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 .
Corruption, in all its categories and forms, is regarded as the nowadays virus which has greatly spread in most institutes and society, a matter that cause a great waste of resources.
According to the reports of international transparency Institute, Iraq is regarded as one of the greatest countries in corruption.
Regardless of the reasons and forms of corruption, the retreat in work – values and ethics are the main reasons behind that.
Being the main source of providing qualified staff "educators" for the working market, the high education institutes face great challenges in standing against corruption inside and outside
... Show MoreThe makers of strife exist in every era and time. They differ in how these temptations are created and the methods used in doing so. In our modern era, they are more; This is due to the presence of information technology and its easy availability at their fingertips, as well as the spread of social networking sites, which are rapidly spreading among ignorant groups and groups that are deficient in their use. Which led the makers of sedition to exploit these matters and create various temptations and spread them among peoples and societies. Today, we cannot predict the future of humanity in light of this huge amount of temptation. What the Holy Qur’an mentioned about the types of temptations in its noble verses and their embodiment in seve
... Show MoreObjective: The current study aimed to prepare a measure for comprehensive knowledge marketing management. In the Iraqi sports institutions under study, identifying the extent of each dimension of comprehensive knowledge marketing management. Research methodology: This study relied on appropriate scientific methods, mainly represented by the descriptive method and the analytical method, and on the case study method because it suits the nature of the study. The study population was determined from the administrative cadres in the Iraqi Sports Federation, and the research sample numbered (86) and was represented as follows: The preparation sample numbered (50) and a percentage amounted to (58.13%), the sample of the exploratory experim
... Show MoreThis paper involved the registration of 1,936 cases of infection of the Leishmania tropica parasite observed at hospitals and health centers in Ramadi, Fallujah, Baghdadi, and Hit during 2017. The results revealed that the highest rates of infection were found in Ramadi and Fallujah. The 1-10 years age group recorded the highest rate at 35.5%. There was no significant difference (p ≥ 0.05) between the sexes. December and January saw the highest rate of infection, where the rate in rural townships was found to be 65.5%, higher than in urban regions which saw a rate of 34.4%. Facial lesions were the most prominent area of infection, recorded at a rate of 41.3%. The study also included an examination of 180 rodents (94 mice and 86 black r
... Show MoreThe research aimed to test the effect of independent variables career plateaus and workaholism on employees loyalty through the influence of the mediator variable organizational socialization. Descriptive approach with survey style on a sample of managers and executives in the Iraqi Drilling Company in Basra's (123) employees. The most important findings of the research are: the existence of a significant effect of the independent variables career plateaus and workaholism in employees loyalty by having a mediator variable organizational socialization and introduced numerical from recommendations. &nbs
... Show MoreThe recent advances in technology, the increased dependence on electrical energy and the emergence of the fourth industrial revolution (Industry 4.0) were all factors in the increased need for smart, efficient and reliable energy systems. This introduced the concept of the Smart Grid (SG). A SG is a potential replacement for older power grids, capable of adapting and distributing energy based on demand. SG systems are complex. They combine various components and have high requirements for real time reliable operation. This paper attempts to provide an overview of SG systems, by outlining SG architecture and various components. It also introduces communication technologies, integration and network management tools that are involved in SG sys
... Show MoreQuality of e-service is one of the critical factors that decide the success or failure of organizations. It may increase competitive advantages as well as enhance the relationships with the customers. Achieving high e-service quality and user satisfaction are challenging since they depend fundamentally on user perception and expectation which can be tricky at times. To date, there is no agreement as to what service quality is, and how it should be measured, whether it is a function of statistical measures of quality including physical defects or managerial judgment, or it is a function of customer perception about the services. This paper deep-dived the quality of e-services offered b
The research work is "The passive voice as a grammatical phenomenon in four selected textbooks". The research deals with the grammatical phenomenon passive in German. The research consists of two parts, the theoretical and the empirical part. The present research work is divided into 3 sections:
The first section includes the definition of passive, passive types, process passive, state passive, passive with modal verbs, and other types of passive. The second section provides illustrations of the four selected textbooks. The third chapter presents the passive voice in textbooks, namely German language teaching for foreigners by Dora Schulz and Heinz Griesbach, Delfin von Aufderstrasse H. and others, Em von Balme, M. and others and
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