Searching for losers

We investigate the following process: N people select b losers by flipping coins. The 0-party continues until there are less than b losers; then the 1-party has to find the other losers by the same process. The average time for this process is about long₂ N, but this result requires rather advanced methods. Furthermore, the average size of a binary tree associated to this process and the average number of coin flippings are computed. The method used in this article can be used to give asympotical solutions of a special type of bivariate recurrences. © 1993 John Wiley & Sons, Inc.     

Experimental study of acoustic probing of electrical space charge in solid insulators

Experimental results are presented on acoustic probing of electric fields in solid insulators. An experimental apparatus and methods are described for acoustic measurements of the bulk space charge density and electric field strength in solid insulators. The sensitivity and spatial resolution of the acoustic probe technique are determined.Institute of Introscopy Research, Polytechnical University, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 62–67, September, 1993.     

Optical absorption bistability in quasi-one-dimensional peierls semiconductors

The optical absorption coefficient γ of a thin film of a Peierls semiconductor has been calculated in the dipole approximation for direct interband transitions as a function of intensity I and central frequency ω₀ of a quasi-monochromatic frequency spectrum near the lower optical transition edge. It is shown that the γ(I, ω₀) dependence is strongly nonlinear, and within a certain region of I and ω₀ variation, not single-valued, which indicates the onset of resonator-free optical bistability with increasing absorption.     

On the exceptional series,and its descendantsLa série exceptionnelle,et sa descendance

Many of the striking similarities which occur for the adjoint representation of groups in the exceptional series (cf. [1–3]) also occur for certain representations of specific reductive subgroups. The tensor algebras on these representations are easier to describe (cf. [4,5,7]), and may offer clues to the original situation.The subgroups which occur form a Magic Triangle, which extends Freudenthal's Magic Square of Lie algebras. We describe these groups from the perspective of dual pairs, and their representations from the action of the dual pair on an exceptional Lie algebra. To cite this article: P. Deligne, B.H. Gross, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 877–881.     

Electromagnetic field singularities

An integral transform based method is given for determining information about the locating and properties of singularities of electromagnetic fields associated with axially symmetric radiating sources.     

Spectra and Transport in Almost Periodic Dimers

We study spectral properties of discrete Schrödinger operators with potentials obtained via dimerization of a class of aperiodic sequences. It is shown that both the nature of the autocorrelation measure of a regular sequence and the presence of generic (full probability) singular continuous spectrum in the hull of primitive and palindromic (four block substitution) potentials are robust under dimerization. Generic results also hold for circle potentials. We illustrate these results with numerical studies of the quantum mean square displacement as a function of time. The numerical techniques provide a very fast algorithm for the time evolution of wave packets.     

An M/G/1 Retrial Queueing System with Two-Phase Service and Preemptive Resume

An M/G/1 retrial queueing system with additional phase of service and possible preemptive resume service discipline is considered. For an arbitrarily distributed retrial time distribution, the necessary and sufficient condition for the system stability is obtained, assuming that only the customer at the head of the orbit has priority access to the server. The steady-state distributions of the server state and the number of customers in the orbit are obtained along with other performance measures. The effects of various parameters on the system performance are analysed numerically. A general decomposition law for this retrial queueing system is established.     

Thoms Effect as Influenced by the Concentration and Molecular Parameters of the Cationic Copolymer of Acrylamide

The Thoms effect observed with water-soluble cationic copolymer of acrylamide was studied in relation to the concentration, molecular weight, and molecular weight polydispersity of the polymeric additive, with its composition and composition polydispersity being constant.     

A nondestructive numerical-experimental method of determining the residual stresses in welded shells of revolution

We propose a numerical-experimental method of determining the residual stresses in welded shells of revolution. We solve the inverse conditionally correct problem of recovering the complete picture of the residual stress state from part of the experimental values obtained by the method of photoelasticity. We apply the numerical spline-collocation method. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 149–151.