Approximation du temps local des surfaces gaussiennes

Summary LetX be a centered stationary Gaussian stochastic process with ad-dimensional parameter (d2),F its spectral measure, (x denotes the Euclidean norm ofx). We consider regularizations of the trajectories ofX by means of convolutions of the formX (t)=( *X)(t) where stands for an approximation of unity (as tends to zero) satisfying certain regularity conditions.The aim of this paper is to recover the local time ofX at a given levelu, as a limit of appropriate normalizations of the geometric measure of theu-level set of the regular approximating processesX . A part of the difficulties comes from the fact that the geometric behavior of the covariance of the Gaussian processX can be a complex one as approaches O.The results are onL ²-convergence and include bounds for the speed of convergence.L ^presults may be obtained in similar ways, but almost sure convergence or simultaneous convergence for the various values ofu do not seem to follow from our methods. In Sect. 3 we have included examples showing a diversity of geometric behaviors, especially in what concerns the dependence on the thickness of the set in which the covariance of the original processX is irregular.Some technical results of analytic nature are included as appendices in Sect. 4.     

Probing adsorbed fibronectin layer structure by kinetic analysis of monoclonal antibody binding

Adsorbed protein layers are often away from equilibrium and thus exhibit history dependent structures. We use the kinetics of monoclonal antibody binding, as measured using optical waveguide lightmode spectroscopy (OWLS), to investigate the structure of adsorbed fibronectin (Fn) layers formed under different kinetic paths. For all of the layers investigated, we find no difference between the apparent adsorption rate constants of (i) monoclonal antibodies specific to Fn's cell binding site (alpha-Fn) and (ii) monoclonal antibodies specific to cytochrome c (alpha-CC, as a control), indicating initial adsorption of antibodies to be non-specific. For certain layers, the saturation density and the initial projected area per antibody differ significantly between alpha-Fn and alpha-CC, suggesting specific binding to follow the initial non-specific attachment. The fraction of antibodies binding specifically to the Fn layer, and the number of Fn binding sites per specific binding event, are estimated in terms of the difference in initial projected areas between alpha-Fn and alpha-CC. For a Fn layer formed at a bulk concentration of 2 microg/mL, we find a decrease in specific binding with an increase in Fn layer formation time, suggesting post-adsorption structural changes of a lower density adsorbed layer diminish binding site availability. Conversely, for a Fn layer formed at a bulk concentration of 40 microg/mL, we find an increase in specific binding with an increase in the aging time of the Fn layer, implying post-adsorption structural changes reveal binding sites for a higher density adsorbed layer.     

Probing electrochemical properties of pi-conjugated thienylenevinylenes/fullerene C(60) adducts by ESI/MS: evidence for dimerized cation-radicals

Oligothienylenevinylenes/C(60) dyads n-C and triads n-C(2) are studied by electrospray mass spectrometry. A clear correlation is observed between the nature of the charged species detected by mass spectrometry, i.e. protonated molecule [M + H], (+) cation radical M(+.) and dication M(++), and the oxidation potentials of the molecules. Moreover, under defined solubility conditions, mass spectrometry provides conclusive evidences for the reversible dimerization of cation-radicals of n-C(2) compounds.     

Comprehensive photokinetic and NMR study of a biphotochromic supermolecule involving two naphthopyrans linked to a central thiophene unit through acetylenic bonds

A photophysical and photochemical study of a biphotochromic compound where two naphthopyran units are linked by an acetylene-thiophene-acetylene bridge has been carried out in toluene. Both fluorescence and intersystem crossing to the triplet manifold were found to compete with the photocoloration process. Two photoproducts (transoid-trans and transoid-cis stereoisomers), absorbing at approximately 480 nm and corresponding to the opening of a single photochromic unit, were detected by spectrophotometric analysis after short irradiation time in diluted solution and identified by 1H-nuclear magnetic resonance (NMR) spectroscopy. After prolonged irradiation at 228 K of highly concentrated solutions (up to 3 x 10(-3) mol dm(-3)), two additional isomers, absorbing at approximately 550 nm, were formed. Their NMR spectra indicate the opening of both photochromic units. An interesting effect of selective vibronic excitation was found, showing that the photoreaction is favored at excited vibronic levels to the detriment of the radiative relaxation.     

Efficient access to functionalised medium-ring systems by radical fragmentation/radical addition to α-iodoketones

Functionalised medium-ring systems of various sizes can be efficiently prepared by a novel approach that embodies a radical-induced fragmentation of bicyclic β-hydroxy ketones, followed by a second radical-coupling reaction. The unexpected reactivity of α-keto radicals is also discussed.     

