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

             Polycystic syndrome (PCOS) is a considerable infertility disorder in adolescents and adult women in reproductive age. Obesity is a vigorous risk factor related to POCS.  This study aims to evaluate the association of obesity and PCOS by investigating several parameters including:  anthropological, biochemical (lipid profile, fasting blood sugar, glucose tolerance test, and hormone levels (LH, FSH, LH/FSH ratio, Estradiol2 and Testosterone),and genetic parameters (Fat mass and Obesity associated gene (FTO) polymorphism at rs17817449) in 63 obese and non-obese PCOS women. The biochemical tests were investigated by colorimetric methods while FTO gene polymorp

The present study was conducted to investigate effect of prey type on the relationship between age of females of Macrocyclops albidus and reproductive performance, which included each of mean number of nauplii, age at first brood, and age at first clutch. Results revealed that the correlation coefficient between the age at first brood and clutch and age of females fed on Artemia was significant P <0.05, being 0.65 and 0.81 respectively, while the correlations were not significant P>0.05 in females fed on mosquito larvae (Culex quinquefasciatus) and Paramecium nauplii. It was also found that the correlation coefficients between mean number of the nauplii and longevity in M. albidus were significant P<0.05 whereas, the correlations were not s

We have investigated in this research, the contents of the electronic cigarette (Viber) and the emergence of the phenomenon of electronic smoking (vibing) were discussed, although the topic of smoking is one of the oldest topics on which many articles and research have been conducted, electronic smoking has not been studied according to statistical scientific research, we tried in this research to identify the concept of electronic smoking to sample the studied data and to deal with it in a scientific way. This research included conducting a statistical analysis using the factor analysis of a sample taken randomly from some colleges in Bab Al-medium in Baghdad with a size of (70) views where  (КМО) and a (bartlett) tests

This article examines the usage features of the phraseological units in Russian political discourse and the peculiarities of the phraseological units’ usage by politicians in their speeches.  The main focus is on the expressive and pragmatic functions of using phraseological units in political texts due to their evaluative and expressive nature.  The present article also examines the structural and stylistic changes of the phraseological units in political discourse.  Moreover, the work provides examples from the speeches of the Minister of Foreign Affairs of the Russian Federation S.V.  Lavrov.  As a result, the author comes to the conclusion that phraseological units make it possible to establish a contact be

The research presented to the concept of social isolation through the manifestations of that concept and its works within the theatrical presentation space, and the diversity of directing experiences that the theatrical field benefited from, as contemporary data that contributed to the production of theatrical speech engaging with various levels of different form and content, and this was revealed through the chapters of the research that included The first chapter (the systematic framework), the second chapter (theoretical framework), which included the first topic (formations of social isolation), the second topic (social isolation in the world stage), and resulted in indicators including:
1- Postmodernism produced intellectual appr

The Department of Art Education in the College of Fine Arts is one of the educational institutions that aims to prepare teachers specialized in teaching art education in secondary schools and other educational institutions, which forces those in charge of preparing the curricula for this section and developing it, taking into account the rapid scientific and technological development. And the subject (Music Appreciation) is one of the subjects taught for the third grades in Art Education departments, and through the exploratory study carried out by the researcher it became clear to him that the Faculties of Fine Arts agreed to define their educational objectives and outputs in the subject (Music Appreciation) in Art Education departments

This research aims to study the methods of reduction of dimensions that overcome the problem curse of dimensionality when traditional methods fail to provide a good estimation of the parameters So this problem must be dealt with directly . Two methods were used to solve the problem of high dimensional data, The first method is the non-classical method Slice inverse regression ( SIR ) method and the proposed weight standard Sir (WSIR) method and principal components (PCA) which is the general method used in reducing dimensions,    (SIR ) and (PCA) is based on the work of linear combinations of a subset of the original explanatory variables, which may suffer from the problem of heterogeneity and the problem of linear

  The audience is one of the important practical elements in the theatrical show and its importance is not confined to its static activity as a receiver element only, rather it went beyond that issue as an effective and influential element in the proceedings of the show and the process of meaning construction, that it gains an active role in the construction and production of the connotation that influences and is influenced by the actor, where the communication channels are open between the two sides, consequently a kind of watching and joint interaction happens between them. Thus, it has become necessary for the actor to create a suitable environment for the onlookers in order for it to be an essential part of the show system. The

The main purpose of this investigation is to evaluate the concentrations of six essential metals (Na⁺, Mg²⁺, K⁺, Ca²⁺, Fe²⁺ and Zn²⁺) in saffron and a farm soil using the neutron activation analysis (NAA) as a nuclear spectrometry method. The stratified random sampling method was used here. The NAA results showed the well uptake of Mg²⁺, K⁺, Ca²⁺, Fe²⁺, and Zn²⁺ in saffron, which is lower than the toxicity range. Based on the contamination factor and geoaccumulation index, soil contamination levels were determined uncontaminated by Zn, moderately contaminated by Na⁺ and Fe²⁺, and strongly contamin