Sur L’Existence De L’Unité Unilatérale Dans Les Algèbres De Banach

One of our main results is a theorem on the existence of a left unit in Banach algebras. As a consequence, we obtain a non-commutative version of a result due to Dixon.      

Inégalités de Morse Holomorphes Singulières

We generalize Demailly’s holomorphic Morse inequalities to the case of a line bundle E equipped with a singular metric on an arbitrary compact complex manifold X. Our inequalities give an estimate of the cohomology groups with values in the tensor power E^⊗k twisted by the corresponding sequence of multiplier ideal sheaves introduced by Nadel. The allowed singularities are of the following type: the metric is locally given by a weight exp(−φ) where with holomorphic f_j. As a consequence, we obtain a necessary and sufficient analytic condition, invariant by bimeromorphism, for a manifold X to be Moishezon. This characterization improves a result given by Ji and Shiffman. We finally recall and improve some results of Kollár in order to show that the corresponding sufficient conditions obtained by Siu and Demailly in the smooth case are not necessary.      

Révision et extension des formules numériques de la théorie des surfaces réciproques

Sans résumé     

The Blackwell and Dubins Theorem and Rényi’s Amount of Information Measure: Some Applications

This survey paper provides first for an overview of how quantum-like concepts could be used in macroscopic environments like economics. The paper then argues for the use of the concept of a quantum mechanical wave function as an ‘information wave function’. A rationale is provided on why such interpretation is reasonable. After having defined the ‘information wave function’, Ψ(q), we argue how | Ψ(q)| ² can be interpreted as a Radon-Nikodym derivative. We consider how we can connect, using the | Ψ(q)| ², the Blackwell and Dubins (Ann. Math. Stat. 33:882–886, 1961) Theorem with Rényi’s (Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, 1961) measure of quantity of information. We also define ‘ambiguity of information’ and ‘multi-sourced information’.     

Régularisation S.C.I. et γ-convergence: Approximations inf-convolutives associées à un référentiel

Summary The well-known Moreau-Yosida approximation is inoperative for nonconvex functionals without an a priori inequality of quadratic type. We point out an inf-convolution approximation (generally locally lipschitz) by a convex function (called « referential ») connected to the «infinite negative growth» of the approximated function. This method is easily extended to problems of - convergence: epi- convergence, epi-hypo-convergence ... Several applications are given to the case of integral functionals and to conditional expectations of integrands.

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article dédié à J. J.Moreau     

Fibrés de Green et Régularité des Graphes C 0-Lagrangiens Invariants par un Flot de Tonelli

In this article, we prove different results concerning the regularity of the C ⁰-Lagrangian invariant graphs of the Tonelli flows. For example :

Comments on “Imprecise probability models for learning multinomial distributions from data. Applications to learning credal networks” by Andrés R. Masegosa and Serafín Moral

We briefly overview the problem of learning probabilities from data using imprecise probability models that express very weak prior beliefs. Then we comment on the new contributions to this question given in the paper by Masegosa and Moral and provide some insights about the performance of their models in data mining experiments of classification.     

Erratum à la Note « f-catégories,tours et motifs de Tate » [C. R. Acad. Sci. Paris,Ser. I 347 (2009) 1137–1342], avec un appendice de Q. Liu et de J. Vitória

The aim of this Note is to correct the hypothesis of Theorem 1.1 (c), (d) of J. Wildeshaus, C. R. Acad. Sci. Paris, Ser. I 347 (2009) 1337–1342. As shown by a counterexample found by Q. Liu and J. Vitória, whose construction is given in the Appendix, the original hypothesis is indeed insufficient to obtain the conclusions of J. Wildeshaus (2009).