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

In this paper two ranking functions are employed to treat the fuzzy multiple objective (FMO) programming model, then using two kinds of membership function, the first one is trapezoidal fuzzy (TF) ordinary membership function, the second one is trapezoidal fuzzy weighted membership function. When the objective function is fuzzy, then should transform and shrinkage the fuzzy model to traditional model, finally solving these models to know which one is better

<p>Photovoltaic (PV) systems are becoming increasingly popular; however, arc faults on the direct current (DC) side are becoming more widespread as a result of the effects of aging as well as the trend toward higher DC voltage levels, posing severe risk to human safety and system stability. The parallel arc faults present higher level of current as compared with the series arc faults, making it more difficult to spot the series arc. In this paper and for the aim of condition monitoring, the features of a DC series arc fault are analyzed by analysing the arc features, performing model’s simulation in PSCAD, and carrying out experimental studies. Various arc models are simulated and investigated; for low current arcs, the heur

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

In view of the large profits made by the sex trade on the one hand, and the minor penalties imposed on the traffickers (brokers) compared with the severe penalties imposed on the drug trade and illegal weapons, on the other hand, this trade has become popular and spread in most countries of the world, and the cornerstones of this trade and A safe haven for them is hotels, especially luxury ones with international brands where their guests are rich and some may look for sex for money. Given the great physical and psychological damage to the victims, this research highlights the civil liability of hotels towards these victims in US and Iraqi law.In order not to limit the

    An analytical procedure has been carried out to measure the charge that may be trapped in an insulator sample of scanning electron microscope. It mainly concerns the determination of the deduced polarization charges by means of mirror effect phenomenon. Several relations related to such issue have been modified so as to be applicable for regarding charges due to polarization in linear and isotropic material. Consequently, the potential arises as a result for both trapped free and polarization charges which is set up. Actually the well-known magnification factor method is adopted to be a case study to implement the introduced approach. Results have clearly showed that the polarization charge significantly influences the Coul

The struggle between two identities is a crucial subject everywhere. Some people travel abroad in quest of a new identity after struggling at home. People migrate and embrace a new identity for different reasons. They find themselves in a state of internal conflict as they navigate the tension between their newly adopted identities and their old ones. The individual is haunted and overwhelmed by their previous experiences. This research explores the universality of the subject matter by examining the motivations underlying the adoption of a new identity in a distinct geographical and temporal context. This paper examines the literary works of Kincaid's Lucy (1990) and Blasim's "The Nightmares of Carlos Fuentes" (2014). Kincaid’s pro

         This is a contribution to study the situation of a dwelling of previous case of kala- azar in the endemic area (AL-Mahmodiya/ AL-Rasheed district) about 25 km south of Baghdad.  In order to assess the possible ecological causes of the incidence and the prevalence of visceral leishmaniasis, in one of the well-known foci of the disease in the central region of Iraq. It was found that the human dwelling position and ecological factors affect the infection with this disease.

Objective: The approximate life span of a silicone maxillofacial prosthesis is as short as1.5–2 years of clinical service, then a new prosthesis should be fabricated. The most common reasonfor re-making the prosthesis is silicone mechanical properties degradation. The aim of this studywas to assess some mechanical properties of VST-30 silicone for maxillofacial prostheses after addi-tion of intrinsic pigments.Methods: Two types of intrinsic pigments (rayon flocking and burnt sienna); each of them wasincorporated into silicone. One hundred and twenty samples were prepared and split into 4 groupsaccording to the conducted tests (tear strength, hardness, surface roughness, and tensile strengthand elongation percentage) with 30 samples for ea