The purpose of this paper is to introduce a new type of compact spaces, namely semi-p-compact spaces which are stronger than compact spaces; we give properties and characterizations of semi-p-compact spaces.

Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be approximately pure submodule of an R-module, if for each ideal I of R. The main purpose of this paper is to study the properties of the following concepts: approximately pure essentialsubmodules, approximately pure closedsubmodules and relative approximately pure complement submodules. We prove that: when an R-module M is an approximately purely extending modules and N be Ap-puresubmodulein M, if M has the Ap-pure intersection property then N is Ap purely extending.

The security of message information has drawn more attention nowadays, so; cryptography has been used extensively. This research aims to generate secured cipher keys from retina information to increase the level of security. The proposed technique utilizes cryptography based on retina information. The main contribution is the original procedure used to generate three types of keys in one system from the retina vessel's end position and improve the technique of three systems, each with one key. The distances between the center of the diagonals of the retina image and the retina vessel's end (diagonal center-end (DCE)) represent the first key. The distances between the center of the radius of the retina and the retina vessel's end (ra

In the present paper, we have introduced some new definitions On D- compact topological group and D-L. compact topological group for the compactification in topological spaces and groups, we obtain some results related to D- compact topological group and D-L. compact topological group.

It is shown that if a subset of a topological space (χ, τ) is δ-semi.closed, then it is semi.closed. By use this fact, we introduce the concept regularity of a topological space (χ, τ) via δ-semi.open sets. Many properties and results were investigated and studied. In addition we study some maps that preserve the δ-semi.regularity of spaces.

In this paper, a new type of supra closed sets is introduced which we called supra β*-closed sets in a supra topological space. A new set of separation axioms is defined, and its many properties are examined. The relationships between supra β*-Ti –spaces (i = 0, 1, 2)   are studied and shown with instances. Additionally, new varieties of supra β*-continuous maps have been taken into consideration based on the supra β*-open sets theory. 

Aerial manipulation of objects has a number of advantages as it is not limited by the morphology of the terrain. One of the main problems of the aerial payload process is the lack of real-time prediction of the interaction between the gripper of the aerial robot and the payload. This paper introduces a digital twin (DT) approach based on impedance control of the aerial payload transmission process. The impedance control technique is implemented to develop the target impedance based on emerging the mass of the payload and the model of the gripper fingers. Tracking the position of the interactional point between the fingers of gripper and payload, inside the impedance control, is achieved using model predictive control (MPD) approach.