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This dissertation depends on study of the topological structure in graph theory as well as introduce some concerning concepts, and generalization them into new topological spaces constructed using elements of graph. Thus, it is required presenting some theorems, propositions, and corollaries that are available in resources and proof which are not available. Moreover, studying some relationships between many concepts and examining their equivalence property like locally connectedness, convexity, intervals, and compactness. In addition, introducing the concepts of weaker separation axioms in α-topological spaces than the standard once like, α-feebly Hausdorff, α-feebly regular, and α-feebly normal and studying their properties. Furthermor

In this research, a new application has been developed for games by using the generalization of the separation axioms in topology, in particular regular, Sg-regular and SSg- regular spaces. The games under study consist of two players and the victory of the second player depends on the strategy and choice of the first player. Many regularity, Sg, SSg regularity theorems have been proven using this type of game, and many results and illustrative examples have been presented

In this paper, some commonly used hierarchical cluster techniques have been compared. A comparison was made between the agglomerative hierarchical clustering technique and the k-means technique, which includes the k-mean technique, the variant K-means technique, and the bisecting K-means, although the hierarchical cluster technique is considered to be one of the best clustering methods. It has a limited usage due to the time complexity. The results, which are calculated based on the analysis of the characteristics of the cluster algorithms and the nature of the data, showed that the bisecting K-means technique is the best compared to the rest of the other methods used.

Suppose R has been an identity-preserving commutative ring, and suppose V has been a legitimate submodule of R-module W. A submodule V has been J-Prime Occasionally as well as occasionally based on what’s needed, it has been acceptable: x ∈ V + J(W) according to some of that r ∈ R, x ∈ W and J(W) an interpretation of the Jacobson radical of W, which x ∈ V or r ∈ [V: W] = {s ∈ R; sW ⊆ V}. To that end, we investigate the notion of J-Prime submodules and characterize some of the attributes of has been classification of submodules.

Abstact:
Nursery is one of educational institution in the process of developing the
social concepts that it includes a quirking the knowledge and experiences that
help the kid to adjust with environment through arrangement words ,
movements and concrete things which are transferred to the kids so as to
realize these concepts .
Social concepts are numbers of words and statements with social nature
which the kids learn through the family or nursery in order to effect their
educational style of independent and helping the others .
The re searcher adopted this theory because of the little studies in the
filed of social concepts in the nursery.
The aims of the study are as following :
1- building tools for

Abstract
Dame Ngaio Edith Marsh (1899-1982), a writer of detective fiction, was born
at Christchurch, New Zealand. Her hero, Chief Detective Inspector Roderick Alleyn,
appears in her first novel, A Man Lay Dead (1934), and in subsequent novels
including Death and the Dancing Footman (1942). She wrote twenty detective novels.
The Dancing Footman, Thomas, listening to a playful song from the smokingroom's
radio where William lay dead after being killed by his brother, Nicholas,
provides the most suspected guest at Highfold with badly needed alibi. The murderer,
Nicholas, plans an almost perfect crime, but the dance of this footman spoils his
scheme. When Alleyn and his group of policemen stage a show in which the

The study aimed to estimate the content of lead and determine the quality of the internal coating of metal cans through electrical conductivity as well as to determine the accuracy of the information card for some types of canned food that available in local markets. The information card test showed that all of these samples contained the name of the food, trade mark, country origin, weight, and components, as was indicated by the company producing in all of them except for the C₁₂ sample which was otherwise, and the batch number was mentioned in all samples except for the C₃ and C₁₇ which was not clear and not mentioned in the C₂₁, and the validity period was observed (produce and fini

Hydro cracking of heavy oil is used in refinery to produce invaluable products. In this research, a model of hydro cracking reactor has been used to study the behavior of heavy oil in hydro cracking under the conditions recommended by literature in terms lumping of feed and products. The lumping scheme is based on five lumps include: heavy oil, vacuum oil, distillates, naphtha and gases. The first order kinetics was assumed for the conversion in the model and the system is modeled as an isothermal tubular reactor. MATLAB 6.1 was used to solve the model for a five lump scheme for different values of feed velocity, and temperature.