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 .

Each organization has values ​​and objectives, tangible and intangible properties of its products. The reflection of properties on the brand constitutes the identity of the brand that contributes to building the customer's convictions about the products or services provided by any organization and its brand in a positive or negative way. This is reflected in purchasing behavior, which may push forward the progress towards marketing goals or deviation from them. Therefore, the current research came to identify the brand identity, its types and the factors affecting them and how they affect to achieve each of the marketing goals. At a time when

Iraqi industrial units face strong competition due to many problems including1- high production costs2- weak interest in studying the market3- lack of government support for their products4- dumping the market with imported products with specifications and a competitive price as well as adopting the traditional cost system in calculating costs that do not provide appropriate information for pricing decisions Which requires studying and analyzing these problems and dealing with them by adopting modern technologies so that they can compete, so the research aims to show the knowledge bases of technology Activity- Based Costing, with an indication of the role of technology Activity- Based Costing in rationalizing the tax In, and the

The variables of quantitative and qualitative Population role in the economic development process and it was said the human center of development and population is the goal of development and its tool , and Iraq suffers from problems in the economic growth and the standard of living and development in general, and if I want him evolution and development sectors must pay for these demographic changes especially , to study and that invest Pmaasb in the interest of the man
The study of the demographic situation in Iraq and at the provincial level to track paths demographic change and its impact on the entry of Iraq to the demographic window due to the change in the age structure of the population and how to use them and invested well in

SARS-CoV-2 stands for severe acute respiratory syndrome coronavirus 2 which is the causative agent of spreading coronavirus disease 2019 that is known as COVID-19 pandemic, the disease leads to severe acute respiratory illness. Matrix metalloproteinases- 9 (MMP-9) plays several important physiological functions. This enzyme could also be implicated in the "cytokine storm" in some way, which may represent one of the possible scianrios during coronavirus infection, in addition to its role in the mechanism of lung fibrosis on molecular basis.. The tissue inhibitors of metalloproteinase (TIMPs) are well characterized for controlling the activity of MMPs in extracellular matrix remodeling. They also considered as signaling molecules anal

SARS-CoV-2 stands for severe acute respiratory syndrome coronavirus 2 which is the causative agent of spreading coronavirus disease 2019 that is known as COVID-19 pandemic, the disease leads to severe acute respiratory illness. Matrix metalloproteinases- 9 (MMP-9) plays several important physiological functions. This enzyme could also be implicated in the "cytokine storm" in some way, which may represent one of the possible scianrios during coronavirus infection, in addition to its role in the mechanism of lung fibrosis on molecular basis.. The tissue inhibitors of metalloproteinase (TIMPs) are well characterized for controlling the activity of MMPs in extracellular matrix remodeling. They also considered as signaling molecules anal

A study of non-diatom algal species composition in twelve sites from Greater Zab River path within
Erbil Province, was carried out from April 2021 to January 2022 with monthly sample collection in twelve studied sites. Among them site 4,5,6,7 and 9 are the first for algal study in this area. The 112 different species of algae belong to 33 genera, 25 families, 13 orders and 4 divisions have been identified. The predominant genera included Spirogyra and Cosmarium 17, 8 taxa respectively. 13 taxa were new recorded to Iraqi
Kurdistan algal flora and 9 of them were new recorded to Iraqi algal flora: Botryosphaerella sudetica, Muriella magna, Gloeotaenium loitlesbergianum, Apiocystis brauniana, Anabaena oscillarioides, C. distentum

Ping message focused on highlighting the fact commodity trading in Iraq, and increased exposure to world merchandise trade imbalance, which dominate Iraq's foreign trade major commodity is oil, and therefore the inability of Iraq to control financial revenue as a result of the fluctuations in the international market, the shortage of commodity products will lead inevitably to the weakness in the ability of the local market to meet the internal demand and due to the lack of flexible production machine For agricultural, industrial and economic sectors are responding to changes in the domestic or external demand which will open the door to merchandise imports to invade these markets, since the adoption of the Iraq oil exports,

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