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 .

Background: Malignant lymphoma is a term that describes primary tumors of the lymphoreticular system, almost all of which arise from lymphocytes.MMP-1 is the most ubiquitously expressed interstitial collagenase, a subfamily of MMPs that cleaves stromal collagens. It is also called collagenase-1.TIMPs which inhibits MMP activity and thereby restrict extracellular matrix breakdown, TIMP-1 is a stromal factor that has a wide spectrum of functions in different tissues. Material and Methods: This study was performed on (68) formalin-fixed, paraffin-embedded blocks, histopathologically diagnosed as lymphoma (head and neck lesions). Immunohistochemical staining of MMP1and TIMP1 was performed on each case of the study sample. Results: The expressio

Background: Bone regeneration in dehiscence and fenestration defect can be improved with the use of platelet rich fibrin (PRF) that provides a scaffold for new bone regeneration. This study was conducted to assess the effectiveness of PRF as a graft material and membrane in dehiscence and fenestration defects. Materials and Methods: This prospective clinical study included patients who received dental implants that demonstrated peri-implant defects which were augmented using Leukocyte- PRF (L-PRF) or Advanced-PRF (A-PRF). Twenty four weeks postoperatively the defect resolution and the density of regenerated bone were assessed by CBCT and re-entry surgery. The assessment also included measurement of primary and secondary implant stability

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

Background: Acute urinary tract infection is a common bacterial infection causing illness in infants and children. At age of seven, 8% of girls and 2% of boys will have at least one episode. Although drinking water and using home remedies are known to help to flush away bacteria and keeps them from sticking to the bladder wall, researches to test the efficacy and safety of hydrochlorothiazide's diuretic effect as adjuvant to the antibiotics in pediatric age groups are lacking, and so this research was to address this subject.

Objectives: To assess the effectiveness   and  the safety of hydrochlorothiazide as adjuvant therapy to the antibiotics in treating acute urinary tract infect

Rainwater harvesting could be a possible solution to decrease the consequences of water scarcity and energy deficiency in Iraq and the Kurdistan Region of Iraq (KRI). This study aims to calculate the water and energy (electricity) saved by rainwater harvesting for rooftops and green areas in Sulaimani city, KR, Iraq. Various data were acquired from different formal entities in Sulaimani city. Moreover, Google Earth and ArcMap 10.4 software were used for digitizing and calculating the total rooftop and green areas. The results showed that for the used runoff coefficients (0.8 and 0.95), the harvested rainwater volumes were 2901563 and 12197131 m³ during the study period (2005 – 2006) and (2019-2020). Moreover, by compa

  Methylotrophs bacteria are ubiquitous, and they have the ability to consume single carbon (C1) which makes them biological conversion machines. It is the first study to find facultative methylotrophic bacteria in contaminated soils in Iraq. Conventional PCR was employed to amplify MxaF that encodes methanol dehydrogenase enzyme. DNA templates were extracted from bacteria isolated from five contaminated sites in Basra. The gene specific PCR detected Methylorubrum extorquens as the most dominant species in these environments. The ability of M. extorquens to degrade aliphatic hydrocarbons compound was tested at the laboratory. Within 7 days, gas chromatographic (GC) studies of remaining utilize

The need for renewable energy sources is higher than ever due to rising global warming, climate change, and ozone depletion. For refrigeration and air conditioning applications, adsorption refrigeration systems are viable alternatives cooling techniques. This study is a topic and part of the M.Sc. thesis. A field solar-powered ice maker unit was created, studied, tested, and evaluated on the 13^th and 30^th of May, 2022. Activated carbon and methanol pair was used to set up a refrigeration system in Baghdad (Al Dora). Experimental tests were carried out outdoors to determine the coefficient of performance COP and specific cooling power SCP of the system. The results showed that the lowest temperature

The study of determing Uranium concentration in samples of teeth is the first of its kind in the Iraq . In this study Uranium concentration has been measured was (32) samples of child teeth distributed on the some of middle and south governorate of Iraq (Muthana – Dekar – Basrah – Najaf – Karbalah – Waset – Babel – Baghdad) . The Uranium concentration in teeth samples has been measured by using fission tracks registration in (CR-39) track detector that caused by the bombardment of (U235) with thermal neutrons falx from (24Am.Be) neutron source that has flux of (5x103n.cm-2S-1). The result obtained show that the Uranium concentrations in governorates were (0.18ppm), (0.172ppm), (0.160ppm), 0.150ppm) (0.89ppm), (0.07ppm) , (0.