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

Traditional nursing interventions for children with Cerebral Palsy (CP) often lack active engagement and show limited improvement in motor function. Play interventions involving manipulative activities may better support motor skill development. Objectives: To evaluate the effect of structured play-based nursing interventions on hand motor skills in children with cerebral palsy. Methods: A quasi-experimental pre-test/post-test design with a control group was used. The study was conducted at the Paediatric Welfare Hospital in Baghdad from November 25, 2024, to February 13, 2025. A non-probability sample of 79 children was identified based on the study criteria; of these, 64 children met the eligibility criteria and agreed to particip

Iraq is located near the northern tip of the Arabian plate, which is advancing northwards relative to the Eurasian plate, and is predictably, a tectonically active country. Seismic activity in Iraq increased significantly during the last decade. So structural and geotechnical engineers have been giving increasing attention to the design of buildings for earthquake resistance. Dynamic properties play a vital role in the design of structures subjected to seismic load. The main objective of this study is to prepare a data base for the dynamic properties of different soils in seismic active zones in Iraq using the results of cross hole and down hole tests. From the data base collected it has been observed that the average ve

Dumping policy considered as one of the policies occurs severe damages to the developing countries apparently this is happens due to the potential weakness in (productive, technical, legislative, legal institutions) comparing with other developed countries who are members in WTO.

Iraq consider as one of the developing countries that has been effected by the dumping policy, the events in Iraq since downfall of the formal regime, and the allied forces domination of Iraq have all together accelerated in the apace of deterioration , particularly , after the temporary coalition authority  has forced Iraq to adopt a free foreign trade policy& exclusion of the state from the market mechanism & to consolidate import and deac

This study was conducted to describe a protocol for the callus establishing culture of Lavandula angustifolia plant and estimating their content of volatile oil. The quantity of volatile oil callus tissues was compared with that of leaves production. Callus was induced from leaf explants on Murashige and Skoog medium (MS) supplemented with Naphthalene acetic acid (NAA) and Benzyl adenine (BA) in different concentrations. Maximum callus fresh weight was obtained in the combination of 10 mg/L BA and 3 mg/L NAA which reached 18 g after four weeks. The results of this work showed that the  quantity of volatile oil from the highest fresh weight callus was 6 ml compared with quantity of 18g of leaves which gave 0.5 ml. Volatile o

In this paper the queuing system (M/Er/1/N) has been considered in equilibrium. The method of stages introduced by Erlang has been used. The system of equations which governs the equilibrium probabilities of various stages has been given. For general N the probability of j stages of service are left in the system, has been introduced. And the probability for the empty system has been calculated in the explicit form.