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- CONTENTS VOLUME 289 - SECTION A
- No. 12 - SESSION OF NOVEMBER 12th 1979
- Group Theory
- In a previous Note we introduced invols whose automorphism group includes elements
of degree 2n-1. We also defined the type of such an element and the genus of a type. We now study the automorphism group and prove the unicity of the genus for all elements in the invol.
- Mathematical Analysis
- .......... Page(s) .......... 595
- We extend to unbounded operators previous results valid for bounded operators [1]. Furthemore, we get a general theorem on the rate of convergence. Applications are given.
- We define the approximate derivative of a positive measure on the real axis and we describe some of its important properties. This notion allows us to give a formula for the density of a positive measure, even when it is neither locally finite nor diffuse. Introducing the set H of increasing homeomorphisms on R, we define the H-derivative of a positive measure, we give a characterization of the semi-finite measures and we get their Lebesgue decomposition from the decomposition of-finite measures.
- Complex Analysis
- .......... Page(s) .......... 601
- Aiming at applications to some deformation problems in complex analytic geometry, we give a version of Nash-Moser implicit function theorem which may be used for spaces like the space of holomorphic functions on a polydisc in Cm. The notion of "loss of differentiability" is here replaced by that of "restriction to a smaller neighbourhood"
- Functional Analysis
- .......... Page(s) .......... 605
- We study properties equivalent to amenability for an action of a locally compact group on a von Neumann algebra M when the action defined by restriction to the centre of M is free. In this case, when M is injective, we show that the crossed product algebra is injective if and only if the action is amenable.
- Construction of elliptic operators and their diffusion invariant by gauge group on spaces of connexions and in the singular quotient space of connexions mod gauge group.
- Optimization
- .......... Page(s) .......... 613
- Let X be a vector space and a functional on X such that:
- : X x X R,
- (i) (x, x) = (x);
- (ii) (x, y) = ((x, x)+(v, y)-2 (x, y))1/2 is a (semi-) distance on X.
- We show, when verifies given hypotheses, that the problem: Inf has a solution in a completed space of (X, ).
- Analytic Geometry
- .......... Page(s) .......... 617
- This Note contains results on order one deformation of analytic cycles. We show that, in general, the order one jet of a one parameter family of cycles does not determine the order one jet of its graph. But we give a generic situation in which this is nevertheless true.
- Probability Theory
- .......... Page(s) .......... 621
- The abstract lifting induced by a lifting of M permits one to construct - in a natural way - Radon measures on a compact space K: this yields a good tool for the extension of Baire measures on a completely regular space. We then study the notion of "lifting compact" space and its stability properties.
- Probability
- .......... Page(s) .......... 625
- A "piecewise expanding transformation" of the square has a finite number of ergodic components, on each of which there exists a unique finite, invariant measure, absolutely continuous with respect to Lebesgue measure. Related results are announced. This extends a paper by Lasota and Yorke to the 2-dimensional case.
- TOME 289 - N° 12 - SERIE A - SCIENCES PHYSIQUES SOMMAIRE
- TABLE DES ARTICLES TOME 289 - N° 12 - SERIE A - SCIENCES PHYSIQUES
- Séance du 12 novembre 1979
- PARTIE SCIENTIFIQUE
- TABLE DES ARTICLES TOME 289 - N° 12 - SERIE A - SCIENCES PHYSIQUES
- CONTENTS VOLUME 289 - SECTION B
- No. 12 - SESSION OF NOVEMBER 12th 1979
- Physics of Continua
- Direct proof, based on microscopic equations and a statistical averaging procedure, of the objectivity or material-frame indifference of the fields which characterize electromagnetic matter as compared to vacuum, within the framework of the Galilean electrodynamics of continua.
- Nuclear Magnetic Resonance
- The motion of the electronic spins in polyacetylene (CH)x is studied by dynamic nuclear polarization for various cistrans compositions. The experimental results show that the characteristic frequency of this motion increases with the concentration in trans isomer.
- SOMMAIRE TOME 289 - N° 12 - SERIE B - SCIENCES PHYSIQUES
- TABLE DES ARTICLES TOME 289 - N° 12 - SERIE B - SCIENCES PHYSIQUES
- Séance du 12 novembre 1979
- PARTIE SCIENTIFIQUE
- TABLE DES ARTICLES TOME 289 - N° 12 - SERIE B - SCIENCES PHYSIQUES
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