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.     

Ground-state properties of LiV2O4 and Li1-xZnx(V1-yTiy)2O4

We present susceptibility, microwave resistivity, NMR and heat-capacity results for Li_1-xZn_x(V_1-yTi_y)₂O₄ with 0 ? x ? 0.3 and 0 ? y ? 0.3. For all doping levels the susceptibility curves can be fitted with a Curie-Weiss law. The paramagnetic Curie-Weiss temperatures remain negative with an average value close to that of the pure compound Θ≈ - 36 K. Spin-glass anomalies are observed in the susceptibility, heat-capacity and NMR measurements for both type of dopants. From the temperature dependence of the spin-lattice relaxation rate we found critical-dynamic behavior in the Zn doped compounds at the freezing temperatures. For the Ti-doped samples two successive freezing transitions into disordered low-temperature states can be detected. The temperature dependence of the heat capacity for Zn-doped compounds does not resemble that of canonical spin glasses and only a small fraction of the total vanadium entropy is frozen at the spin-glass transitions. For pure LiV₂O₄ the spin-glass transition is completely suppressed. The temperature dependence of the heat capacity for LiV₂O₄ can be described using a nuclear Schottky contribution and the non-Fermi liquid model, appropriate for a system close to a spin-glass quantum critical point. Finally an ( x / y , T )-phase diagram for the low-doping regime is presented. Received 16 March 2001 and Received in final form 30 October 2001     

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.     

Cyclic and telechelic ladder polymers derived from tetrahydroxytetramethylspirobisindane and 1,4‐dicyanotetrafluorobenzene

5,5′,6,6′‐Tetrahydroxy‐3,3,3′,3′‐tetramethylspirobisindane was polycondensed with 1,4‐dicyanotetrafluorobenzene in four different solvents at 70 °C. In dimethylformamide, N‐methylpyrrolidone, and sulfolane exclusively, cyclic polymers were detectable by matrix‐assisted laser desorption/ionization time‐of‐flight (MALDI‐TOF) mass spectrometry up to masses around 13,000 Da. In dimethyl sulfoxide, linear byproducts were also found. Higher temperatures caused degradation reactions catalyzed by potassium carbonate. Polycondensations performed with the addition of 4‐tert‐butyl catechol or 2,2′‐dihydroxy binaphthyl yielded linear telechelic oligomers. Equimolar mixtures of linear and cyclic ladder polymers were examined by MALDI‐TOF mass spectra to determine how the end groups and the cyclic structure influenced the signal‐to‐noise ratio. The results suggested a preferential detection of the linear chains. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5344–5352, 2006     

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.