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.     

On the distribution of the number of customers in the symmetric M/G/1 queue

We consider an M/G/1 queue with symmetric service discipline. The class of symmetric service disciplines contains, in particular, the preemptive last-come-first-served discipline and the processor-sharing discipline. It has been conjectured in Kella et al. [1] that the marginal distribution of the queue length at any time is identical for all symmetric disciplines if the queue starts empty. In this paper we show that this conjecture is true if service requirements have an Erlang distribution. We also show by a counterexample, involving the hyperexponential distribution, that the conjecture is generally not true. AMS Subject Classifications Primary—60K25; Secondary—90B22     

Electroencephalogram (EEG) time series classification: Applications in epilepsy

Epilepsy is among the most common brain disorders. Approximately 25–30% of epilepsy patients remain unresponsive to anti-epileptic drug treatment, which is the standard therapy for epilepsy. In this study, we apply optimization-based data mining techniques to classify the brain's normal and epilepsy activity using intracranial electroencephalogram (EEG), which is a tool for evaluating the physiological state of the brain. A statistical cross validation and support vector machines were implemented to classify the brain's normal and abnormal activities. The results of this study indicate that it may be possible to design and develop efficient seizure warning algorithms for diagnostic and therapeutic purposes. Research was partially supported by the Rutgers Research Council grant-202018, the NSF grants DBI-980821, CCF-0546574, IIS-0611998, and NIH grant R01-NS-39687-01A1.     

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.