On the equivalence between the energy and virial routes to the equation of state of hard-sphere fluids

The energy route to the equation of state of hard-sphere fluids is ill defined since the internal energy is just that of an ideal gas, and thus it is independent of density. It is shown that this ambiguity can be avoided by considering a square-shoulder interaction and taking the limit of vanishing shoulder width. The resulting hard-sphere equation of state coincides exactly with the one obtained through the virial route. Therefore, the energy and virial routes to the equation of state of hard-sphere fluids can be considered as equivalent.     

Le problème de la réduction des intégrales électroniques dans la méthode L.C.A.O. améliorée

Résumé L'auteur reprend les principes de la méthode L.C.A.O. améliorée en vue d'une justification plus complète des procédés employés. La théorie des perturbations permet d'une façon simple de tenir compte de la corrélation entre les électrons grâce à l'introduction d'une fonction universelle de la distance entre deux électrons. Le problème est ainsi ramené de l'échelle moléculaire à l'échelle atomique. On montre que la corrélation entre les électrons entraîne la réduction des intégrales atomiques. Le problème de la réduction des intégrales coulombiennes est traité en détail. La possibilité de négliger les autres intégrales biélectroniques est ensuite examiné. Enfin est étudié le problème de la réduction des intégrales de coeur.

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The principles of the improved LCAO theory are investigated to give a better justification for its methods. Perturbation theory allows a simple account for electronic correlation, when a universal function of interelectronic distance is introduced. The problem is hereby reduced from molecular to atomic scale. The reduction of electronic energy integrals by correlation is shown, especially for Coulomb integrals. The possibility of neglecting the other bielectronic integrals is examined. Finally the problem of core integral reduction is studied.

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Zusammenfassung Die Grundlagen der verbesserten LCAO-Methode werden untersucht, um dieses Verfahren besser zu rechtfertigen. Mit einer allgemeinen Funktion des Abstandes je zweier Elektronen und der Störungstheorie läßt sich die Elektronenkorrelation auf einfache Weise berücksichtigen. Damit wird das Problem vom molekularen auf den atomaren Maßstab zurückgeführt. Die Elektronenkorrelation bringt eine Reduktion der Elektronenenergieintegrale mit sich; die Coulombintegrale werden im einzelnen behandelt. Anschließend wird die Möglichkeit untersucht, die übrigen Zweielektronenintegrale zu vernachlässigen. Schließlich wird die Reduktion der Rumpfintegrale behandelt.

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Nous tenons à remercier très vivement le Docteur Chr. K. Jørgensen (Cyanamid European Research Institut, Genève) pour les intéressants échanges de vue que nous avons eu sur les divers problèmes évoqués dans cet article ainsi que le Docteur G. Berthier (Institut de Biochimie théorique, Paris) et Monsieur H. v. Hirschhausen.     

Study of the ternary system FeCrTe around the composition FeCr2Te4

The system FeCrTe was investigated around the composition FeCr₂Te₄. FeCr₂Te₄ is a metastable compound. Single crystals with Fe_0·93Cr_1·76Te₄ composition were grown by vapor transport or the Bridgman method. These crystals are metallic and anisotropic ferromagnets.     

On approximation by bivariate incomplete polynomials

In this paper we prove that given certain convex domains Δ on the plane, ε>0, andf∈C(Δ) such thatf=0 on θ²Δ={(θ² x,θ² y):(x,y)?Δ} (0<θ<1), a polynomialp(x, y) of the form $$p(x,y) = \sum\limits_{\theta n \leqslant k + l \leqslant n} {a_{kl} x^k y^l }$$ exists such that ∥f?p∥ _C(Δ) ≤ε. The admissible convex domains include triangles and parallelograms with a vertex at the origin and sections of unit disk.     

Formal orthogonal polynomials revisited. Applications

From some results concerning the formal orthogonal polynomials, already proved in [5], we develop new properties of generalized adjacent polynomials which correspond to a change in the weight function. A new structure of the singular blocks is given. These results have a direct application to Lanczos methods, theG and -algorithms.     

Beiträge zur Chemie der Pyrrolo[3,2-c]azepine und der Pyrrolo [3,2-b]azepine

Some chemical transformations in the series of the pyrrolo [3,2-b]azepines and the pyrrolo[3,2-c]azepines are reported: alkylation at the pyrrolo nitrogen and/or the azepino nitrogen, reduction of the lactam group by means of LiAlH₄, preparation of lactim ethers and amidines, substitution in position 2 by MANNICH reaction, bromination and condensation with oxalyl chloride or chloral hydrate, and the cyclocondensation with dimethylmalonyl chloride. The structures of the 2-substitution products have been evaluated by NMR.-spectroscopy.     

Recherches sur la structure électronique de composés soufrés (méthode L.C.A.O. améliorée)

Improved L.C.A.O. method primitively built for conjugated molecules holding only atoms of second row in the periodic classification is extended to molecules holding atoms of the third row. The application is done for thiophen, thioketones, SO₂ and SO₃. d orbitals are not introduced in this study. Discussion about results shows that d orbitals must be introduced when the sulphur atom is strongly positively charged like in sulphur oxides.     

Consequence of boar edible tissue consumption on urinary profiles of nandrolone metabolites. II. Identification and quantification of 19-norsteroids responsible for 19-norandrosterone and 19-noretiocholanolone excretion in human urine

In previous work (Le Bizec et al., Rapid Commun. Mass Spectrom. 2000; 14: 1058), it was demonstrated that a boar meal intake could lead to possible false accusations of abuse of 17beta-nortestosterone in antidoping control. The aim of the present study was to identify and quantify endogenous 19-norsteroids in boar edible tissue at concentrations that can alter the steroid urinary profile in humans, and lead to excretion of 19-norandrosterone (19-NA) and 19-noretiocholanolone (19-NE). The samples were analysed in two laboratories. The methodologies used for extraction and detection (GC/MS(EI) and LC/MS/MS(APCI+)) are compared and discussed. 19-Norandrostenedione (NAED), 17beta- and 17alpha-nortestosterone (bNT, aNT), and 17beta- and 17alpha-testosterone (bT, aT) were quantified. The largest concentrations of NAED and bNT were observed in testicles (83 and 172 microg/kg), liver (17 and 63 microg/kg) and kidney (45 and 38 microg/kg). A correlation between the bNT and NAED content of a typical meal prepared with boar parts and the excreted concentrations of 19-NA and 19-NE in human urine was demonstrated.