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 .

Background: The hybrid compounds hold promise for developing novel pharmaceuticals, potentially exhibiting greater activity, mainly against viruses and cancer diseases, than their components.

Objective: In this study, researchers explored the potential synergistic effects of hybrid molecules by designing and synthesizing a series of isatin-gallate hybrids, denoted as N’-(5-substituted-2-oxoindolin-3-ylidene)-3,4,5-trihydroxybenzohydrazide (3a–d).

Methods: Isatin-gallate hybrids (3a–d) were synthesized by reacting gallic hydrazide with each of the isatin analogs (2a–d). The structures of all produced comp

Cost is the essence of any production process for it is one of the requirements for the continuity of activities so as to increase the profitability of the economic unit and to support the competitive situation in the market. Therefore, there should be an overall control to reduce the cost without compromising the product quality; to achieve this, the management should have detailed credible and reliable information about the cost to be measured, collected, understood and to analyze the causes for the spread of deviations and obstacles the management faces, and to search for the factors that trigger the emergence of these deviations and obstacles

 The research dealt with two variables first in the field of human resources represented by the empowerment of workers  and second in operations through improved process in the framework of standards Quality Award European containing nine basic criteria (Leadership, Strategy, partnerships and resources, the results of the individuals, the results of the customer, the results of the community), including human resources and operations has been selected and the Ministry of Industry and Minerals as a community to search , which covered most of the industrial sectors of Iraq through the selection of a single company of every industrial sector and thus became the research sample (6 ) industrial companies in addition to the C

Oil sector is one of the most important sectors affecting the ecological balance, as activity contributes to the oil companies to influence their working environment, both during the oil exploration and extraction process or during transfer from one place to another process. We will try through this research put an environmental audit program proposal takes into account all the financial aspects, commitment and performance, according to the laws and regulations and agreements as well as relevant international standards, was based on research on the premise that the development of an environmental proposal auditing program that includes environmental controls on oil industry phases which helps reduce or minimize environmental pollutants B

This paper tackles with principal component analysis method (PCA ) to dimensionality reduction in the case of linear combinations to digital image processing and analysis. The PCA is statistical technique that shrinkages a multivariate data set consisting of inter-correlated variables into a data set consisting of variables that are uncorrelated linear combination, while ensuring the least possible loss of useful information. This method was applied to a group of satellite images of a certain area in the province of Basra, which represents the mouth of the Tigris and Euphrates rivers in the Shatt al-Arab in the province of Basra.

Sara and other kid's Agony: - Back to Innocence to Save Iraq

Humans knew writing and to blog motivated by the need for registration and documentation, and tried from the very beginning of research to find the most suitable material for this purpose, he used many different materials in form, nature, and composition, so it is written on the mud by the ancient Sumerian people in different forms and when the text is long Numbered as the pages of the book at the present time, this research will deal with the damage to manuscripts and then find ways to address them.

A Survey Study Of A Sample Of The Public Of Baghdad  Governorate

The current study aimed to identify the most prominent psychological and behavioral repercussions of the exposure of the elderly to the news of the Corona pandemic and to determine the mechanisms of their exposure. On an intended sample on both sides of (Al-Karkh and Al-Rasafa) and the simple random sample was adopted to choose the place of distribution of the questionnaire and the intentional sample.

 The research concluded several results, most TV news is still a primary source of information and that most of the sample move between stations to see more information about the pandemic and that the presentation of views confuses the elderly ،There

Abstract

                  The study aimed to prepare a practical guide for procedures for auditing the strategies of municipal institutions in achieving sustainable development by adopting the idea of ​​the audit matrix through which a classified report is prepared according to the dimensions of sustainable development, by preparing a specialized audit program for the purpose of auditing strategies for achieving sustainable development and emptying the results of the application of each of the paragraphs The program in the audit matrix that was prepared for the purpose of determining the impact of each observation and linkin