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

The aim of this research is to recognize the tasks undertaken by   the   headmasters   of   intermediate   schools   concerning   time- administration,   in   accordance   to   the   viewpoints   of   the headmasters   of   intermediate   schools   in   the   Administration   of Education   of   Al-Karkh   the   Third.   The   sample   of   this   research consists   of   (60)   headmasters   and &n

The aim of this study is to develop the science textbook for the 1st intermediate grade by analyzing it according to life skills. Its core areas were mental skills, environmental skills, and health skills. The analysis tool was used after verifying its validity and stability in analyzing the science textbook for the 1st intermediate grade, and the results of the study resulted in the inclusion of mental skills on a high percentage of repetitions, while we find that this percentage is low in the inclusion of environmental and health skills. The study recommended the importance of achieving balance and justice in including skills in the science textbook for the 1st intermediate grade, by emphasizing the environmental and health skills by incr

Background: Osteoarthritis is a chronic pathology of the joints causing disability and morbidity. Diacerein is a disease-modifying agent indicated for osteoarthritis management with enhanced performance and have much lower side effects profile than conventional non-steroidal anti-inflammatory drugs. Oral administration of Diacerein is associated with a laxative effect, thus causing treatment discontinuation. Aim: This study aimed to evaluate the activity of Diacerein novasome-based transdermal gel compared with standard oral treatment in the management of induced osteoarthritis in a rat model. Materials and methods: A single intra-articular injection of monosodium iodoacetate was administered to the left knee joint, resulting in the develop

Background: The problem of difficult gallbladder is not clearly defined and associated with real missing of therapeutic approaches that decreased morbidity. Moreover, the difficult gallbladder was reported as a contributing risk factor for biliary injury due to raised difficulty in surgical dissection within Calot’s triangle. The aim of this study is to determine the surgical outcomes of the open fundus-first cholecystectomy in lowering the rate of lethal intraoperative risks.

Subjects and Methods: Our prospective study conducted during the period of January 2019 to December 2022 at Ibn Sina specialized hospital, Khartoum, Sudan, for two hundred and fifty-three patients underw

Background Obstructing dentinal tubules is a valuable approach for managing dentin hypersensitivity. Although various agents promote dentin remineralization, direct comparisons between theobromine, bioactive glass (BAG), and nano-hydroxyapatite (Nano-HAP) under simulated oral conditions remain limited. To fill this gap, this in vitro study aimed to evaluate and compare the effectiveness of these three treatments on exposed cervical dentin. The assessment focused on their chemical, morphological, and mechanical effects on dentin. Materials and methods Forty-eight human dentin slabs were obtained from the cervical portions of twelve sound premolar teeth. Baseline Raman spectroscopy and VMH tests were done to exclude outliers. All specimens we

Background: University dental students perceived a higher level of stress prior to the final exam associated with raised salivary cortisol levels which could be considered as a useful noninvasive biomarker for measuring acute stress. Using a Helkimo anamnestic and clinical dysfunction scoring for temporomandibular disorders can give a better insight about the association of this marker and temporomandibular joint disorders. The aim of this study was to evaluation level of salivary cortisol in stressor students with temporomandibular disorder and the relation between this marker in relation to temporomandibular disorder severity. This might give a better understanding to the role of psychological stress as an etiological factor for developin

The purpose of this research that, the performance budget  is the best style of budget styles that can help and contribute in forming preparing federal typical budget in Iraq , By taking advantage of the application of the principles of scientific rules that would ensure optimal allocation and investment of the financial resources of the state and achieve the best performance and the lowest possible cost, both with regard to the administrative and accounting side, reducing the waste of public money, so that can enhance the success , power , and safety of financial activity of managerial system that it focuses on the magnetite and quality of the work done and the objectives wanted to meet. so application of performance budget require

This research aims primarily to highlight personal tax exemptions A comparative study with some Arab and European regulations. And by conducting both theoretical comparative analyses. Most important findings of the study is the need to grant personal and family exemptions that differ according to the civil status of the taxpayer (single or married). In other words, the exemption increases as the number of family members depend on its social sense. Also taking into account some incomes that require a certain effort and looking at the tax rates, it is unreasonable for wages to be subject to the same rates applied to commercial profits.