Sur la méthode des approximations successives pour les équations aux derivées partielles du deuxième ordre

Sans résumé Extrait d'une lettre à M. Mittag-Leffler.     

Use of N-benzyl-2-naphthohydroxamic acid as a highly selective reagent for solvent extraction and spectrophotometric determination of vanadium(V)

N-Benzyl-2-naphthohydroxamic acid extracts vanadium(V) selectively and quantitatively into chloroform from 2-8.5M hydrochloric acid in the presence of Mo(VI), Zr(IV) and Ce(IV). The extraction takes place quickly and gives a stable reddish-violet extract which shows an absorption maximum at 505 nm with molar absorptivity of (5.34 +/- 0.05) x 10(3) 1.mole(-1).cm(-1). The optimum range for the determination is 2.2-7.4 ppm of vanadium(V) in the final solution. The method has been used for the determination of vanadium in steels.     

Preparation of 125I-Lanreotide and its biodistribution in murine model of melanoma

Lanreotide, a somatostatin analogue, was radioiodinated with ¹²⁵I to explore the possibility of using ¹²³I labeled lanreotide as a diagnostic radiopharmaceutical for tumors overexpressing somatostatin (SST) receptors. Radioiodination was carried out with ¹²⁵I using chloramine T as the oxidant. The labeling yield was >90%. Characterization of ¹²⁵I-Lanreotide was carried out by paper electrophoresis as well as HPLC. ¹²⁵I-Lanreotide was purified by chromatography using a C18 Sep-Pak column. Radiochemical purity of the purified ¹²⁵I-Lanreotide thus obtained was >99%. Significant tumor uptake of ¹²⁵I-Lanreotide was observed in C57BL/6 mice bearing melanoma.     

Theories of Gravitation

This paper presents a systematic study of the theories of gravitation that have been proposed. We restrict ourselves to an investigation of the linear approximation since new connections with experiment can be expected in this order in χ only. It turns out that all theories that differ from general relativity contain a scalar field and describe gravitation by a mixture of scalar and tensor interactions. The scalar has negative energy in theories with light deflection larger than the Einstein value. As a consequence instabilities of cosmic systems and continuous creation result in this case. Furthermore, the emission of gravitational radiation with negative energy could be the energy source of the quasars. The question of the mass renormalization of the scalar is investigated. No unique answer is possible at present. Finally a new class of gravitational theories is given.     

Physical chemistry of binary organic eutectic and monotectic alloys; 1,2,4,5-tetrachlorobenzene−β-naphthol and 1,2,4,5-tetramethylbenzene-succinonitrile systems

Phase diagrams of 1,2,4,5-tetrachlorobenzene–β-naphthol and 1,2,4,5-tetramethylbenzene–succinonitrile systems which are organic analogues of a nonmetal–nonmetal and a nonmetal–metal system, respectively, show the formation of a simple eutectic (melting point 103.7°C) with 0.71 mole fraction of β-naphthol in the former case and a monotectic (melting point 76.0°C) with 0.07 mole fraction of succinonitrile and a eutectic (melting point 52.5°C) with 0.97 mole fraction of succinonitrile in the latter case. The growth behaviour of the pure components, the eutectics and the monotectic studied by measuring the rate of movement of the solid–liquid interface in a capillary, suggests that the data obey the Hillig–Turnbull equation, v=u(ΔT)ⁿ, where v is the growth velocity, ΔT is the undercooling and u and n are constants depending on the nature of the materials involved. From the values of enthalpy of fusion determined by the DSC method using Mettler DSC-4000 system, entropy of fusion, interfacial energy, enthalpy of mixing and excess thermodynamic functions were calculated. The optical microphotographs of pure components and polyphase materials show their characteristic features.     

Effect of γ irradiation on the heat capacity of Rb2ZnBr4 in the vicinity of phase transitions

Heat capacity of Rb₂ZnBr₄ as a function of γ irradiation dose has been measured within the 85–300 K range by the adiabatic calorimeter technique. It is shown that, as the irradiation dose increases, the heat capacity peak in the vicinity of the incommensurate-commensurate first-order phase transition (PT) decreases, and the transition temperature T _c increases. The heat capacity peak in the region of the second-order PT at T ₃=112 K does not depend on γ irradiation, both in magnitude and in position, just as the heat capacity throughout the remainder of the temperature range studied. Fiz. Tverd. Tela (St. Petersburg) 40, 1106–1108 (June 1998)     

Representations of the cyclically symmetric q-deformed algebra U q(so3)

An algebra homomorphism from the nonstandard q-deformed (cyclically symmetric) algebra U _q(so₃) to the extension Û _q(sl₂) of the Hopf algebra U _q(sl₂) is constructed. Not all irreducible representations (IR) of U _q(sl₂) can be extended to representations of Û _q(sl₂). Composing the homomorphism with irreducible representations of Û _q(sl₂) we obtain representations of U _q(so₃). Not all of these representations of U _q(so₃) are irreducible. Reducible representations of U _q(so₃) are decomposed into irreducible components. In this way we obtain all IR of U _q(so₃) when q is not a root of unity. A part of these representations turn into IR of the Lie algebra so₃ when q 1.