Discrete degenerate representations of non-compact unitary groups

Two degenerate principal series of irreducible unitary representations of an arbitrary non-compact unitary groupU(p,1) are derived. These series are determined by the eigenvalues of the first and second-order invariant operators, which are shown to possess a discrete spectrum. The explicit form of the corresponding harmonic functions is derived and the properties of the discrete representations are discussed in detail. Moreover, in the Appendix, we derive the properties of the corresponding degenerate representations of an arbitrary compactU(p) group.On leave of absence from Institute of Nuclear Research, Warsaw, Poland.On leave of absence from Institute of Physics of the Czechoslovak Academy of Sciences, Prague, Czechoslovakia.     

A kinematical study of Kirchhoff-Rayleigh flow

Summary A method of calculating the separated flow of a viscous fluid is proposed, which allows to split up properly the boundary condition problem from the viscous phenomena. The theory is developed for the flow past a plate and yields wakes of finite extension having an underpressure which depends directly on the amount of vorticity diffusion and dissipation occurring in the fluid. Application of the method to real flows shows good agreement between the calculated and the measured velocity distributions in front of the plate and in the wake.

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Résumé Une méthode de calcul de l'écoulement décollé d'un fluide visqueux est proposée qui permet de séparer clairement le problème aux limites des phénomènes visqueux. La théorie est développée pour l'écoulement autour d'une plaque et donne des sillages de longueur finie ayant une dépression de culot directement dépendante de l'intensité de la diffusion et dissipation de la vorticité se produisant dans le fluide. L'application de la méthode à des écoulements réels montre une bonne concordance entre les répartitions de vitesse calculées et mesurées sur le devant de la plaque et dans le sillage.

     

Conductivite electrique des magnetites finement divisees substituees a l'aluminium et au chrome

The magnetites substituted for aluminium and chromium show a high conductivity decrease as well as a change in the conduction type under vacuum when passing from the inverse to the normal spinel during substitution. This type of conduction is confirmed by the study of oxygen chemisorption at temperatures close to room temperature. At higher temperatures, volume oxidation is accompanied by a sharp change in conductivity, which differs depending on whether the spinel is inverse or normal.     

Random time change and recurrent boundary

The purpose of this paper is to study some properties of random time changes in recurrent potential theory. In particular we show that the Martin recurrent boundary is not invariant under a random time change. We then obtain a characterization of random time change destroying a boundary point. We also give some complement about the recurrent boundary connected with “special additive functionals”. We have for example a representation at the boundary of solutions of the Poisson's equation $\text{?(I-U}{}_1\text{)=-U}{}_1\text{(x,·)}$ by using local time at x.     

Norme composée et norme associée généralisée d'une matrice

Sans résumé     

Studies related to the synthesis of maytansinoids.

Two approaches to the partial synthesis of C₁–C₅ of a bis-nor maytansinoid $\text{1}$ have been investigated starting on the one hand with (S)-(?)-malic acid and on the other, with D-(+)-ribonolactone.     

Density of states of crystalline chlorine and bromine

The interpolation method for calculation of the density of states g(ν) of Gilat and Raubenheimer has been extended to monoclinic crystals. Numerical results are given for Cl₂ at 118 K and Br₂ at 130 and 250 K.