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 biggest problem of structural materials for fusion reactor is the damage caused by the fusion product neutrons to the structural material. If this problem is overcomed, an important milestone will be left behind in fusion energy. One of the important problems of the structural material is that nuclei forming the structural material interacting with fusion neutrons are transmuted to stable or radioactive nuclei via (n, x) (x; alpha, proton, gamma etc.) reactions. In particular, the concentration of helium gas in the structural material increases through deuteron- tritium (D-T) and (n, α) reactions, and this increase significantly changes the microstructure and the properties of the structural materials. T

Recently, several concepts and expressions have emerged that have often preoccupied the world . around the concept of environment and sustainability. This is due to the negative and irresponsible impact of man and his innovations in various industrial and technological fieldsthat have damaged the natural environment. Architecture and cities at the broader level are some of the man made components that caused these negative impacts and in the same time affected by them. What distinguishes architectural and urban projects is the consumption of large . quantities of natural resources and production larger amounts of waste and pollution, along the life of these projects. At the end of the twentieth century and the beginning of the twenty-fir

This study concerns the role of activated carbon (AC) from palm raceme as a support material for the enhancement of lipase-catalyzed reactions in an aqueous solution, with deep eutectic solvent (DES) as a co-solvent. The effects of carbonization temperature, impregnation ratio, and carbonization time on lipase activity were studied. The activities of Amano lipase from Burkholderia cepacia (AML) and lipase from the porcine pancreas (PPL) were used to investigate the optimum conditions for AC preparation. The results showed that AC has more interaction with PPL and effectively provides greater enzymatic activity compared with AML. The optimum treatment conditions of AC samples that yield the highest enzymatic activity were 0.5 (NaOH (

Biomarkers such as Interleukin-6 (IL-6), Procalcitonin (PCT), C-reactive protein (CRP) and Neutrophil-Lymphocyte Ratio (NLR) have a role in the pathogenesis of severe coronavirus disease 2019 (COVID-19). The aim of this study was to explore the differences between serum levels of such biomarkers in severe and non-severe COVID-19 cases and compare them with normal people and to evaluate the sociodemographic variables and chronic diseases effect on the severity of COVID-19. The study included 160 subjects, divided into two groups, a case group of 80 patients, and a control group of 80 normal persons. The case group was divided into two subgroups: 40 severe COVID-19 patients and 40 patients with non-severe disease. Blood IL-6 was asses

The topic of (pilgrims) of the old and modern subjects at the same time, as it extends his foot and is associated with the beginning of speech and argument, a modern because it is based on studies and research (and the theory of pilgrims) from (Austin and Cyril) through (Charles Breman) to (Aristotle) ), It is worth mentioning here to mention the role of (Hazem al - Qartagni) in mentioning the value of the pilgrimage of hair and saying the use of persuasion in the hair, is palatable and acceptable. Hence our research applied these views, and we chose the pendants as a model for that matter.

The research utilizes data produced by the Local Urban Management Directorate in Najaf and the imagery data from the Landsat 9 satellite, after being processed by the GIS tool. The research follows a descriptive and analytical approach; we integrated the Markov chain analysis and the cellular automation approach to predict transformations in city structure as a result of changes in land utilization. The research also aims to identify approaches to detect post-classification transformations in order to determine changes in land utilization. To predict the future land utilization in the city of Kufa, and to evaluate data accuracy, we used the Kappa Indicator to determine the potential applicability of the probability matrix that resulted from

The Quality  function deployment (QFD)  tool is an important  tool of total quality management because its a link between two important parts customer and production process of the product, using advanced House of quality, which contributed to provide more details about improving the product before it had a vision for the future of the product be improved. Also the identification of the two competitors (Alwazeer , Altouri) bases on the survey of retailers  which they identified five competitors products (Alwazeer , Altouri , Ferry , Jif , Dina)for the product (Zahi). Then House of quality  to product (Zahi) has been developed  By using a Kano Model  to classify of customer's requirements for the

the research ptesents a proposed method to compare or determine the linear equivalence of the key-stream from linear or nonlinear key-stream