997 resultados para Moré, Charles-Albert, comte de, 1758-1837.


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"Extrait de la Revue des questions historiques, juillet 1888."

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Twenty-three line edition.

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References: Vicaire col. 389, Bitting p. 555.

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The problem of global optimization of M phase-incoherent signals in N complex dimensions is formulated. Then, by using the geometric approach of Landau and Slepian, conditions for optimality are established for N = 2 and the optimal signal sets are determined for M = 2, 3, 4, 6, and 12.

The method is the following: The signals are assumed to be equally probable and to have equal energy, and thus are represented by points ṡi, i = 1, 2, …, M, on the unit sphere S1 in CN. If Wik is the halfspace determined by ṡi and ṡk and containing ṡi, i.e. Wik = {ṙϵCN:| ≥ | ˂ṙ, ṡk˃|}, then the Ʀi = ∩/k≠i Wik, i = 1, 2, …, M, the maximum likelihood decision regions, partition S1. For additive complex Gaussian noise ṅ and a received signal ṙ = ṡie + ṅ, where ϴ is uniformly distributed over [0, 2π], the probability of correct decoding is PC = 1/πN ∞/ʃ/0 r2N-1e-(r2+1)U(r)dr, where U(r) = 1/M M/Ʃ/i=1 Ʀi ʃ/∩ S1 I0(2r | ˂ṡ, ṡi˃|)dσ(ṡ), and r = ǁṙǁ.

For N = 2, it is proved that U(r) ≤ ʃ/Cα I0(2r|˂ṡ, ṡi˃|)dσ(ṡ) – 2K/M. h(1/2K [Mσ(Cα)-σ(S1)]), where Cα = {ṡϵS1:|˂ṡ, ṡi˃| ≥ α}, K is the total number of boundaries of the net on S1 determined by the decision regions, and h is the strictly increasing strictly convex function of σ(Cα∩W), (where W is a halfspace not containing ṡi), given by h = ʃ/Cα∩W I0 (2r|˂ṡ, ṡi˃|)dσ(ṡ). Conditions for equality are established and these give rise to the globally optimal signal sets for M = 2, 3, 4, 6, and 12.

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La Bibliothèque du Code civil de Charles-Chamilly de Lorimier et Charles-Albert Vilbon, parue au cours de la seconde moitié du XIXe siècle, demeure un des ouvrages de référence marquants de la production juridique québécoise. Les artisans de cet ouvrage présentent le droit civil comme un héritage du passé. L’oeuvre, par sa valorisation des anciens auteurs, propose une lecture du Code civil qui s’inscrit dans la tradition. En même temps, elle se révèle un outil adapté à la transformation que connaît alors la pratique du droit. La Bibliothèque constitue un témoin éloquent de l’évolution de la culture juridique québécoise.