On the stability of retrial queues

We consider the following Type of problems. Calls arrive at a queue of capacity K (which is called the primary queue), and attempt to get served by a single server. If upon arrival, the queue is full and the server is busy, the new arriving call moves into an infinite capacity orbit, from which it makes new attempts to reach the primary queue, until it finds it non-full (or it finds the server idle). If the queue is not full upon arrival, then the call (customer) waits in line, and will be served according to the FIFO order. If λ is the arrival rate (average number per time unit) of calls and μ is one over the expected service time in the facility, it is well known that μ > λ is not always sufficient for stability. The aim of this paper is to provide general conditions under which it is a sufficient condition. In particular, (i) we derive conditions for Harris ergodicity and obtain bounds for the rate of convergence to the steady state and large deviations results, in the case that the inter-arrival times, retrial times and service times are independent i.i.d. sequences and the retrial times are exponentially distributed; (ii) we establish conditions for strong coupling convergence to a stationary regime when either service times are general stationary ergodic (no independence assumption), and inter-arrival and retrial times are i.i.d. exponentially distributed; or when inter-arrival times are general stationary ergodic, and service and retrial times are i.i.d. exponentially distributed; (iii) we obtain conditions for the existence of uniform exponential bounds of the queue length process under some rather broad conditions on the retrial process. We finally present conditions for boundedness in distribution for the case of nonpatient (or non persistent) customers. This revised version was published online in June 2006 with corrections to the Cover Date.     

Effects of the Structural Rigidity of Polymethine Dye Molecules on Quenching of Their Photoluminescence by an Electric Field and Charge Photogeneration in Poly(N-epoxypropylcarbazole)

For photoconducting poly(N-epoxypropylcarbazole) films doped with cationic polymethine dyes used as an example, it was found that an increase in dye molecular rigidity increased the photoconductivity of the films in the region of dye absorption, quenching effect of an electric field on photoluminescence, and concentration ratio of photogenerated triplet electron–hole pairs to singlet pairs. The effects were enhanced by an increase in the quantum energy of excitation light. The results are explained by a decrease in the dissipation rate of the electronic excitation energy of dye molecules upon growing their rigidity, which accelerates singlet–triplet intersystem crossing in the photogenerated electron–hole pairs via the spin–lattice relaxation mechanism.     

Structure and Adsorption Properties of Nanocrystalline Silicon

The structure of the particles of nanocrystalline silicon synthesized in argon plasma with added oxygen is studied. An amorphous shell composed of silicon oxide is formed on the surface of silicon nanoparticles. The particles form clusters with a fractal structure. The adsorption of nitrogen on a powder of nanocrystalline silicon at 77 K is studied, and adsorption isotherms obtained for nanocrystalline silicon and nonporous silica adsorbents with identical specific surface areas are compared. The values of surface fractal dimension of powdered nanocrystalline silicon are calculated using the Frenkel-Halsey-Hill equation for multilayer adsorption under the dominant contribution of van der Waals or capillary forces. It is shown that surface fractal dimension is a structure-sensitive parameter characterizing both the morphology of clusters and the structure (roughness) of the surface of particles and their aggregates.__________Translated from Kolloidnyi Zhurnal, Vol. 67, No. 4, 2005, pp. 541–547.Original Russian Text Copyright © 2005 by Tutorskii, Belogorokhov, Ishchenko, Storozhenko.     

Layer-by-Layer electrostatic self-assembly of polyelectrolyte nanoshells on individual carbon nanotube templates

Carbon nanotubes have been featured prominently in the nanotechnology research for some time, yet robust strategies for noncovalent chemical modification of the nanotube surface are still missing. Such strategies are essential for the creation of functional device architectures. Here, we present a new general procedure for carbon nanotube modification based on polyelectrolyte layer-by-layer assembly. We have built multilayer structures around individual carbon nanotube bridges by first modifying the nanotube surface with a pyrene derivative followed by layer-by-layer deposition of polyelectrolyte macroions on the nanotube. Transmission electron microscopy and scanning confocal fluorescence microscopy images confirm the formation of nanometer-thick amorphous polymer nanoshells around the nanotubes. These multilayer polyelectrolyte shells on individual carbon nanotubes introduce nearly unlimited opportunities for the incorporation of various functionalities into nanotube devices, which, in turn, opens up the possibility of building more complex multicomponent structures.     

Cyclization of alpha-Oxo-oximes to 2-substituted benzoxazoles

Reactions of oximes 9, 17, and 19 with electrophiles 15a-f and 24 in the presence of anhydrous potassium carbonate or triethylamine give 2-substituted condensed ring oxazoles 10, 16a-c, 18a-d, 20a-c, and 25 in a new general route to these compounds.     

From oxides of internal perfluoroolefins to fluorocontaining camphor thiazolinylhydrazones

The reaction of oxides of internal trans- and cis-perfluoroolefins with (1S, 4S)- or racemic camphor thiosemicarbazone leads to the formation of trans- and cis-isomers of (1S, 4S)- or racemic camphor 5′-fluoro-4′-hydroxy-4′,5′-di(perfluoroalkyl)-1′,3′-thiazolinyl-2′-hydrazones, respectively. Unsymmetrical dodecafluoro-2,3-epoxyhexane yields a mixture of regioisomeric hydrazones. The molecular structure of the trans-isomer of (1S, 4S)-camphor 5′-fluoro-4′-hydroxy-4′,5′-bis(trifluoromethyl)-1′,3′-thiazolinyl-2′-hydrazone has been established by X-ray crystallography. The quite rare example of cocrystallization of two diastereomers of the latter in homochiral crystal (sp. group P2₁) has been revealed.     

Experimental study of the gas-phase hydrofluorination of perchloroethylene over a chromium-based catalyst

Summary Gas-phase hydrofluorination of perchloroethylene to pentafluoroethane in the presence of a chromium-magnesium catalyst at 0.4 MPa and 330-390°C has been studied. А reaction scheme taking into account the formation of by-products is suggested. An erratum to this article is available at .     

Pyrylocyanines. 11. Symmetrical tetraphenyl-substituted pyrylo-2-cyanines

Symmetrical polymethine dyes (monomethylidyne, carbo-, and dicarbocyanines), viz., 4,6-diphenylpyrylium, -thiopyrylium, and -pyridinium derivatives, were synthesized. It follows from a comparison of the absorption spectra of pyrylo-2-cyanines and their heteroanalogs with the spectra of the corresponding 4 isomers that these dyes differ from one another with respect to the positions, intensities, and forms of the bands. The pyrylocarbo- and -dicarbocyanines and their sulfur analogs are more deeply colored than their isomers, while the reverse regularity is observed in the pyridocyanine series. The long-wave bands in the spectra of all of the isomers are accompanied by more intensive transitions to the vibrational sublevels than in the case of the isomers.See [1] for Communication 10.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, pp. 898–902, July, 1980.     

Laws of the lattice of all $${\mathfrak {X}}$$ -local formations of finite groups

Ricerche di Matematica - Let $${\mathfrak {X}}$$ be a class of simple groups with a completeness property $$\pi ({\mathfrak {X}}) = \mathrm {char} \, {\mathfrak {X}}$$ . A formation is a class of...