Quantum automorphism groups of finite graphs

A quantum analogue of the automorphism group of a finite graph is introduced. These are quantum subgroups of the quantum permutation groups defined by Wang. The quantum automorphism group is a stronger invariant for finite graphs than the usual automorphism group. We get a quantum dihedral group .

     

Nanoscopic scale studies of LiFePO4 as cathode material in lithium-ion batteries for HEV application

We present a review of the structural properties of LiFePO₄. Depending on the mode of preparation, different impurities can poison this material. These impurities are identified and a quantitative estimate of their concentrations is deduced from the combination of X-ray diffraction analysis, Fourier transform infrared spectroscopy, Raman spectroscopy, and magnetic measurements. An optimized preparation provides samples with carbon-coated particles free of any impurity phase, insuring structural stability and electrochemical performance that justify the use of this material as a cathode element a new generation of lithium secondary batteries.     

Nanocrystalline Li<Subscript>2</Subscript>TiO<Subscript>3</Subscript> electrodes for supercapattery application

Nanocrystalline Li₂TiO₃ was successfully synthesized using solid-state reaction method. The microstructural and electrochemical properties of the prepared material are systematically characterized. The X-ray diffraction pattern of the prepared material exhibits predominant (002) orientation related to the monoclinic structure with C2/c space group. HRTEM images and SAED analysis reveal the well-developed nanostructured particles with average size of ～40 nm. The electrochemical properties of the prepared sample are carried out using cyclic voltammetry (CV) and chronopotentiometry (CP) using Pt//Li₂TiO₃ cell in 1 mol L^?1 Li₂SO₄ aqueous electrolyte. The Li₂TiO₃ electrode exhibits a specific discharge capacity of 122 mAh g^?1; it can be used as anode in Li battery within the potential window 0.0–1.0 V, while investigated as a supercapacitor electrode, it delivers a specific capacitance of 317 F g^?1 at a current density of 1 mA g^?1 within the potential range ?0.4 to +0.4 V. The demonstration of both anodic and supercapacitor behavior concludes that the nanocrystalline Li₂TiO₃ is a suitable electrode material for supercapattery application.     

Decomposing Oriented Graphs into Six Locally Irregular Oriented Graphs

An undirected graph G is locally irregular if every two of its adjacent vertices have distinct degrees. We say that G is decomposable into k locally irregular graphs if there exists a partition \(E_1 \cup E_2 \cup \cdots \cup E_k\) of the edge set E(G) such that each \(E_i\) induces a locally irregular graph. It was recently conjectured by Baudon et al. that every undirected graph admits a decomposition into at most three locally irregular graphs, except for a well-characterized set of indecomposable graphs. We herein consider an oriented version of this conjecture. Namely, can every oriented graph be decomposed into at most three locally irregular oriented graphs, i.e. whose adjacent vertices have distinct outdegrees? We start by supporting this conjecture by verifying it for several classes of oriented graphs. We then prove a weaker version of this conjecture. Namely, we prove that every oriented graph can be decomposed into at most six locally irregular oriented graphs. We finally prove that even if our conjecture were true, it would remain NP-complete to decide whether an oriented graph is decomposable into at most two locally irregular oriented graphs.     

Layer-by-layer self-assembled polyelectrolyte multilayers with embedded liposomes: immobilized submicronic reactors for mineralization

The development of chemical reactions in nanospaces is of paramount importance for the development of active nanodevices, particularly in nanofluidics. It has been shown in a previous paper that phospholipid vesicles can be incorporated without spontaneous bilayer rupture into poly-L-glutamic acid/poly(allylamine) (PGA/PAH) multilayered polyelectrolyte films. The aim of the present study was to use such a system as an "embedded submicronic reactor" able to trigger precipitation of calcium phosphates within closed spaces through an enzymatic reaction, the enzyme also being encapsulated in the vesicle interior. To this aim, large unilamellar vesicles (LUVs) were produced containing calcium ions as active ions in the mineralization process, spermine as an activator of crystal growth, and alkaline phosphatase as a catalyst to convert phosphate esters into phosphates. After stabilization by adding a layer of poly-(D-lysine), these vesicles were embedded in a (PGA-PAH)n film. A paranitrophenyl phosphate containing solution was then put in contact with this film. It is shown by means of infrared spectroscopy in the attenuated total reflection mode that, consecutively to this contact, calcium phosphates are growing inside the embedded vesicles. By using scanning near-field fluorescence microscopy, it is demonstrated that the alkaline phosphatase enzymes are most probably located inside the vesicles after their embedding. In addition, atomic force microscopy was used to show, after chemical removal of the organic top layer of the film, that the inorganic platelets produced after the precipitation reaction are localized in volumes of similar size and shape as that of the vesicles into which the phosphate ester hydrolysis and subsequent precipitation reaction did occur.     

