Endomorphism Rings and Isogenies Classes for Drinfeld Modules of Rank 2 Over Finite Fields

Let $\Phi$ be a Drinfeld $\mathbf{F}_{q}[T]$-module of rank 2, over a finite field $L$, a finite extension of $n$ degrees of a finite field with $q$ elements $\mathbf{F}_{q}$. Let $m$ be the extension degrees of $L$ over the field $\mathbf{F}_{q}[T]/P$, $P$ is the $\mathbf{F}$-characteristic of $L$, and $d$ the degree of the polynomial $P$. We will discuss about a many analogies points with elliptic curves. We start by the endomorphism ring of a Drinfeld $\mathbf{F}_{q}[T]$-module of rank 2, End$_{L}\Phi$, and we specify the maximality conditions and non maximality conditions as a $\mathbf{F}_{q}[T]$-order in the ring of division End$_{L}\Phi \otimes _{\mathbf{F}_{q}[T]}$, in the next point we will interested to the characteristic polynomial of a Drinfeld module of rank 2 and used it to calculate the number of isogeny classes for such module, at last we will interested to the Characteristic of Euler-Poincare $\chi_{\Phi}$ and we will calculated the cardinal of this ideals.Comment: 1

Post-disaster 4G/5G Network Rehabilitation using Drones: Solving Battery and Backhaul Issues

Drone-based communications is a novel and attractive area of research in cellular networks. It provides several degrees of freedom in time (available on demand), space (mobile) and it can be used for multiple purposes (self-healing, offloading, coverage extension or disaster recovery). This is why the wide deployment of drone-based communications has the potential to be integrated in the 5G standard. In this paper, we utilize a grid of drones to provide cellular coverage to disaster-struck regions where the terrestrial infrastructure is totally damaged due to earthquake, flood, etc. We propose solutions for the most challenging issues facing drone networks which are limited battery energy and limited backhauling. Our proposed solution based mainly on using three types of drones; tethered backhaul drone (provides high capacity backhauling), untethered powering drone (provides on the fly battery charging) and untethered communication drone (provides cellular connectivity). Hence, an optimization problem is formulated to minimize the energy consumption of drones in addition to determining the placement of these drones and guaranteeing a minimum rate for the users. The simulation results show that we can provide unlimited cellular service to the disaster-affected region under certain conditions with a guaranteed minimum rate for each user.Comment: 2018 IEEE Global Communications Conference: Workshops: 9th International Workshop on Wireless Networking and Control for Unmanned Autonomous Vehicle

Facial expressions emotional recognition with NAO robot

Human-robot interaction research is diverse and covers a wide range of topics. All aspects of human factors and robotics are within the purview of HRI research so far as they provide insight into how to improve our understanding in developing effective tools, protocols, and systems to enhance HRI. For example, a significant research effort is being devoted to designing human-robot interface that makes it easier for the people to interact with robots. HRI is an extremely active research field where new and important work is being published at a fast pace. It is crucial for humanoid robots to understand the emotions of people for efficient human robot interaction. Initially, the robot detects human face by Viola- Jones technique. Later, facial distance measurements are accumulated by geometric based facial distance measurement method. Then facial action coding system is used to detect movements of measured facial points. Finally, measured facial movements are evaluated to get instant emotional properties of human face in this research; it has been specifically applied to NAO humanoid robot