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 Imsatfia Moheddine Mathematics , 2012, Abstract: In this paper we present a Hamiltonian formulation of multisymplectic type of an invariant variational problem on smooth submanifold of dimension $p$ in a smooth manifold of dimension $n$ with $p  Eeva Suvitie Mathematics , 2012, DOI: 10.1016/j.jnt.2012.03.007 Abstract: We study a mean value of the shifted convolution problem over the Hecke eigenvalues of a fixed non-holomorphic cusp form. We attain a result also for a weighted case. Furthermore, we point out that the proof yields analogous upper bounds for the shifted convolution problem over the Fourier coefficients of a fixed holomorphic cusp form in mean.  Chao Bao Mathematics , 2014, Abstract: The entropy of a hypersurface is given by the supremum over all F-functionals with varying centers and scales, and is invariant under rigid motions and dilations. As a consequence of Huisken's monotonicity formula, entropy is non-increasing under mean curvature flow. We show here that a compact mean convex hypersurface with some low entropy is diffeomorphic to a round sphere. We will also prove that a smooth self-shrinker with low entropy is exact a hyperplane.  A. Mohammad-Djafari Physics , 2001, Abstract: To handle with inverse problems, two probabilistic approaches have been proposed: the maximum entropy on the mean (MEM) and the Bayesian estimation (BAYES). The main object of this presentation is to compare these two approaches which are in fact two different inference procedures to define the solution of an inverse problem as the optimizer of a compound criterion. Keywords: Inverse problems, Maximum Entropy on the Mean, Bayesian inference, Convex analysis.  Mathematics , 2010, Abstract: We present an intrinsic formulation of the kinematic problem of two$n-$dimensional manifolds rolling one on another without twisting or slipping. We determine the configuration space of the system, which is an$\frac{n(n+3)}2-$dimensional manifold. The conditions of no-twisting and no-slipping are decoded by means of a distribution of rank$n$. We compare the intrinsic point of view versus the extrinsic one. We also show that the kinematic system of rolling the$n$-dimensional sphere over$\mathbb R^n$is controllable. In contrast with this, we show that in the case of$SE(3)$rolling over$\mathfrak{se}(3)\$ the system is not controllable, since the configuration space of dimension 27 is foliated by submanifolds of dimension 12.