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

   The aim of this paper is to introduce and study new class of fuzzy function called fuzzy semi pre homeomorphism in a fuzzy topological space by utilizing fuzzy semi pre-open sets. Therefore, some of their characterization has been proved; In addition to that we define, study and develop corresponding to new class of fuzzy semi pre homeomorphism in fuzzy topological spaces using this new class of functions.

     The primary purpose of this subject is to define new games in ideal spaces via set. The relationships between games that provided and the winning and losing strategy for any player were elucidated.

Personification in Arab poetry is not confined to the abstract items in nature: it trespasses them to include more than that. We found after reviewing the anthologies of the poets tens of the personified items are full of human attributes - via personification- such as speaking, moving, feeling human feelings.. Personification formed a remarkable feature in the relationship between poets and war, which was clear in the Pre-Islamic poetry, because it occupied the minds of the ancient Arab mindset. The poets have envisioned war as ugly as a force that brings destruction and devastation. The paper aims at stating the position in which poets personified war with female tributes. Thus, it is impregnated, conceived, and produced birth like a w

Abstract

This study identified the developing of a range of students' geography learning skills and the change in their attitudes toward fieldwork as a consequence of leaning experiences that occurred within a field trip. The sample of the study consisted of (27) students within a special topic course enrolled in Geography Department at Umm Al-Qura University in Saudi Arabia in semester 2, 2018. A range of students' geography learning skills were measured by the skills questionnaire that consisted of 12 geography skills after completing field work. Changes in students' at

A finite element is a study that is capable of predicting crack initiation and simulating crack propagation of human bone. The material model is implemented in MATLAB finite element package, which allows extension to any geometry and any load configuration. The fracture mechanics parameters for transverse and longitudinal crack propagation in human bone are analyzed. A fracture toughness as well as stress and strain contour are generated and thoroughly evaluated. Discussion is given on how this knowledge needs to be extended to allow prediction of whole bone fracture from external loading to aid the design of protective systems.

The current study included the anatomical structure of the metatarsal bone in sheep in terms of the traditional structural description of the bone, as it was found that the metatarsal bone in the fore and hind limbs of adult sheep had no visible differences between it and animals, especially ruminants. The metacarpal \tarsal bone No. 3 was cylindrical in shape, with the presence of the metacarpal \tarsal bones 2 and 4 declines, articulated from the proximal end with the metacarpal and metatarsal bones whereas from the distal part with the fetlock joint and the first phalanx bone. The aim of the study is to determine whether the environment and its changes in Iraq have affected the animals and their bones in terms of length, thicknes