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.     

A mixed-valence polyoxovanadate(III,IV) cluster with a calixarene cap exhibiting ferromagnetic V(III)-V(IV) interactions

A series of compounds (cat)[V6O6(OCH3)8(calix)(CH3OH)] was obtained under anaerobic conditions and solvothermal reaction of VOSO4 with p-tert-butylcalix[4]arene (calix) in methanol using different types of bases (Et4NOH, NH4OH, pyridine, Et3N). All compounds contain the same polyoxo(alkoxo)hexavanadate anion [V6O6(OCH3)8(calix)(CH3OH)]- (1) exhibiting a mixed valence {VIIIVIV5O19} core with the so-called Lindqvist structure coordinated to a calix[4]arene macrocycle and cocrystallizing with the conjugated acid of the base (cat = Et4N+, NH4(+), pyridinium, Et3NH+) involved in the synthesis process. The structures have been fully established from X-ray diffraction on single crystals and the mixed valence state has been confirmed by bond valence sum calculations. The magnetic behavior of all compounds are the same because of the polyalkoxohexavanadate anion [V6O6(OCH3)8(calix)(CH3OH)]- (1) and have been interpreted by DFT calculations. Thus the V(III)...V(IV) interactions are found to be weakly ferromagnetic (<5.5 cm(-1)) while the V(IV)...V(IV) are antiferromagnetic (-17.6; -67.6 cm(-1)). The set of the coupling exchange parameters allows a good agreement with the magnetic experimental data.     

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     

Solvation of UCl6(2-) anionic complex by MeBu3N(+), BuMe2Im(+), and BuMeIm(+) cations

The complexes [MeBu 3N] 2[UCl 6] and [BuMe 2Im] 2[UCl 6] were characterized in the solid state and in solution of [MeBu 3N][Tf 2N], [BuMe 2Im][Tf 2N], and [BuMeIm][Tf 2N] room-temperature ionic liquids using single-crystal XRD, EXAFS, electrochemistry, UV-visible absorption spectroscopy, and NMR. In the solid state and in solution, the existence of hydrogen bonding between the UCl 6 (2-) complex and the ionic liquid cations was revealed by these techniques. The MeBu 3N (+) cation interacts with UCl 6 (2-) via the protons on the alpha-carbon atoms of nitrogen. The protons of the imidazolium ring account for the interaction between the BuMe 2Im (+) cation and the UCl 6 (2-) anion. For the BuMeIm (+) cation the major interaction was confirmed between the most acidic proton on C(2) and the chlorides of UCl 6 (2-). The experimental results also show that the intensity of the interaction between the UCl 6 (2-) anion and the cation varies with the ionic liquid cation in the following order: MeBu 3N (+) approximately BuMe 2Im (+) < BuMeIm (+).     

Investigation of the two-step spin crossover complex Fe[5-NO2-sal-(1,4,7,10)] using density functional theory

A quantum chemical study of the Fe[5-NO2-sal-(1,4,7,10)] ((1,10-bis(5-nitrosalicylaldehyde)-1,4,7,10-tetra-ezdecane-O,O',N,N',N' ',N' ')iron(II)) molecule was performed using density functional theory (DFT). Starting from the different X-ray crystallographic structures, geometry optimizations have been performed. These calculations confirmed the conformational isomerism of this complex in each spin states of the molecule ((1)A(1g) and (5)T(2g)). Each employed DFT method (B3LYP, B3LYP*, BP86, HCTH407) reproduced correctly the structural differences between the two calculated conformers when compared to the experimental structures. Furthermore, electronic polarizabilities have been calculated in each spin state and for each conformer. These calculations revealed a higher polarizability in the singlet state in agreement with the measured higher dielectric constant in this state.     

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.