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 .

This research paper looks to put its hands on sufi symbols which are applied by the algerian poet د abdallah hammadi د in his poetical works . the symbols it relies on are : ( symbolisme of wine . symbolisme of light . symbolisme of night . sufisme and nature , femal symbols ) .
From these symbols we try to show its range of ability to apply it , with trying to determine its meaningful , dimensions .

The importance of the heritage of the Iraqi heavy symbolism and connotations where contacted habits rights and beliefs from antiquity to the present, in addition to being represented with data aesthetic it is an expression philosophical concepts associated implications incentives cultural aesthetic of the content of the intellectual including contents of semantics and symbols and the dimensions of the meanings Sayings , to turn form a legacy popularly moving window to communicate worth studying its details and search function on the character and identity and origins . Where have emerged in recent years, a phenomenon characterized by inventing new designs by modernist styles that have entered into technical system design and effectivenes

The research aims to improve the performance of the Directorate of Maysan water by reconciling the objectives of the employees of the directorate with the objectives of the Directorate itself, as well as to identify the strengths and weaknesses in the performance of the Directorate (Leadership - Individuals - Knowledge - Operations - Financial) and presented to experts and arbitrators of specialized, and the researchers have relied on the case study methodology as a descriptive approach is comprehensive analysis, and draws on more than one approach, method and scientific design, has been interviewed a number of experts in the Directorate Maysan's water Identify the weaknesses and strengths of the Directorate, the research has rea

Reishi Mushroom, Ganoderma, is considered one of important wood-decaying medicinal mushrooms. This study aimed to identify three samples of this genus in Mosul city in February and April 2019. Three species of Ganoderma were collected from three various trees including Eucalyptus, Morus, and Olea (olive) in Mosul City, Northern Iraq. Their identifications and their DNA sequences were genetically identified by using PCR techniques according to detect nuclear ribosomal internal transcribed spacer (ITS) regions. Results exhibited the finding of Ganoderma resinaceum, Ganoderma applanatum, and Ganoderma sp. This study is first attempt to identify Reishi Mushroom by molecular methods in Iraq. Thus, the current study is considered new good d

The leaf miners Pegoinya terbrans (Rondani) and P. bicolor (Wiedemann) (Diptera; Anthomyiidae) were newly recorded in Iraq. Host plants of these leaf miners and P. cunicularia (Rondani) were identified: P. bicolor was found to be monophagous, whereas P. terbrans and P. cunicularia were oligophagous . It was found that Cirsixim syriaca and Silybum marianum were more susceptible to P. terbrans than the other ones. Infectivity and severity of infestation were estimated for most susceptible weeds against P. terbrans and P.bicolor. These leaf miners. Have two generations a year.

This study was aimed to investigate the genetic variability of 26 rice genotypes and evaluation at two locations in Sulaimani governorate, Gaba and Chawtan which were completely different in their environmental condition during the season of 2019. The performances of the genotypes were analyzed at both locations as well as the average of both. Simple coefficients of correlation were used to assess the grain yield components and their relationships. Path analysis was used to determine the direct and indirect effects of such components on grain yield plant^-1. The genotypes were grouped based on the agro-morphological features using cluster analysis. Almost all of the traits at both locat

Background: Dysfunction of sinoatrial node is a set of abnormal rhythms which are resulted from the sinoatrial node malfunction of the sinus node, the chief natural cardiac pacemaker. The common, and occasionally, the single method for treatment of heart arrhythmias was implantation of pacemaker, which reduce symptoms exactly occurs after implantation. Aim: To detect the role of smoking on cardiac electrophysiology parameters in sinus node dysfunction in Iraqi patients such as SNRT and AH. Methods: A cross sectional study, was conducted on 59 patient ranging between 20-50 years old and involving 35 female and 24 male patients, suffering from an unexplained symptoms of sinoatrial node dysfunction (SND). The enrolled participants were gathere