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.

        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

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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

Countries have faced the challenges of high levels of public debt and seek to define the optimum limits to reduce risks to which the financial system can be exposed and its impact on the economy as a whole. Hence the importance of research in studying the impact of internal and external public debt components on indicators of stability of the financial system for the period 2005-2017 for the purpose of knowing the extent of the financial stability indicators response to the high level of the public debt from its optimum ratio, as the aim of the research is to estimate and analyze the dynamic relationship of short and long term between the components of public debt and indicators of financial stability using the (ARDL) model that

اضاءات على الانتخابات الشريعية في العراق عام 2010

Abstract                                           

           The developments of technology and information that is sweeping the world based on the factors of pressure on the accounting profession in general, and the authors of the accounting information. That becouse the makers of administrative decisions have become in need of new information fit and the environmental situation of the new competition and try to enter new markets,