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 process of coordination and joint cooperation between SAIs and internal auditors in the public sector is considered one of the very important matters in performing efficient audits and are of high quality, especially if this coordination and cooperation is implemented in accordance with international standards, as it leads to avoiding duplication in auditing work. And the distribution of work in a distribution that achieves the objectives of auditing in general and is of general benefit to the economic unit.

The research problem lies in the weakness of the relationship between internal auditing and external auditing as a result of not applying INTOSAI Standard (9150) coordination and joint cooperation

An essential tool for studying the web is its ability to show how energy moves through an ecosystem. Understanding and elucidating the relationship between species variety and their placement within the inclusive trophic dynamics is also beneficial. A food web ecological model with prey and two rival predators under fear and wind flow conditions is developed in this article. The boundedness and positivity of the system’s solution are established mathematically. The stability and existence constraints of the system’s equilibria are examined. The proposed system’s persistence limitations are established. Additionally, the bifurcation analysis of every potential equilibrium is examined using the Sotomayor theorem. To describe the

The concept of rehabilitation provided an essential richness in the conservation philosophy through sustaining buildings life and adapting them to the contemporary use through a vision which looks at the present and future . In Iraq , the existence of historical buildings and the traditional fabric in the cities required the urban development which enhanced the interests of planning and architectural fields especially the building rehabilitation which requires the architectural intervention , and all that led to elaborate the problem of research which is " The confusion in the concepts of monumental, historical and traditional buildings in Iraq, As well as The insufficient knowledge about rehabilitation and the acts related to it through

         Fibromyalgia (FM) is a common, debilitating, and chronic pain syndrome. The women are more likely to have more tender points on examination than are their male counterparts. Iraqi study showed that FM occur in 1.5% among adolescents of Iraqi population. In compare to normal healthy women, present study was revealed that Iraqi women with FM have significant elevation of calcium (p = 0.003) with significant reduction of magnesium (p = 0.001), whereas the inorganic phosphorous was not differs (p = 0.31). In conclusion, magnesium and calcium would play a crucial role in etiopathogenesis of fibromyalgia.

Key words: calcium, magnesium, phosphorous, Fibromyalgia.

In this study the prevalence of acute, sub-acute and chronic toxoplasmosis were monitored in a group of Iraqi pregnant women according to the anti-T.gondii antibodies (IgG and IgM), as well as the levels of both progesterone and estrogen hormones were measured using mini-VIDAS®technique. This study demonstrated that there was high prevalence of chronic toxoplasmosis (31.70%) when it compared with acute and sub-acute type, results also showed that the acute toxoplasmosis always related with low concentration of both progesterone and estrogen which were (5.35 ± 7.15 ng/ml) and (70.66 ± 51.08 pg/ml) respectively

The research dealt with the impact of reinsurance on the financial surplus of the National Insurance Company by focusing on reinsurance in the marine insurance / merchandise branch. The aim of this research was to show the impact of reinsurance indicators (reinsurance ratios, retention ratios, commission rates earned) on reinsurance operations Data on the research variables were collected based on the inductive and deductive approach in the analysis of information for the financial reports of the National Insurance Company of the Marine Insurance Branch and the insurance portfolio (goods) for the period from 2010 to 2017, and for the purpose of obtaining results was used M a number of statistical methods commensurate with the nature of t

Background: Crohn's disease (CD) is an immunological disorder associated with chronic inflammatory process of several unspecific regions of gastrointestinal tract but frequently detected in the terminal Ilium and proximal colon or both. This disease frequently presented with various oral manifestations as a consequence of inflammatory process of the disease, nutritional deficiency or medications side effects. Several therapeutic approaches have been developed for CD management that are targeting the inflammatory process and directed at controlling the host immune response. Immunosuppressants such as Azathioprine and anti-TNF α agents as well as the combination of them have been widely used as an effective therapeutic modality with a bett

Abstract: In the present work, the heat transfer of Nano Aluminum Oxide -NAO- has been studied practically to define the appropriate insulation conditions.  This study focuses on finding of the amount of heat transfer through a glass substrate that is coated with nanoalumina doped on PMMA matrix. The optical and thermal properties were systematically investigated. The density of heat flow rate, was calculated in the range values (240-260) W/m2 while the optimum values confine between (250-260) W/m2 at temp. (25-35)C^o. The results showed that the thermal insulation of the sample was significantly enhanced at temp. (30-50)C^o. The simulated net heat transfer through window decreased linearly with incr

The current research aims to reveal the level of satisfaction of the mentors with the evaluation of their performance according to gender (male - female) and to formulate the predictive equation for the level of performance (dependent variable) from knowing the level of satisfaction with the evaluation (independent variable). (16 paragraphs) contains alternatives to the answer that measures the level of satisfaction (weak, medium, and high) (1,2,3), that is, with a hypothetical average of (32). It consisted of 100 educational counselors consisting of 45 males and 55 females, the results of the research concluded that the level of satisfaction with performance is below the mean when compared with the hypothetical average of the scale of s