Up to isometries,a deformation is a continuous function of its metric tensorAux isométries près,une déformation est une fonction continue de son tenseur métrique

If the Riemann–Christoffel tensor associated with a field of class $\text{C}{}^2$ of positive definite symmetric matrices of order three vanishes in a connected and simply connected open subset $\text{Ω?}\text{R}{}^3$, then this field is the metric tensor field associated with a deformation of class $\text{C}{}^3$ of the set $\text{Ω}$, uniquely determined up to isometries of $\text{R}{}^3$. We establish here that the mapping defined in this fashion is continuous, for ad hoc metrizable topologies. To cite this article: P.G. Ciarlet, F. Laurent, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 489–493.     

Arithmetic functions with linear recurrence sequences

We obtain asymptotic formulas for all the moments of certain arithmetic functions with linear recurrence sequences. We also apply our results to obtain asymptotic formulas for some mean values related to average orders of elements in finite fields.     

Über die Identifizierung von Alkoholen mit 1-Chlormethyl-isatin

Monatshefte für Chemie - Chemical Monthly - Primary, secondary and tertiary aliphatic alcohols quickly react with 1-chloromethyl-isatin (1) to give good yields of alkoxymethylisatines4-novel...     

A new approach to phosphoserine and phosphothreonine analysis in peptides and proteins: chemical modification,enrichment via solid-phase reversible binding,and analysis by mass spectrometry

beta-Elimination of the phosphate group on phosphoserine and phosphothreonine residues and addition of an alkyldithiol is a useful tool for analysis of the phosphorylation states of proteins and peptides. We have explored the influence of several conditions on the efficiency of this PO(4)(3-) elimination reaction upon addition of propanedithiol. In addition to the described influence of different bases, the solvent composition was also found to have a major effect on the yield of the reaction. In particular, an increase in the percentage of DMSO enhances the conversion rate, whereas a higher amount of protic polar solvents, such as water or isopropanol, induces the opposite effect. We have also developed a protocol for enrichment of the modified peptides, which is based on solid-phase covalent capture/release with a dithiopyridino-resin. The procedure for beta-elimination and isolation of phosphorylated peptides by solid-phase capture/release was developed with commercially available alpha-casein. Enriched peptide fragments were characterized by MALDI-TOF mass spectrometric analysis before and after alkylation with iodoacetamide, which allowed rapid confirmation of the purposely introduced thiol moiety. Sensitivity studies, carried out in order to determine the detection limit, demonstrated that samples could be detected even in the low picomolar range by mass spectrometry. The developed solid-phase enrichment procedure based on reversible covalent binding of the modified peptides is more effective and significantly simpler than methods based on the interaction between biotin and avidin, which require additional steps such as tagging the modified peptides and work-up of the samples prior to the affinity capture step.     

Fibre optic fluorometric enzyme sensors for hydrogen peroxide and lactate,based on horseradish peroxidase and lactate oxidase

An optical biosensor for the determination of hydrogen peroxide based on immobilized horseradish peroxidase is described. The fluorescence of the dimeric product of the enzyme catalysed oxidation of homovanillic acid is utilized to determine the concentration of H₂O₂. The membrane-bound enzyme is attached to a bifurcated fibre bundle permitting excitation and detection of the fluorescence by a fluorometer. The response of the sensor is linear from 1 to 130 M hydrogen peroxide; the coefficient of variation is 3%. The sensor is stable for more than 10 weeks. The operating pH for maximal sensor response is 8.15. This allows the sensor to be used in combination with oxidase reactions producing hydrogen peroxide, as is demonstrated with a co-immobilized lactate oxidase-horseradish peroxidase optode for the determination of L-lactate. The fluorescence intensity of this sensor depends linearly on the concentration of lactate between 3 and 200 M and a throughput of 10 samples per hour is possible. The precision is in the same range as that of the monoenzyme optode. The lifetime of the bienzyme sensor for lactate is considerably shorter than that of the peroxidase sensor; it is limited by the stability of the immobilized lactate oxidase enzyme. The sensor has been applied to the determination of lactate in control serum.     

