Pure Mathematics for Theoretical Computer Science

In this work, we study p-Lindelöf spaces, a concept which is "stronger" than Lindelöf spaces. Every p-compact space is proven to be p-Lindelöf space, so the concept of p-Lindelöf is a generalization of the concept of p-compact. Most of the theorems which are valid for p-compact spaces will be also valid for p-Lindelöf spaces, (with a slight modification). We also study local p-Lindelöf spaces with many related theorems and examples.

The set of all isometries on a metric space X with the usual composition of functions form a group and it is called the group of isometries and is denoted by I(X). In this paper we study the generalization of the concepts of minimal sets, stability and attraction, from dynamic system into the topological transformation group (I(X),X).We find that the collection of all minimal sets of I(X)-space is the collection of all the closures of orbits of X and we found some useful results about stability and attraction and we fixed the relationship among it's kinds.

The main purpose of this paper is to study some results concerning the generalized derivation D defined on semi-prime ring R, we obtain a derivation d which commuting and 2-commuting on R. Also, we present many examples to clarify the validity of our work.

In this paper, we find the formula of Cauchy – Pompeiu's integral in the octal of unit disk  of the complex plain, by using the reflection method to determine the Integral's Cauchy – Pompeiu's operator. Also, we give many related examples about the novel formula.

Nowadays, Automatic Meter Reading (AMR) systems are applied in many technologically advanced countries. Many researchers proved that Wireless Sensor Networks (WSN) is one of the most overwhelming technologies for meters information collection systems. In this research, we proposed a network design for the WSN to collect the electric meters information in Jableh city-Syria using mobile gateway. We improved the performance of IEEE 802.15.4 protocol using Guaranteed Time slots (GTS) according to our application need. WE also deduced the mathematical equations that describe the protocol and thus we could get pre-simulation results. We used NS 2.35 and SUMO 0.32.0, and we found that by choosing the appropriate values for the protocol parameters according to our network design and method of collection, we could achieve the reliable collection of electric meters for a gateway speed of up to 70 Km/h which is considered an improvement of the protocol performance compared to other literature studies.