On the recovery of a curve isometrically immersed in a Euclidean space

It is known from differential geometry that one can reconstruct a curve with n?1 prescribed curvature functions, if these functions can be differentiated a certain number of times in the usual sense and if the first n?2 functions are strictly positive. We establish here that this result still holds under the assumption that the curvature functions belong to some Sobolev spaces, by using the notion of derivative in the distributional sense. We also show that the mapping that associates with such prescribed curvature functions the reconstructed curve is of class $\text{C}{}^{\mathrm{\infty }}$. To cite this article: M. Szopos, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

DC corona discharge influence on chemical composition in mixtures of natural gas with air and its combustion exhaust with air

Experiments in dc supplied corona discharge in natural gas + air mixture and in combustion exhaust of natural gas + air mixture were realized. The influence of discharge on CO, CO₂, NO _x and other minority components was studied using IR absorption spectrometry. Production of NCO radicals in gas and consequent formation of NCO containing surface layers on a plate electrode was detected. In natural gas + air mixture after about 1 min oxygen poor combustion exhaust was produced due to slow combustion by corona discharge. Occurrence of various pulses in discharge current was typical.     

Thermochemically induced binding of methyl orange to polycations containing primary amine groups

The thermochemical transformation of electrostatically formed complexes of methyl orange (MO) with polycations containing primary amine groups such as ammonium salts afforded new polymers with a high concentration of covalently bound 4‐N,N‐dimethylaminoazobenzene groups in the side chain. Poly(allylamine hydrochloride) and poly(β‐aminoethylene acrylamide hydrochloride) were employed as support polycations for MO. The transformation of sulfonate–ammonium ion pairs into sulfonamide bonds, via heating at an elevated temperature, was supported by the polymer properties before and after the thermal treatment. The polymer structure changes were monitored with elemental analysis, Fourier transform infrared, ¹H NMR, and ultraviolet–visible absorption spectroscopy, and thermogravimetric analysis. The spacer length between the backbone and azobenzene structures used as side chains strongly influenced the polymer properties before and after the heat‐induced reaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5898–5908, 2006     

Indirect fluorometric determination of diclofenac sodium.

A simple and easy method of analysis for diclofenac sodium is reported. A spectrofluorometric method for the microdetermination of diclofenac sodium has been developed through its reaction with cerium(IV) in an acidic solution and measurement of the fluorescence of the Ce(III) ions produced. Under the optimum experimental conditions for the oxidation reaction, 1.0 M H2SO4 with 90 min of heating time (100 degrees C), the range of application is 124.3-600 ng mL(-1) and the limit of detection is 72.7 ng mL(-1). The proposed method was applied to the determination of diclofenac sodium in pharmaceutical tablets. The results of the analysis show a good agreement with those obtained by the official USP 27 HPLC method.     

Unusual volumetric and hydration behavior of the catanionic system sodium undecenoate: sodecyltrimethylammonium bromide

Following the studies on the effect of double bonds in the surfactant hydrophobic tail on the formation of mixed surfactant aggregates, we studied the viscosity and density of the system Sodium 10-undecenoate (SUD)–decyltrimethylammonium bromide (DTAB)–water. We found that the partial molar volume (pmv) and intrinsic viscosity of both, micellised and unmicellised mixtures, are non-ideal, dependent on the mixture composition and related to structural changes in micelles. These phenomena are caused by the presence of the double bond at the distal extreme of the SUD molecule, which has some affinity with water by formation of hydrogen bonds. In particular, as far as we know, this is the first report on non-ideal behavior of the pmv in mixed micelles.     

The aqueous cationic system sodium undecenoate-dodecyltrimethylammonium bromide at low concentration

The aqueous sodium undecenoate (SUD) –dodecyltrimethylammonium bromide (DTAB) catanionic system was studied at low concentration. The system did not precipitate, even at a 1:1 SUD:DTAB proportion, but showed the formation of a coacervate in a range of surfactant mixture compositions. Micelles have a preferential composition of 0.37 mole fraction of SUD. This behavior is attributed to the presence of the double bond at the distal extreme of the SUD molecule, which can form hydrogen bonds with water. Consequently, the –CH=CH₂ group is situated at the interface between the hydrocarbon micelle core and water, reducing the interfacial free energy. Structural computations demonstrate that the mentioned SUD proportion produces complete coverage of the micelle surface by the double bonds.     

Synthesis and properties of 1-(6-methoxy)-2-benzothiazolyl)-2-pyridones

Substituted ]-(6-methoxy-2-benzothiazolyt)-2-pyridones were prepared from 2-amino-6-methoxybenzathiazate through N-(6-methoxy-2-benzothiazotyl) cyanvorearmileaznd-3-aryl-N-(6-methoxy-2-benzothiazolyt)-2-cyano-2-propenamides. The cyclization of the latter with malonodinitrile in the presence of piperidine gave the corresponding pyridones. The structures of the synthesized compounds were confirmed by¹H NMR and mass spectral data.Department of Organic Chemistry, Mass Spectrometry Laboratory, Slovak Technical University, 812 37 Bratislava, Slovakia. Published in Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1402–1404, October, 1995. Original article submitted August 24, 1995.     

Tröger's base scaffold in racemic and chiral fashion as a spacer for bisdistamycin formation. Synthesis and DNA binding study

‘Head-to-head’ oligo-N-methylpyrrole peptide dimers linked by a methano[1,5]diazocin scaffold are presented in racemic as well as chiral fashion. Their DNA binding activities were assayed on calf thymus DNA, poly(dA-dT)₂, and poly(dC-dG)₂ by NMR and ECD spectroscopies, and fluorescence probe displacement assay. The presented dimers prefer AT sequences, but show higher affinity to poly(dC-dG)₂ than distamycin A. The (4R,9R) configuration of methanodiazocin bridge was found to be better suited for interaction with ct-DNA and poly(dA-dT)₂ than (4S,9S) configuration.     

Resonance assignments and secondary structure analysis of E. coli thioredoxin by magic angle spinning solid-state NMR spectroscopy

De novo site-specific 13C and 15N backbone and sidechain resonance assignments are presented for uniformly enriched E. coli thioredoxin, established using two-dimensional homo- and heteronuclear solid-state magic angle spinning NMR correlation spectroscopy. Backbone dihedral angles and secondary structure were derived from the statistical analysis of the secondary chemical shifts, and are in good agreement with solution values for the intact full-length thioredoxin, with the exception of a small number of residues located at the termini of the individual secondary structure elements. A large number of cross-peaks observed in the DARR spectra with long mixing times correspond to the pairs of carbon atoms separated by 4-6 angstroms, suggesting that DARR could be efficiently employed for observation of medium- and long-range correlations. The 108 amino acid residue E. coli thioredoxin is the largest uniformly enriched protein assigned to this degree of completeness by solid-state NMR spectroscopy to date. It is anticipated that with a combination of two-dimensional correlation experiments and high magnetic fields, resonance assignments and secondary structure can be generally derived for other noncrystalline proteins.