Some graphs with chromatic number three

A question of P. Erdös is solved by showing that certain graphs have chromatic number at most three. The proof proceeds by showing a conjecture of Erdös and Bollobás holds, namely, that under certain circumstances, a graph which contains an odd circuit must contain an odd circuit with diagonal.     

Equations fonctionnelles et systèmes induits en théorie ergodique

Sans résuméEquipe de Recherche n 1 «Processus stochastiques et applications», associèe au C.N.R.S.     

On Fatou's Lemma in several dimensions

Probability Theory and Related Fields -     

Le spectre d'absorption infrarouge de l'acétate de méthyle perdeutéré

Résumé Les spectres d'absorption infrarouge de l'acétate de méthyle et de l'acétate de méthyle perdeutéré ont été étudiés de 300 à 4000 cm^–1. La comparaison des spectres a permis l'attribution certaine des bandes de l'acétate de méthyle, en particulier de la bande observée vers 1245 cm^–1 qui correspond à une vibration concernant la liaison C-O.

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Summary The infrared absorption spectra of methyl acetate and the perdeuterated methyl acetate have been studied from 300 to 4000 cm^–1. The comparison of the spectra has made it possible to attribute certain of the bands of methyl acetate, in particular the band observed around 1245 cm^–1, which corresponds to a vibration involving the C-O bond.

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Zusammenfassung Die Absorptionsspektren von Methylacetat der Zusammensetzung CH₃COOCH₃ und CD₃COOCD₃ im Infrarot wurden zwischen 300 und 4000 cm^–1 untersucht. Der Vergleich dieser Spektren führte zur sicheren Zuordnung der Banden des Methylacetats, insbesondere der bei 1245 cm^–1 gelegenen Bande, die der C-O-Bindung zugehört.

     

Application of Watson's centrifugal distortion theory to water and light asymmetric tops. General methods. Analysis of the ground state and the ν2 state of D2O16

Watson's reduced Hamiltonian proved adapted for treating the rotation of light molecules which show very large effects of centrifugal distortion. In order to determine which terms are required and which are negligible (choice of an effective model), we have studied the order of magnitude of the terms from a theoretical point of view. This order depends on the coefficient and the operator. It is shown (1) that the order of the coefficients depends not only on the degree of the components of the angular momentum but also on the asymmetry of the molecule and (2) that the factor due to the operator depends on the asymmetry and on the rotational quantum numbers J and K_?1. It is established that diagonal and off-diagonal terms are of similar importance for small K_?1 while, for large K_?1, the diagonal terms are the leading ones. Further, the number of terms of high degree may be reduced by numerically telescoping the series. The terms to be retained are best determined by a statistical analysis. Terms resulting from telescoping completely or partially lose their original meaning.The previous theory has been applied to the ground state and to the ν₂ state of D₂O¹⁶. Thirteen new microwave lines are reported in this paper. In the rotational analysis, microwave and infrared data were used simultaneously: 22 constants could be determined for the groundstate and only nine for the ν₂ state. The constants related to the z-axis are most affected in the latter. The A, B, C constants corresponding to the standard Hamiltonian, i.e., the Kivelson-Wilson Hamiltonian, are, in MHz:

$\text{A}{}_{\mathrm{gr}}\text{=462 291.70, B}{}_{\mathrm{gr}}\text{=217 982.29, C}{}_{\mathrm{gr}}\text{=145 301.13, A}{}_{\mathrm{v2}}\text{=498 746, B}{}_{\mathrm{v2}}\text{=219 960, C}{}_{\mathrm{v2}}\text{=143 672.}$

     

Étude de l'adsorption électrochimique de l'oxygène sur des lames minces d'or par la mesure de leur résistance électrique

The electrical resistance changes of thin gold film electrodes of preferential orientation [111] with film thickness and potential have been studied. The applicability of the Fuchs-Sondheimer (FS) relation to the decrease of resistance observed at the first negative polarization and the first few potential sweeps for different thicknesses have shown that this phenomenon is due to a surface process, interpreted as a cleaning of the electrodes. The resistance changes observed during the electrochemical adsorption and desorption of oxygen also obey the FS relation. The analysis of the resistance variation with the charge exchanged during these reactions has allowed us to show that the electrochemical adsorption of oxygen, on these gold films occurs by a two-dimensional island mechanism with formation of different structures of the surface layer. The values of the resistivity change caused by the adsorption of 1% oxygen atoms (with respect to the total number of metal atoms in the films) at low coverage have been compared with those observed in other systems (metal-gas, metal-metal).