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 the variable structure control theory is utilized to derive a discontinuous controller to the magnetic levitation system. The magnetic levitation system model is considered uncertain, which subjected to the uncertainty in system parameters, also it is open-loop unstable and strongly nonlinear. The proposed variable structure control to magnetic levitation system is proved, and the area of attraction is determined. Additionally, the chattering, which induced due to the discontinuity in control law, is attenuated by using a non-smooth approximate. With this approximation the resulted controller is a continuous variable structure controller with a determined steady state error according to the selected control

Maximizing the net present value (NPV) of oil field development is heavily dependent on optimizing well placement. The traditional approach entails the use of expert intuition to design well configurations and locations, followed by economic analysis and reservoir simulation to determine the most effective plan. However, this approach often proves inadequate due to the complexity and nonlinearity of reservoirs. In recent years, computational techniques have been developed to optimize well placement by defining decision variables (such as well coordinates), objective functions (such as NPV or cumulative oil production), and constraints. This paper presents a study on the use of genetic algorithms for well placement optimization, a ty

Background: Osteoid osteoma(OO) is a relatively common benign skeletal neoplasm of unknown etiology that is composed of osteoid and woven bone, usually seen in adolescent and young males Although, the clinical, radiological and scintigraphic features of OO have been well described, these features may be misleading or altered in the cases of lesser trochanter of the femur which is relatively uncommon location for OO with a few number of cases reported up to date. Case Presentation: We report a case of a 20-year-old man who presented with painful limpThe pain had begun six months earlier and was made worse by walking and by exercise., with normal initial X-rays .The diagnosis was made after six months when typical Computed tomography, magneti

Presentation of urinary calculus ranges from painful urination to acute retention. Diagnosed by x-ray pelvis and non-contrast CT and removal of stone by various methods is the management. Variety in symptoms, sometimes make clinical diagnosis difficult until radiological investigations confirm it. In this case presentation, initial diagnosis was made of Urethrocutaneous fistula may be due to distal stricture, but on investigating, he was diagnosed as urethral calculus in urethral diverticulum , as the reason for his symptoms

This study employs a critical discourse analysis approach to investigate the linguistic and discursive mechanisms employed by the prominent Russian online news platform Gazeta.ru in its coverage of social news. Drawing on an interdisciplinary framework integrating critical discourse analysis (CDA), media discourse analysis, and sociolinguistic perspectives, the research examines how language is used to construct and disseminate societal narratives. The analysis focuses on a dataset of Gazeta.ru articles published in March 2024, encompassing topics such as health, travel, and consumer affairs. Through a multi-level analytical approach, the study explores macro-level discursive strategies and microlevel linguistic choices, unveiling the intri