On Physically Secure and Stable Slotted ALOHA System

In this paper, we consider the standard discrete-time slotted ALOHA with a finite number of terminals with infinite size buffers. In our study, we jointly consider the stability of this system together with the physical layer security. We conduct our studies on both dominant and original systems, where in a dominant system each terminal always has a packet in its buffer unlike in the original system. For N = 2, we obtain the secrecy-stability regions for both dominant and original systems. Furthermore, we obtain the transmission probabilities, which optimize system throughput. Lastly, this paper proposes a new methodology in terms of obtaining the joint stability and secrecy regions.Comment: 7 Pages, 8 Figures, Allerton 200

On the generalization some intgeral inequalities and their applications

In this paper, a general integral identity for convex functions is derived. Then, we establish new some inequalities of the Simpson and the Hermite-Hadamard's type for functions whose absolute values of derivatives are convex. Some applications for special means of real numbers are also provided