Maximum directed cuts in digraphs with degree restriction

For integers m, k≥1, we investigate the maximum size of a directed cut in directed graphs in which there are m edges and each vertex has either indegree at most k or outdegree at most k. © 2009 Wiley Periodicals, Inc. J Graph Theory     

Synthesis of novel alkylamino zinc(II) phthalocyanines

The synthesis of tetramethyl‐tetraphthalimidomethyl‐phthalocyaninato zinc(II) ( 6 ) and tetramethyl‐tetraaminomethyl‐phthalocyaninato zinc(II) ( 7 ) is described.     

Crosslinking and ageing of C labelled polyisoprene part 1: Synthesis and polymerisation of 4-C-isoprene

4-¹³C-isoprene was prepared by the Wittig reaction. All reaction steps were optimised using unlabelled compounds. By reaction with triphenyl phosphine, ¹³C labelled methyl iodide afforded labelled methyl-triphenyl phosphine iodide in 84% yield. This reacted with meth acrolein with production of 4-¹³C-isoprene in 64% yield. Labelled polyisoprene was prepared by anionic polymerisation initiated by t-butyl lithium. Based on ¹³CH₃I the overall yield is ca 30%. The polymer was characterized by ¹H and ¹³C NMR spectroscopy. The contribution of each microstructure was [cis 1-4, 72%]; [trans 1-4, 10%]; [3-4, 18%].     

New access to 1,3-diketones from aldehydes

A simple and efficient methodology to introduce an 1,3-diketone motif from various aldehyde precursors in three steps with good overall yields is described using β-ketosulphone 7 as masked equivalent of acetone.     

High-resolution heteronuclear correlation spectroscopy in solid state NMR of aligned samples

A new two-dimensional scheme is proposed for accurate measurements of high-resolution chemical shifts and heteronuclear dipolar couplings in NMR of aligned samples. Both the (1)H chemical shifts and the (1)H-(15)N dipolar couplings are evolved in the indirect dimension while the (15)N chemical shifts are detected. This heteronuclear correlation (HETCOR) spectroscopy yields high-resolution (1)H chemical shifts split by the (1)H-(15)N dipolar couplings in the indirect dimension and the (15)N chemical shifts in the observed dimension. The advantages of the HETCOR technique are illustrated for a static (15)N-acetyl-valine crystal sample and a (15)N-labeled helical peptide sample aligned in hydrated lipid bilayers.     

Design and synthesis of novel spirocyclopropyl cyclohexane-1,3-diones and -1,3,5-triones for their incorporation into potent HPPD inhibitors

We report the design and the efficient synthesis of novel spirocyclopropyl cyclohexane-1,3-dione and -1,3,5-trione units to be incorporated into potent HPPD inhibitors. New routes involving original combinations of synthetic equivalents of α-cyclopropyl ketone-α-anion and α-cyclopropyl ester-β-cation are described.     

Optical characterization of photochromic effect

Photochromic powders are powders whose color is sensitive to UV irradiation. When such a powder is exposed to the sunlight or any other UV rays, it becomes darker and then looks back progressively to its initial color. An optical method has been set up in order to quantify these colors variations. We can then quantify the variations in the colorimetric space, and the time response of the coming back phenomenon.     

Sur les oscillations du processus de Poisson composéOn the oscillations of compound empirical processes

In this paper, we describe the local behaviour of compound Poisson processes based on a Poisson process and a sequence of independent and identically distributed random weights. These results are motived by their natural counterparts in the theory of empirical processes. To cite this article: M. Maumy, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 705–708.