In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

Our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

the student of the structure of the city and its constituent elements will clearly sense the invisible relationships that underlie the different forms of urban activity, which in turn are defined by the generality of the urban patterns in that city, which will vary clearly according to the location in the city. These relations will be embodied in their true form in the interactions between the different uses of the earth, and the change that will result from their regularity in the form of entities in independent groups, which may share with each other a component of it.
Therefore, the process of controlling the functional interactions between the uses of the urban land and the awareness of t

This study revolves around the rapid changes of science and a comparison of the formal and practical aspects and the reason behind summoning the changes and their types, which are subject to the influence of the recipient. This transformation represents formal and intellectual production cycles and formal functional generation that is subject to the goals of the system of multiple differences at the level of time and place. It meets the needs and the request for change, but access to it comes through multiple systems and portals that are different from the normal and the usual, so this study was called (meta and its dimensions in the designed biological formation (virtual reality environment - a model). The research seeks to find solutio

The study aims to build a proposed training program for school leaders in the Sultanate of Oman on the planning practices of the Kaufman model in light of the needs and challenges of reality. It also aims to identify the challenges facing school leaders in practicing the stages of strategic planning. To achieve these objectives, the study adopted the descriptive approach due to its suitability to the nature of the study. A questionnaire was used to collect the needed data. The study sample included (225) individuals from school principals, their assistants and senior teachers in post-basic education in the Sultanate of Oman. After processing the data statistically, the study concluded that the reality of planning practices for school lea

Prepositions have a key function, which is to associate parts of a sentence, called letters In addition, it adds the meanings of the verbs to the names, ie reached by them, and called by the coffin characters Qualities..

          I chose to search for the meaning of the preposition "from" in Surat Maryam to know its meanings in terms of originality and expansion, so the title of the research (the meanings of preposition "from" in terms of originality and expansion in Surat Maryam model(

The construction sector consumes large amounts of energy during the lifetime of a building. This consumption starts with manufacturing and transferring building materials to the sites and demolishing this building after a long time of occupying it. The topic of energy conservation and finding the solution inside the building spaces become an important and urgent necessity. It is known that the roof is exposed to a high amount of thermal loads compared to other elements in a building envelope, so this needs some solutions and treatments to control the flow of the heat through them. These solutions and treatments may be achieved by using nanomaterials. Recently, nanomaterials have high properties, so that this made them go

Most cities in the world are suffering from the problem of solid waste and the resting adverse impact on the environment and public health, in particular the spread of diseases, insects and rodents, As well as the proliferation of nuisance odors result of provided by the responsible parties, As wall as weak environmental awareness among those who dwell in dealing in environmentally sound disposal of solid waste, this study was  bembgesan  first intake of solid waste and the kinds of concept and components by land use, As wall as the effects of solid waste on the environment spatial, factors affecting the quality and quantity of solid waste, the second topic was included as a study field presented the historical city of Baghdad

Abstract

The term public budget defects became nowadays a chronic, economical phenomenon, almost all the countries weather advanced or development country suffered from it, despite the different visions to economic schools of a thought to accept or reject the deficit in public budget but the prevailed opinion that is needed to rule the role of the state by reducing the public spending which led to continuous deficits in public budget and the consequent upon increase in government borrowing, increase taxes on income and wealth, thus weakening the in contrive for private investment which contributed to the increase of in flationary stagnation, it became a duty to state covered by the lack of financial sources

The international reporting auditor witness rapidly developed over the past years, where profession began give attention to the development of auditor reporting and improve its informational report through the issuance and amendment of some relevant international auditing standards. The reality of the situation refers to the failure to inform the auditor in Iraq in  many areas, including: Clearly defined management responsibility for the preparation of financial and auditor's responsibility to express an opinion on these statements and Amendment of opinion when the financial statements as a whole is free from material misstatement based on the evidence is sufficient and appropriate audit, or not to build the auditor's ability to obt