A method for the systematic resolution of unbranched α-acetoxyalkyl- and aralkylaldehydes: synthesis of 11R and 11S-hete

It is shown that oxazolidines derived from racemic unbranched α-acetoxyaldehydes and ?-ephedrine have predictable chromatographic mobilities, with the R-isomer always having a higher R_f-value. This resolution has been used to prepare $\text{11R}$ and $\text{11S}$-HETE.     

Methanofullerene Molecular Scaffolding: Towards C60-substituted poly(triacetylenes) and expanded radialenes,preparation of a C60–C70 hybrid derivative,and a novel macrocyclization reaction

The synthesis of (E)-hex-3-ene-l, 5-diynes and 3-methylidenepenta-1, 4-diynes with pendant methano[60]-fullerene moieties as precursors to C₆₀-substituted poly(triacetylenes) (PTAs, Fig. 1) and expanded radialenes (Fig. 2) is described. The Bingel reaction of diethyl (E)-2, 3-dialkynylbut-2-ene-1, 4-diyl bis(2-bromopropane-dioates) 5 and 6 with two C₆₀ molecules (Scheme 2) afforded the monomeric, silyl-protected PTA precursors 9 and 10 which, however, could not be effectively desilylated (Scheme 4). Also formed during the synthesis of 9 and 10 , as well as during the reaction of C₆₀ with thedesilylated analogue 16 (Scheme 5 ), were the macrocyclic products 11, 12 , and 17 , respectively, resulting from double Bingel addition to one C-sphere. Rigorous analysis revealed that this novel macrocyclization reaction proceeds with complete regio- and diastereoselectivity. The second approach to a suitable PTA monomer attempted N, N′-dicyclohexylcarbodiimide(DCC)-mediated esterification of (E)-2, 3-diethynylbut-2-ene-l, 4-diol ( 18 , Scheme 6) with mono-esterified methanofullerene-dicarboxylic acid 23 ; however, this synthesis yielded only the corresponding decarboxylated methanofullerene-carboxylic ester 27 (Scheme 7). To prevent decarboxylation, a spacer was inserted between the reacting carboxylic-acid moiety and the methane C-atom in carboxymethyl ethyl 1, 2-methano[60]fullerene-61, 61-dicarboxylate ( 28 , Scheme 8), and DCC-mediated esterification with diol 18 afforded PTA monomer 32 in good yield. The formation of a suitable monomeric precursor 38 to C₆₀-substituted expanded radialenes was achieved in 5 steps starting from dihydroxyacetone (Schemes 9 and 10), with the final step consisting of the DCC-mediated esterification of 28 with 2-[1-ethynyl(prop-2-ynylidene)]propane-1, 3-diol ( 33 ). The first mixed C₆₀-C₇₀ fullerene derivative 49 , consisting of two methano[60]fullerenes attached to a methano[70]fullerene, was also prepared and fully characterized (Scheme 13). The C_s-symmetrical hybrid compound was obtained by DCC-mediated esterification of bis[2-(2-hydroxy-ethoxy)ethyl] 1, 2-methano[70]fullerene-71, 71-dicarboxylate ( 46 ) with an excess of the C₆₀-carboxylic acid 28 . The presence of two different fullerenes in the same molecule was reflected by its UV/VIS spectrum, which displayed the characteristic absorption bands of both the C₇₀ and C₆₀ mono-adducts, but at the same time indicated no electronic interaction between the different fullerene moieties. Cyclic voltammetry showed two reversible reduction steps for 49 , and comparison with the corresponding C₇₀ and C₆₀ mono-adducts 46 and 30 indicated that the three fullerenes in the composite fullerene compound behave as independent redox centers.     

A L-RNA aptamer chiral stationary phase for the resolution of target and related compounds

In this paper, we report for the first time an aptamer-based chiral stationary phase (CSP) able to resolve racemates of both target and various related compounds. The enantiomers of tyrosine and analogues (11 enantiomeric pairs) were separated using an immobilized tyrosine-specific L-RNA aptamer as CSP and an aqueous buffer (8 mM Tris-HCl buffer, 25 mM NaCl, 5 mM MgCl2; pH 7.4) as mobile phase, at a column temperature of 10 degrees C. It appeared that the carboxylic and amino groups as well as the aromatic side chain of amino acid controlled the stereospecific recognition. Modifications on the polar groups were strongly detrimental for enantioselectivity while the replacement of the phenolic group by some bicyclic aromatic residues of different polarity, size or shape did not impair the enantioselective interaction. In addition, the effects of the mobile phase composition and column temperature upon the retention and stereoselective properties of the CSP were assessed. Finally, it was found that the immobilized RNA aptamer could be used under hydro-organic mobile phase conditions without alteration of the stationary phase stability.