Simulation du drapé des tissus par maillages adaptatifsAdaptive meshing for cloth draping

Numerical simulation methods regarding fabric and cloth draping are generally based on mechanical models. These models are usually applied to uniform grids representing the true geometry of the fabric. Fabrics being a very flexible material, wrinkles appear on its surface when submitted to free or constrained motion. The main problem of the simulation is to represent realistically cloth surface motion. This is strongly dependent on the surface discretization. We present a new cloth animation scheme based on adaptive surface discretization. It can be seen as a multi-grid method which allows us to obtain realistic simulations. We propose also a new mechanical model well suited to our adaptive meshing strategy. A numerical example is given to show the efficiency of the method. To cite this article: J. Villard et al., C. R. Acad. Sci. Paris, Ser. I 335 (2002) 561–566.     

Regio- and stereoselectivities in Diels-Alder cyclodimerizations of orthoquinonoid cyclohexa-2,4-dienones

The [4+2] cyclodimerization of cyclohexa-2,4-dienone derivatives of the orthoquinone monoketal and orthoquinol types has been the topic of numerous investigations over the last 50 years in the aim of rationalizing the extraordinary level of regio-, site-, and stereoselectivities observed in these processes. In particular, the double diastereo-π-facial differentiation expressed in cyclodimerizations of chiral orthoquinols (i.e., 6-alkyl-6-hydroxycyclohexa-2,4-dienones) is an important aspect of these transformations, for they relate to the construction of several natural products. The experimental and theoretical results that are described in this article offer a comprehensive understanding of the factors controlling these site-specific regio- and diastereoselectivities. Our interpretation of these results relies on a combination of Woodward-Hoffmann and Salem-Houk secondary orbital interactions and Cieplak-type hyperconjugative effects in bispericyclic C₂-symmetric transition states.     

Automated analysis of geosmin, 2-methyl-isoborneol, 2-isopropyl-3-methoxypyrazine, 2-isobutyl-3-methoxypyrazine and 2,4,6-trichloroanisole in water by SPME-GC-ITDMS/MS

This paper describes a method of determining the following compounds in water characterised by complex matrices (raw waters and drinking waters): geosmin, 2-methylisoborneol (2-MIB), 2-isobutyl-3-methoxypyrazine (IBM), 2-isopropyl-3-methoxypyrazine (IPM) and 2,4,6-trichloroanisole (TCA). The method is carried out using headspace solid-phase microextraction (HS-SPME) combined with gas chromatography (GC) and ion trap mass spectrometry (ITMS). Several parameters of extraction and desorption were optimised through the use of a Combi PAL autosampler to automate various tasks (temperature extraction, extraction time, stir speed). Quantities of NaCl and the liquid volume/total volume ratio were also optimised. Double fragmentation (tandem MS/MS) was optimised on the target compounds. The method resulted in good linearity obtained for concentrations of 1 to 100?ng?L^?1 and provided detection limits of approximately below 1?ng?L^?1. Good precision (1–8%) was obtained. This method was successfully applied to the analysis of earthy and musty odours in municipal raw source waters with high concentrations of natural organic matter and in the corresponding treated waters. This is the first time MS/MS has been used to analyse odorous compounds in waters destined for human consumption. In addition, the method as developed is simple to use and lends itself to easy interpretation of chromatograms.     

Measurement of Aluminum–Carbon Distances Using S‐RESPDOR NMR Experiments

It is demonstrated that reliable aluminum–carbon distances can be measured in samples with ¹³C natural abundance by NMR spectroscopy. Overcoupled resonators, with only one radio‐frequency synthesizer and one amplifier, are used to irradiate in the same pulse sequence ²⁷Al and ¹³C nuclei, which differ by only 3.6 % in Larmor frequencies. The combination of ²⁷Al saturation pulse with heteronuclear dipolar recoupling yields dipolar dephasing of the ¹³C signal, which only depends on the Al? C distance and the efficiency of the saturation pulse. Therefore, reliable distances can be obtained by rapid fitting of experimental data to an analytical expression. It is demonstrated that with natural isotopic abundance this approach allows recovery of Al? C distances of 216 pm for the covalent bond in lithium tetraalkyl aluminates, commonly used as a co‐catalyst in olefin polymerization processes, and which range from 274 to 381 pm for the three carbon atoms in aluminum lactate. The accuracy of the measured internuclear distances is carefully estimated.     

Stereoselective functionalization of pyrrolidinone moiety towards the synthesis of salinosporamide A

An important feature of the synthesis of salinosporamide A, a potent proteasome inhibitor, is the establishment of the quaternary stereocenter at C3. A new route has been developed based on the methylation of a functionalized pyrrolidinone. Direct methylation reaction led to the unwanted diastereomer; however, by means of a Corey–Chaykovsky reaction followed by LiAlH₄ epoxide opening, the desired alcohol was obtained. The pyrrolidinone was elaborated through a key allylation reaction between a tertiary allyltitanium reagent and an aldehyde bearing a spiroketal moiety in α-position.