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 .

    In this paper, the ability of using corn leaves as low-cost natural biowaste adsorbent material for the removal of Indigo Carmen (IC) dye was studied. Batch mode system was used to study several parameters such as, contact time (4 days), concentration of dye (10-50) ppm, adsorbent dosage (0.05-0.25) gram, pH (2-12) and temperature (30-60) oC. The corn leaf was characterized by Fourier-transform infrared spectroscopy device before and after the adsorption process of the IC dye and scanning electron microscope device was used to find the morphology of the adsorbent material. The experimental data was imputing with several isotherms where it fits with Freundlich (R2 = 0.9937) and followed pseudo second order kinetic. The hi

As human societies grow, the problem of waste management becomes one of the pressing issues that need to be addressed. Recycling and reuse of waste are effective waste management measures that prevent pollution and conserve natural resources. In this study, the possibility of using glass waste as an alternative was used as a partial weight substitute for fine aggregates with replacement ratios of 10, 20, 30, and 40% by the weight, and formed into test models (15 cm * 15 cm ) cube and (15 cm * 30 cm) cylinder, then matured and tested their strength compression and tensile strength at the age of 7 and 28 days and compared with a reference or conventional concrete with a mixing ratio (1: 1.5: 3) as well as testing its worka

Diabetic nephropathy (DN) is the foremost cause of end-stage renal disease. Early detection of DN can spare diabetic patients of severe complications. This study aimed to evaluate the diagnostic value of red cell distribution width (RDW) and neutrophil-lymphocyte ratio (NLR) in the detection of DN in patients with type 2 diabetes mellitus (T2DM). This cross-sectional study included a total of 130 patients with T2DM, already diagnosed with T2DM. The albumin creatinine ratio (ACR) in urine samples was calculated for each patient, according to which patients were divided into two groups: with evidence of DN when ACR ? 30 mg/g, and those with no evidence of DN when ACR < 30 mg/g. According to multivariate analysis, each of disease duration (OR

In this paper, the ability of using corn leaves as low-cost natural biowaste adsorbent material for the removal of Indigo Carmen (IC) dye was studied. Batch mode system was used to study several parameters such as, contact time (4 days), concentration of dye (10-50) ppm, adsorbent dosage (0.05-0.25) gram, pH (2-12) and temperature (30-60) ^oC. The corn leaf was characterized by Fourier-transform infrared spectroscopy device before and after the adsorption process of the IC dye and scanning electron microscope device was used to find the morphology of the adsorbent material. The experimental data was imputing with several isotherms where it fits with Freundlich (R² = 0.9

     The radio drama is considered to be one of the arts that is discovered after a long period of theater's discovery. Initially , it was the broad framework of the theater's work when radio was broadcasting the shows on the huge theaters. This beginning encouraged many of the radio specialists to correlate plays with radio and make a novice and distinctive type of art. Thus, radio drama made its first step including the following   ( plays, short and long series drama as well as other types of radio arts). Because of the above mentioned , the researcher is stimulating  to study directing techniques to process the radio drama script ( Khata'a play as a sample).

The first chapter deals with the

In this study, two active galaxies (NGC4725, NGC4639) have been chosen to study their morphological and photometric properties, by using the IRAF ISOPHOTE ELLIPS task with griz-filters. Observations are obtained from the Sloan Digital Sky Survey (SDSS) which reaches now to the DATA Release (DR14). The data reduction of all images (bias and flat field) has been done by SDSS Pipeline. The surface photometric investigation was performed like the magnitude. Together with isophotal contour maps, surface brightness profiles and a bulge/disk decomposition of the images of the galaxies, although the disk position angle, ellipticity, and inclination of the galaxies have been done. Also, the color of galaxies was studied, where chromatic distribution

The absence of ecological perception in the local urbanization resulted in the lack of a clear conception of achieving sustainability in its simplest form in the urban reality and in the city of Baghdad in particular. The research assumes the possibility of achieving urban sustainability in Iraqi cities by applying the cities for the most effective methods to implemented ecological solutions and introducing appropriate urban planning tools and improve the living environment. The research focuses on the ability to define some aspects to achieve a sustainable local urban identity from global experiences. This was performed by proposing a scheduled theoretical framework, through which the features of sustainability can be extrapolated from the

The environmental problems that have emerged recently as a result of pressure on the environment due to the increase in population size, especially in urban cities, where this increase was accompanied by the need for housing as well as the need for services and activities. This led to the establishment of many vertical residential buildings represented by residential complexes within the urban fabric of the city of Baghdad. As part of following the methodology of urban dictation policies in empty areas, and to accommodate the largest number of residents as a result of the multiplicity of floors and housing, these buildings must be subject to the standards and requirements of sustainability at the level of their spatial location and their