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

Background: Dyslipidemia is defined as an abnormally high level of various lipids in the blood. It is considered a major risk for atherosclerosis and coronary artery disease. Genetic susceptibility can have a significant influence on the development and progression of dyslipidemia. ApoB-100 R3500Q mutation and ApoE variants are among those genetic risks for dyslipidemia. This study aims to assess the possible contribution of ApoB and ApoE variants on lipid profile among a group of early-onset ischemic heart disease (IHD) patients in comparison to a group of controls. Methods: Forty patients with dyslipidemia and early-onset IHD without chronic conditions likely to cause derangement of lipid levels were recruited to this case-control study

Background: Trigeminal neuralgia (TN), or Tic Douloureux, is one of the most common neuropathic pains. Gamma knife stereotactic radiosurgery (GNSRS) has been considered one of the procedures for treating primary TN. Objective: This study evaluates the effectiveness of GNSRS in treating primary TN in patients who are unresponsive to medical treatment in a single-center experience. Subjects and Methods: This study was conducted on 180 patients from January 2018 to October 2021. The study utilized the Barrow Neurological Institute (BNI) pain intensity score to assess pain before and after GNSRS treatment. Results: A total of 180 patients with primary TN were included in this study, 108 female with a 1.5:1 female: male ratio.  Results

   As a result of the entry of  multinationals companies in Iraq for investing in the joint projects through conducting agreements and contracts for work on important and strategic projects to get the necessary funds and various experiences which characterize the foreign participant sides that Iraq currently needs them and because of the non-applying the accounting processing stipulated in the unified accounting system in addition to the absence of a local accounting bases as well as the default of the participant contracts on indicating the accounting methods about those projects which are considered one of the bases that enables auditors in the public sector to depend on it, thus the research paper deals with studying an

The study of triples seeks to deal with the comprehensive nature of the Qur’an texts, and the choice fell on the trilogy of great torment, pain, and humiliation in the Noble Qur’an - an objective study, the title of this research, in which I tried to shed light on these terms, and the nuances between them, and in particular torment The eschatological terminology varied, which can be summed up in three terms, namely the great, the painful, and the offensive. The types of torment, the pain is the painful one that is described by the severity of pain and its horror, as for the humiliating punishment, it is that which humiliates the one who has fallen on it, and the diversity of torment is due to the diversity of sins.

This study represents an optical biosensor for early skin cancer detection using cysteine-cupped CdSe/CdS Quantum Dots (QDs). The study optimizes QD synthesis, surface, optical functionalization, and bioconjugation to enhance specificity and sensitivity for early skin cancer cell detection. The research provides insights into QD interactions with skin cancer biomarkers, demonstrating high-contrast, precise cellular imaging. Cysteine-capped CdSe/CdS absorption spectra reveal characteristic peaks for undamaged DNA, while spectral shifts indicate structural changes in skin-cancer-damaged DNA. Additionally, fluorescence spectra show sharp peaks for undamaged DNA and notable shifts and intensity variations when interacting with skin cancer. This