Microstructure and electrical properties of BaTiO<Subscript>3</Subscript> and (Ba,Sr)TiO<Subscript>3</Subscript> ferroelectric thin films on nickel electrodes

Nickel thin films have been sputtered on standard Si/SiO₂ substrates with TiO₂ as an adhesive layer. The thermal stability of these substrates was analyzed. SEM images show an increase in grain size with annealing temperature. They were found to be stable till 800°C, beyond which the nickel layer disintegrated. These substrates were used for deposition of BaTiO₃ and (Ba,Sr)TiO₃ dielectric thin films under a reducing atmosphere. The dielectric thin films were processed with various pyrolysis and annealing temperatures in order to optimize the dielectric properties. Increased pyrolysis temperatures showed an increase in the grain size. Results on these nickelised substrates were finally compared with dielectric films deposited on platinized silicon substrates under identical conditions but crystallized in an oxygen atmosphere.     

4,4-Disubstituierte Imidazol-Derivate aus der Umsetzung von 3-Amino-2H-azirinen mit Salicylamid

4,4-Disubstituted Imidazole Derivatives from the Reaction of 3-Amino-2H-azirines with Salicylamide Reaction of 3-amino-2H-azirines 1a–c with salicylamide ( 7 ) in MeCN leads to imidazoles 10 and 11 in different rates, depending on the conditions. In the case of 1a and 1b, 11a and 11b , respectively, have been obtained as the main product at 50°; in reactions at 80°, 10a and 10b are the favored products (Tables 1 and 2). 2,2-Dimethyl-3-(N-methyl-N-phenylamino)-2H-azirine ( 1c ) reacts with 7 in MeCN mainly to 2-(2-hydroxyphenyl)-5,5-dimethyl-3,5-dihydroimidazol-4-one ( 10a ); in boiling toluene, 11c is formed with low preference (Table 3). The structure of the products has been established by spectroscopic means, and in the case of 10b and 11c , by X-ray crystallography. Two different reaction mechanisms for the formation of the products are discussed (Scheme 2).     

Preparation,Structure, and Reactivity of Thioxo and Imino Derivatives of the Triolide (and Pentolide) from (R)-3-Hydroxybutanoic Acid

Reaction of the triolide 1 from (R)-3-hydroxybutanoic acid with Lawesson's reagent 5 leads to the mono-, di-, and trithio derivatives 6–8 which can be isolated in pure form (20–40% yields), and which have crystal structures very similar to the parent triolide 1 (Fig. 1). Similarly, pentolide 3 is converted to mixtures of various thio derivatives, three of which are separated ( 10–12 ) by HPLC and fully characterized. The X-ray structures of the mono- and of one of the dithiopentolides ( 10, 12 ) differ remarkably from each other (Fig. 3). Reduction of the thiotriolides 6–8 (NaBH₄, R₃SnH, Cl₃SiH, Raney-Ni) gives 12-membered rings containing up to three ether groups (chiral crown ethers, 15, 17–19 ) in poor yields. The thiotriolides react spontaneously and in yields of up to 96% with ammonia, certain primary amines, and hydroxylamine to give imine and oxime derivatives with intact 12-membered-ring backbones ( 20, 22–24, 30 , see crystal structures in Figs. 4–7). The rigid structure of all the derivatives of triolide 1 puts the C?O, C?S, and C?NR O-, S-, and N-atoms in juxtaposition (a feature reminiscent of the side chains in the iron-binder enterobactin, Fig. 6). Imines containing PPh₂ groups are prepared ( 30, 33, 35 ) from the thiotriolides and tested as chiral ligands for Pd^II-catalyzed 1,3-diphenyallylations (→ 37 , enantiomer ratio up to 77:23). The reactions described demonstrate that multiple reactions of the triolide 1 from (R)-3-hydroxybutanoic acid which proceed through tetrahedral intermediates are possible without ring opening – the skeleton is remarkably stable, and this might be exploited as a template for bringing up to three pendent substituents into close proximity to allow a study of their interactions and cooperative properties. Also, the di- and trithio derivatives 7 and 8 could be used for cross-linking in molecules containing primary NH₂ groups.