This paper generalizes and improves the results of Margenstren, by proving that the number of -practical numbers  which is defined by   has a lower bound in terms of . This bound is more sharper than Mangenstern bound when  Further general results are given for the existence of -practical numbers, by proving that the interval contains a -practical for all

We used to think of grammar as the bones of the language and vocabulary as the flesh to be added given that language consisted largely of life generated chunks of lexis. This “skeleton image” has been proverbially used to refer to that central feature of lexis named collocation- an idea that for the first 15 years of language study and analysis gave a moment‟s thought to English classroom material and methodology.
The work of John Sinclair, Dave Willis, Ron Carter, Michael McCarthy, Michael Lewis, and many others have all contributed to the way teachers today approach the area of lexis and what it means in the teaching/learning process of the language. This also seems to have incorporated lexical ideas into the teaching mechanis

The concept of the order sum graph associated with a finite group based on the order of the group and order of group elements is introduced. Some of the properties and characteristics such as size, chromatic number, domination number, diameter, circumference, independence number, clique number, vertex connectivity, spectra, and Laplacian spectra of the order sum graph are determined. Characterizations of the order sum graph to be complete, perfect, etc. are also obtained.

  The research includes studying melodic and rhythmic properties, In the audio format for Iraqi musicians. The audio form is one of the important methodological forms in Arab music in general and Iraqi music in particular. It showcases its characteristics, features, internal form, and how important it is in Iraqi music.
Addressed ((the systematic framework)) presenting the research problem and the need for it. Its importance, purpose and limitations of its research, which included music ((Khaled Muhammad Ali)) as a human limit to reveal its characteristics in the composition of the audio form. And define the terms included in the research. And included ((theoretical framework)) on three topics .. The first: composing. The second

The place and environment in which the artist lives is considered one of the influences and drivers active in him, thus determining his style and artistic direction later, and in our research we have dealt with the effect of place and environment in the drawings of Nuri al-Rawi and the extent of their reflection on the general, so the research came within two frameworks: The first is the methodological framework that represents We have the problem of the research, its importance, its goal and the limits of research in it in addition to defining terms. As for the theoretical framework, the study dealt with two topics, the first of which included the topic (Nuri the narrator, the environment and the place) dealing with the role and effect

Summarized the idea of research is marked by "changes in the process of mass communication by using the international network of information" by specifying what data networking and mass communication is the transformation processes in the mass communication network where research aims to:1. Diagnostic data and transformations in the process of mass communication network.2. Provide a contact form commensurate with the characteristic mass of the International Network of electronic information, and research found to provide a communicative model called the (human contact network). In short (HCN) Humanity Communication Net also reached conclusions concerning the search process and communicative transformations and changes that have taken pla

The management of the exchange rate of the most important tools of economic policy because of its wide area in achieving stability and economic growth through the provision of stability in the exchange rate of the currency of the country concerned , as well as the impact and influence of money supply and then treat the economic crisis monetary and reduce the risk of currency exchange rate .For the management of the exchange rate in Iraq has passed through several stages , from installation to link to a basket of currencies to float freely , and we are dealing with in this research regard to the achievements of monetary policy , especially after the enjoyment of independence on according to the Iraqi Central Bank Law No. 56 of 2004 and Ma

The tourism activity is one of the pillars on which the economy of any country is based , the importance of the tourism sector is reflected in its potential to become an effective development alternative in many countries, especially Iraq ,this has a direct impact on the national economy as an important source in attracting hard currency and eliminating unemployment. Adding the Iraqi Marshlands to the list of effects makes it contribute to diversification of sources of income and stimulating rest of the economic sectors, the potentials and qualifications possessed by Iraq in the field of tourism and monuments have a significant impact on the state budget if they were exploited optimally. The research aims at identifying the contr

 Quality is the key to success in today's world, which is based mainly on competition in the provision of high quality services through the application of the modern management method which is called  total  quality management in organizations. This includes describing the provision of health services and satisfaction of patients .              .                                                 &nbsp