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 .

Egypt and Ethiopia have connected in a strong relation as there are historical facts that
deepen these relations, one of these is Egypt's cooperation in establishing the first economic
and financial banking system in Ethiopia.
Beside the religious relation between The Egyptian and Ethiopian churches the Nile River is
considered one of the effective connections
That strong then the relations as it leads to some tension between the two countries because
Ethiopia believes that Egypt seeks to control the river tries to build its project over the Blue
Nile means a threat to the Ethiopian national security.
The tension continues even after the revolution of 25th of January 2011because the Nahda
dam which is a clear t

The current research aims to know the extent of the impact of performance evaluation in its dimensions as an explanatory variable in the behavioural and attitudinal work outputs with its dimensions as a response variable in order to reach appropriate solutions through which the University of Fallujah seeks to achieve its goal in the process of diagnosing the axes of strength and to benefit from them in the process of strengthening the status and sobriety of the academic position of the professor and the researcher relied on The descriptive and analytical approach in carrying out this study, and data was collected from university professors, including leaders, heads of departments and divisions, who numbered (97) teachers. And fie

The current study was carried out to study a high injection dose of the ethanolic extract thymus vulgaris leaf (500 ug /Kg) against the immune response combination with partially purified extracted Lipopolysaccharide ( LPS) from Proteus mirablis.Study groups were included four groups; Group I :treated with normal saline. Group II : treated with LPS antigen, Group III: injected subcutaneously ((500 ug /Kg) from ethanolic extract thymus vulgaris, group IV : injected subcutaneously (500 ug /Kg) from ethanolic extract thymus vulgaris leaf and LPS antigen, the immunological assays were measured through the phagocytic activity as (non specific immunity) after day 8 by using the phagocytic activity index.After day I4 the lymphocyte proliferations

Wellbore instability is one of the most common issues encountered during drilling operations. This problem becomes enormous when drilling deep wells that are passing through many different formations. The purpose of this study is to evaluate wellbore failure criteria by constructing a one-dimensional mechanical earth model (1D-MEM) that will help to predict a safe mud-weight window for deep wells. An integrated log measurement has been used to compute MEM components for nine formations along the studied well. Repeated formation pressure and laboratory core testing are used to validate the calculated results. The prediction of mud weight along the nine studied formations shows that for Ahmadi, Nahr Umr, Shuaiba, and Zubair formations

Background: Knowing the indications for a cesarean section will help to have a better understanding of this common obstetrical procedure and prepare for the high level of care management that it entails. Aims of the study: The goal of this study was to determine the factors that influence caesarean section indications among women who visited AL-Dewaniya Maternity and Pediatric Hospital, as well as the relationship between caesarean section women's indications and socio-demographic data. Methodology: A descriptive cross-sectional study design is conducted for the period of December 26th 2020 to June 1st 2021 at Al Dewaniya Maternity and Pediatric Hospital. The validity of the questionnaire is determined through a panel of experts and reliabi

The optimal combination of aluminum quality, sufficient strength, high stress to weight ratio and clean finish make it a good choice in driveshafts fabrication. This study has been devoted to experimentally investigate the effect of applying laser shock peening (LSP) on the fatigue performance for 6061-T6 aluminum alloy rotary shafts. Q-switched pulsed Nd:YAG laser was used with operating parameters of 500 mJ and 600 mJ pulse energies, 12 ns pulse duration and 10 Hz pulse repetition rate. The LSP is applied at the waist of the prepared samples for the cyclic fatigue test. The results show that applying 500 mJ pulse energy yields a noticeable effect on enhancing the fatigue strength by increasing the required number of cycles to fracture the

In this research, a simple experiment in the field of agriculture was studied, in terms of the effect of out-of-control noise as a result of several reasons, including the effect of environmental conditions on the observations of agricultural experiments, through the use of Discrete Wavelet transformation, specifically (The Coiflets transform of wavelength 1 to 2 and the Daubechies transform of wavelength 2 To 3) based on two levels of transform (J-4) and (J-5), and applying the hard threshold rules, soft and non-negative, and comparing the wavelet transformation methods using real data for an experiment with a size of 26 observations. The application was carried out through a program in the language of MATLAB. The researcher concluded that

The existing study aimed to assess four soil moisture sensors’ capacitive (WH51 and SKU: S EN0193) and resistive (Yl69 and IC Station) abilities, which are affordable and medium-priced for their accuracy in six common soil types in the central region of Iraq. The readings’ calibration for the soil moisture sensor devices continued through two gravimetric methods. The first depended on the protocols’ database, while the second was the traditional calibration method. The second method recorded the lowest analysis error compared with the first. The moderate-cost sensor WH51 showed the lowest standard error (SE), MAD , and RMSE and the highest R² in both methods. The performance accuracy of WH51 was close to readings shown by the manufac