This letter proposes a robust beamforming (BF) scheme to enhance physical layer security (PLS) of the downlink multibeam satellite system in presence either uncoordinated or coordinated eavesdroppers (Eves). Specifically, with knowing only approximate locations Eves, we aim at maximizing worst-case achievable secrecy rate (ASR) legitimate user (LU), subject constraints per-antenna transmit powe...

The dueling bandit is a learning framework wherein the feedback information in the learning process is restricted to a noisy comparison between a pair of actions. In this research, we address a dueling bandit problem based on a cost function over a continuous space. We propose a stochastic mirror descent algorithm and show that the algorithm achieves an O( √ T log T )-regret bound under strong ...

In this paper, we give a fundamental convexity preserving for spectral functions. Indeed, we investigate infimal convolution, Moreau envelope and proximal average for convex spectral functions, and show that this properties are inherited from the properties of its corresponding convex function. This results have many applications in Applied Mathematics such as semi-definite programmings and eng...

This article deals with the different classes of convexity and generalizations. Firstly, we reveal the new generalization of the definition of convexity that can reduce many order of convexity. We have showed features of algebra for this new convex function. Then after we have constituted Hermite-Hadamard type inequalities for this class of functions. Finally the identity has been revealed for ...

For any finite horizon Sinai billiard map T on the two-torus, we find t_*>1 such that for each t in (0,t_*) there exists a unique equilibrium state $\mu_t$ $- t\log J^uT$, and is T-adapted. (In particular, SRB measure \log J^uT$.) We show exponentially mixing Holder observables, pressure function $P(t)=\sup_\mu \{h_\mu -\int J^uT d \mu\}$ analytic (0,t_*). In addition, P(t) strictly convex if o...

In numerous applications of image processing, e.g. astronomical and medical imaging, data-noise is well-modeled by a Poisson distribution. This motivates the use of the negative-log Poisson likelihood function for data fitting. (The fact that application scientists in both astronomical and medical imaging regularly choose this function for data fitting provides further motivation.) However diff...

This note gives a simple method for obtaining inequalities for ratios involving 3log-convex functions. As an example, an inequality for Wallis’s ratio of Gautchi-Kershaw type is obtained. Inequalities for generalized means are also considered.

Log-concave and Log-convex sequences arise often in combinatorics, algebra, probability and statistics. There has been a considerable amount of research devoted to this topic in recent years. Let {xi}i≥0 be a sequence of non-negative real numbers. We say that {xi} is Log-concave ( Log-convex resp.) if and only if xi−1xi+1 ≤ xi (xi−1xi+1 ≥ xi resp.) for all i ≥ 1 (relevant results can see [2] an...