The main objective of this research is to study and to introduce a concept of strong fully stable Banach -algebra modules related to an ideal.. Some properties and characterizations of full stability are studied.

      In this paper, a modified three-step iteration algorithm for approximating a joint fixed point of non-expansive and contraction mapping is studied. Under appropriate conditions, several strong convergence theorems and Δ-convergence theorems are established in a complete CAT (0) space. a numerical example is introduced to show that this modified iteration algorithm is faster than other iteration algorithms. Finally, we prove that the modified iteration algorithm is stable. Therefore these results are extended and improved to a novel results that are stated by other researchers. Our results are also complement to many well-known theorems in the literature. This type of research can be played a vital role in computer programming

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.

In this paper we introduce a new class of operators on Hilbert space. We
call the operators in this class, n,m- powers operators. We study this class
of operators and give some of their basic properties.

      Throughout this paper, a generic iteration algorithm for a finite family of total asymptotically quasi-nonexpansive maps in uniformly convex Banach space is suggested. As well as weak / strong convergence theorems of this algorithm to a common fixed point are established. Finally, illustrative numerical example by using Matlab is presented.

The operative system of theatrical performance depends on the construction of the scenographic space, as it constitutes the most aesthetic effect of the recipient, and the body of the theatrical discourse that contains the signs of the show, and it comes as an embodiment of the directing vision of the show director, so most of the world directors resorted to attention to the output treatment to establish the scenographic space, and thus it possesses a contrast in The embodiment of the directing vision according to the stylistic and hermeneutical dimension of the director, so the two researchers found the importance of studying the topic, and the study came under the title (Directing Treatments of the Scenographic Space in the Iraqi Theat

In this paper, we introduce a new type of Drazin invertible operator on Hilbert spaces, which is called D-operator. Then, some properties of the class of D-operators are studied. We prove that the D-operator preserves the scalar product, the unitary equivalent property, the product and sum of two D-operators are not D-operator in general but the direct product and tenser product is also D-operator.

Digital forensic is part of forensic science that implicitly covers crime related to computer and other digital devices. It‟s being for a while that academic studies are interested in digital forensics. The researchers aim to find out a discipline based on scientific structures that defines a model reflecting their observations. This paper suggests a model to improve the whole investigation process and obtaining an accurate and complete evidence and adopts securing the digital evidence by cryptography algorithms presenting a reliable evidence in a court of law. This paper presents the main and basic concepts of the frameworks and models used in digital forensics investigation.