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 trade balance is considered as a way to join the national economy with the world, So it is the mirror that reflect the economic center of the country and it is point to competitive ability of it, The tariff and the exchange rate perform a great role to motivate the domestic production and improve the trade balance if we direct them to achieve the same purpose. The Iraqi economic has trade balance which achieve overabundant during the years of studying because of the oil exports, while the other exports represent a small percentage it is hardly remember, and expansion in imports from other side causes exhaustion in oil revenues, and this make the trade balance in permanent

Background:The demand for esthetic orthodontic appliances is increasing so that the esthetic orthodontic archwires were introduced. This in vitro study was designed to evaluate the surface roughness offiber-reinforced polymer composite (FRPC) archwires compared to coated nickel-titanium (NiTi) archwires immersed in artificial saliva. Materials and Methods:Three types of esthetic orthodontic archwires were used: FRPC (Dentaurum), Teflon coated NiTi (Dentaurum) and epoxy coated NiTi (Orthotechnology). They were round (0.018 inch) in cross section and cut into pieces of 15 mm in length.Forty pieces from each type were divided into four groups; one group was left at a dry condition and the other three groups were immersed in artificial saliva (

This study was conducted to determine the ability of water treatment system (Vortisand) to reduce some chemical and physical properties for tigris river raw water, It consisted of turbidity, electrical conductivity, pH, total hardness, calcium Hardness as well as temperature in order to determine the unit`s efficiency for reducing their concentration as compared to those in the water produced by some classical potable water projects (Dora and Wathba) in Baghdad. Samples were collected during the cold months (December 2016 and January 2017) and during the hot months (May and June 2017). The results showed that this system has the ability to reduce some properties such as turbidity, the values were 215NTU in raw water and decreased to NTU

This research studies the comparison of deep neural network models and performance evaluation to predict the gold prices of time series, where the gold prices contain high fluctuations and non-linear patterns that are difficult to capture using traditional models, which makes predicting them a significant challenge. Therefore, the focus was on using deep learning models represented by (LSTM), (Bi-LSTM), (GRU) and (Bi-GRU). The results showed the superiority of the (Bi-GRU) model according to comparison criteria (MSE), (RMSE), (MAE), and (R∧2) compared to other models because it was able to understand the time patterns better by processing the data in both directions and provided superior performance, which indicates its effectiveness, eff

It is well known that petroleum refineries are considered the largest generator of oily sludge which may cause serious threats to the environment if disposed of without treatment. Throughout the present research, it can be said that a hybrid process including ultrasonic treatment coupled with froth floatation has been shown as a green efficient treatment of oily sludge waste from the bottom of crude oil tanks in Al-Daura refinery and able to get high yield of base oil recovery which is 65% at the optimum operating conditions (treatment time = 30 min, ultrasonic wave amplitude = 60 micron, and (solvent: oily sludge) ratio = 4). Experimental results showed that 83% of the solvent used was recovered meanwhile the main water

In a hybrid cooling solar thermal systems , a solar collector is used to convert solar energy into heat energy in order to super heat the refrigerant leaving the compressor, and this process helps in the transformation of refrigerant state from gaseous state to the liquid state in upper two-thirds of the condenser instead of the lower two-thirds such as in the traditional air-conditioning systems and this will reduce the energy needed to run the process of cooling .In this research two systems with a capacity of 2 tons each were used, a hybrid air-conditioning system with an evacuated tubes solar collector and a traditional air-conditioning system . The refrigerant of each type was R22.The comparison was in the amou