A complete metric space is a well-known concept. Kreyszig shows that every non-complete metric space  can be developed into a complete metric space , referred to as completion of .

We use the b-Cauchy sequence to form  which “is the set of all b-Cauchy sequences equivalence classes”. After that, we prove  to be a 2-normed space. Then, we construct an isometric by defining the function from  to ; thus  and  are isometric, where  is the subset of  composed of the equivalence classes that contains constant b-Cauchy sequences. Finally, we prove that  is dense in ,  is complete and the uniqueness of  is up to isometrics

The local resolving neighborhood  of a pair of vertices  for  and  is if there is a vertex  in a connected graph  where the distance from  to  is not equal to the distance from  to , or defined by . A local resolving function  of  is a real valued function   such that  for  and . The local fractional metric dimension of graph  denoted by , defined by  In this research, the author discusses about the local fractional metric dimension of comb product are two graphs, namely graph  and graph , where graph  is a connected graphs and graph  is a complate graph &

The metric dimension and dominating set are the concept of graph theory that can be developed in terms of the concept and its application in graph operations. One of some concepts in graph theory that combine these two concepts is resolving dominating number. In this paper, the definition of resolving dominating number is presented again as the term dominant metric dimension. The aims of this paper are to find the dominant metric dimension of some special graphs and corona product graphs of the connected graphs  and , for some special graphs  . The dominant metric dimension of  is denoted by  and the dominant metric dimension of corona product graph G and H is denoted by .

Slag of aluminum is a residue which results during the melting process of primary and secondary aluminum production. Salt slag of aluminum is hazardous solid waste according to the European Catalogue for Hazardous Wastes. Hence, recovery of aluminum not only saves the environment, but also has advantages of financial and economic returns. In this research, aluminum was recovered and purified from the industrial wastes generated as waste from both of State Company for Electrical and Electronic Industries (Baghdad/AlWaziriya) and General Company for Mechanical Industries (Babylon/-Al-Escandria). It was found that these wastes contain tiny proportions of other elements such as iron, copper, nickel, titanium, lead, and potassium. Wastes were

Summary:

This research revolves around the probing of those whom Ibn Hajar said, "He has a vision", its significance, and the ruling on the connection and transmission to it.  The number of narrators reached fifty-one (51) narrators, among whom it was said, “He has a vision, whether it is definite or possibly. Some of them had a vision and companionship.”They are eleven (11) narrators, And among them were those who had visions and had no company, and their number was twenty-one (21) narrators, and among them were those who had no vision and nor company, and their number is nineteen (19) narrators.
As a result , whoever said about him “has a vision” and has companions, his hadith is connected, even i

The topic of the partnership between the public and private sectors with great interest by researchers around the world after making sure that the process of economic and social development depends on a combination of resources and energies and expertise of both the public and private sectors in the creation and operation of the various projects , the economic development of the growing proved the failure of both sectors in achieving greater economic growth Klaaly separately in many countries , especially developing countries with a socialist approach , led one way or another to adopt most of the countries economic reform programs promoted by international organizations and institutions ( such as the IMF and the World Bank ) of i

Abstract

The research aims to determine the role of the efficiency of Human Resources Information System in the effectiveness of Employees Performance Appraisal System in the Ministry of Higher Education and Scientific Research / Center for the ministry, it was touching the researchers need the ministry to devise methods that employ outputs Human Resources Information System in the organization surveyed for the development of methods and levels of process evaluate the performance of its employees, in order to identify the extent of the role played by human resources information system in the process of assessing the performance of employees, we raised the question of the President as follows:

The research deals with solar energy as one of the sources of renewable energies available in Iraq, which can be utilized. The research aims to identify the design pillars of the use of solar energy in street furniture and its relationship to formal variables. The research limits included street furniture manufactured by JCDecaux in Boston during the period 2015-2016, and included the theoretical framework which consists of two sections: solar energy (its beginnings and uses), and solar energy and its uses in Street furniture design.

As far as the research procedures and methodology are concerned, it adopted the descriptive approach in describing and analyzing the sample models in addition to describing and analyzing the sample i

This paper describes a new proposed structure of the Proportional Integral Derivative (PID) controller based on modified Elman neural network for the DC-DC buck converter system which is used in battery operation of the portable devices. The Dolphin Echolocation Optimization (DEO) algorithm is considered as a perfect on-line tuning technique therefore, it was used for tuning and obtaining the parameters of the modified Elman neural-PID controller to avoid the local minimum problem during learning the proposed controller. Simulation results show that the best weight parameters of the proposed controller, which are taken from the DEO, lead to find the best action and unsaturated state that will stabilize the Buck converter system performan