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.     

Mössbauer and magnetic studies of parent material from argentine pampas soils

In order to establish a correlation between the different types of soils using hyperfine and magnetic parameters as climatic and environmental proxies, we have studied the differentiation of soil developed around 38.5° south latitude, in the central Pampas of Argentina, by means of Mössbauer spectroscopy and environmental magnetism. The soils transect (climosequence) investigated stretches from the drier west (around 64° W) to the more humid east (at around 59° W) in the Buenos Aires Province, covering a distance of 600 km. The soils studied developed during recent Holocene geologic times in a landscape characterized by small relict plateaus, slopes and depressions, dunes and prairies. The parent material consists of eolian sandy silts overlying calcrete layers. The low mean annual precipitation in the western parts of the region gives rise to soils without B-horizons, which limits the agricultural use of land. The preliminary results show an increase of the paramagnetic Fe³⁺ relative concentration from west to east in the soils investigated. Magnetite is probably mainly responsible for the observed enhancement in the susceptibility values. The magnetic response of the parent material is similar to that of the loess part of the previously investigated loess–paleosol sequences of the Argentine loess plateau.     

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.     

Syntheses of halogenated ethenyl isocyanide chromium complexes as organometallic precursor molecules for ethenyl and ethynyl isocyanides

The radical alkylation of tetraethylammonium pentacarbonyl(cyano)chromate 1 yielded the halogenated ethyl isocyanide complexes [(CO)5Cr(CN-CClX-CClYF)] 3 (a, X= Cl, Y= F; b, X = F, Y= F and c, X=Y= Cl). Dehalogenation of 3 using zinc in diethyl ether gave [(CO)5Cr(CN-CX=CFY)] 4. The compounds 4a, b reacted with various nucleophiles exclusively at the difluoromethylene group. The unstable phosphorane 5, which is formed on reaction of 4b with trimethylphosphane, decomposed thermally and on hydrolysis yielding pentacarbonyl(1,2-difluoroethenyl isocyanide)chromium (6). The cyano substituent can be introduced in the beta position of the isocyanide function by reaction of 4a, b with potassium cyanide, leading to the formation of [(CO)5Cr(CN-CX=CF-CN)] (7). Reactions of 4a, b with organolithium or organomagnesium compounds yielded [(CO)5Cr(CN-CX=CF-R)] (8) and [(CO)5Cr(CN-CF=CF-C...C-CF=CF-NC)Cr(CO)5] (10). The trimethylsilyl group in 8a, b, d could be removed by a solution of potassium carbonate in methanol leading to [(CO)5Cr(CN-CX=CF-Cn-H)] (11) (n=2,4). Octacarbonyldicobalt reacted with 8e under coordination of the C-C triple bond to the hexacarbonyldicobalt fragment, resulting in the cluster compound 12. The crystal and molecular structure of 8i, 11 a, b, and 12 were elucidated by X-ray crystallography. The alkenyl and alkynyl isocyanides CN-CCl=CF2 (13a), CN-CF=CF2 (13b), CN-CCl=CClF (13c), CN-CF=CFH (14), CN-CC-H (15), CN-CC-CN (16), and CN-CCl=CF-CN (17) were obtained by flash vacuum pyrolysis of 4a, 4b, 4c, 6, and 7a, respectively.     

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.