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

            This study tests the effect of a large number of independent variables that control the growth of the total productivity, which amounted to 112 variables, gathered from what is mentioned in the specialized theoretical and applied literature. The data for these variables were taken from global reports of sound international organizations and reliable databases covering the period 1991-2016. The data of the dependent variable, the growth of the total factor productivity, were taken from the database of the world development indicators. The study covered 61 countries for which data were available. The study included three regression models to explain

The city has normal natural state, and the man has a usual movement, change and search for the new .Also, the city has a usual change and transform in its time, place and quality (sizes)structures. The city has a solid memory diving into the past and the future and reflects The real present, and this memory has a timing layers change into real materialistic place making the city has accumulated overlapping circles which is hard to break u , and it broadcasts the lockup timing density ,in which there is no visual record precisely, it is just like((the social record)) that evaluates the un visual relationships between the components and parts of the city (community and form) in a visual quiet exhibition and transform change inside.

The current research aims to develop the skills of the kindergarten students in designing and implementing a theater for gauntlets made of cardboard materials. To study this, the researcher determined to build teaching plans for design and implementation skills according to (Kolb model).
The results of this research showed the effectiveness of teaching plans according to (Kolb's model) in developing skills of design and implementation (theater for gauntlets made of cardboard materials) for the students of the Kindergarten Department - the experimental group. Which had a positive effect to reach the desired results in the design and implementation of the gauntlet theater and dealing with cardboard materials

Thermal energy storage is an important component in energy units to decrease the gap between energy supply and demand. Free convection and the locations of the tubes carrying the heat-transfer fluid (HTF) have a significant influence on both the energy discharging potential and the buoyancy effect during the solidification mode. In the present study, the impact of the tube position was examined during the discharging process. Liquid-fraction evolution and energy removal rate with thermo-fluid contour profiles were used to examine the performance of the unit. Heat exchanger tubes are proposed with different numbers and positions in the unit for various cases including uniform and non-uniform tubes distribution. The results show that

Almost all thermal systems utilize some type of heat exchanger. In a lot of cases, evaporators are important for systems like organic Rankine cycle systems. Evaporators give a share in a large portion of the capital cost, and their cost is significantly attached to their size or transfer area. Open-cell metal foams with high porosity are taken into consideration to enhance thermal performance without increase the size of heat exchangers. Numerous researchers have tried to find a representation of the temperature distribution closer to reality due to the different properties between the liquid and solid phases. Evaporation heat transfer in an annular pipe of double pipe heat exchanger (DPHEX) filled with cooper foam is investigated numerical

Background: Chief complaint of patients attending dental clinic represents the first step towards treatment plan. However, most of patients are not aware but the extent and severity of periodontal disease, which could be also, misdiagnose by the dentist. Aim of the study: To investigate whether reported chief complaint(s) are consistent with oral hygiene status Materials and methods: Records of 1102 patients, attending periodontics clinics in the college of dentistry/ university of Baghdad, were used to determine ten most commonly reported chief complaints. Sample of patients was further subdivided according to gender and age. In addition, plaque and gingival index were recorded to determine oral hygiene status. Results: Patients mostly

The research aims to develop alternatives to transportation at the entrance to the Educational City (University of Baghdad) during the morning and evening peaks, which result from of the traffic congestion at the entrances to the educational city (the University of Baghdad), and affects the emotional, functional, and social performance of the whole city, and leads to hotbeds of confluence and congestion at the entrances in the morning and evening peaks. This movement was measured on the ground for pedestrians and vehicles. Some criteria were adopted to determine the density of road length to the area and density of roads for the number of users and the rate of the area served by roads. The research reviews the experiences of some