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 .

Abstract

This research  aims to reform the Iraqi public budget through going into the challenges the budget faces in applying item-line budget in its preparation, implementation and control; which encourage extravagance and waste instead of rationalizing expenditures. This  is shown in the data analysis of Federal public budget laws in Iraq for the years from 2005 till 2013; there was a continuous increase in the aggregate public expenditures in the public budget for the years previously mentioned, as the public expenditures growth has reached into the percent 284.71% in 2013. In addition the public budget for these years (2005-2013) is being prepared with planned deficit without confirming that

Nowhere is American author Shirley Jackson’s (1916-1965) social and political criticism is so intense than it is in her seminal fictional masterpiece “The Lottery”. Jackson severely denounces injustice through her emphasis on a bizarre social custom in a small American town, in which the winner of the lottery, untraditionally, receives a fatal prize. The readers are left puzzled at the end of the story as Tessie Hutchinson, the unfortunate female winner, is stoned to death by the members of her community, and even by her family. This study aims at investigating the author’s social and political implications that lie behind the story, taking into account the historical era in which the story was published (the aftermath of th

Abstract

 This research deals will the declared production planning operation in the general company of planting oils, which have  great role in production operations management who had built mathematical model for correct non-linear programming according to discounting operation during raw materials or half-made materials purchasing operation which concentration of six main products by company but discount included just three products of raw materials, and there were six months taken from the 1^st half of 2014 as a planning period has been chosen . Simulated annealing algorithm  application on non-linear model which been more difficulty than possible solution when imposed restric

We use of multi-choice Goal Programming (MCGP), which is a developed model of Goal Programming where it is used in circumstances of the multiplicity and difference of goals when choosing between decision alternatives in cases of allocating resources, as it is a model that seeks to find the closest and best solutions to the specific values ​​of the goals within the aspiration levels, as the first goal in the multi-choice goal programming model that is used to reduce the total cost of storage and shortage, while the other goal was to reduce the difference between the real demand that the hospitals need from the blood transfusion center and the units that already achieved. The case Iraqi Center

In this paper we study the selection of cognitive elements and criteria of the inflectional structure of the Russian and Arabic languages in the process of speech communication. Phonetic-physiological principle is the main parameter by which the elements and criteria of cognitive activity in the presented study are distinguished. On the basis of the above mentioned parameter, we select the investigated criteria and elements. The first criterion is semantic, reflects the accordance of the elements of thinking to sound combinations in the studied languages, and allows us to distinguish the second criterion – morphonological. The second criterion depends on the phonetic changes of these combinations occurring in the process of speech activit

По мнению ученых, исследующих современные деривационные процессы, „начиная со второй половины XX в., активизируются новые социолингвистические и коммуникативные факторы”, определяющие специфику современного словотворчества в ряде типологически близких славянских языков [Нещименко 2010: 39]. В результате возросшего влияния масс-медиа на коллективное сознание носителей языка, на существующий вербальный

The accession of countries to the World Trade Agreement and the openness of markets to each other without restrictions led to the emergence of the philosophy of "a world without borders and business units without countries", which required adapting the modern business environment to that philosophy, which is considered as objectives for the activities of the units that must be implemented in order to achieve competition. The objective of the units has changed from making profit to meeting the desires of customers, which is what imposed a new role for management accounting as a field of knowledge renewed in it visions of competitiveness between units. Because of the increasing needs for information in light of environmental change

Abstract The study aims to clarify the value of auditing economic units and how it can be measured, which is one of the most important challenges to matching the Value Relevance of Accounting Information. The problem of the study was identified with questions that revolve around the extent to which it is possible to measure the value of auditing in Iraqi economic units and the extent to which the value of auditing affects the adequacy of accounting information. Through reviewing the studies discussing this topic, it was found that auditing can provide value through the performance of the auditor and adding value to the economic unit subject to audit. The study recommended the need to study the situational factors of auditing, whether exter

The role of internal control is based on the effectiveness of the budget through an analysis of the reality of the budget in the research sample as it was studied in the preparation and preparation stages and the implementation stage. The sample showed that the sample did not comply with what is stated in the Ministry of Finance publication of instructions and ceilings. In the process of preparing and resulting from the occurrence of deviations in large proportions both in the discussion of the Ministry of Finance or when implementation as a low rate of implementation and the absence of allocations for some items, although there is a need for them as well as the transfer of large proportions of transfers both up or down and the purpose o