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.     

Spectral-luminescent properties of oxazole derivatives with annelated aromatic and heterocyclic rings in neutral and acid media

An investigation was carried out of the spectral-luminescent and acid-base properties at the stage of formation of the hydrogen bond and during the protonation of compounds with annelated aromatic and heterocyclic rings, obtained by introduction of bridging groups -CH=CH- (I), -CH=N- (II) and -CO-N(CH₃)-(III) in the 4- and 2-positions of the molecules of 4-substituted derivatives of 2,5-diphenyloxazole. The nature of the reaction center was estabished, and an analysis was carried out of its sensitivity to the electronic influence of the substituents, and the reasons for the observed differences in the properties of compounds of various reaction series are discussed. A comparative analysis of the fluorescent properties of the neutral and protonated forms of the oxazole derivatives studied was made and the conclusion that the generation is possible of laser emission by the protonated forms of compounds of the reaction series (I) was confirmed.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 28, No. 4, pp. 343–349, July–August, 1992.     

Structurally Controlled Porphyrin-Aggregation Process in Phospholipid Membranes

Abstract— Structurally controlled aggregation course for five porphyrins (etioporphyrin [EP], 5-mono- and 5,15-di-[ p -tol-yl]etioporphyrin [TP and DTP], 5,10,15,20-tetrakis[ p -tol-y1]porphin [TTP], and 5,10,15,20-tetrakis[3,5-di- tert -bu-tylphenyl]porphin [TBP]) in dipalmitoyl-phosphatidyl-choline liposomes has been monitored by fluorescence and absorption spectroscopy. While TBP shows no tendency to aggregate in liposomes, EP, TP, DTP and TTP form a porphyrin-enriched domain in membrane interior with time. The further aggregation steps within porphyrin clusters resulting in formation of stacked porphyrin aggregates have been observed for EP, TP and DTP.     

Supramolecular Assembly Formation in Monolayers of tert-Butyl Substituted Copper Phthalocyanine and Tetrabenzotriazaporphin

The effect is studied of the layer formation conditions on the molecular arrangement of copper tetra- tert-butyl phthalocyanine (CuPctBu₄) and copper tetra- tert-butyl tetrabenzotriazaporphin (CuThptBu₄) at the air–water interface. The decrease in initial surface concentration of these compounds is shown to affect the molecular orientation, as indicated by the increase in the area per molecule. The data are interpreted in terms of formation of CuPctBu₄ and CuThptBu₄ monolayers with a face-on molecular arrangement when the initial surface concentration is sufficiently small (N less than 1.6 × 10^–7 mole/m² for CuPctBu₄ and N less than 4 × 10^–7 mole/m² for CuThptBu₄) and changes in the molecular orientation to edge-on when the N values are higher. It is emphasized that the edge-on orientation on the water surface is not only a molecular but a collective property of the azaporphyrine supramolecular assembly.     

IR spectral study of the effect of the reaction medium on the state of cobalt in a 10% Co/Al2O3 catalyst for aliphatic hydrocarbons from CO and H2

Diffuse scattering IR spectroscopy was used to study the 10% Co/Al₂O₃ catalyst for the synthesis of aliphatic hydrocarbons from CO and H₂. Ionic and metallic cobalt forms were identified in the IR spectroscopy. The adsorption of CO on these forms is accompanied by the appearance of linear and bridged complexes. After prolonged treatment of the catalyst by a CO + 2H₂ mixture, the ions and surface of metallic cobalt remain available for the adsorption of CO. Modification of the surface of metallic cobalt occurs upon the action of the reaction medium. This modification is seen in a bathochromic displacement of the IR bands for the adsorbed and linear CO forms. This displacement is accompanied by a reduction in the strength of the metal-carbon bond in the Co^o-CO complex.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2640–2643, November, 1990.     

Theoretical and Experimental Studies of the Nature of the Catalytic Activity of VO x /TiO2 Systems

The states of supported vanadium and the nature of activation of ammonia adsorbed on vanadium sites of V _x /Ti₂ catalysts are studied by ⁵¹V NMR spectroscopy and diffuse-reflectance IR Fourier-transform (DRIFT) spectroscopy using cluster quantum chemical calculations of N₃ adsorption. We employ the V _x /Ti₂ catalyst of two types: the monolayer catalyst in which vanadium is located on the surface of well-crystallized anatase and the catalyst in which vanadium embedded in the anatase lattice at a rather great depth. It is shown that ammonia is predominantly adsorbed on Lewis acid sites of the monolayer catalyst, whereas most of N₃ adsorbed on the catalyst containing bulk vanadium is in the form of ammonium ions. Analysis of experimental and calculated data suggests that, in the monolayer catalyst, N₃ molecules in the selective reduction of nitrogen oxides are activated on Lewis acid sites. Ammonia activation involves the dissociation of the N–H bond in a coordinated molecule, which results in the formation of the amide V–N₂ group and a water molecule coordinated by a V⁵⁺ ion. It is likely that, in the case of the catalyst containing bulk vanadium, this reaction occurs with the predominant participation of ammonium ions.     

Supramolecular chirogenesis in zinc porphyrins: equilibria, binding properties, and thermodynamics

Complexation mechanism, binding properties and thermodynamic parameters of supramolecular chirality induction in the achiral host molecule, syn (face-to-face conformation) ethane-bridged bis(zinc porphyrin), upon interaction with chiral monoamine and monoalcohol guests have been studied by means of the UV-vis, CD, (1)H NMR, and ESI MS techniques. It was found that the chirogenesis process includes three major equilibria steps: the first guest ligation to a zinc porphyrin subunit of the host (K(1)), syn to anti conformational switching (K(S)), and further ligation by a second guest molecule to the remaining ligand-free zinc porphyrin subunit (K(2)), thus forming the final bis-ligated species possessing supramolecular chirality. The validity of this equilibria model is confirmed by the excellent match between the calculated and experimentally observed spectral parameters of the bis-ligated species. The second ligation proceeds in a cooperative manner as K(2) > K(1) for all supramolecular systems studied, regardless of the structure of the chiral ligand used. The binding properties are highly dependent on the nature of the functional group (amines are stronger binders than alcohols) and on the structure of the chiral guests (primary and aliphatic amines have overall binding constant values greater than those of secondary and aromatic amines, respectively).