Jensen's inequality for g-expectation: part 1

Briand et al. (Electron. Comm. Probab. 5 (2000) 101–117) gave a counterexample and proposition to show that given g,g-expectations usually do not satisfy Jensen's inequality for most of convex functions. This yields a natural question, under which conditions on g, do g-expectations satisfy Jensen's inequality for convex functions? In this paper, we shall deal with this question in the case that g is convex and give a necessary and sufficient condition on g under which Jensen's inequality holds for convex functions. To cite this article: Z. Chen et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Comparative investigation of ruthenium-based metathesis catalysts bearing N-heterocyclic carbene (NHC) ligands

Exchange of one PCy3 unit of the classical Grubbs catalyst 1 by N-heterocyclic carbene (NHC) ligands leads to "second-generation" metathesis catalysts of superior reactivity and increased stability. Several complexes of this type have been prepared and fully characterized, six of them by X-ray crystallography. These include the unique chelate complexes 13 and 14 in which the NHC- and the Ru-CR entities are tethered to form a metallacycle. A particularly favorable design feature is that the reactivity of such catalysts can be easily adjusted by changing the electronic and steric properties of the NHC ligands. The catalytic activity also strongly depends on the solvent used; NMR investigations provide a tentative explanation of this effect. Applications of the "second-generation" catalysts to ring closing alkene metathesis and intramolecular enyne cycloisomerization reactions provide insights into their catalytic performance. From these comparative studies it is deduced that no single catalyst is optimal for different types of applications. The search for the most reactive catalyst for a specific transformation is facilitated by IR thermography allowing a rapid and semi-quantitative ranking among a given set of catalysts.     

Multiparametric microsensor chips for screening applications

The identification of drug targets for pharmaceutical screening can be greatly accelerated by gene databases and expression studies. The identification of leading compounds from growing libraries is realized by high throughput screening platforms. Subsequently, for optimization and validation of identified leading compounds studies of their functionality have to be carried out, and just these functionality tests are a limiting factor. A rigorous preselection of identified compounds by in vitro cellular screening is necessary prior to using the drug candidates for the further time consuming and expensive stage, e.g. in animal models. Our efforts are focused to the parallel development, adaptation and integration of different microelectronic sensors into miniaturized biochips for a multiparametric, functional on-line analysis of living cells in physiologically environments. Parallel and on-line acquisition of data related to different cellular targets is required for advanced stages of drug screening and for economizing animal tests.     

Einkristalle von CoNbO4 mit AlNbO4-Struktur

Single Crystals of CoNbO₄ with AlNbO₄ Structure The hitherto unknown single crystals of CoNbO₄ were prepared. CoNbO₄ has AlNbO₄ structure with monoclinic symmetry (space group C?C2/m; a = 1212.9; b = 374.9; c = 651.2 pm; β = 107.6°). X-ray investigations shows on ordered arrangement of Co³⁺ and Nb⁵⁺ with well defined differences in respect to oxocobaltates with Columbite type (CoNb₂O₆ = Co_0.33Nb_O.66O₂) and Rutil type (CoNbO₄ = Co_0.5-xNb_0.5+xO₂; 0 ? × ? 0.166) structure.     

Anomalous behaviour of the Landé factors and the chemical shift close to the dissociation limit of the B state of molecular iodine

Resonances in a modulated light beam have been observed on five transitions in the visible band system of I₂. Landé factors g_J and chemical shifts g₁ have been measured for levels very close to the dissociation limit of the B state.     

Novel open-chain and cyclic conformationally constrained (R)- and (S)-α,α-disubstituted tyrosine analogues

A series of novel open-chain and cyclic conformationally constrained (R)- and (S)-α,α-disubstituted tyrosine analogues 1a–e were synthesized in good yields and high optical purities (Schemes 1 and 2). The absolute configurations of these tyrosine analogues were unambiguously determined based on the X-ray structures of the precursor diastereoisomeric peptides of type 4 and 5 . Four of these structures are described (Figs. 1–4), showing β-turn type-I geometries for dipeptides 4a, 5b , and 4c and an extended conformation for peptide 5c (Table 3). The conversion of the free amino acids 1a–c into suitably protected building blocks 11a–d and 15d,e for peptide synthesis is discussed (Schemes 3 and 4).     

