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

المقال منشور على موقع مجلة الفورين بوليسي الأميركية (Foreign Policy) على الانترنت في 27 أيلول/سبتمبر 2019. يُشير مصطلح العزل (Impeachment) في الثقافة السياسية الأميركية إلى مجموعة الإجراءات التي يتم بموجبها عزل الرئيس من منصبه، وهذه الإجراءات هي بمثابة عملية طويلة تجري داخل الكونجرس، وتتم وفقاً لخطوات يؤدي فيها كل من مجلسيّ النواب والشيوخ دوراَ. ولا يعني القيام بهذه الإجراءات أن يتم عزل الرئيس، فقد تتم إ

With the spread of global markets for modern technical education and the diversity of programs for the requirements of the local and global market for information and communication technology, the universities began to race among themselves to earn their academic reputation. In addition, they want to enhance their technological development by developing IMT systems with integrated technology as the security and fastest response with the speed of providing the required service and sure information and linking it The network and using social networking programs with wireless networks which in turn is a driver of the emerging economies of technical education. All of these facilities opened the way to expand the number of students and s

In this research, the effect of multi-walled carbon nanotubes (MWCNTs) on the alumina/chromia (Al₂O₃/Cr₂O₃) nanocomposites has been investigated. Al₂O₃/Cr₂O₃-MWCNTs nanocomposites with variable contents of Cr₂O₃ and MWCNTs were fabricated using coprecipitation process and followed by spark plasma sintering. XRD analysis revealed a good crystallinity of sintered nanocomposites samples and there was only one phase presence of Al₂O₃-Cr₂O₃ solid solution. Density, Vickers microhardness, fracture toughness and fracture strength have been measured in the sintered samples. The results show tha

This study examined the tagged (the matter, its ruling, and examples of its applications in Ahmadiyya interpretations), the study of devising formulas of commissioning, especially the matter from the book of interpretation, which is: (Ahmadiyyeh’s interpretations), and the contemplative of the nature of (Ahmadiyya’s interpretations) realizes that the cognitive, linguistic and juristic knowledge product and the verses of judgments And other is the focus of this immortal travel, as it is truly a comprehensive book containing what the students of knowledge, scholars and the general public need in terms of interpreting the legal verses, and it is not possible to reach an understanding of the Book of God Almighty, and to clarify his purpo

The research aims to determine the effectiveness of auditing in light of the relationship between the governance of investment policy and the cost of debt in companies listed on the Iraqi Stock Exchange. The problem of the research is to raise the question about the effect of the governance of investment policy and the cost of debt on the effectiveness of auditing and auditors. During the research, the most important of them were: the existence of an impact relationship on the effectiveness of auditing through the relationship between the governance of investment policy and the cost of debt. The companies listed in the Iraqi Stock Exchange lack an effective proposed guide or framework dealing with the governance of investment policy desp

In this investigation, metal matrix composites (MMC_s) were manufactured by using powder technology. Aluminum 6061 is reinforced with two different ceramics particles (SiC and B₄C) with different volume fractions as (3, 6, 9 and 12 wt. %). The most important applications of particulate reinforcement of aluminum matrix are: Pistons, Connecting rods etc. The specimens were prepared by using aluminum powder with 150 µm in particle size and SiC, B₄C powder with 200 µm in particle size. The chosen powders were mixed by using planetary mixing setup at 250 rpm for 4hr.with zinc stearate as an activator material in steel ball milling. After mixing process the powders were compacted by hydraulic

Aim: The current study was aimed to determine the relationship between the orthodontic force applied by monobloc and the salivary level of alkaline phosphatase (ALP) and lactate dehydrogenase (LDH) enzymes, considering the time factor after insertion of the appliance and whether there is a correlation between these enzymes. Materials and methods: A sample of 28 growing patients requiring orthodontic treatment with myofunctional appliance (Monoblock) was taken for the current study with an age range 9 to 12 years,all patients had Angle's class II division 1 malocclusion with no or mild crowding, the sample was selected using simple random sampling. Only 16 subjects (10 males and 6 females) were included who follow certain inclusion criteria.

      This research investigates the type and the significant relationship between roaming management and self-efficacy and its impact on excellence in providing hotel service. To achieve this, the applied approach was adopted through  A questionnaire was designed and developed for the collected data. It has consisted of three parts. The firsts section included nine questions to measure the dimensions of management by roaming. The second section includes nine questions to measure the effectiveness of the two employees. The last section includes   12   questions to measure the excellence of the hotel service. The research sample included  43  employees' responding to this