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 problem of the tagged research (experimentation in the works of the artist Muhammad al-Kinani is an analytical study) dealt with the nature of the concept of experimentation and its work in the works of Muhammad al-Kinani. Which adopts the removal of the concept of style and artistic style and takes the experience away from the pattern of repetition The importance of the research comes through the identification of the materials founding the artistic work. The current research benefits the specialists in the field of arts from the students of studies with a new and renewed formulation of creativity. The research objectives shed light on the contemporary experiences of the artist Muhammad Al-Kinani and its importance in benefiting res

This is a contextual study in face and isotope science, and I have made it in one of the terms faces and isotopes, which is the word (bad). Quranic also, and that is at every aspect they mentioned.
The nature of the research required that it be divided into three sections:
The first topic: I singled it out to show the types of contextual connotations.
- The second topic: I singled it out to define the word bad and its meaning.
- The third topic: I devoted it to the study of the word bad and explaining the significance of the Quranic context on the additional meaning and the original meaning.
Conclusion: It mentioned the most important results, which are:
1- The significance of the Quranic context is one of the most impo

The place in which the person lives and his geographical and social environment have a great impact on building his personality, belief and culture, Islam has alerted the importance of the Muslim to make sure to choose the appropriate place in which he resides and dwells in that it is compatible with his religion and belief in order to ensure communication with Islamic knowledge in a way that enhances his belief Arabization occurs when a person makes himself an Arab by living the life of the Bedouins, and creates the morals of the Bedouins from the inhabitants of the Badia with its harshness, cruelty, ignorance and lack of understanding in religion and far from the sources of knowledge of Islamic knowledge. Blasphemy and polytheism, and

Research summary

Informing means informing and informing, which is conveying information to someone and confirming his narration with it. Accordingly, information is its main content..and it has multiple means, including visual, audio and read, and it has become the dominant role in the process of socialization, and much of what we hear, read, or watch in the media is not devoid of a goal, and expresses that scientifically as “charged with values” ( Value Loaded)..Values that are: the set of beliefs that the individual holds towards things, meanings, and various aspects of activity, which direct his desires and attitudes towards them, and determine for him acceptable and unacceptable behavior, right and wrong, and all of this

The research (The Aesthetics of Lumia Art in Contemporary Textile Arts: An Analytical Study) included four chapters, the first to explain the research problem summarized by the question: Does the art of Lumia achieve aesthetic values in contemporary textile arts?, and aims to: Identify the aesthetics of Lumia art and its applied uses in contemporary textile arts, within the time period (2013-2022). The third chapter included: research procedures and sample analysis (4) models according to the descriptive analytical approach, and the fourth chapter dealt with: results, conclusions and recommendations as well as sources.

Abstract

  The study aims to find out the impact of expectations and perceptions in determining the position of the customer service quality received by him. Represent the expectations and perceptions customer’s key of service quality determinants. The customer's requirements and needs main pivot, who must be built all events and activities and efforts of service organizations, including the hotel and organizations that operate in an environment known as highly competitive , intensification and  complexity of the conditions set by the customer and increasing day after day. The study sample of three Luxury hotels in Kurdistan region of Iraq a model. The use of service quality m

This study aimed to detect of contamination of milk and local soft cheese with Staphylococcus aureus and their enterotoxins with attempt to detect the enterotoxin genes in some isolates of this bacteria. A total of 120 samples, 76 of raw milk and 44 of soft cheese were collected from different markets of Baghdad city. Enterotoxins in these samples were detected by VIDAS Set 2 system and it was found that enterotoxin A is present in a rate of 44.74% in milk samples and in a rate 54.50% in cheese samples. While other enterotoxins B, C, D, E were not found in any rate in any samples.
Through the study 60 isolates obtained from milk and cheeses were identified as Staphylococcus aureus by cultural, morphological and biochemical test by u

Soil invertebrates community an important role as part of essential food chain and responsible for the decomposition in the soil, helps soil aeration , nutrients recycling and increase agricultural production by providing the essential elements necessary for photosynthesis and energy flow in ecosystems.The aim of the present study was to investigate the soil invertebrates community in one of the date palms plantation in Aljaderia district South of Baghdad, , and their relationships with some physical and chemical properties of the soil , as Five randomly distributed replicates of soil samples were collected monthly. Invertebrates samples were sorted from the soil with two methods, direct method to isolate large invertebrates and indirec

Due to the importance of the extraction process in many engineering and medical industries, in addition to great interest in medicinal plants, in this research, microwave-assisted extraction has been applied to extract some active compounds from Rosmarinus officinalis leaves.  The optimal extraction conditions were then determined by calculating the ratio and extraction efficiency. The process has also been described through kinetic study by applying five  kinetic models, the Hyperbolic diffusion model,  Power low model, the First order reaction  model, Elovich's model, and Fick's second law diffusion model and determining their compatibility with the studies operation, and determining the kinetic constants for each model. The result