Rate of reactions between D2O and CaxAlyOz

The rate of the reaction between D₂O and the calcium aluminum oxides Ca₃Al₂O₆, Ca₅Al₆O₁₄, CaAl₂O₄, and CaAl₄O₇ was investigated by on-line neutron diffraction powder methods at temperatures from room temperature to 100°C. The rate of the reaction increases with increasing calcium content of the compounds and with increasing temperature for each of the compounds. The crystallographic stable hydrate Ca₃Al₂(OD)₁₂ is obtained from CaAl₄O₇ and CaAl₂O₄ at temperatures above 63°C, from Ca₅Al₆O₁₄ at temperatures above 49°C, and from Ca₃Al₂O₆ at temperatures as low as 7°C.     

Structure and properties of the dendron-encapsulated polyoxometalate (C(52)H(60)NO(12))(12)[(Mn(H(2)O))(3)(SbW(9)O(33))(2)], a first generation dendrizyme

Combining analytical and theoretical methods, we present a detailed study of a heteropolytungstate cluster encapsulated in a shell of dendritically branching surfactants, namely (C(52)H(60)NO(12))(12)[(Mn(H(2)O))(3)(SbW(9)O(33))(2)], 3. This novel surfactant-encapsulated cluster (SEC) self-assembles spontaneously from polyoxometalate-containing solutions treated with a stoichiometric amount of dendrons. Compound 3 exhibits a discrete supramolecular architecture in which a single polyoxometalate anion resides in a compact shell of dendrons. Our approach attempts to combine the catalytic activity of polyoxometalates with the steric properties of tailored dendritic surfactants into size-selective catalytic systems. The structural characterization of the SEC is based on analytical ultracentrifugation (AUC) and small-angle neutron scattering (SANS). The packing arrangement of dendrons at the cluster surface is gleaned from molecular dynamics (MD) simulations, which suggests a highly porous shell structure due to the dynamic formation of internal clefts and cavities. From analysis of the MD trajectory of 3, a theoretical neutron-scattering function is derived that is in good agreement with experimental SANS data. Force field parameters used in MD simulations are partially derived from a quantum mechanical geometry optimization of [(Zn(H(2)O))(3)(SbW(9)O(33))(2)](12)(-), 2b, at the density functional theory (DFT) level. DFT calculations are corroborated by X-ray structure analysis of Na(6)K(6)[(Zn(H(2)O))(3)(SbW(9)O(33))(2)].23H(2)O, which is isostructural with the catalytically active Mn derivative 2a. The combined use of theoretical and analytical methods aims at rapidly prototyping smart catalysts ("dendrizymes"), which are structurally related to naturally occurring metalloproteins.     

Novel diode laser-compatible fluorophores and their application to single molecule detection, protein labeling and fluorescence resonance energy transfer immunoassay

We describe a series of new long-wave absorbing and fluorescing cyanine dyes and labels (based on a general logic for the design of such dyes), their spectra, covalent and noncovalent linkage to proteins, their use in single molecule detection (SMD) and as donors and acceptors, respectively, in fluorescence resonance energy transfer studies. The new labels represent water-soluble and reactive fluorophores whose quantum yields increase substantially if noncovalently or covalently bound to proteins. Due to their strong absorptions between 550 and 700 nm they are excitable by light-emitting diodes or diode lasers. Their high absorbances (epsilon around 100,000) and adequate fluorescence quantum yields (phi up to 0.68 if bound to proteins) along with their availability as reactive NHS esters make them viable labels for proteins and oligomers, e.g. in context with SMD or fluorescence energy transfer immunoassay which is demonstrated for the system HSA/anti-HSA.     

Neutral loss of amino acid residues from protonated peptides in collision-induced dissociation generates N- or C-terminal sequence ladders

The widespread occurrence of the neutral loss of one to six amino acid residues as neutral fragments from doubly protonated tryptic peptides is documented for 23 peptides with individual sequences. Neutral loss of amino acids from the N-terminus of doubly charged tryptic peptides results in doubly charged y-ions, forming a ladder-like series with the ions [M + 2H](2+) = y(max) (2+), y(max - 1) (2+), y(max - 2) (2+), etc. An internal residue such as histidine, proline, lysine or arginine appears to favor this type of fragmentation, although it was sometimes also observed for peptides without this structure. For doubly protonated non-tryptic peptides with one of these residues at or near the N-terminus, we observed neutral loss from the C-terminus, resulting in a doubly charged b-type ion ladder. The analyses were performed by Q-TOF tandem mass spectrometry, facilitating the recognition of neutral loss ladders by their 2+ charge state and the conversion of the observed mass differences into reliable sequence information. It is shown that the neutral loss of amino acid residues requires low collision offset values, a simple mechanistic explanation based on established fragmentation rules is proposed and the utility of this neutral loss fragmentation pathway as an additional source for dependable peptide sequence information is documented.