Lack of Invariant Property of the Erlang Loss Model in Case of <Emphasis Type="Italic">MAP</Emphasis> Input

The BMAP/PH/N/0 model with three different disciplines of admission (partial admission, complete rejection, complete admission) is investigated. Loss probability is calculated. Impact of the admission discipline, variation and correlation coefficients of inter-arrival times distribution, and variation of service times distribution on loss probability is analyzed numerically. As by-product, it is shown by means of numerical results that the invariant property of the famous Erlang M/G/N/0 system, which was proven by B. A. Sevastjanov, is absent in case of the MAP input. AMS subject classification: Primary 60K25, 60K20 This revised version was published online in June 2005 with corrected coverdate     

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.     

Oxidative Coupling of Anionic Abnormal N‐Heterocyclic Carbenes: Efficient Access to Janus‐Type 4,4′‐Bis(2H‐imidazol‐2‐ylidene)s

The oxidative coupling of anionic imidazol‐4‐ylidenes protected at the C2 position with [MnCp(CO)₂] or BH₃ led to the corresponding 4,4′‐bis(2H‐imidazol‐2‐ylidene) complexes or adducts, in which the two carbene moieties are connected through a single C?C bond. Subsequent acidic treatment of the later species led to the corresponding 4,4′‐bis(imidazolium) salts in good yields. The overall procedure offers practical access to a novel class of Janus‐type bis(NHC)s. Strikingly, the coplanarity of the two NHC rings within the mesityl derivative 4,4′‐bis(IMes), favored by steric hindrance along with stabilizing intramolecular C?H???π aryl interactions, allows the alignment of the π‐systems and, as a direct consequence, significant electron communication through the bis(carbene) scaffold.     

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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