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 Jean-Francois Burnol Mathematics , 2004, Abstract: Une danse avec co-Poisson: 1 Introduction: Sommes, Propriete de support, Co-sommes, Mellin et dz\^eta, Fonctions entieres et meromorphes 2 Docteur Poisson et Mister Co: Des theoremes de co-Poisson, Lemmes sur les sommes et les co-sommes, Preuve du theoreme 2.4, Un theoreme de Poisson presque s\^ur, Formule integrale de co-Poisson, Sommes de Riemann, Un autre theoreme de co-Poisson ponctuel 3 Etudes sur une formule de M\"untz: Dz\^eta et Mellin, Distributions temperees et formule de M\"untz, La transformation de Fourier de la fonction dz\^eta, Fonctions de carres integrables 4 Entrelacement et fonctions meromorphes: Convolution multiplicative, Le theoreme d'entrelacement, Transformation de Mellin, Propriete S et transformees de Mellin entieres, Fonctions moderees et propriete S, Distributions homogenes et quasi-homogenes, Propriete S-etendue et fonctions meromorphes, Exemples ----- A dance with co-Poisson: 1 Introduction 2 Dr Poisson and Mister Co 3 Studies on a formula of M\"untz 4 Intertwining and meromorphic functions
 Revista Colombiana de Estadística , 2011, Abstract: We developed an asymptotically optimal hypothesis test concerning the homogeneity of a Poisson process over various subintervals. Under the null hypothesis, maximum likelihood estimators for the values of the intensity function on the subintervals are determined, and are used in the test for homogeneity. Una prueba de hipótesis asintótica para verificar homogeneidad de un proceso de Poisson sobre ciertos subintervalos es desarrollada. Bajo la hipótesis nula, estimadores máximo verosímiles para los valores de la función intensidad sobre los subintervalos mencionados son determinados y usados en el test de homogeneidad.
 Laurent Stolovitch Mathematics , 2004, Abstract: We are interested in analytic singular Poisson structures with a non zero linear part at the singularity. Using recent work of the author about holomorphic normalization of commutative familly of singular vector fields, we obtain results about normalization of holomorphic Poisson structures.
 Mathematics , 2014, Abstract: We prove a conjecture of Etingof and the second author for hypertoric varieties, that the Poisson-de Rham homology of a unimodular hypertoric cone is isomorphic to the de Rham cohomology of its hypertoric resolution. More generally, we prove that this conjecture holds for an arbitrary conical variety admitting a symplectic resolution if and only if it holds in degree zero for all normal slices to symplectic leaves. The Poisson-de Rham homology of a Poisson cone inherits a second grading. In the hypertoric case, we compute the resulting 2-variable Poisson-de Rham-Poincare polynomial, and prove that it is equal to a specialization of an enrichment of the Tutte polynomial of a matroid that was introduced by Denham. We also compute this polynomial for S3-varieties of type A in terms of Kostka polynomials, modulo a previous conjecture of the first author, and we give a conjectural answer for nilpotent cones in arbitrary type, which we prove in rank less than or equal to 2.
 Mathematics , 1999, Abstract: Let g be a quasitriangular Lie bialgebra over a field k of characteristic zero, and let g^* be its dual Lie bialgebra. We prove that the formal Poisson group F[[g^*]] is a braided Hopf algebra. More generally, we prove that if (U_h,R) is any quasitriangular QUEA, then (U_h', Ad(R)|_{U_h' \otimes U_h'}) --- where U_h' is defined by Drinfeld --- is a braided QFSHA. The first result is then just a consequence of the existence of a quasitriangular quantization (U_h,R) of U(g) and of the fact that U_h' is a quantization of F[[g^*]]. ----- Soit g une big\ebre de Lie quasitriangulaire sur un corps k de characteristique zero, et soit g^* sa big\ebre de Lie duale. Nous prouvons que le groupe de Poisson formel F[[g^*]] est une algebre de Hopf tress\'ee. Plus en g\'en\'eral, nous prouvons que, si (U_h,R) est une QUEA quasitriangulaire, alors (U_h', Ad(R)|_{U_h' \otimes U_h'}) --- o\u U_h' est definie par Drinfeld --- est une QFSHA tress\'ee. Le premier r\'esultat est alors une consequence de l'existence d'une quantification quasitriangulaire (U_h,R) de U(g) et du fait que U_h' est une quantification de F[[g^*]].
 Mathematics , 2006, Abstract: The space $\Gamma_X$ of all locally finite configurations in a Riemannian manifold $X$ of infinite volume is considered. The deRham complex of square-integrable differential forms over $\Gamma_X$, equipped with the Poisson measure, and the corresponding deRham cohomology are studied. The latter is shown to be unitarily isomorphic to a certain Hilbert tensor algebra generated by the $L^2$-cohomology of the underlying manifold $X$.
 Physics , 2012, Abstract: We present a study of constrained mechanical systems and of their quantisation, emphasising the importance of the role played by Poisson brackets in the study of gauge theories.
 F. Alcalde Cuesta Mathematics , 1994, Abstract: A surjective submersion $\pi : M \to B$ carrying a field of simplectic structures on the fibres is symplectic if this Poisson structure is minimal. A symplectic submersion may be interpreted as a family of mechanical systems depending on a parameter in $B$. We give some conditions to find a closed form which represent the foliated form $\sigma$ gluing the symplectic forms on the fibres. This is the first step to prequantize all these systems at once. We will indeed exhibit an integrality condition which does not depend on the closed form representing $\sigma$: if the fibres are 1-connected and $H^3(B;Z)=0$, then there exists a $S^1$-principal fibre bundle with a connection whose curvature represents $\sigma$ iff the group of spherical periods of $\sigma$ is a discrete subgroup of R. The symplectic integration of a Poisson manifold $(M,\Lambda)$ is a symplectic groupoid $(\Gamma,\eta)$ with 1-connected fibres such that the space of units with the induced Poisson structure is isomorphic to $(M,\Lambda)$. This notion was introduced by A. Weinstein in order to quantize Poisson manifolds by quantizing their symplectic integration. We show that if the symplectic integration is prequantizable, then there exists a unique prequantization which is trivial over $M$. We show that the symplectic integration of a minimal Poisson manifold is prequantizable iff the group of spherical periods is discrete. Moreover we prove that a {\em totally aspherical} Poisson manifold (any vanishing cycle is trivial and the $\pi_2$ of the leaves is zero) is prequantized in the sense of Weinstein by a trivial fibre bundle.
 Matemáticas : Ense？anza Universitaria , 2007, Abstract: The Lipschitz spaces (Rn), > 0 are de ned and characterized in terms of partial derivatives of the Poisson integrals. In this paper we show a characterization of the functions of (Rn), in terms of the Riemann-Liouville,s non integer order derivative of the Poisson integral. For this we generalize to the non integer case some propierties of the kernel and Poisson integral,s partial derivatives.
 Mathematics , 2005, Abstract: Starting from the problem of describing cohomological invariants of Poisson manifolds we prove in a sense a `no-go'' result: the differential graded Lie algebra of de Rham forms on a smooth Poisson manifold is formal.
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