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

Steganography is a mean of hiding information within a more obvious form of
communication. It exploits the use of host data to hide a piece of information in such a way
that it is imperceptible to human observer. The major goals of effective Steganography are
High Embedding Capacity, Imperceptibility and Robustness. This paper introduces a scheme
for hiding secret images that could be as much as 25% of the host image data. The proposed
algorithm uses orthogonal discrete cosine transform for host image. A scaling factor (a) in
frequency domain controls the quality of the stego images. Experimented results of secret
image recovery after applying JPEG coding to the stego-images are included.

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This research studying the phenomenon of Doppler (frequency Doppler) as a method through which the direction and speed of the blood cells flows in blood vessels wear measured. This Doppler frequency is relied upon in medicine for measuring the speed of blood flow, because the blood flow is an important concept from the concepts of medicine. It represents the function and efficient of the heart and blood vessels in the body so any defect in this function will appear as a change in the speed of blood flow from the normal value assumed. As this speed changes alot in cases of  disease and morbidity  of the heart, so in order to identify the effect of changing the Doppler frequency on the speed of blood flow and the relationship of

مشكلة البحث

              وتعد مرحلة المراهقة من اصعب المراحل التي يمر بها الفرد واخطرها اذ يطلق عليها بمرحلة التفكير المجرد ، وهي مرحلة حاسمة في حياته اذ تتكون لديه معالم الشخصية .أنهم خزين الامة الحقيقي من الطاقات الحيوية التي لا تنضب لذا يجب الاهتمام بهذه الشريحة من المجتمع وتطويرهم وتوجيههم لاسلم الطرق للحفاظ على مستقبلهم ومستقبل الا

The issue, the existence of God Almighty, and the creativity of the universes including the whale, and assets and how diversified, and faith in him and his lordship and divinity, is a delicate issue, and very important and dangerous, and it occupied human thought old and new, and still occupy it until God takes the land and on it. Many complex issues of thought, behavior, and ethics have resulted in the belief of many communities in the existence of the Almighty, having ruled their minds, depicting their beliefs and distancing their thoughts about slippage and abuse. When they looked at the wonders of creatures and the minutes of the assets, they thought about the planetary and astronomical motion systems. His existence was denied by ath

مشكلة البحث واهميته:-

          اخذ موضوع العولمة قدراً وافياً من الاهتمام سواء على المستوى الاكاديمي او على مستوى اجهزة الاعلام والرأي العام ومختلف التيارات السياسية والاقتصادية والاجتماعية ، فلا يخلو أي لقاء اقتصادي او سياسي او اجتماعي من الحديث عن العولمة اذ نشرت العديد من الابحاث والدراسات وعقدت الكثير من الندوات والمؤتمرات لدراسة العولمة وبيان اثارها ولعل ذل

Theatrical production mechanisms were determined according to the extents of the theatrical performance, the directing plan, and the ideas that the theatrical performance seeks to convey to the audience. Accordingly, theatrical production mechanisms differ between one theatrical performance and another according to the requirements of each of them and the surrounding circumstances that accompany the production of theatrical performance, and in order to search for production mechanisms and their repercussions on the show. Theatrical The current research was divided into four chapters, namely (Chapter One - Methodology), which identified the research problem in the following question: What are the production mechanisms and their implicatio

The professional skepticism is one of the fundamental concepts necessary for practicing the audit profession, without which the auditor can not reach a reasonable assurance as to the correctness of the evidence and the information obtained by the auditing department. The auditor's possession of the characteristics of professional skepticism and his practice of professional skepticism during the audit process lead to an increase The quality of audit and thus raise the confidence of the financial community in the audit profession again after the exposure of several crises led to the loss of financial society confidence in the audit profession.

The aim of the study is to measure the impact of professional sk