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

Abstract

 The issue of inequality in distribution of income and / or consumption expenditure is related to economic welfare because there is an inverse relationship between the economic welfare on the one hand, and the degree of inequality, on the other hand. Despite the fact that inequality is considered as normal phenomenon in every society, but if it exceeded certain limits it will lead to undesirable economic, social and political consequences. Therefore, the availability of indicators about inequality is a necessary tool for planning and evaluation of economic development programs. So, current study is aiming at measuring and analyzing the degree of inequality in distribution of consumpti

The aim of this essay is to use a single-index model in developing and adjusting Fama-MacBeth.  Penalized smoothing spline regression technique (SIMPLS) foresaw this adjustment.  Two generalized cross-validation techniques, Generalized Cross Validation Grid (GGCV) and Generalized Cross Validation Fast (FGCV), anticipated the regular value of smoothing covered under this technique. Due to the two-steps nature of the Fama-MacBeth model, this estimation generated four estimates: SIMPLS(FGCV) - SIMPLS(FGCV), SIMPLS(FGCV) - SIM PLS(GGCV), SIMPLS(GGCV) - SIMPLS(FGCV), SIM PLS(GGCV) - SIM PLS(GGCV). Three-factor Fama-French model—market risk premium, size factor, value factor, and their implication for excess stock returns and portfolio return

Rice (Oryza sativa) is a fundamental food for the majority of world population. Cyclin Dependent Kinase -A (CDKA) accelerates transition through different stages of cell cycle and contributes in gametes formation. In the present investigation, a CDKA encoding gene along with the corresponding protein were characterized in O. sativa Indica Group, O. glaberrima,  O. barthii, O. brachyantha, O. glumipatula, O. longistaminata, O. meridionalis, O. nivara, O. punctata and O. rufipogon using in silico analyses. The results reflected little variation in most species except O. longistaminata and O. brachyantha. Compared with the remaining species, O. longistaminata

Apart from graduating five-star doctors, a particular medical college has the mission to motivate and offer researchers the opportunity to publish high-quality researches on various health problems and disseminate updated medical knowledge to a wide range of local and international readers. This could be accomplished by establishing a medical journal and releasing issues regularly

The spectacular film is a type of feature films which has specific elements that contribute in increasing the aesthetics of the shape in its structure. The researcher started studying this type of films by researching the spectacular film concept, the history of its development, who are its most important stars and then tackling the Indian cinema represented by Bollywood, which is considered a school for this type of film. The researcher addressed the most important influential elements that entre in its production as well as studying these elements that contribute to building the shape including the configuration, movements of cameras, lenses, the lighting, colors, costumes etc. and what influence they have in forming a special aestheti

Binary mixtures of three, heavy oil-stocks was subjected to density measurements at temperatures of 30, 35 and 40 °C. and precise data was acquired on the volumetric behavior of these systems. The results are reported in terms of equations for excess specific volumes of mixtures. The heavy oil-stocks used were of good varity, namely 40 stock, 60 stock, and 150 stock. The lightest one is 40 stock with °API gravity 33.69 while 60 stock is a middle type and 150 stock is a heavy one, with °API gravity 27.74 and 23.79 respectively. Temperatures in the range of 30-40 °C have a minor effect on excess volume of heavy oil-stock binary mixture thus, insignificant expansion or shrinkage is observed by increasing the temperature this effect beco

Background: Worldwide gastric cancer is the fifth most common cancer with poor prognosis. In early stages, it is hard to distinguish gastric cancer from benign gastric diseases, resulting in delayed diagnosis. There is a need to develop a biomarker for differentiating between gastric cancer and benign gastric diseases. Serum cholinesterase is synthesized in liver and released into plasma, and it has an important role in oncogenesis.

Objectives: To determine the correlation between serum cholinesterase activity and gastric cancer, in comparison to benign gastric diseases.

Subjects and Methods: A case control study carried out at Medical City Direct