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

Simulation of free convection heat transfer in a square enclosure induced by heated thin plate is represented numerically. All  the enclosure walls have constant temperature lower than the plate’s temperature. The flow is assumed to be two-dimensional. The discretized equations were solved stream function, vorticity, and energy equations by finite difference method using explicit technique and Successive Over- Relaxation method. The study was performed for different values of Rayleigh number ranging from 10³ to 10⁵ for different angle position of heated thin plate(0°, 45°, 90°). Air was chosen as a working fluid (Pr = 0.71). Aspect ratio of center of plate to the parallel left wall A₂

This work deals with thermal cracking of heavy vacuum gas oil which produced from the top of vacuum distillation unit at Al- DURA refinery, by continuous process. An experimental laboratory plant scale was constructed in laboratories of chemical engineering department, Al-Nahrain University and Baghdad University. The thermal cracking process was carried out at temperature ranges between 460-560^oC and atmospheric pressure with liquid hourly space velocity (LHSV) equal to 15hr^-1.The liquid product from thermal cracking unit was distilled by atmospheric distillation device according to ASTM D-86 in order to achieve two fractions, below 220^oC as a gasoline fraction and above 220^oC as light cycle o

Research Summary
      Praise be to God, Lord of the worlds, and prayers and peace be upon the most honorable of the prophets and messengers, our master Muhammad, and on the good God and his righteous companions.
      For the most truthful hadith is the Book of God Almighty, and the best guidance is the guidance of the Prophet, may God bless him and grant him peace. If any)). Our good predecessor took care of collecting what they were able to collect and arrange from the words of the prophecy issued by our master Muhammad, peace and blessings be upon him, and wrote works on them including forms of support, parts, dictionaries, and mosques. About me, if any, in order to re

The study aimed to reveal the level of knowledge and tendencies of high- study students specializing in curriculum and teaching methods at King Khalid University towards harmonious strategies with brain-based learning (BBL). And Then, putting a proposed concept to develop knowledge and tendencies of high-study students specializing in curriculum and teaching methods at King Khalid University towards harmonious strategies with Brain-based learning (BBL). For achieving this goal, a cognitive test and a scale of tendency were prepared to apply harmonious strategies with brain-based learning. The descriptive approach was used because it suits the goals of the study. The study sample consisted of (70) male and female students of postgraduate

The importance of research and study of classical Persian literature is not overlooked.  So far, there have been many studies in this area.  But there are still some things that need more research.  Persian grammar is one of the most important branches of Persian literature.  This section has always been converted at different times.  One of the issues that has been neglected in the studies of classical literature is the study of the technical tales of past and past poetry.  These texts can be studied from different perspectives.  Because Persian is a mixed language, it is possible to combine language terms with each other or to add prefixes and suffixes to express new concepts. They can be used by exam

The study of Terracotta in Mesopotamia is one of the important
technical topics that gave us valuable information ،whether from a
technical or cultural point of view

Atmospheric transmission is disturbed by scintillation, where scintillation caused more beam divergence. In this work target image spot radius was calculated in presence of atmospheric scintillation. The calculation depend on few relevant equation based on atmospheric parameter (for Middle East), tracking range, expansion ratio of applied beam expander's, receiving unit lens F-number, and the laser wavelength besides photodetector parameter. At maximum target range Rmax =20 km, target image radius is at its maximum Rs=0.4 mm. As the range decreases spot radius decreases too, until the range reaches limit (4 km) at which target image spot radius at its minimum value (0.22 mm). Then as the range decreases, spot radius increases due to geom

A nonlinear filter for smoothing color and gray images
corrupted by Gaussian noise is presented in this paper. The proposed
filter designed to reduce the noise in the R,G, and B bands of the
color images and preserving the edges. This filter applied in order to
prepare images for further processing such as edge detection and
image segmentation.
The results of computer simulations show that the proposed
filter gave satisfactory results when compared with the results of
conventional filters such as Gaussian low pass filter and median filter
by using Cross Correlation Coefficient (ccc) criteria.