This paper introduces some properties of separation axioms called α -feeble regular and α -feeble normal spaces (which are weaker than the usual axioms) by using elements of graph which are the essential parts of our α -topological spaces that we study them. Also, it presents some dependent concepts and studies their properties and some relationships between them.

The undetected error probability is an important measure to assess the communication reliability provided by any error coding scheme. Two error coding schemes namely, Joint crosstalk avoidance and Triple Error Correction (JTEC) and JTEC with Simultaneous Quadruple Error Detection (JTEC-SQED), provide both crosstalk reduction and multi-bit error correction/detection features. The available undetected error probability model yields an upper bound value which does not give accurate estimation on the reliability provided. This paper presents an improved mathematical model to estimate the undetected error probability of these two joint coding schemes. According to the decoding algorithm the errors are classified into patterns and their decoding

The research aims to identify the level of functional engagement and hope-based thinking of kindergarten teachers, identify if there is a significant difference in functional engagement and hope-based thinking in terms of specialization and years of service for kindergarten teachers, identify if there is a significant correlation between functional engagement and hope-based thinking of kindergarten teachers. The current research is determined by kindergarten teachers in the Second Rusafa Baghdad Education Directorate for the academic year (2022-2023). In order to achieve the objectives of the research, the researcher prepared a functional engagement scale, which consists of (45) items in three areas: Perceptual and functional engagement

Die Forschung geht  um das wichtigste Thema für die literarischen Studien, die um die literarische Übersetzung und die Deutlichkeit dem Leser gekreist sind. Die literarische Übersetzung ist ein schwieriger Prozess, der auf vielseitigen Faktoren beruht ist, damit es erfolgreich gelungen ist. Dies ist auch ein gemeinsamer Prozess durch das Kunstwerk zwischen dem Autor und Übersetzer, so dass der erste Schritt in der vorliegenden Forschung wie folgendes lautet: muss es der Autor genau bestimmt wird, wie er die methodischen Grundprinzipien des Wekes im Dienst der zentralen Idee formuliert, und wie er die literarische Gestalt durch die voll erfassende Vorstellung des Wekes dichtet. Denn die literarische Arbeit besteht aus zwei Teilen

Let M be a prime Γ-ring satisfying abc  abc for all a,b,cM and
,  with center Z, and U be a Lie (Jordan) ideal. A mapping d :M M
is called Γ- centralizing if u d u Z  [ , ( )] for all uU and  .In this paper
, we studied Lie and Jordan ideal in a prime Γ - ring M together with Γ -
centralizing derivations on U.

  We live in a world where cultures and visions overlap .. Therefore, every society seeks to create a harmonization that is in line with the data of those special cultures and reproduces those cultures and defines their paths. There are cultures based on historical action and experience and others that work on historical displacement, and art is one of the most important means of transmitting cultures and establishing their aesthetic harmony. This research is concerned with studying (cultural patterns and their representations in contemporary Mexican painting) and it falls into four chapters. The first chapter is devoted to explaining the research problem, its importance, the need for it, the goal of the research, and identifying th

The Present research aimed at identifying:   

1- The level of environmental stress among preparatory students

2- The level of self-rebellion  among preparatory students

3- The correlation between the two variables of research (environmental stress and self-rebellion) and the extent to which the independent variable contributes to the variable of the middle school students. 

The current research has determined the students of the fifth stage of the preparatory stage and all the branches in the departments of education in Baghdad province the morning study for the academic