This paper contains an equivalent statements of a pre-  space, where  are considered subsets of with the product topology. An equivalence relation between the preclosed set  and a pre-  space, and a relation between a pre-  space and the preclosed set  with some conditions on a function  are found. In addition, we have proved that the graph  of  is preclosed in if  is a pre-  space, where the equivalence relation  on  is open.

     On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that

Coagulation is the most important process in drinking water treatment. Alum coagulant increases the aluminum residuals, which have been linked in many studies to Alzheimer's disease. Therefore, it is very important to use it with the very optimal dose. In this paper, four sets of experiments were done to determine the relationship between raw water characteristics: turbidity, pH, alkalinity, temperature, and optimum doses of alum [   .14 O] to form a mathematical equation that could replace the need for jar test experiments. The experiments were performed under different conditions and under different seasonal circumstances. The optimal dose in every set was determined, and used to build a gene expression model (GEP). The models were co

The selective information broadcasting service is one of the important services in libraries and information centers, as it is the link between the source and the beneficiary and between related sources, as it links similar sources through keywords and then sends them to beneficiaries, which contributes to reducing the time and effort spent by beneficiaries in obtaining sources or information. Therefore, the application of this service is an important matter and gives a positive indicator in the progress of the library towards the integration of its services. From this standpoint, this research came to answer some questions, including: 1. What are the outlets for beneficiaries (the research community) in obtaining information sources? 2. Wh

The research aims to identify the availability of some basic competencies that are required to be available to workers in digital agricultural Extension from the point of view of senior management, middle management, and, employees with Post-graduate education degrees, represented by the following: Transition to digital agricultural Extension for sustainable and smart family farms, benefiting from international expertise and experiences in applying for Digital agricultural Extension, preparing and implementing Extension messages through platforms, factors affecting the effectiveness of digital agricultural Extension and its platforms, following up and evaluating the activities and programs of the digital Extension platform. The research pop

Congenital valvular pulmonary stenosis accounts for 5-10% of all congenital heart disease. Balloon pulmonary valvuloplasty is a safe and effective method in reduction of moderate to severe valvular pulmonary stenosis. This retrospective study done in Hawler surgical specialty cardiac center on pediatric patients who had pulmonary valve stenosis (with echocardiographic peak gradient 2:50mmHg) and treated by balloon pulmonary valvuloplasty. A total of 178 cases were involved, 93(52.25%) patient was male and 85 (47.75%) patients was female. 160 patient (89.89%) were treated with single balloon method 18 patient (10.11%) were managed by double balloon method technique. Follow up period of these patients range from 1 year to 10 years (mean of 5.

The research aims to identify the reality of the management strategy followed in the treatment of solid waste in the city of Baquba, and what strategies are used to treat solid waste, and the extent of the application of these strategies, through personal interviews with leading cadres in the Directorate of Baquba Municipality, their assistants and heads of departments, they numbered (55) Individuals. The descriptive method was adopted through a questionnaire prepared to measure the extent of the implementation of the strategy of solid waste management in the city of Baquba and using statistical tools including (arithmetic mean, standard deviation, relative importance, the gap). The research reac

The problem of the paper focused on the role of the learning organization in the crisis management strategy, and the extent of the actual interest in both the learning organization and the crisis management and aimed at diagnosing and analyzing that and surrounding questions. The Statistical Package for the Social Sciences (SPSS) program was used to calculate the results and the correlation coefficient between the two main variables. The methodology was descriptive and analytical. The case study was followed by a questionnaire that was distributed to a sample of 31 teachers. The paper adopted a seven-dimensional model of systemic thinking that encourages questioning, empowerment, provision of advanced technologies, and strategic lea

Background: Atrial fibrillation (AF) stands as the most prevalent cardiac arrhythmia, with associated risks of stroke and systemic thromboembolism. While vitamin K antagonists, specifically warfarin, have historically been the mainstay for stroke prevention in AF, they come with inherent limitations.

Aim: This review seeks to offer a comprehensive analysis of the efficacy, safety, and clinical advantages of novel oral anticoagulants (NOACs) compared to traditional warfarin in AF management.

Method: A meticulous examination of pivotal clinical trials, meta-analyses, and recent research publications was conducted.

     This aims tackles the importance of the organizational energy of the hotel organizations that search the success in the business field to penetrate in the whole tourist markets, and to draw the policies and firm rules which must be framed with the administrative strategies that contributed in creativity and achievement the targets besides provide a future vision due to its position among the competitive henceforth achieving the activity. This is what the chapters tackle in the theoretical side. Also many general questions have been arisen to determinate the importance of the research and many other special questions that express the problem of the study. To limit the levels of study alter