The research is an article that teaches some classes of fully stable Banach - Å modules. By using Unital algebra studies the properties and characterizations of all classes of fully stable Banach - Å modules. All the results are existing, and they've been listed to complete the requested information.

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

which is much useful in the Arabic Language generally in the Holly Quran especially. It is the pronoun  I have taken in the semantic aspect from it and I have done on the surra sabba which varities  the semantical pronoun in it among the pronoun of the speaker the conscience of the addressee the absent  such the the siprat pronoun that comes in it with the explanation for its importance and its work and this is the subject of the first unit which I advanced it from the concept of the pronoun Linguistically and convention. After that I have lighten in some meanings which I have done in the surrat as a semantic , magnification , proud, reprimand and others which I ended my research I have reached the results from it

Cancer is in general not a result of an abnormality of a single gene but a consequence of changes in many genes, it is therefore of great importance to understand the roles of different oncogenic and tumor suppressor pathways in tumorigenesis. In recent years, there have been many computational models developed to study the genetic alterations of different pathways in the evolutionary process of cancer. However, most of the methods are knowledge-based enrichment analyses and inflexible to analyze user-defined pathways or gene sets. In this paper, we develop a nonparametric and data-driven approach to testing for the dynamic changes of pathways over the cancer progression. Our method is based on an expansion and refinement of the pathway bei

Anomaly detection is still a difficult task. To address this problem, we propose to strengthen DBSCAN algorithm for the data by converting all data to the graph concept frame (CFG). As is well known that the work DBSCAN method used to compile the data set belong to the same species in a while it will be considered in the external behavior of the cluster as a noise or anomalies. It can detect anomalies by DBSCAN algorithm can detect abnormal points that are far from certain set threshold (extremism). However, the abnormalities are not those cases, abnormal and unusual or far from a specific group, There is a type of data that is do not happen repeatedly, but are considered abnormal for the group of known. The analysis showed DBSCAN using the

Let A be a unital algebra, a Banach algebra module M is strongly fully stable Banach A-module relative to ideal K of A, if for every submodule N of M and for each multiplier θ : N → M such that θ(N) ⊆ N ∩ KM. In this paper, we adopt the concept of strongly fully stable Banach Algebra modules relative to an ideal which generalizes that of fully stable Banach Algebra modules and we study the properties and characterizations of strongly fully stable Banach A-module relative to ideal K of A.

Topological indices provide important insights into the structural characteristics of molecular graphs. The present investigation proposes and explores a creative graph on a finite group G, which is known as the RIG. This graph is designated as ΓRS G2(4) indicating a simple undirected graph containing elements of G. Two distinct ertices are regarded as nearly the same if and only if their sum yields a non-trivial involution element in G. RIGs have been discovered in various finite groups. We examine several facets of the RIG by altering the graph through the conjugacy classes of G. Furthermore, we investigate the topological indices as applications in graph theory applying the distance matrix of the G2(4) group.

The research problem can be summarized through focusing on the environment that surrounds students and class congestion, how these factors affect directly or indirectly the academic achievement of students, how these factors affect understanding the scientific material that the student receives in this physical environment, how classroom’s components such as seats, space With which the student can move, the number of students in the same class,  the lighting, whether natural or artificial, and is this lighting sufficient or not enough, the nature of the wall paint old or modern, is it comfortable for sight, the blackboard if it is Good or exhausted,  In addition to air-conditioning sets in summer and winter, this is on the on

In this paper, we introduce the concept of cubic bipolar-fuzzy ideals with thresholds (α,β),(ω,ϑ) of a semigroup in KU-algebra as a generalization of sets and in short (CBF). Firstly, a (CBF) sub-KU-semigroup with a threshold (α,β),(ω,ϑ) and some results in this notion are achieved. Also, (cubic bipolar fuzzy ideals and cubic bipolar fuzzy k-ideals) with thresholds (α,β),(ω ,ϑ) are defined and some properties of these ideals are given. Relations between a (CBF).sub algebra and-a (CBF) ideal are proved. A few characterizations of a (CBF) k-ideal with thresholds (α, β), (ω,ϑ) are discussed. Finally, we proved that a (CBF) k-ideal and a (CBF) ideal with thresholds (α, β), (ω,ϑ) of a KU-semi group are equivalent relations.