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: Although underdeveloped in Iraq, telehealth was one tool used to continue health service provision during the COVID-19 pandemic. Aim: To assess women’s experiences and satisfaction with gynaecological and obstetric telehealth services in Iraq during the COVID-19 pandemic. Methods: Free telehealth services were provided by 4 obstetrician-gynaecologists associated with private clinics in 2020–2021. All patients who accessed the services between June 2020 and February 2021 were invited to complete a postconsultation survey on their experience and satisfaction with services. Results were analysed using descriptive statistics and logistic regression conducted using SPSS version 25. Results: A total of 151 (30.2%) women re

ABSTRACT                                                                                            

The study aims to identify the level of health services provided in private suites to government hospitals from the perspective of the recipi

      It is frequently asserted that an advantage of a binary search tree implementation of a set over linked list implementation is that for reasonably well balanced binary search trees the average search time (to discover whether or not a particular element is present in the set) is O(log N) to the base 2 where N is the number of element in the set (the size of the tree).  This paper presents an experiment for measuring and comparing the obtained binary search tree time with the expected time (theoretical), this experiment proved the correctness of the hypothesis, the experiment is carried out using a program in turbo Pascal with recursion technique implementation and a statistical method  to prove th

Half of the oil production of the worldwide is a result  of the water flooding  project. But the main concern of this process is mobility control of the injected fluid, because the unfavorable mobility ratio leads to fingering effect. Adding polymer to the injection water increase the water viscosity, therefore, the displacement will be more stable and have a greater sweep efficiency.

   Using of polymer flooding has received more attention these days. Polymer has great potential in the Middle East region, especially in reservoir with high temperature and salinity.

   The main objective of this work is to show the effect of shear rate, salinity, temperature, polymer concentration on polymer v

In this research, we have added nano anatase TiO₂ as a partial replacement of Portland cement by a weight percentage of (0.25 to 1%) for the development of properties for protection against bacteria. The control mix was made by using "the cement to sand" proportion about (1: 2.75) with the "water to cement" proportion of (0.5) to study the structure, porosity, water absorption, density, mechanical properties, as well as anti-bacterial behavior. Inspections have been done such as scanning electron microscopy (SEM), and atomic force microscope (AFM) for mortar. Experimental results showed that after the addition of Nano powders in cement mortar, the structural properties improved significantly with the development of hydration o

Copper selenide (Cu2Se) thin films were prepared by thermal evaporation at RT with thickness 500 nm. The heat-treating for (400 &500) K for the absorber layer has been investigated. This research includes, studying the structural properties of X-ray diffraction (XRD) that show the Cu2Se thin film (Cubic) and has a polycrystalline orientation prevalent (220). Moreover, studying the effect of annealing on their surface morphology properties by using Atomic Force Microscopy AFM. Optical properties were considered using the transmittance and absorbance spectra had been recorded when wavelength range (400 - 1000) nm in order to study the absorption coefficient and energy gap. It was found that these films had allowed direct transitio

Polypyrrole (PPy) nanocomposites were prepared using chemical oxidation and were combined with manganese oxide (MnO2) nanoparticles. The PPY-MnO2 nanocomposite was synthesized by integrating PPy nanofibers with varying volume ratio percentages of MnO2 dopant (10, 30, and 50% vol. ratio). The structural features of the PPy and PPy-MnO2 nanocomposite were investigated using X-ray diffraction (XRD).  Fourier transfor infrared (FTIR) spectroscopy was used to demonstrate the molecular structures of primary materials and the final product of PPy, MnO2, and PPy- MnO2 nanocomposites. Field Emission Scanning Electron Microscopy (FESEM) showed that the morphology of PPy consisted of a network of nanofibers. Increasing the volume ratios of ma

In this study, hydroxyapatite (HAP, Ca10(PO4)6(OH)2) has been prepared as bioceramic material with biological specifications useful to used for orthopedic and dental implant applications. Wet chemical processing seems to form the fine grain size and uniform characteristic nanocrystalline materials by the interstice factors controlling which affected the grain size and crystallinity in order to give good mechanical and/or constituent properties similar as natural bone. Fluorinated hydroxyapatite [4-6 wt% F, (FHA, Ca10(PO4)6(OH)2–Fx] was developed in new method for its posses to increased strength and to give higher corrosion resistance in biofluids than pure HAP moreover reduces the risk of dental caries. The phase's and functional groups