A vector in a separable infinite dimensional Hilbert space is called disk-cyclic for bounded operator if the orbit α : 0, α∈;|∝| 1is dense in. The useful tool used to discover codisk-cyclic operation is called the disk-cyclic Criterion. In this paper we will show that some equivalent conditions of the

The whole world and the Arab world, especially an important part of this international system, is undergoing a radical transformation at all levels. This mosaic of political, economic, social and military relations and alliances, whether based on the special interests of the major Powers or on the basis of mutual interests, The major transformations to social, economic, political and military conflict and these transformations still bear more surprises, at all levels, nothing remains constant, all changed, relations changed and alliances changed and loyalties fell and the principles of the M changed and the spectacular imperial economies collapsed and the will of the masses was no longer fixed.

This study examines the dynamic relationship between stock market and economic activity in the United States to verify the possibility of using financial indicators to monitor the turning points in the expected path of future economic activity. Has been used methodology (Johansen - Juselius) for the Co-integration and causal (Granger) to test the relationship between the (S & P 500 , DJ) index  and gross domestic product (GDP) in the United States for the period
(1960-2009). The results of the analysis revealed the existence of a causal relationship duplex (two-way) between the variables mentioned. which means the possibility of the use stock market indicators to pre

This study investigates the challenges encountered by first-grade intermediate students in learning the Arabic language. It aims to identify specific obstacles that hinder language acquisition and proficiency among this demographic. Through qualitative and quantitative methods, including surveys and interviews with students, teachers, and parents, the research highlights key issues such as limited vocabulary, difficulties in grammar, lack of engagement with the material, and inadequate teaching resources. The findings reveal a complex interplay between cognitive, social, and educational factors that contribute to these challenges. The study underscores the need for targeted interventions, such as enhanced pedagogical strategies and improved

Some experiments need to know the extent of their usefulness to continue providing them or not. This is done through the fuzzy regression discontinuous model, where the Epanechnikov Kernel and Triangular Kernel were used to estimate the model by generating data from the Monte Carlo experiment and comparing the results obtained. It was found that the. Epanechnikov Kernel has a least mean squared error.

   Singled current study on the subject of shorthand in structure designs logos (Iraqi sports clubs model), as the current study Tdmt four chapters, was in the first chapter defines the research problem and its significance, as well as the aim of the research in the know shorthand formal in structure designs logos (Iraqi sports clubs model ), and identifies Find time limits: - slogans Iraqi sports clubs for the years (1956 - 1970), because it represented the years to include designs slogans official Iraqi sports clubs that have been elected in this period for the purpose of examining the reality of the design in the current search. And it represented the spatial limits: - the Republic of Iraq - Iraqi slogans designs sports

Preserving the independence and sovereignty of the countries of the South Caucasus region, establishing political and economic stability in the region, and supporting regional cooperation are the main elements of Turkish foreign policy towards the region. The South Caucasus region, which has historical and cultural ties between it and Turkey, is a bridge that links Turkey to Central Asia.                     

     Turkey later developed advanced relations with Azerbaijan and Georgia. However, the same momentum was not achieved in terms of relations with Armenia because of the conflict over Nagorny Karabakh

Research summary

Perhaps the methods of mask that Arab poets resorted to in our time are due to the conditions of oppression and political and social repression that the Arab poet suffered from; So he strived to circumvent it, and it became a justification for hiding behind it. The research is available on a number of topics that lead to the definition of the mask technique and the beginning of its prevalence in Arabic literature after the Second World War, especially in recent decades by benefiting from historical stories, fairy tales and legends of all kinds. As well as defining the mask idiomatically and linguistically, and the beginning of its use in ancient religious rituals, and the special place it had in Greek plays. Poets

Abstract

    All of us are indispensable for this rule (the most important and important) individuals, whether we were groups of leaders or followers of peoples or countries because the rule provides adequate guarantees for the correct positions and drawing the plan for successful decision-makers matching with the balances of Sharia without incompatibility between religious or worldly interests or legal positions and therefore in the framework of the most important appointment And distinguish it from the important from the interests or the appointment of the most important and distinguish from the important from the evils and through this rule we learn about the scientific and practical solutions t