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

Native speakers of English from different parts of the world have different accents,but the differences of accents are mainly the result of differences in the sound of  vowels  and consonants . The actual use of all these sounds in combination leads the speaker to produce a number of segments which only appear on the production level and realized on the perceptual  one . RP pronunciation represents the teachable variety in all Iraqi universities because it is the most acceptable and understandable accent all over the world and not only in South East London ..The structure of the English syllable in RP  pronunciation is influenced by the appearance of certain allophones especially aspiration and glottalization which ch

This study has been done for testing the effectiveness and efficiency of probiotic in its ability to inhibit Aspergillus flavus , which secretes the aflatoxin B1 and compare it with materials that were approved to be effective in the inhibition of the growth of fungi and break down and reduction of mycotoxin. these are the filax substance and ozone gas. A laboratory experiment has been conducted to determine the isolates out of the fungus producing the aflatoxin B1.the isolate producing aflatoxin B1 has grown on the yellow corn seed. the probiotic was added along with the filax and they have been exposed to ozone gas and then they were stored from 30 days. A bio test was con conducted to knw the effects of biological toxin on the broiler me

Erbil city is located in the northern Iraq with a population of over one million people. Due to water crises farmers usually use wastewater and well water for the agricultural production. In this study six stations were designed to sample waste water and three from well water to define waste water and ground water characteristics. In this study, Residual Na⁺ Carbonate, Mg⁺⁺ hazard, salinity hazard, Kelley index, %sodium, total hardness, permeability index, potential salinity, sodium adsorption ratio, and Irrigation Water Quality Index (IWQI) were determined. The order of average cation concentrations in water was Mg²⁺> Ca²⁺ > Na⁺ > K⁺. While the proportion of main

Purpose: This research seeks to provide a point of view based on the creation of sustainable value to the customer of the banks in the context of total quality management and relationship marketing. It aims to develop a model to measure the value of sustainable customer peduncular under total quality management PAL (administrative leadership, involvement of employees, continuous improvement, process improvement, staff training), through the mediation of relationship marketing and objective dimensions (administrative leadership, involvement of employees, continuous improvement, improving processes , staff training), and to explore any of the variables and dimensions more influential in the creation of sustainable value to the cust

The world has seen in recent years as a result of rapid changes in the information and communication revolution until his limbs became distant as if a small screen can be controlled at the touch of which resulted in a stunning advance in all areas of life button, these changes were not accompanied by all the positive development, but it has many drawbacks on humans resulted in many of the psychological, social, intellectual and cultural problems.

As it is the cultural alienation of the most important challenges faced by the community in light of the tremendous technological progress and rapid jumps that exceeded all expectations in addition to the economic, social and political changes experienced by the country led to the desire

Most studies indicated that the values ​​of atmospheric variables have changed from their general rates due to pollution or global warming etc. Hence, the research indicates the changes of direct solar radiation values ​​over a whole century i.e. from 1900 to 2000 depending on registered data for four cities, namely (Mosul - Baghdad - Rutba - Basra. Moreover, attemptsto correlate the direct solar radiation with the temperature values have been ​​recorded over that period. The results showed that there is a decreasing pattern of radiation quantities over time throughout the study period, where the value of direct radiation over the city of Baghdad 5550 w/m² was recorded in the year 1900, but this ratio decreased cle

The research aims to reveal the availability of skills to develop the tax assessor when carrying out the tax examination process. The study was conducted in the branches of the General Tax Authority in the province of Baghdad (the General Authority for Taxes, Adhamiya branch, the General Authority for Taxes, Rusafa branch, Al-Bayaa branch, New Baghdad tax branch) was approved The descriptive approach to achieve the research objectives represented by answering the following two questions: 1- What are the necessary skills that should be available in the performance of the tax examiner? 2- Are the skills of developing a tax evaluator available? The two researchers used the closed questionnaire as a tool for their research. The quest

In the analysis of multiple linear regression, the problem of multicollinearity and auto-correlation drew the attention of many researchers, and given the appearance of these two problems together and their bad effect on the estimation, some of the researchers found new methods to address these two problems together at the same time. In this research a comparison for the performance of the Principal Components Two Parameter estimator (PCTP) and The (r-k) class estimator and the r-(k,d) class estimator by conducting a simulation study and through the results and under the mean square error (MSE) criterion to find the best way to address the two problems together. The results showed that the r-(k,d) class estimator is the best esti

Self-driving automobiles are prominent in science and technology, which affect social and economic development. Deep learning (DL) is the most common area of study in artificial intelligence (AI). In recent years, deep learning-based solutions have been presented in the field of self-driving cars and have achieved outstanding results. Different studies investigated a variety of significant technologies for autonomous vehicles, including car navigation systems, path planning, environmental perception, as well as car control. End-to-end learning control directly converts sensory data into control commands in autonomous driving. This research aims to identify the most accurate pre-trained Deep Neural Network (DNN) for predicting the steerin