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 .

A solid Phase Extraction (SPE) cartridges followed by HPLC-UV method is described for the simultaneous quantitative determination of benzidine (BZ) and its substituted 3, 3’-dichlorobenzidine (DCB) and 3, 3’-Dimethylbenzidine (DMB). The Benzidines were separated by liquid chromatography using a C-18 column with UV detector at wave length of 280nm. The mode of Flow was isocratic. The mobile phase was consisted of 75:25 methanol: water, column temperature 50C°, and Flow Rate 1.8ml/min. Calibration curves were linear (R2 = 0.9979-0.9995). LOD (26.36-33.67) µg/L, LOQ (109.98-186.11) µg/L, the Robustness (2.99-4.35), Ruggedness (2.93-3.65).Conditions of extraction by (SPE) cartridges were optimized, the resin used is Octadecyl silica (ODS

Background: Multiple myeloma (MM) is characterized by clonal proliferation of malignant plasma cells within the bone marrow. In most patients, monoclonal immunoglobulin heavy chains or light chains are produced and are associated with organ dysfunction. The growth factor B-cell activating factor (BAFF) plays an important role in the pathogenesis of multiple myeloma due to its ability to promote B-cell survival, expansion, and differentiation. Objective:  to measure the circulatory level of B-cell activating factor in multiple myeloma patients in relapsed and remission states and explore its possible correlations with the clinical staging, β2-microglobulin, and interleukin-6. Methods: This cross-sectional study was performed on 60

Background and Purpose: Coronavirus has posed an unfamiliar threat to the world. Despite such circumstances, Malaysians continue to stay optimistic by keeping abreast with updates and mostly by seeking refuge in hopeful and consoling messages shared by fellow citizens. This study identified Facebook postings with positive messages, posted by Malaysians during the Movement Control Order (MCO) implemented by the Malaysian government as a form of prosocial behaviour.   Methodology: Through an analytic framework consisting of Positive Discourse Analysis and Critical Discourse Analysis, 15 Facebook postings related to COVID-19 were selected and identified as positive discourse, which were coded and categorised using a thematic analysi

Four photosensitizers were used to test inhibitory effect of Helicobacter pylori bacteria using
low power helium: neon red laser radiation. Biopsies were collected from 176 patients and H. pylori were
isolated, identified and bacterial suspension was prepared. Samples of this suspension were mixed with
various low concentrations of the test sensitizer. The mixture samples were exposed to different laser
radiation doses. The samples were then inoculated and the inhibition zones were studied and compared
with their analogues of control samples. The most effective sensitizer with optimum concentration and
irradiation dose was determined. Statistical analysis of results was performed. The sensitizers' toluidine
blue and

Many water supplies are now contaminated by anthropogenic sources such as domestic and agricultural waste, as well as manufacturing activities, the public's concern about the environmental effects of wastewater contamination has grown. Several traditional wastewater treatment methods, such as chemical coagulation, adsorption, and activated sludge, have been used to eliminate pollution; however, there are several drawbacks, most notably high operating costs, because of its low operating and repair costs, the usage of aerobic waste water treatment as a reductive medium is gaining popularity. Furthermore, it is simple to produce and has a high efficacy and potential to degrade pollu

Investigations made and soil samples brought from 14 sites in different areas, including Abu Ghraib and Al Anbar. Tests and measurements made in the Microbiology Laboratory at the College of Agriculture, University of Anbar. Department of Soil Sciences and water Resources, in order to isolate bio-fertilizers and test isolates fixing nitrogen in atmosphere and solvents for phosphorous compounds efficiency. The experiment included isolating and diagnosis of bacteria from rhizosphere soils of different plants that were brought from different agricultural areas, 74 isolates obtained by soils alleviation, and then the bio-chemical morphological and microscopic characteristics of these soils studied. The results showed that the most abundant and

Prediction of penetration rate (ROP) is important process in optimization of drilling due to its crucial role in lowering drilling operation costs. This process has complex nature due to too many interrelated factors that affected the rate of penetration, which make difficult predicting process. This paper shows a new technique of rate of penetration prediction by using artificial neural network technique. A three layers model composed of two hidden layers and output layer has built by using drilling parameters data extracted from mud logging and wire line log for Alhalfaya oil field. These drilling parameters includes mechanical (WOB, RPM), hydraulic (HIS), and travel transit time (DT). Five data set represented five formations gathered