Homogenization of a Ginzburg–Landau functional

We consider a nonlinear homogenization problem for a Ginzburg–Landau functional with a (positive or negative) surface energy term describing a nematic liquid crystal with inclusions. Assuming that sizes and distances between inclusions are of the same order ?, we obtain a limiting functional as $?\to 0$. We generalize the method of mesocharacteristics to show that a corresponding homogenized problem for arbitrary, periodic or non-periodic geometries is described by an anisotropic Ginzburg–Landau functional. We give computational formulas for material characteristics of an effective medium. To cite this article: L. Berlyand et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Annihilating measures of the algebra R(X)

A special class of “analytic measures” in the totality of measures orthogonal to the algebra of rational functions on a compact set X?C is introduced. It is proved that there always exist nontrivial (i.e., nonzero) analytic measures provided that R(X) ≠ C(X). We also give sufficient conditions in order to have the linear span of analytic measures be weak (1) dense in the whole annihilator of the algebra R(X).     

Catalytic dehydrogenation of ethanol into acetaldehyde and isobutanol using mono- and multicomponent copper catalysts

The purpose of this work was to investigate biomass-derived ethanol dehydrogenation into acetaldehyde using several mono- and multicomponent (CuO, ZnO and Cr₂O₃)-containing catalysts supported on industrial size Al₂O₃ beads. The catalysts, prepared with either solution combustion or incipient wetness method, were characterized by using various physico-chemical methods, such as EDXA, SEM-EDXA, TEM, XRD, XPS, pyridine adsorption desorption FTIR, and ζ-potential measurements. The results revealed that the multicomponent catalysts exhibited superior activity compared to the metal oxide catalysts containing only one metal oxide. In addition, the most selective catalyst towards acetaldehyde formation, with 50% selectivity at 55% conversion of ethanol at 300 °C and WHSV 1 h^?1 was CuOCr₂O₃/Al₂O₃ prepared by using the solution combustion method, indicating that this inexpensive and rapid catalyst preparation method is promising for other applications.     

Catalytic Oxo/Imido Heterometathesis by a Well‐Defined Silica‐Supported Titanium Imido Complex

Grafting Ti(=NtBu)(Me₂Pyr)₂(py)₂ (Me₂Pyr= 2,5‐dimethylpyrrolyl, py=pyridine) onto the surface of silica partially dehydroxylated at 700 °C gives the well‐defined silica‐supported Ti imido complex (≡SiO)Ti(=NtBu)(Me₂Pyr)(py)₂, which is fully characterized by IR and solid‐state NMR spectroscopy as well as elemental and mass balance analyses. While stoichiometric imido‐transfer reactivity is typical for Ti imides, the obtained surface complex is unique in that it enables catalytic transformations involving Ti imido and oxo intermediates. In particular, it efficiently catalyzes imidation of carbonyl compounds with N‐sulfinylamines by oxo/imido heterometathesis.     

α‐Sila‐Dipeptides: Synthesis and Characterization

The first two α‐sila‐dipeptides, 7 and cyclo‐sila‐dipeptide 8 , were synthesized and characterized by several methods, including X‐ray crystallography. Bulky t‐BuMe₂Si substituents provide some kinetic stabilization to the synthesized molecules. 7 and 8 are the first examples of a “Si for C switch” in the central α‐position of an amino acid or a peptide, in which silicon is bonded to both the amino and the carbonyl groups.     

Dearomatization of oxa- or selenadiazolopyridines with neutral nucleophiles as an efficient approach to pharmacologically relevant nitrogen compounds

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CF3-Carbenoid functionalization of N-(pyrimidin-2-yl)indole catalyzed by cobalt complexes: Ligand control of selectivity

The carbonyl cobalt complex Cp*Co(CO)I₂ catalyzes carbenoid Co alkylation of N-(pyrimidin-2-yl)indole with methyl 3,3,3-trifluoro-2-diazopropionate regioselectively giving 2-substituted indole, while the N,N’-ligated cations [CpCo(L)I]⁺ (L = bipy, phen) provide 3-substitution exclusively. The structure of [CpCo(phen)I]PF₆ was investigated by X-ray diffraction.

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Bohr's power series theorem in several variables

Generalizing a classical one-variable theorem of Bohr, we show that if an -variable power series has modulus less than in the unit polydisc, then the sum of the moduli of the terms is less than in the polydisc of radius .