Arbres de Markov Triplet et fusion de Dempster–Shafer

The hidden Markov chains (HMC) (X,Y) have been recently generalized to triplet Markov chains (TMC), which enjoy the same capabilities of restoring a hidden process X from the observed process Y. The posterior distribution of X can be viewed, in an HMC, as a particular case of the so called “Dempster–Shafer fusion” (DS fusion) of the prior Markov with a probability q defined from the observation Y=y. As such, when we place ourselves in the Dempster–Shafer theory of evidence by replacing the probability distribution of X by a mass function M having an analogous Markov form (which gives again the classical Markov probability distribution in a particular case), the result of DS fusion of M with q generalizes the conventional posterior distribution of X. Although this result is not necessarily a Markov distribution, it has been recently shown that it is a TMC, which renders traditional restoration methods applicable. The aim of this Note is to present some generalizations of the latter result: (i) more general HMCs can be considered; (ii) q, which can possibly be a mass function Q, is itself a result of the DS fusion; and (iii) all these results are finally specified in the hidden Markov trees (HMT) context, which generalizes the HMC one. To cite this article: W. Pieczynski, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Homomo rphisms of the g roup $$L^1_s$$ into the g roup $$L^1_ r$$ fo r r ≤ 3

We determine all homomorphisms of the differential group L¹_sL^1_s with arbitrary s ≥ 2 into the group L¹_rL^1_r for r ≤  3.     

Towards a metallic quasi‐d9 system without copper: AgO at high pressure

AgO is a prototypical mixed‐valence compound, with markedly different coordination environment of dumbbell Ag(1+) and low‐spin square‐planar Ag(3+) which render it a narrow band gap semiconductor. The hybrid HSE06 functional reproduces fairly well the band gap of its P 2₁/c form at ambient conditions (ΔE_exp = 1.0–1.1 eV, ΔE_theor = 0.94 eV) and suggest progressive band gap decrease with external pressure with metallization at 50 GPa via band overlap. Dynamic (phonon) instability appears at the onset of metallization leading to a structural phase transition to a more stable but still metallic $$P\stackrel{?}{1}$$ form. The density of electronic states at the Fermi level of the $$P\stackrel{?}{1}$$ polymorph is small and a pseudo‐gap at the Fermi level is preserved.

Illustration of the predicted P2₁/c → $$P\stackrel{?}{1}$$ transformation.     

Local Symmetry Group in the General Theory of Elastic Shells

We establish the local symmetry group of the dynamically and kinematically exact theory of elastic shells. The group consists of an ordered triple of tensors which make the shell strain energy density invariant under change of the reference placement. Definitions of the fluid shell, the solid shell, and the membrane shell are introduced in terms of members of the symmetry group. Within solid shells we discuss in more detail the isotropic, hemitropic, and orthotropic shells and corresponding invariant properties of the strain energy density. For the physically linear shells, when the density becomes a quadratic function of the shell strain and bending tensors, reduced representations of the density are established for orthotropic, cubic-symmetric, and isotropic shells. The reduced representations contain much less independent material constants to be found from experiments.     

Ferrocene‐Donor and 4,5‐Dicyanoimidazole‐Acceptor Moieties in Charge‐Transfer Chromophores with π Linkers Tailored for Second‐Order Nonlinear Optics

A series of new nonlinear optical chromophores ( 1 – 15 ) that were comprised of ferrocene‐donor and 4,5‐dicyanoimidazole‐acceptor moieties and various π linkers of different length were synthesized. Support for the presence of significant D ? A interactions in these NLO‐phores was obtained from the evaluation of the quinoid character of the 1,4‐phenylene moieties and their electronic absorption spectra, which featured intense high‐energy (HE) bands that were accompanied by less‐intense low‐energy (LE) bands. The redox behavior of these compounds was investigated by cyclic voltammetry (CV) and by rotating‐disc voltammetry (RDV); their electrochemical gaps decreased steadily from 2.64 to 2.09 V. In addition to the experimentally obtained data, DFT calculations of their absorption spectra, HOMO/LUMO levels, and second‐order polarizabilities (β) (?2ω,ω,ω) were performed. A structure–property relationship study that was performed by systematically altering the π linker revealed that the intramolecular charge‐transfer and nonlinear optical properties of these inorganic–organic hybrid D? π? A systems ( 1 – 15 ) were primarily affected by: 1) The presence of olefinic/acetylenic subunits; 2) the length of the π linker; and 3) the spatial arrangement (planarity) of the π linker.     

Porosity of closed carbon nanotubes compressed using hydraulic pressure

Experimental data of nitrogen adsorption (T = 77.3 K) from gaseous phase measured on commercial closed carbon nanotubes are presented. Additionally, we show the results of N₂ adsorption on compressed (using hydraulic press) CNTs. In order to explain the experimental observations the results of GCMC simulations of N₂ adsorption on isolated or bundled multi-walled closed nanotubes (four models of bundles) are discussed. We show that the changes of the experimental adsorption isotherms are related to the compression of the investigated adsorbents. They are qualitatively similar to the theoretical observations. Taking into account all results it is concluded that in the “architecture” of nanotubes very important role has been played by isolated nanotubes.     

Abnormal Ionic Conductivities in Halide NaBi3O4Cl2 Induced by Absorbing Water and a Derived Oxhydryl Group

In hunting for safe and cost‐effective materials for post‐Li‐ion energy storage, the design and synthesis of high‐performance solid electrolytes (SEs) for all‐solid‐state batteries are bottlenecks. Many issues associated with chemical stability during processing and storage and use of the SEs in ambient conditions need to be addressed. Now, the effect of water as well as oxyhdryl group (^.OH) on NaBi₃O₄Cl₂ are investigated by evaluating ionic conductivity. The presence of water and ^.OH results in an increase in ionic conductivity of NaBi₃O₄Cl₂ owing to diffusion of H₂O into NaBi₃O₄Cl₂, partially forming binding ^.OH through oxygen vacancy repairing. Ab initio calculations reveal that the electrons significantly accumulate around ^.OH and induce a more negative charge center, which can promote Na⁺ hopping. This finding is fundamental for understanding the essential role of H₂O in halide‐based SEs and provides possible roles in designing water‐insensitive SEs through control of defects.     

Ultrafast Excited State Dynamics in a First Generation Photomolecular Motor

Efficient photomolecular motors will be critical elements in the design and development of molecular machines. Optimisation of the quantum yield for photoisomerisation requires a detailed understanding of molecular dynamics in the excited electronic state. Here we probe the primary photophysical processes in the archetypal first generation photomolecular motor, with sub-50 fs time resolved fluorescence spectroscopy. A bimodal relaxation is observed with a 100 fs relaxation of the Franck-Condon state to populate a red-shifted state with a reduced transition moment, which then undergoes multi-exponential decay on a picosecond timescale. Oscillations due to the excitation of vibrational coherences in the S₁ state are seen to survive the ultrafast structural relaxation. The picosecond relaxation reveals a strong solvent friction effect which is thus ascribed to torsion about the C−C axle. This behaviour is contrasted with second generation photomolecular motors; the principal differences are explained by the existence of a barrier on the excited state surface in the case of the first-generation motors which is absent in the second generation. These results will help to provide a basis for designing more efficient molecular motors in the future.