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 communication, introduce the split Mersenne and Mersenne-Lucas hybrid quaternions, also obtaining generating functions and Binet formulas for these hybrid quaternions and investigating some properties among them.

Is the subject of the mind took a dimension in philosophy and psychology , and has cared psychologists this topic to a large extent , I started education institutions interest in the capabilities of intelligence since the early twentieth century , and the development of interest in them until he arrived to find Standards and Criteria to identify the degree IQ of any individual , and began to educational institutions interested in mental talent and talented .

The United States is the country chock first of these research projects , but they devoted all their attention on the wish talent mental and Gifted , until I got to the projects, the so-called time ( ( wars of the mind ) ) and projects Schools gifted

Atherosclerosis is the most common causes of vascular diseases and it is associated with a restriction in the lumen of blood vessels. So; the study of blood flow in arteries is very important to understand the relation between hemodynamic characteristics of blood flow and the occurrence of atherosclerosis.

looking for the physical factors and correlations that explain the phenomena of existence the atherosclerosis disease in the proximal site of LAD artery in some people rather than others is achieved in this study by analysis data from coronary angiography as well as estimating the blood velocity from coronary angiography scans without having a required data on velocity by using some mathematical equations and physical laws. Fif

Abstract

The aim of this research is to determine how well the Cubing Technique affects the Iraqi EFL students' composition writing, vocabulary, and meta-cognitive awareness of writing strategies. The sample of (64) secondary-school female students in the fifth grade is drawn from two classrooms and split into two equal groups: the experimental group and the control group, each of which consists of (32) students. A quasi-experimental design is applied. The performance test and Meta-cognitive Writing Strategies questionnaire are given as a pre-test for equalizing the two groups after ensuring their validity and reliability. Then, they are administrated as a posttest in both groups. According to the results, the si

Abstract

 Nano-crystalline ZSM-5 zeolite was synthesized by hydrothermal method using chelating agent and two gel compositions:Compositionɪ:Al₂O₃:86SiO₂:5.5TPA:12.7Na₂O:3.4Trien:3320H₂O.Compositionɪɪ:Al₂O₃:68SiO₂:5.4TPA:10Na₂O:2.6Trien:2626H₂O.Study of hydrothermal reaction factors on characteristics of nano- sized zsm-5 has been carried on ,among them are crystallization temperature, crystallization time and concentration of template ( TPAOH ) solution. Synthesis was accomplished in PTFE lined autoclave ( reactor ) . The product were characterized by X-ray diffraction ( XRD ),Atomic force microsc

In this work, we study the effect of doping Sn on the structural and optical properties of pure cadmium oxide films at different concentrations of Tin (Sn) (X=0.1,0.3 and 0.5) .The films prepared by using the laser-induced plasma at wavelength of laser 1064 nm and duration 9 ns under pressure reached to 2.5×10^-2 mbar. The results of X-ray diffraction tests showed that the all prepared films  are polycrystalline. As for the topography of the films surface, it was measured using AFM , where the results showed that the grain size increases with an increase in the percentage of doping  in addition to an increase in the average roughness. The optical properties of all films have also been studied through the absorbance s

Obliquely deposited (70o) Bi, Sb, and Bi-Sb alloy thin films have been prepared by thermal
resistive technique. Structural properties of these films were studied using XRD. Their resistance and
voltage responsivity for Nd:YAG and CO2 laser pulses have been recorded as function of operating
temperature between 10 oC and 120 oC. It was found that the maximum responsivity for these detectors
can be obtained at 75 oC. On the other hand, the dependence of responsivity on the width of detectors was
investigated.

study aimed to recognize the relationship shyness and depression and to recognize the differences between the genders, according to the variable of shyness and depression, the sample consisted (214) students, (141) female (73) male, and the sample responded scale of shyness and Inventory beck for depression, The Results of this study show that: the sample has a low degree shyness and a high degree depression, . There are no statistically significant differences according to gender variable in shyness, and there are statistically significant differences according to gender variable in depression favor for male, and there are statistically significant relationships between the variables of the study at lev