In this thesis, we study the topological structure in graph theory and various related results. Chapter one, contains fundamental concept of topology and basic definitions about near open sets and give an account of uncertainty rough sets theories also, we introduce the concepts of graph theory. Chapter two, deals with main concepts concerning topological structures using mixed degree systems in graph theory, which is M-space by using the mixed degree systems. In addition, the m-derived graphs, m-open graphs, m-closed graphs, m-interior operators, m-closure operators and M-subspace are defined and studied. In chapter three we study supra-approximation spaces using mixed degree systems and primary object in this chapter are two topological

     The cozy partitions achieved more creativity by emerging with many topics in representation theory and mathematical relations. We find the precise number of cozy tableaux in the case  with any number of  and . Specifically, we use the MATLAB programme that coincided with the mathematical solution in giving precision to these numbers in this case.

The literature shows conflicting outcomes, making it difficult to determine how e-learning affects the performance of students in higher education. The effect of e-learning was studied and data has been gathered with the utilization of a variety of qualitative and quantitative methods, especially in relation to students' academic achievements and perceptions in higher education, according to literature review that has been drawn from articles published in the past two decades (2000-2020). The development of a sense of community in the on-line environment has been identified to be one of the main difficulties in e-learning education across this whole review. In order to create an efficient online learning community, it could be claim

Let R be associative; ring; with an identity and let D be unitary left R- module; . In this work we present semiannihilator; supplement submodule as a generalization of R-a- supplement submodule, Let U and V be submodules of an R-module D if D=U+V and whenever Y≤ V and D=U+Y, then annY≪R;. We also introduce the the concept of semiannihilator -supplemented ;modules and semiannihilator weak; supplemented modules, and we give some basic properties of this conseptes

In the present paper, a simply* compact spaces was introduced it defined over simply*- open set previous knowledge and we study the relation between the simply* separation axioms and the compactness, in addition to introduce a new types of functions known as 𝛼𝑆 𝑀∗ _irresolte , 𝛼𝑆 𝑀∗ __𝑐𝑜𝑛𝑡𝑖𝑛𝑢𝑜𝑢𝑠 and 𝑅 𝑆 𝑀∗ _ continuous, which are defined between two topological spaces.

The subject of the provisions of prayer on the chairs of the important topics in the jurisprudence they fall under the door of the people of excuses, and this section of the important doors in Islamic jurisprudence because it permeates scourge, as prayer is one of the pillars of this religion, and the first thing to be held accountable on the Day of Resurrection prayer If the peace reconciled the rest of his work and spoil corrupted all his work, the street wise was interested in this matter and put him provisions overlooked by many people these days became insulted him and do not pardon him, and do not know the rules and provisions approved by Shara, and the omission of one of these provisions is possible To lead to the invalidity of hi

 Let R be a commutative ring with 10 and M is a unitary R-module . In this paper , our aim is to continue studying 2-absorbing submodules which are introduced by  A.Y. Darani and F. Soheilina . Many new properties and characterizations are given .

This study sought to determine malformation caused by Ochratoxin-A (OTA) on mouse embryos. Twenty adult female white Swiss mice (mus msculus) were divided into four groups, with five females per group, and with one male placed with two females in a cage. Avaginal plug was observed in the early morning and the day of mating was considered as day of pregnancy followed by the first day of pregnancy. Three sub lethal concentrations of OTA were applied to the respective groups (other than the control), 1mg/kg, 2mg/kg and 4mg/kg. The animals were given 0.1 ml per 10 gm body weight per concentration of OTA once a day during days 7-14 of pregnancy. The control group animals were given distilled water. The pregnant mice were dissected, and the embry

In this paper mildly-regular topological space was introduced via the concept of mildly g-open sets. Many properties of mildly - regular space are investigated and the interactions between mildly-regular space and certain types of topological spaces are considered. Also the concept of strong mildly-regular space was introduced and a main theorem on this space was proved.

     Our aim in this work is to investigate prime submodules and prove some properties of them. We study the relations between prime submodules of a given module and the extension of prime submodules. The relations between prime submodules of two given modules and the prime submodules in the direct product of their quotient module are studied and investigated.