Ergodicity of Jackson-type queueing networks

This paper gives a pathwise construction of Jackson-type queueing networks allowing the derivation of stability and convergence theorems under general probabilistic assumptions on the driving sequences; namely, it is only assumed that the input process, the service sequences and the routing mechanism are jointly stationary and ergodic in a sense that is made precise in the paper. The main tools for these results are the subadditive ergodic theorem, which is used to derive a strong law of large numbers, and basic theorems on monotone stochastic recursive sequences. The techniques which are proposed here apply to other and more general classes of discrete event systems, like Petri nets or GSMPs. The paper also provides new results on the Jackson-type networks with i.i.d. driving sequences which were studied in the past.The work of this author was supported in part by a grant from the European Commission DG XIII, under the BRA Qmips contract.The work of this author was supported by a sabbatical grant from INRIA Sophia Antipolis.     

First dicyanamide-bridged spin-crossover coordination polymer: synthesis, structural, magnetic, and spectroscopic studies

We report here on the synthesis and characterisation of a first iron(II) spin-crossover coordination polymer with the dca spacer ligand, having the formula [Fe(aqin)2(dca)]ClO4.MeOH (aqin=8-aminoquinoline, dca=dicyanamide), which displays a two-step complete spin transition. Variable-temperature magnetic susceptibility measurements and M?ssbauer spectroscopy have revealed that the two relatively gradual steps are centred at 215 and 186 K and are separated by an inflection point at about 201 K, at which 50 % of the complex molecules undergo a spin transition. The two steps are related to the existence of two crystallographically inequivalent metal sites, as confirmed by the structural and M?ssbauer studies. The crystal structure was resolved at 293 K (HS form) and 130 K (LS form). Both spin-state structures belong to the triclinic P1 space group (Z=2). The complex assumes a linear chain structure, in which the active iron(II) sites are linked to each other by anionic dicyanamide ligands acting as chemical bridges. The Fe-Fe distances through the dca ligand are 8.119(1) and 7.835(1) A in the high-spin and low-spin structures, respectively. The polymeric chains extend along a (1, 0, -1) axis and are packed in sheets, between which the perchlorate anions and methanol molecules are inserted. The complex molecules are linked together by pi-stacking interactions and H-bonding between the H-donor aqin ligands and the perchlorate ions. These structural features provide a basis for cooperative interactions in the crystal lattice. Analysis of the two-step spin-crossover character in this compound suggests that covalent interactions through the spacer ligand do not provide the main mechanism of cooperativity.     

Circular choosability via combinatorial Nullstellensatz

A p‐list assignment L of a graph G assigns to each vertex v of G a set of permissible colors. We say G is L‐(P, q)‐colorable if G has a (P, q)‐coloring h such that h(v) ? L(v) for each vertex v. The circular list chromatic number of a graph G is the infimum of those real numbers t for which the following holds: For any P, q, for any P‐list assignment L with , G is L‐(P, q)‐colorable. We prove that if G has an orientation D which has no odd directed cycles, and L is a P‐list assignment of G such that for each vertex v, , then G is L‐(P, q)‐colorable. This implies that if G is a bipartite graph, then , where is the maximum average degree of a subgraph of G. We further prove that if G is a connected bipartite graph which is not a tree, then . © 2008 Wiley Periodicals, Inc. J Graph Theory 59: 190–204, 2008     

Superelectrophilic activation of 4-heterocyclohexanones. Implications for polymer synthesis. A theoretical study

The stability and the reactivity of mono- and diprotonated 4-heterocyclohexanones as well as cyclohexanone in triflic acid have been studied at the PBE0/aug-cc-pvtz//PBE0/6-31+G** level of theory. In all cases the first protonation is an exergonic process occurring at a carbonyl oxygen except for 4-piperidone where a nitrogen atom is protonated fist. Second protonation is only slightly endergonic for all studied molecules except for cyclohexanone where the second protonation is very unfavorable thermodynamically. According to calculations, diprotonated 4-heterocyclohexanones are much more active in the reactions of triflic acid mediated polyalkoxyalkylation with aromatic hydrocarbons compared to monoprotonated ones. The increase of the reactivity of diprotonated 4-heterocyclohexanones is due to inductive effect rather than through space electrostatic influence as follows from the electronic structure analysis of dications. Moreover, the second protonation reduces the possibility of an aldol condensation side reaction, reducing the enol electrophilicity rendering heterocyclohexanones as promising monomers for superacid mediated polyhydroxyalkylation.     

