We develop in this paper an amelioration of the method given by S. Bobkov and M. Ledoux in [BL00]. We prove by Prékopa-Leindler Theorem an optimal modified logarithmic Sobolev inequality adapted for all log-concave measure on Rn. This inequality implies results proved by Bobkov and Ledoux, the Euclidean Logarithmic Sobolev inequality generalized in the last years and it also implies some convex...

We firstly describe a maximal inequality for dual Sobolev spaces W−1,p. This one corresponds to a “Sobolev version” of usual properties of the Hardy-Littlewood maximal operator in Lebesgue spaces. Even in the euclidean space, this one seems to be new and we develop arguments in the general framework of Riemannian manifold. Then we present an application to obtain interpolation results for Sobol...

We propose a new Integral Probability Metric (IPM) between distributions: the Sobolev IPM. The Sobolev IPM compares the mean discrepancy of two distributions for functions (critic) restricted to a Sobolev ball defined with respect to a dominant measure μ. We show that the Sobolev IPM compares two distributions in high dimensions based on weighted conditional Cumulative Distribution Functions (C...

different methods exists for jamming mitigation and we should choose a method based an the jammer type and other parameters. one of the jammers is narrow band fm jammer and we use subspace projection techniques for the suppression of this type of jammer. in subspace projection technique, we estimate the if of signals and construct the subspace vector that is orthogonal to jammer vector by incre...

This paper introduces a defense approach against end-to-end adversarial attacks developed for cutting-edge speech-to-text systems. The proposed algorithm has four steps. First, we use the short-time Fourier transform to represent speech signals with 2D spectrograms. Second, iteratively find safe vector using spectrogram subspace projection operation. operation minimizes chordal distance adjustm...

In this paper we present several extensions of theoretical tools for the analysis of Discontinuous Galerkin (DG) method beyond the linear case. We define broken Sobolev spaces for Sobolev indices in [1,∞), and we prove generalizations of many techniques of classical analysis in Sobolev spaces. Our targeted application is the convergence analysis for DG discretizations of energy minimization pro...

The Hausdorf moment problem (HMP) over the unit interval in an L 2 -setting is a classical example of ill-posed inverse problem. Since various applications can be rewritten terms HMP, it has gathered significant attention literature. From point view regularization special interest because occurrence non-compact forward operator with non-closed range. Consequently, HMP constitutes one few exampl...

Let $mathcal{A}$ be a Banach algebra with BAI and $E$ be an introverted subspace of $mathcal{A}^prime$. In this paper we study the quotient Arens regularity of $mathcal{A}$ with respect to $E$ and prove that the group algebra $L^1(G)$ for a locally compact group $G$, is quotient Arens regular with respect to certain introverted subspace $E$ of $L^infty(G)$. Some related result are given as well.

The above inequality implies a logarithmic Sobolev inequality for q. We get an explicit lower bound for the logarithmic Sobolev constant of q under the assumptions that: (i) the local specifications of q satisfy logarithmic Sobolev inequalities with constants ρi, and (ii) they also satisfy some condition expressing that the mixed partial derivatives of the Hamiltonian of q are not too large rel...