solution. AFM was applied for surface morphology examination, XRD measurements were carried out for phase composition and texture analysis, electron probe microanalysis was used for alloy chemical composition studies, while electrochemical techniques were applied for corrosion performance evaluation. The pulse plated Zn–Ni coatings appeared to consist of the γ-Zn₂₁Ni₅ phase and the composition of the alloy depended on the plating parameters. The grain size, lattice imperfection and homogeneity of grain distribution were established to be the main factors determining corrosion behaviour of the coating. Presented at the 4th Baltic Conference on Electrochemistry, Greifswald, March 13–16, 2005     

Dipole moments and structure of poly(epoxypropylcarbazole)

The mean-square molecular dipole moments 〈μ²〉 of carbazole, N-ethylcarbazole and of the sequence of poly(epoxypropylcarbazole) (PEPCa) oligomers of various molecular weights have been evaluated in solutions of these organic compounds in dioxan. For PEPCa the values of 〈μ²〉 have also been determined in the solid state. On the basis of the experimental results and of molecular mechanics calculations it has been shown that the orientation of the lateral group of PEPCa favors noninteracting racemic dyads. The temperature-dependence of the effective dipole moment of solid PEPCa follows the Onsager theory above 295 K.