Courbure totale des feuilletages des surfaces

The sum of the total curvatures of two orientable orthogonal foliations on the unit sphereS ²⊂R ³ is at least 4Π. The total curvature of a foliation with saddle singularities on a closed hyperbolic surfaceM is at least (12 Log 2–6 Log 3) ... |χ(M)|.      

Dynamique des automorphismes des surfaces projectives complexes

We study the dynamics of automorphisms of complex projective surfaces. Letbe such an automorphism whose topological entropy is not zero. We construct a probability measure associated toand the complex structure. This measure is -invariant, ergodic and has maximal entropy. This is the unique measure satisfying these properties and periodic points are equidistributed with respect to this measure.     

Température des Flammes,Rayonnement des Gaz incandescents et des Flammes

Ohne Zusammenfassung

---

Température des Flammes, Rayonnement des Gaz incandescents et des Flammes G. Ribaud, Conférences d'actualités scientifiques et industrielles X, 43 Seiten. Hermann & Cie., Paris 1930. Preis geh. Frs. 5

     

Continuite-Besov des operateurs definis par des integrales singulieres

Our purpose is to give necessary and sufficient conditions for continuity, on Besov spaces \(\dot B_p^{s,q} \) , of singular integral operators whose kernels satisfy: $$|\partial _x^\alpha K(x, y)| \leqslant C_\alpha |x - y|^{ - n - |\alpha |} for|\alpha | \leqslant m,$$ where m ∈ ? and 0 < s < m. The criterion is compared to the M.Meyer theorem [11] where 0 _p ^s,q spaces for s?1. For 0 _p ^s,p space is characterized by the localization and by Besov-capacity. In particular we show that the BMO ₁ ^s,1 space is characterized by generalized Carleson conditions.     

La somme des chiffres des carrés

In this article we answer a question proposed by Gelfond in 1968. We prove that the sum of digits of squares written in a basis q ⩾ 2 is equidistributed in arithmetic progressions.     

Quelques proprietes des systemes generateurs minimaux des monoides

In this paper we give some results about minimal generating systems of a monoïd M. The main tool is a relation denoted “S” which is finer than the relation “J”.     

Neuer Beweis des Primzahlsatzes und Beweis des Primidealsatzes

Ohne Zusammenfassung     

Axiomatisations simples des theories des corps de rolle

Using Becker's results we obtain here a simple first order axiomatization, looking like those by Artin-Schreier and also written in the language of fields, for the theory of Rolle fields (i.e. fields with the Rolle's property for every order). In fields having a finite number of orders, we characterize Rolle fields as those which are pythagorean at level 4 and do not admit any algebraic extension of odd degree. Then we give an axiomatization for Rolle fields having exactly 2ⁿ orders (n≥0); in fact, for n=0 we recover an axiomatization of the theory of real-closed fields and for n=1 we get exactly an axiomatization given for the theory of chain-closed fields by the author in [G1]. Finally we prove that a Rolle field with exactly 2ⁿ orders is the intersection of n+1 real closures of the field.      

Théorie des genres analytique des fonctionsL p-adiques des corps totalement réels

Sans résumé     

Extension des fonctions holomorphes dans les pseudo-ellipsoïdes

Sans résumé Received 17 April 1996; in final form 9 July 1996     

Presentation geometrique des methodes de calcul des valeurs propres

Summary We present a survey of recent work on the convergence of methods for computing eigenvalues and eigenvectors of matrices. We try to maintain a geometric point of view and give pride of place to the R algorithm.

---

---

Cet article a été ecrit pendant le sejour de l'auteur en laboratoire d'Analyse Numérique de l'Université de Paris 6     

Zur Bestimmung des Volumens des Fundamentalbereichs der unimodularen Gruppe

Ohne Zusammenfassung