The critical temperature for the BCS equation at weak coupling

For the BCS equation with local two-body interaction λV(x), we give a rigorous analysis of the asymptotic behavior of the critical temperature as γ»0. We derive necessary and sufficient conditions onV(x) for the existence of a nontrivial solution for all values of γ>0.     

Free-base tripyrrins

The hitherto unavailable free-base tripyrrins HTrpy have been prepared by cyanide promoted demetallation of a nickel(ii) tripyrrin and by acid-induced condensation of a diformylpyrrole and an alkylpyrrole with a sterically shielded alpha-position.     

Characterization of nanoporous gold electrodes for bioelectrochemical applications

The high surface areas of nanostructured electrodes can provide for significantly enhanced surface loadings of electroactive materials. The fabrication and characterization of nanoporous gold (np-Au) substrates as electrodes for bioelectrochemical applications is described. Robust np-Au electrodes were prepared by sputtering a gold-silver alloy onto a glass support and subsequent dealloying of the silver component. Alloy layers were prepared with either a uniform or nonuniform distribution of silver and, post dealloying, showed clear differences in morphology on characterization with scanning electron microscopy. Redox reactions under kinetic control, in particular measurement of the charge required to strip a gold oxide layer, provided the most accurate measurements of the total electrochemically addressable electrode surface area, A(real). Values of A(real) up to 28 times that of the geometric electrode surface area, A(geo), were obtained. For diffusion-controlled reactions, overlapping diffusion zones between adjacent nanopores established limiting semi-infinite linear diffusion fields where the maximum current density was dependent on A(geo). The importance of measuring the surface area available for the immobilization was determined using the redox protein, cyt c. The area accessible to modification by a biological macromolecule, A(macro), such as cyt c was reduced by up to 40% compared to A(real), demonstrating that the confines of some nanopores were inaccessible to large macromolecules due to steric hindrances. Preliminary studies on the preparation of np-Au electrodes modified with osmium redox polymer hydrogels and Myrothecium verrucaria bilirubin oxidase (MvBOD) as a biocathode were performed; current densities of 500 μA cm(-2) were obtained in unstirred solutions.     

Asymptotic analysis of 3D thin anisotropic plates with a piezoelectric patch

We consider a thin elastic plate with piezo patches mounted on top of it. Electrodes are located on the upper and, depending on the devices, at the lower surface of the patches. This piezo actuator is coupled to an elastic body. We develop an asymptotic procedure to derive a two‐dimensional approximation of the entire structure. As a result, we obtain an inhomogeneous fourth‐order plate equation with piecewise smooth coefficients for the vertical displacement coupled to a second‐order in‐plane problem. The analysis and the resulting asymptotic limits help clarifying the modeling issue concerning active piezo devices in multidimensional smart structures. Copyright © 2012 John Wiley & Sons, Ltd.     

Asymptotics for estimation of quantile regressions with truncated infinite-dimensional processes

Many processes can be represented in a simple form as infinite-order linear series. In such cases, an approximate model is often derived as a truncation of the infinite-order process, for estimation on the finite sample. The literature contains a number of asymptotic distributional results for least squares estimation of such finite truncations, but for quantile estimation, results are not available at a level of generality that accommodates time series models used as finite approximations to processes of potentially unbounded order. Here we establish consistency and asymptotic normality for conditional quantile estimation of truncations of such infinite-order linear models, with the truncation order increasing in sample size. We focus on estimation of the model at a given quantile. The proofs use the generalized functions approach and allow for a wide range of time series models as well as other forms of regression model. The results are illustrated with both analytical and simulation examples.