Trigonometric moment problems for arbitrary finite subsets of

We consider finite subsets satisfying the extension property, i.e. the property that every collection of complex numbers which is positive-definite on is the restriction to of the Fourier coefficients of some positive measure on . A simple algebraic condition on the set of trigonometric polynomials with non-zero coefficients restricted to is shown to imply the failure of the extension property for . This condition is used to characterize the one-dimensional sets satisfying the extension property and to provide many examples of sets failing to satisfy it in higher dimensions. Another condition, in terms of unitary matrices, is investigated and is shown to be equivalent to the extension property. New two-dimensional examples of sets satisfying the extension property are given as well as explicit examples of collections for which the extension property fails.

     

Hemoabzymes different strategies for obtaining artificial hemoproteins based on antibodies

Besides existing models of chemical or biotechnological origin for hemoproteins like peroxidases and cytochromes P450, catalytic antibod ies (Abs) with a metalloporphyrin cofactor represent a promising alter native route to catalysts tailored for selective oxidation reactions. A brief overview of the literature shows that, until now, the first strategy for obtaining such artificial hemoproteins has been to produce antipor phyrin Abs, raised against various free-base, N-substituted, Sn-,Pd-,or Fe-porphyrins. Four of them exhibited, in the presence of the corre sponding Fe-porphyrin cofactor, a significant peroxidase activity, with k_cat/K_m values of 10² to 5 × 10³/M/s. This value remained low when com pared to that of peroxidases, probably because neither a proximal ligand of the Fe, nor amino acid residues participating in the catalysis of the heterolytic cleavage of the O—O bond of H₂O₂, have been induced in those Abs. This strategy has been shown to be insufficient for the elabo ration of effective models of cytochromes P450, because only one set of Abs, raised againstmeso-tetrakis(para-carboxyvinylphenyl)porphyrin, was reported to catalyze the nonstereoselective oxidation of styrene by iodosyl benzene using a Mn-porphyrin cofactor, and attempts to gener ate Abs having binding sites for both the substrate and the metallopor phyrin cofactor, using as a hapten a porphyrin covalently linked to the substrate, were not successful. A second strategy is then proposed, which involves the chemical labeling of antisubstrate Abs with a metallopor phyrin. As an example, preliminary results are presented on the covalent linkage of an Fe-porphyrin to an antiestradiol Ab, in order to obtain semisynthetic catalytic Abs able to catalyze the selective oxidation of steroids.     

A remark on Carathéodory balls

Member of URA CNRS D 1322 Groupes de Lie et Géométrie     

A global attracting set for the Kuramoto-Sivashinsky equation

New bounds are given for the L²-norm of the solution of the Kuramoto-Sivashinsky equation $$\partial _t U(x,t) = - (\partial _x^2 + \partial _x^4 )U(x,t) - U(x,t)\partial _x U(x,t)$$ , for initial data which are periodic with periodL. There is no requirement on the antisymmetry of the initial data. The result is $$\mathop {\lim \sup }\limits_{t \to \infty } \left\| {U( \cdot ,t)} \right\|_2 \leqslant const. L^{8/5} $$ .     

Electrophilic Nitration of Electron-Rich Acetophenones

Summary. It is demonstrated that electron-rich disubstituted acetophenones react according to various electrophilic nitration conditions that generally lead to ipso substitution accompanying the conventional reaction. The hydroxy substituent does not seem prone to favor such behaviour.     

Novel synthetic approach for optical resolution of cryptophanol-A: a direct access to chiral cryptophanes and their chiroptical properties

The separation by crystallization of the pair of cryptophane diastereomers 1 a and 1 b, obtained in 1:1 ratio by treating racemic anti cryptophanol-A (2) with (-)-camphanic acid chloride, provided a substantial amount of optically pure material (diastereomeric excess>98 %). Subsequent hydrolysis afforded the optically pure cryptophanol-A enantiomers (+)-2 and (-)-2, which were submitted to nucleophilic substitution reactions to provide cryptophane-A (+)-3 and cryptophane monoester (-)-4 in optically pure form. The chiroptical properties of the new cryptophanes 1-4 were investigated by using circular dichroism spectroscopy, and the absolute configuration of the molecules was clearly established. These new cryptophanes represent additional interesting examples for studying the Cotton effect of interacting multichromophoric systems. Moreover, this novel approach presents numerous advantages over the other methods developed so far to obtain optically pure cryptophanes, and compounds (-)-2, (+)-2, and (-)-4 can give access to new enantiopure functionalized cryptophanes with host-guest properties similar to those of cryptophane-A.