Let R be commutative ring with identity and let M be any unitary left R-module. In this paper we study the properties of ec-closed submodules, ECS- modules and the relation between ECS-modules and other kinds of modules. Also, we study the direct sum of ECS-modules.

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 aim of this paper is to generate topological structure on the power set of vertices of digraphs using new definition which is Gm-closure operator on out-linked of digraphs. Properties of this topological structure are studied and several examples are given. Also we give some new generalizations of some definitions in digraphs to the some known definitions in topology which are Ropen subgraph, α-open subgraph, pre-open subgraph, and β-open subgraph. Furthermore, we define and study the accuracy of these new generalizations on subgraps and paths.

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.

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

In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise closure topological spaces, fibrewise wake topological spaces, fibrewise strong topological spaces over B. Also, we introduce the concepts of fibrewise w-closed (resp., w-coclosed, w-biclosed) and w-open (resp., w-coopen, w-biopen) topological spaces over B; Furthermore we state and prove several Propositions concerning with these concepts.

Gangyong Lee, S.Tariq Rizvi, and Cosmin S.Roman studied Rickart modules.

The main purpose of this paper is to develop the properties of Rickart modules .

We prove that each injective and prime module is a Rickart module. And we give characterizations of some kind of rings in term of Rickart modules.

The effect of thickness variation on some physical properties of hematite α-Fe2O3 thin films was investigated. An Fe2O3 bulk in the form of pellet was prepared by cold pressing of Fe2O3 powder with subsequent sintering at 800 . Thin films with various thicknesses were obtained on glass substrates by pulsed laser deposition technique. The films properties were characterized by XRD, and FT-IR. The deposited iron oxide thin films showed a single hematite phase with polycrystalline rhombohedral crystal structure .The thickness of films were estimated by using spectrometer to be (185-232) nm. Using Debye Scherrerś formula, the average grain size for the samples was found to be (18-32) nm. Atomic force microscopy indicated that the films had

Jordan  curve  theorem  is  one  of  the  classical  theorems  of  mathematics, it states  the  following :  If    is a graph of  a  simple  closed curve  in  the complex plane the complement  of   is the union of  two regions,  being the common  boundary of the two regions. One of  the region   is  bounded and the other is unbounded. We introduced in this paper one of Jordan's theorem generalizations. A new type of space is discussed with some properties and new examples. This new space called Contractible -space.

The present work aims to study the effect of using an automatic thresholding technique to convert the features edges of the images to binary images in order to split the object from its background, where the features edges of the sampled images obtained from first-order edge detection operators (Roberts, Prewitt and Sobel) and second-order edge detection operators (Laplacian operators). The optimum automatic threshold are calculated using fast Otsu method. The study is applied on a personal image (Roben) and a satellite image to study the compatibility of this procedure with two different kinds of images. The obtained results are discussed.