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.     

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 .     

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...     

The studies of the effect of photostimulated changes in thin carbon films

Photostimulated changes in thin carbon films deposited onto fused silica substrates by reactive magnetron sputtering and irradiated by the light of the first (1060nm) and the second (530nm) harmonics of a QW-switched Nd³⁺ AVG laser were investigated. The changes are supposed to be connected with the reordering of chemical bounds.     

Asymmetrical nonbridgehead nitrogen-17: Complete separation into antipodes and absolute configuration of chiralic n-alkoxyisoxazolidines

trans-Stereospecificity of the amidation of 1-alkoxyisoxazolidine-3,3-dicarboxylic ester (1) has been elucidated. Alkaline hydrolysis of monester 4 yielded the salt 6 which after its ion exchange in the form of S(?) and R-(+)-phenylethylammonium salts was completely separated into the enantiomeric salts (+10 and ?10). Esterification and amidation of these salts afforded antipodes 2 S-( +12) and 2 R-( ?12) containing only a nitrogen asymmetric center. Optical purities of the products were established on the basis of their NMR spectra with shift-reagent. Molecular and crystal structure as well as an absolute configuration of +10 were detected by means of X-ray analysis.