Fuzzy Markov Chains and Decision-Making

Decision-making in an environment of uncertainty and imprecision for real-world problems is a complex task. In this paper it is introduced general finite state fuzzy Markov chains that have a finite convergence to a stationary (may be periodic) solution. The Cesaro average and the -potential for fuzzy Markov chains are defined, then it is shown that the relationship between them corresponds to the Blackwell formula in the classical theory of Markov decision processes. Furthermore, it is pointed out that recurrency does not necessarily imply ergodicity. However, if a fuzzy Markov chain is ergodic, then the rows of its ergodic projection equal the greatest eigen fuzzy set of the transition matrix. Then, the fuzzy Markov chain is shown to be a robust system with respect to small perturbations of the transition matrix, which is not the case for the classical probabilistic Markov chains. Fuzzy Markov decision processes are finally introduced and discussed.     

Two photon absorption and coherent control with broadband down-converted light

We experimentally demonstrate two-photon absorption with broadband down-converted light (squeezed vacuum). Although incoherent and exhibiting the statistics of a thermal noise, broadband down-converted light can induce two-photon absorption with the same sharp temporal behavior as femtosecond pulses, while exhibiting the high spectral resolution of the narrow band pump laser. Using pulse-shaping methods, we coherently control two-photon absorption in rubidium, demonstrating spectral and temporal resolutions that are 3-5 orders of magnitude below the actual bandwidth and temporal duration of the light itself. Such properties can be exploited in various applications such as spread-spectrum optical communications, tomography, and nonlinear microscopy.     

Facile synthetic access to and biological evaluation of the macrocyclic core of apoptolidin

Oxidative cleavage of the C-20/C-21 bond in apoptolidin (1) provides two fragments of similar complexity, facilitating a divide-and-diversify strategy for the determination of the structural basis for apoptolidin's biological activity, the remarkably selective induction of apoptosis in sensitive cell lines. The ability of compounds derived from this cleavage to inhibit mitochondrial F(0)F(1)-ATPase is reported. [structure: see text]     

Probabilistic representation and approximation for coupled systems of variational inequalities

Our study is dedicated to the probabilistic representation and numerical approximation of solutions of coupled systems of variational inequalities. We interpret the unique viscosity solution of a coupled system of variational inequalities as the solution of a one-dimensional constrained BSDE with jumps. This new representation allows for the introduction of a natural probabilistic numerical scheme for the resolution of these systems.     

Sur les représentations linéaires des groupes clos

Sans résumé     

Surface morphology of Ge‐modified 3C‐SiC/Si films

The influence of Ge deposition prior to carbon interaction with 3° off‐axis Si(111) substrates on the structural and morphological properties of the formed silicon carbide (SiC) layer is studied. In situ reflection high‐energy electron diffraction (RHEED) and X‐ray diffraction (XRD) revealed the formation of the cubic silicon carbide (3C‐SiC) modification. In situ spectroscopic ellipsometry measurements revealed a decreasing 3C‐SiC thickness with increasing Ge predeposition. Atomic force microscopy (AFM) studies revealed that the surface overlayer morphology is mainly formed by periodic step arrangements whose relevant geometric parameters, i.e. lateral separation, height and terrace width, depend on the Ge content. Besides the changes of the step morphology, the surface roughness and the grain size and the strain of the formed 3C‐SiC decreases with increasing germanium precoverage. Copyright © 2008 John Wiley & Sons, Ltd.     

SiC polytypes process affected by Ge predeposition on Si(111) substrates

Structural and optical measurements were performed on silicon carbide (SiC) samples containing several polytypes. The SiC samples investigated were grown on (111) Si substrates by solid source molecular beam epitaxy (SSMBE). Several quantities of Ge were predeposited before the growth procedure. The influence of Ge on the SiC polytypes formation was studied by X-Ray, FTIR and μ-Raman characterizations methods. The spectra of the samples with less than one Ge monolayer exhibit a mixture of 2H, 15R and 3C–SiC polytypes. This mixture is due to the mismatch between the heterostructure layers. We propose that the Ge predeposition in the heterostructure can be used to stabilize and unify the polytypes formation.     

Sur des familles remarquables d'hypersurfaces isoparamétriques dans les espaces sphériques

Sans résumé     

Synthesis,Crystal Structure and IR Spectra of Complexes of Mn(II) by Indole-2-Carboxylic or Isoquinoline-1-Carboxylic Acids and 1,10-Phenanthroline

Abstract  

Two ternary complexes of manganese(II) indole-2-carboxylate (2-IC⁻) or isoquinolinecarboxylate (IQC⁻) with 1,10-phenanthroline (phen) in methanol or in dimethylacetamide (DMA) were synthesized and studied by X-ray diffraction and IR spectra. [Mn(C₉H₆NO₂)₂(C₁₂H₈N₂)₂]·CH₄O (1) crystallizes in the triclinic space group P-1 with cell parameters of a = 10.548(2) ?, b = 14.168(3) ?, c = 14.580(3) ?, α = 62.35(2)°, β = 69.16(2)°, γ = 78.61(2)°, V = 1802.4(6) ?³ and Z = 2; [Mn(C₁₀H₆NO₂)₂(C₁₂H₈N₂)].C₄H₉NO (2) crystallizes in the monoclinic space group P2₁/a with cell parameters of a = 15.304(5) ?, b = 12.871(5) ?, c = 17.421(5) ?, β = 114.39(1), V = 3125(2) ?³ and Z = 4. In 1, Mn is six-coordinate by two bidentate phen ligands and two 2-IC⁻ ligands and exhibits a very distorted octahedral geometry. This complex is solvated by methanol involved in hydrogen bonding. In 2, Mn atom is surrounded by one bidentate phen ligand and two bidentate IQC⁻ ligands. The complex exhibits a distorted octahedral geometry around the Mn^II atom. The crystal structure is completed by a disordered DMA solvate molecule. The IR spectra of both compounds are slightly different in the range 4000–2400 cm⁻¹ which may be attributed to hydrogen bond lack in 2.