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 .

Iraq is changing from the centralized system of governance to the decentralized system, which assumes devolution of more authorities to the local governments of Iraqi provinces and cities. This puts a responsibility on the academics to produce more research work on the best framework for this change, to ensure the best results. The main objective of this research is to suggest a policy for the decentralized transformation in domain of Urban and Regional Planning in Iraq. A suggested program for the transformation is involved in the paper as well, with analysis for the new relationships between different levels of planning authorities depending on democracy. In addition, a description for planning process flows from bottom to top.

In this research want to make analysis for some indicators and it's classifications that related with the teaching process and the            scientific level for graduate studies in the university by using analysis of variance for ranked data for repeated measurements instead of the ordinary analysis of variance . We reach many conclusions  for the                         

important classifications for each indicator that has affected on   the teaching process.         &nb

Teresa Fitzpatrick presents a connection between oppressed women and the plant of Wisteria in gothic fiction in her article “Wisteria: A Female Eco-Gothic Metaphor in American Fiction Through the Ages.” The connection between women and nature is common in literature as women are usually compared to the beauty or ferocity of flowers, rivers, or natural phenomena in general. The connection extends to the architecture and sort of plants that appear in gothic literature. Gothic novels have routinely been connected to the secrets and life stories of women who cannot have the liberty to live or share them outside their homes. A fearful house with a prisoned person, ghost, or a secret is mostly normally found in gothic writing. Women have exce

BACKGROUND: Three-dimensional (3D) printing is an evolving technology that has been used recently in a wide spectrum of applications. AIM: The objective is to evaluate the application of 3D printing in various neurosurgical practice. PATIENTS AND METHODS: This pilot study was conducted in the neurosurgical hospital in Baghdad/Iraq between July 2018 and July 2019. An X, Y, and Z printer was used. The working team included neurosurgeons, biomedical engineers, and bio-technicians. The procedure starts with obtaining Magnetic resonance imaging (MRI) or computed tomography (CT) scan in particular protocols. The MRI, and CT or angiography images were imported into a 3D programmer for DICOM images called 3D slice where these files con

The photoconductivity and its dependence on light intensity have been investigated in a-Ge20Se80 thin films as a function of temperature between (293–323)K. The result showed that the photoconductivity and photosensitivity increase with increase of annealing temperature. This behavior is interpreted in terms of the dispersive diffusion –controlled recombination of localized electrons and holes.

Fish are regarded as a crucial indicator of alterations in the aquatic environment due to their position at the apex of the food chain. Monitoring these alterations is crucial for identifying modifications in the aquatic ecosystem. The principal elements influencing fish health are temperature, pH, dissolved oxygen, salinity, pesticide contamination, microplastics, and algal presence. These elements substantially influence fish health regarding development, reproduction, respiration, oxygen stress, and the internal enzymes associated with digesting and other metabolic functions. Alterations in global environmental conditions and anthropogenic pollutants result in modifications to fish populations, their lives, and their behavior and

Conflict is a common but complicated phenomenon. It has been extensively researched in many domains, including philosophy, sociology, psychology, and linguistics. Using the Critical Discourse Approach, this study examines the issue of self-society conflict in The Handmaid’s Tale. The significance of this work lies in the identification and explanation of the discursive strategies that force the ideological polarization of the positively portrayed self versus the negatively portrayed other. The purpose of this study is to answer two questions: what are the discursive strategies used in The Handmaid’s Tale to create a positive or negative representation, and how are these strategies implemented? Five extracts from The Handmaid’s

The inflammatory response is a crucial aspect of the tissues’ responses to deleterious inflammogens. This complex response involves leukocytes cells such as macrophages, neutrophils, and lymphocytes, also known as inflammatory cells. In response to the inflammatory process, these cells release specialized substances which include vasoactive amines and peptides, eicosanoids, proinflammatory cytokines, and acute-phase proteins, which mediate the inflammatory process by preventing further tissue damage and ultimately resulting in healing and restoration of tissue function. This review discusses the role of the inflammatory cells as well as their by-products in the mediation of inflammatory process. A brief insight into the role of natural an

The current research aims to find out the role of transformational leadership in decision-making wise, to cope with the decline in some of the banking performance indicators as a result of the absence of the modern concept of the leadership of those so-called B (Transformational Leadership) and preventing benefit from the advantages in the banks, and I test the research on a sample of the Iraqi private banks through applied to a sample (77) Mdermvud and Associate Director and Advisor to the Chairman of the Department, the distributors (7) banks, and used the head of the questionnaire as a tool to collect data and information. For the purpose of access to the results, the research sought to test two hypotheses two main hypotheses sub pop