A large closed queueing network with autonomous service and bottleneck

This paper studies the queue-length process in a closed Jackson-type queueing network with the large number N of homogeneous customers by methods of the theory of martingales and by the up- and down-crossing method. The network considered here consists of a central node (hub), being an infinite-server queueing system with exponentially distributed service times, and k single-server satellite stations (nodes) with generally distributed service times with rates depending on the value N. The service mechanism of these k satellite stations is autonomous, i.e., every satellite server j serves the customers only at random instants that form a strictly stationary and ergodic sequence of random variables. Assuming that the first k-1 satellite stations operate in light usage regime the paper considers the cases where the kth satellite station is a bottleneck node. The approach of the paper is based both on development of the method from the paper by Kogan and Liptser [16], where a Markovian version of this model has been studied, and on development of the up- and down-crossing method. This revised version was published online in June 2006 with corrections to the Cover Date.     

Synchronization structures in the chain of rotating pendulums

Nonlinear Dynamics - The collective behavior of the ensembles of coupled nonlinear oscillator is one of the most interesting and important problems in modern nonlinear dynamics. In this paper, we...     

[3+2] Annulation of 2-substituted 3-nitro-2H-chromenes with mercaptoacetaldehyde: stereoselective synthesis of tetrahydro-4H-thieno[3,2-c]chromen-3-ols

Chemistry of Heterocyclic Compounds - A diastereoselective method was developed for the synthesis of 4-trifluoromethyl- and 4-phenyl-substituted...     

Translation-rotation coupling and heat transfer in orientationally-disordered phase of CCl4

The isochoric thermal conductivity of an orientationally-disordered phase of CCl₄ is analysed within a model in which heat is transferred by phonons and above the phonon mobility edge by ”diffusive” modes migrating randomly from site to site. The mobility edge ω₀ is found from the condition that the phonon mean-free path cannot become smaller than half the phonon wavelength. The contributions of phonon-phonon, one-, and two-phonon scattering to the total thermal resistance of solid CCl₄ are calcualted under the assumption that the different scattering mechanisms contribute additively. An increase in the isochoric thermal conductivity with temperature is explained by suppression of phonon scattering at rotational excitations due to a decrease in correlation in the rotation of neighbouring molecules.     

Alkylation of narrow rim calix[4]arenes in a DMSO-NaOH medium

An effective method of 5,11,17,23-tetra-tert-butyl-25,26-dialkoxy-27,28-dihydroxy-calix[4]arenes and 25,26,27,28-tetraalkoxycalix[4]arenes synthesis by alkylation of tetrahydroxycalix[4]arenes in a DMSO-NaOH medium was developed.     

Reactivity of spiroanthraceneoxazolidines with cyclopropanes: An approach to the oxindole alkaloid scaffold

The reaction of N-methylspiro[anthracene-oxazolidine] with spiro[cyclopropane-3,3′-indolin]-2-ones in the presence of MgI₂ formed the corresponding spiro[pyrrolidine-3,3′-indolin]-2-ones in 42–65% yields. The use of N-benzylspiro[anthracene-oxazolidine] in this reaction led to the formation of a mixture of the corresponding N-methyl- and N-benzylpyrrolidines.     

Localization for random potentials supported on a subspace

We consider the lattice Schrödinger operator acting onl ² ( ^d ) with random potential (independent, identically distributed random variables), supported on a subspace of dimension 1 v <d. We use the multiscale analyses scheme to prove that this operator exhibits exponential localization at the edges of the spectrum for any disorder or outside the interval [-2d, 2d] for sufficiently high disorder.     

New 4-pentafluorosulfanyl and 4-perfluoroalkylthio derivatives of 1-chloro-2-nitro- and 1-chloro-2,6-dinitrobenzenes

New 4-pentafluorosulfanyl and 4-perfluoroalkylthio derivatives of 1-chloro-2-nitrobenzene and 1-chloro-2,6-dinitrobenzene were prepared from the corresponding bis(4-chloro-3-nitrophenyl)disulfide and bis(4-chloro-3,5-dinitrophenyl)disulfide, respectively. The SF₅ derivatives were obtained by fluorination of the disulfides with AgF₂ according to Sheppard’s method, while perfluoroalkylation was carried out by means of thermolytic reactions with xenon(II) bis(perfluoroalkylcarboxylates). The introduction of fluorine-containing, electron-withdrawing substituents into the aromatic ring (in the presence of other deactivating groups) reinforces the activation of the halogen substituent towards nucleophilic attack. Several nucleophilic substitution reactions have been carried out with these compounds, and as a result, some N- and S-containing groups were introduced in the benzene ring. For example, the previously unknown SF₅, CF₃S, and C₂F₅S analogues of trifluralin (Treflan^®) were prepared and characterized. Additional synthetic possibilities for heterocyclic chemistry are presented on the basis of reactions of the new 1-chloro-2,6-dinitrobenzene derivatives with ethyl thioglycolate wherein fluorine-containing derivatives of benzothiazole N-oxide were obtained as the main products.     

Structure of Dibenzocrown Ethers and their H-Bonded Adducts. 2. Structure Peculiarities of Supramolecular Assemblages Formed by [1.5]Dibenzo-18-Crown-6 and Some NH-Donors

[1.5]Dibenzo-18-crown-6 ([1.5]DB18C6) forms the H-bonded supramolecular complexes with 3-nitro-1H-1,2,4-triazole (1:1), 2,4(1H,3H)-pyrimidinedithione (1:1), 1,2,5-oxadiazole-3,4-diamine monohydrate (1:1:1), ethanedithioamide (1:1) and 1,2-hydrazinedicarbothioamide (2:3). The first two complexes are discrete molecular adducts, two next complexes represent different types of tapes, while in the last complex the components are linked into 3D grid. In all cases, the formation of co-crystals results in the substitution of all or part of supramolecular homosynthons by heterosynthons and in the changing of supramolecular architecture.This revised version was published online in July 2005 with a corrected issue number.