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
Allah the Almighty has honored many of his slaves in the high houses for their efforts in building the scientific edifice of this nation, by demonstrating what is needed from the legal provisions for all the relations between them, and the actions that they emanate from. The tasks of the abbreviations and Almstsot, and deposited in the mabahith after various investigations and precious precious matters and showed all the human needs in his life and what is expected to happen, even on the rarest possibilities, and their efforts that left the nation on the cases of Goliath. , And Ask They are in Dar dignity with the best creatures and make us a share of those good things, and Odamna to obey Him and His pleasure until death, and forgive us
... Show MoreThe aim of the research is to identify the reality of strategic planning in the National Insurance Company and its importance in building institutional work and to identify the requirements that enable this company to successfully implement strategic planning and the obstacles that limit its application and then achieve the marketing objectives of this company. This study started from the fact that there is a problem represented by the main question that was stated.  
... Show MoreThe study aims budget in grades use of smart phones to individuals (sample) according variable sex (males and females) and used researcher descriptive analytical method consisted sample of (300) students have chosen the way stratified random, and the study variables (academic achievement of students, sex and the use of Smart phones) resolution was adopted as a tool for data collection. The most important results of the study that females are more commonly used for smart phones, as well as the existence of a positive relationship between the inverse statistically significant use of smart phones and the rate of school for students and the use of smart phones h
... Show MoreHygienic engineering has dedicated a lot of time and energy to studying water filtration because of how important it is to human health. Thorough familiarity with the filtration process is essential for the design engineer to keep up with and profit from advances in filtering technology and equipment as the properties of raw water continue to change. Because it removes sediment, chemicals, odors, and microbes, filtration is an integral part of the water purification process. The most popular technique for treating surface water for municipal water supply is considered fast sand filtration, which can be achieved using either gravity or pressure sand filters. Predicting the performance of units in water treatment plants is
... Show MoreNonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though
... Show MoreThe current study examined the impact of using PowerPoint presentation on EFL student’s attendance, achievement and engagement. To achieve the aim of this study, three null hypotheses have been posed as follows: There is no statistically significant difference between the mean score of the experimental group attendance and that of the control one; there is no statistically significant difference between the mean score of the experimental group achievement and that of the control one, and there is no statistically significant difference between the mean score of the experimental group engagement and that of the control one. To verify a hypothesis, a sample of sixty students is chosen randomly from the third year, department of English,
... Show MoreBackground: Different diagnostic definition and criteria have been recommended by different expert groups for the diagnosis of metabolic syndrome, however, it’s prevalence in the same population could differ depending on the definition used yielding different results. In Iraq, there is a lack of research comparing these different diagnostic definitions.
Objective: To find out the most suitable metabolic syndrome definition to be used for Iraqi people.
Methods: 320 participants were recruited for this study, 53.4% men and 46.6% women, aged between 25-85 years, visiting Baghdad Teaching Hospital, the prevalence of metabolic syndrome according to different definition
... Show MoreThis paper presents experimental results regarding the behaviours of eight simply supported partially prestressed concrete beams with internally unbonded tendons, focusing particularly on the effect of three different variables: concrete compressive strength,