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

Many academics have concentrated on applying machine learning to retrieve information from databases to enable researchers to perform better. A difficult issue in prediction models is the selection of practical strategies that yield satisfactory forecast accuracy. Traditional software testing techniques have been extended to testing machine learning systems; however, they are insufficient for the latter because of the diversity of problems that machine learning systems create. Hence, the proposed methodologies were used to predict flight prices. A variety of artificial intelligence algorithms are used to attain the required, such as Bayesian modeling techniques such as Stochastic Gradient Descent (SGD), Adaptive boosting (ADA), Decision Tre

There are many studies dealt with handoff management in mobile communication systems and some of these studies presented handoff schemes to manage this important process in cellular network. All previous schemes used relative signal strength (RSS) measurements. In this work, a new proposed handoff scheme had been presented depending not only on the RSS measurements but also used the threshold distance and neighboring BSS power margins in order to improve the handoff management process. We submitted here a threshold RSS as a condition to make a handoff when a mobile station moves from one cell to another this at first, then we submitted also a specified margin between the current received signal and the ongoing BS's received signal must be s

The study aims to build a water quality index that fits the Iraqi aquatic systems and reflects the environmental reality of Iraqi water. The developed Iraqi Water Quality Index (IQWQI) includes physical and chemical components. To build the IQWQI, Delphi method was used to communicate with local and global experts in water quality indices for their opinion regarding the best and most important parameter we can use in building the index and the established weight of each parameter. From the data obtained in this study, 70% were used for building the model and 30% for evaluating the model. Multiple scenarios were applied to the model inputs to study the effects of increasing parameters. The model was built 4 by 4 until it reached 17 parame

Abstract: Residual ridge resorption is chronic, progressive, irreversible and cumulative condition associated with teeth loss. Management of a residual ridge with severe resorption to fulfill the patient’s esthetic and functional requirements is quite difficult for the practitioner and also in the construction of an acceptable appliance. As the height of the edentulous ridge reduces the mandibular denture will be improperly function. Severe resorption of the mandibular alveolar ridge may cause instability and discomfort of the convention acrylic resin denture. Dealing with this condition requires clinical skills and knowledge. Treating the severely resorbed mandibular ridge is a challenging effort for prosthodontics. This research present