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

This study aimed at analyzing and studying the strategic and geopolitical importance of the Sahel region, which increased the regional competition for the resources of the region, especially the energy resources that have been and continue to be one of the axes of conflict and competition between these forces.
The researcher tried to review the competition between the international force, France, the United States of America, China, Algeria and Libya, and the African coast. We note that there is a positive correlation between the severity of the conflict and the intensity of the competition of the major powers to control the countries of the region and the extent of political and economic stability These countries are directly affecte

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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              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

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

        The searchers opinions are variant in determining the extent of impacting political risk in the host country on foreign direct investment decision. (Aharoni,1966) found, in his questionary study for group of foreign companies operating in India, that a political stability is one of the two most important factors, besides the market size, in the attraction of foreign investment, and its availability means that whether this  specific country  is good for foreign investment. On the other side, (Green and Benntt, 1972) are present a variant opinion to Aharonis opinion. They are reach to result state that a political instability do not impact on the general distribution of foreign i

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

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Acceptable Bit Error rate can be maintained by adapting some of the design parameters such as modulation, symbol rate, constellation size, and transmit power according to the channel state.

An estimate of HF propagation effects can be used to design an adaptive data transmission system over HF link. The proposed system combines the well known Automatic Link Establishment (ALE) together with variable rate transmission system. The standard ALE is modified to suite the required goal of selecting the best carrier frequency (channel) for a given transmission. This is based on measuring SINAD (Signal plus Noise plus Distortion to Noise plus Distortion), RSL (Received Signal Level), multipath phase distortion and BER (Bit Error Rate) fo

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