Sur une conjecture de M. Kac

Summary We consider the following heat conduction problem. Let K be a compact set in Euclidean space ³. Suppose that K is held at the temperature 1, while the surrounding medium is at the temperature 0 at time 0. Following Spitzer we investigate the asymptotic behaviour of the integral E _K (t) which represents the total energy flow in time t from the set K to the surrounding medium ³–K. An asymptotic expansion is given for E _K (t) which refines a theorem due to Spitzer. This expansion also verifies and improves a formal calculation of Kac. Similar results are proved in higher dimensions. Up to the constant m(K), the quantity E _K (t) can be interpreted as the expected value of the volume of the Wiener sausage associated with K and a d-dimensional Brownian motion. This point of view both plays a major role in the proofs and leads to a probabilistic interpretation of the different terms of the expansion.     

Nouveaux thiochlorures de molybdène(II): Mo6Cl10Y (Y = S,Se, Te): Structure et propriétés magnétiques et électriques

The thiochlorides Mo₆Cl₁₀Y (Y = S, Se, Te) have been prepared; they are isostructural with Nb₆I₁₁, space group Pccn, and have four formula units per unit cell. The X-ray structure of Mo₆Cl₁₀Se has been determined from three-dimensional single-crystal counter data and refined to a final R value of 0.053 for 3350 independent reflections. The most important result concerning this structure is a statistical distribution of the Se atom on the unit (Mo₆X′₈) with $\text{X′ ?}\text{7}\text{8}\text{Cl}\text{+}\text{1}\text{8}\text{Se}$: so the compound Mo₆Cl₁₀Se must be formulated $\text{(Mo}{}_6\text{Cl}{}_7\text{Se)Cl}{}_{\mathrm{<mtext>4</mtext><mtext>2</mtext>}}\text{Cl}{}_{\mathrm{<mtext>2</mtext><mtext>2</mtext>}}$. The diamagnetic and dielectric behavior of these new thiochlorides is discussed.     

Etude asymptotique des enlacements du mouvement brownien autour des droites de l'espace

Summary The existence of a joint asymptotic distribution for the windings of a three-dimensional Brownian motion around a finite number of straight lines is obtained. This complements the recent studies, by Pitman- Yor, and the authors, of the joint asymptotic distribution for the windings of planar Brownian motion around a finite number of points.The following principle governs the passage from results in the plane to results in space:Let B be a three-dimensional Brownian motion, and P ₁, ..., P _k, k planes which intersect two by two. Then, the convergences in distribution concerning the planar Brownian motions B ⁱ (1ik), defined respectively as the orthogonal projections of B on P _i (1ik), take place jointly, and the corresponding limit variables are independent.     

160Tb nuclear orientation in yttrium single crystal

First experimental results of¹⁶⁰Tb nuclear orientation in yttrium single crystal matrix are described. The influence of external magnetic field in combination with the crystal field interaction is discussed.     

Influence of the pyridine methyl substituent position on the chemical changes of the NCS groups in the thermal decomposition of coordination compounds of the type Cu(NCS)2L2

The influence of the position of the CH₃ group in picoline and lutidine ligands on the degree of chemical change of the NCS groups in coordination compounds of the type Cu(NCS)₂L₂ (whereL=2-, 3- and 4-picoline, and 2,3-, 2,4-, 2,5-, 2,6-, 3,4- and 3,5-lutidine) is dealt with. The most marked effect of the CH₃ group is found to be exerted in position 4. This effect of the methyl group on the degree of chemical change points to the mutual influence of the ligands in coordination compounds of Cu(II).

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Zusammenfassung Der Artikel befaßt sich mit dem Einfluß der Lage der CH₃ Gruppe in Pikolinen und Lutidinen als Liganden auf den Grad der chemischen Änderungen der Gruppen NSC in Koordinationsverbindungen des Typs Cu(NCS)₂L₂ (L=2-, 3- und 4-Pikoline, 2,3-, 2,4-, 2,5-, 2,6-, 3,4- und 3,5-Lutidine). Der ausgeprägteste Effekt der CH₃ Gruppe wurde in der Position 4 beobachtet. Dieser Einfluß der Methylgruppe auf das Ausmaß der chemischen Änderungen deutet auch auf die gegenseitige Wirkung der Liganden in Koordinationsverbindungen von Cu(II).

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Résumé L'article a trait à l'influence de la position du groupe CH₂ dans les picolines et lutidines, en tant que ligands, sur le degré des changements chimiques des groupes SCN dans les composés de coordination du type Cu(SCN)₂L₂ (L=2-, 3 et 4-picoline, 2,3-, 2,4-,2,5-, 2,6-, 3,4- et 3,6-lutidine). L'effet le plus prononcé du groupe CH₃ s'observe en position 4. Cette influence du groupe méthyle sur le degré des changements chimiques indique aussi l'influence mutuelle des ligands dans les composés de coordination du Cu(II).

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- , , NCS Cu(NCS)₂,L₂, L=2-, 3- 4- , 2.3-, 2.4-, 2.5-, 2.6-, 3.4- 3.5-. , 4. Cu(II).