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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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

Nowadays, people's expression on the Internet is no longer limited to text, especially with the rise of the short video boom, leading to the emergence of a large number of modal data such as text, pictures, audio, and video. Compared to single mode data ,the multi-modal data always contains massive information. The mining process of multi-modal information can help computers to better understand human emotional characteristics. However, because the multi-modal data show obvious dynamic time series features, it is necessary to solve the dynamic correlation problem within a single mode and between different modes in the same application scene during the fusion process. To solve this problem, in this paper, a feature extraction framework of

The speaker identification is one of the fundamental problems in speech processing and voice modeling. The speaker identification applications include authentication in critical security systems and the accuracy of the selection. Large-scale voice recognition applications are a major challenge. Quick search in the speaker database requires fast, modern techniques and relies on artificial intelligence to achieve the desired results from the system. Many efforts are made to achieve this through the establishment of variable-based systems and the development of new methodologies for speaker identification. Speaker identification is the process of recognizing who is speaking using the characteristics extracted from the speech's waves like pi

   What linguists mentioned about the infinitive and its use in the linguistic levels of speech, whether with its verb, or what was mentioned in the difference between the infinitive and the noun of the source, are matters that are related to the phenomenon of hearing in speech, a need necessitated by the nature of the linguistic law

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

With the growing use of electronic commerce has worked many companies, especially public shareholding to take advantage of them treated in the trade, so that the e-commerce part of the corporate environment, and this has made a career of accounting and auditing facing new challenges to the sophistication of the information and the rapid growth in the market for electronic commerce. And raised many questions about the ability of the audit profession to facing these challenges and how to audit operations of e-commerce and how to give confidence on websites, this sense it has become necessary keep the internal control systems of this technology and what has caused changes to the accounting system, and evolve to fit the developments that hav