Let G be a graph, each edge e of which is given a weight w(e). The shortest path problem is a path of minimum weight connecting two specified vertices a and b, and from it we have a pre-topology. Furthermore, we study the restriction and separators in pre-topology generated by the shortest path problems. Finally, we study the rate of liaison in pre-topology between two subgraphs. It is formally shown that the new distance measure is a metric

Essential approaches involving photons are among the most common uses of parallel optical computation due to their recent invention, ease of production, and low cost. As a result, most researchers have concentrated their efforts on it. The Basic Arithmetic Unit BAU is built using a three-step approach that uses optical gates with three states to configure the circuitry for addition, subtraction, and multiplication. This is a new optical computing method based on the usage of a radix of (2): a binary number with a signed-digit (BSD) system that includes the numbers -1, 0, and 1. Light with horizontal polarization (LHP) (↔), light with no intensity (LNI) (⥀), and light with vertical polarization (LVP) (↨) is represen

Soft closure spaces are a new structure that was introduced very recently. These new spaces are based on the notion of soft closure operators. This work aims to provide applications of soft closure operators. We introduce the concept of soft continuous mappings and soft closed (resp. open) mappings, support them with examples, and investigate some of their properties.

تهدف هذه الدراسة للتعرف على السياسات اإلاسرائيلية المتبعة على الارض والمتمثلة في االاستيطان
الاستعماري والطرق التفافية، ومصادرة الاراضي وجدار الضم والتوسع العنصري، بالاضافة إلى التصنيف
الاداري للمناطق في الضفة الغربية حسب ما جاء في اتفاقية أوسلو، والتي من شأنها التأثير على تلك
المناطق، وال سيما قطاع اإلسكان الذي يعد من أهم القطاعات التي تتر كب وبالتحديد في منطقة الدراسة،
وسوف تحاول هذه الدراسة تس

      Let  R  be a commutative ring  with identity  and  E  be a unitary left  R – module .We introduce  and study the concept Weak Pseudo – 2 – Absorbing submodules as  generalization of weakle – 2 – Absorbing submodules , where a proper submodule  A of  an  R – module  E is  called  Weak Pseudo – 2 – Absorbing  if   0 ≠ rsx   A   for  r, s  R , x  E , implies that  rx   A + soc ( E ) or  sx  A + soc (E)  or   rs  [ A + soc ( E ) E ]. Many basic  properties, char

     In this paper, we introduce new definitions of the - spaces  namely the    - spaces  Here,  and  are natural numbers that are not necessarily equal, such that . The space  refers to the n-dimensional Euclidean space,  refers to the quaternions set and  refers to the N-dimensional quaternionic space. Furthermore, we establish and prove some properties of their elements. These elements are quaternion-valued N-vector functions defined on , and the  spaces  have never been introduced in this way before.

         The purpose and goal of the research revolve around the diagnosis of intellectual capital as the logical indicator to study an effective human resource management practice and its influential role in determining the overall quality management of higher education institutions and scientific research in Baghdad.

       To achieve the purpose of the research, an upgraded standard questionnaire was used to collect data and distribute it to the selected sample in a statistical manner from the study population of (5) institutions affiliated with the Ministry of Higher Education and Scientific Resear

There is a mutual relationship between the form of a text and its meaning so as separating these two or devaluating the role of one of them leads to the absence of the value therein. Thus, a translation is important as to how it relates the details of a text. That is, the text has special features which go beyond form, and these set out its distinctiveness. Here, we tackle Saleh al-Jafari's Arabic translation of  "Rubbayat al-Khayyam" of Naysapour descriptively and analytically by depending on extracts from the original text. This translation is evaluated on the basis of Spanish critic Maria Carmen Valero Garces. Herein, we discuss the effectiveness of this theory in the criticism of literary texts. It has been concluded that al-Jaf

The research has deal with the relationship between organizational justice and empowerment and their impact on the achievement of organizational commitment in the office of Labour and Vocational Training. To study the research problem which is represented a sense that employees with low levels of organizational justice and empowerment and the reflection on the organizational commitment of the employees, so that Has been collecting data and information relating to research by designing a questionnaire, were distributed to a sample of (50) people in the office mentioned, and the results of the study to confirm the research hypotheses. and the key results of the research was the presence of correlation relationships and the effect o