Artificial boundary conditions on polyhedral truncation surfaces for three-dimensional elasticity systemsConditions aux limites artificielles sur des surfaces polyhédrales de troncature pour des systèmes d'élasticité tridimensionalle

For a three-dimensional exterior problem in the framework of anisotropic elasticity, artificial boundary conditions are constructed on a polyhedral truncation surface. These conditions do not need an explicit formula for the fundamental matrix. An approach to adapt the shape of truncation surfaces to the shape of the enclosed cavity is discussed. To cite this article: S. Langer et al., C. R. Mecanique 332 (2004).     

Self adjoint extensions of differential operators in application to shape optimizationExtensions autoadjointes d'opérateurs différentiels et application à l'optimisation de forme

Two approaches are proposed for the modelling of problems with small geometrical defects. The first approach is based on the theory of self adjoint extensions of differential operators. In the second approach function spaces with separated asymptotics and point asymptotic conditions are introduced, and the variational formulation is established. For both approaches the accuracy estimates are derived. Finally, the spectral problems are considered and the error estimates for eigenvalues are given. To cite this article: S.A. Nazarov, J. Sokolowski, C. R. Mecanique 331 (2003).     

On Range and Local Time of Many-dimensional Submartingales

We consider a discrete-time process adapted to some filtration which lives on a (typically countable) subset of ? ^d , d≥2. For this process, we assume that it has uniformly bounded jumps, and is uniformly elliptic (can advance by at least some fixed amount with respect to any direction, with uniformly positive probability). Also, we assume that the projection of this process on some fixed vector is a submartingale, and that a stronger additional condition on the direction of the drift holds (this condition does not exclude that the drift could be equal to 0 or be arbitrarily small). The main result is that with very high probability the number of visits to any fixed site by time n is less than  $n^{\frac{1}{2}-\delta}$ for some δ>0. This in its turn implies that the number of different sites visited by the process by time n should be at least  $n^{\frac{1}{2}+\delta}$ .     

Thermophysical study of graphene nanoflakes by differential scanning calorimetry

Journal of Thermal Analysis and Calorimetry - Combustion heats of graphene nanoflakes (GNFs) of different thicknesses produced by chemical vapor deposition method were measured for the first time...     

Riemann-Roch and Abel-Jacobi theory on a finite graph

It is well known that a finite graph can be viewed, in many respects, as a discrete analogue of a Riemann surface. In this paper, we pursue this analogy further in the context of linear equivalence of divisors. In particular, we formulate and prove a graph-theoretic analogue of the classical Riemann-Roch theorem. We also prove several results, analogous to classical facts about Riemann surfaces, concerning the Abel-Jacobi map from a graph to its Jacobian. As an application of our results, we characterize the existence or non-existence of a winning strategy for a certain chip-firing game played on the vertices of a graph.     

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