In this paper, we define some generalizations of topological group namely -topological group, -topological group and -topological group with illustrative examples. Also, we define grill topological group with respect to a grill. Later, we deliberate the quotient on generalizations of topological group in particular -topological group. Moreover, we model a robotic system which relays on the quotient of -topological group.

Relation on a set is a simple mathematical model to which many real-life data can be connected. A binary relation  on a set  can always be represented by a digraph. Topology on a set  can be generated by binary relations on the set . In this direction, the study will consider different classical categories of topological spaces whose topology is defined by the binary relations adjacency and reachability on the vertex set of a directed graph. This paper analyses some properties of these topologies and studies the properties of closure and interior of the vertex set of subgraphs of a digraph. Further, some applications of topology generated by digraphs in the study of biological systems are cited.

Abstract:
the system of Administrative Control in organizations meets the need to check on the optimal use and proper resources and conservation to achieve the objectives sought by the organization, hence the system of Administrative Control  is part of the overall system in any organization that has undergone evolution always to be able to keep up with progress in the development of other sciences, and that the growth of coherence between subordinates in the organization means the ability to influence the opinions, ideas and attitudes to change it for directions the organization and its values ​​and this is reflected positively on the coherence of the organization, the researcher interest of the imp

The main purpose of this work is to introduce the concept of higher N-derivation and study this concept into 2-torsion free prime ring we proved that:Let R be a prime ring of char. 2, U be a Jordan ideal of R and be a higher N-derivation of R, then , for all u U , r R , n N .

The study aimed to : - To determine whether there are significant differences between Fartlek training and the increase in the molecular biology (VEGF - basal fibroblast growth factor) for arena and field players in an (800m) youth event. - Determine whether there are statistically significant differences between Fartlek training and the increase in molecular biology and some physical variables for the players (800m) in the arena and field for youth. - Determine whether the Fartlek training method is the most appropriate to achieve statistically significant differences in the research variables for the players (800m) in the arena and field for youth. The researchers used the experimental method for its suitability and the nature of the rese

Given the importance that the Iraqi banking system in general and Islamic banks in particular, there must be effective supervisory oversight of these banks, as supervisory oversight has an essential and effective role in the development and evaluation of the performance of banks, through the application of legal controls and rules. Banking aimed at making sure that its financial centers are safe, protecting depositors' funds, and achieving both monetary and economic stability. This research studied and evaluates the mechanisms and tools used by the Central Bank of Iraq in the supervision and supervision of these banks. Therefore, the research aimed to measure the type and direction of the relationship between the requirements of supervis

The security of information represent the available  protection of  information and its component and guaranty the its safety and confidentiality. The absent or lack or stop of security of information and without maximum benefit may lead to lose confidence and make it burden on the company. So we must protect the company and information from the damages which may lead to the frailer of performance and loses of the company and its workers. So the security of information considered one of the potential  and controlling basis to protect individuals and companies from the damages. To insure the security  and confidentiality of information there are delicate,  proper and trusted ways, like FIRE WALL, PASS WORD, SYPHAR