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 .

The present study aimed at identifying the role of supervisory and training practices in the field   education program in achieving course objectives from the perspective of the student teachers in the Faculty of Science and Arts in sharourah, and its relationship to some variables (gender, specialization,estimation). To achieve this, the researcher used the descriptive-analytical method, and the study tool was designed, which consists of (24) items distributed on two axes: the objectives of field education and supervisory and training practices.Then, the study tool was applied to the research sample represented in the entire study community, which consists of (65) male and female students in the Faculty of Sciences and Arts in

Augmented reality technology is a modern technique used in all fields, including: medicine, engineering and education, and has received attention from officials in the educational process at present; The focus of this research is on the degree of use of augmented reality among field experience students in the project's optimal investment program for teaching staff and their difficulties, applied to a sample of 75 students, through a questionnaire prepared by the researcher as a tool to determine the degree of use, as well as difficulties. The researcher addressed the subject through two main axes to determine the degree of use, as well as the difficulties preventing teachers and learners from using this technique. The results of the rese

The research aims to determine the factors affecting the woman’s use of electronic marketing in social networking sites, and to know the extent of the sample’s use of social networking sites for electronic shopping purposes. The research tool used the questionnaire form that was designed in its final form after presenting it to the arbitrators and it included a set of questions and a five-Likert scale, and used the spss statistical program to perform the statistical operations that were laid out in tables showing the frequencies, percentages and percentages Salary, mean, standard deviation, and correlation using the Spearman correlation coefficient, the Ka2 square test, the F test, the Alpha Cronbach test, and arrived at Searching to

   In southern Iraq, the Yamama Formation has been a primary carbonate resource since the Lower Cretaceous era. This study covers Siba Field, which is located in southeastern Iraq. This paper will be devoted to a YC unit of study. The most crucial step in reservoir management is petrophysical characterization. The primary goal of this research is to assess the reservoir features and lithology of the Yamama (YC) Formation in the Siba region. Accessible excellent logs include sonic, density, neutron, gamma-ray, SP, and resistivity readings. The Interactive Petrophysics (IP4.4) program examined and estimated petrophysical features such as clay volume, porosity, and water saturation. The optimum approach was the neutron density and clay vo

In this paper, a simulation of the electrical performance for Pentacene-based top-contact bottom-gate (TCBG) Organic Field-Effect Transistors (OFET) model with Polymethyl methacrylate (PMMA) and silicon nitride (Si3N4) as gate dielectrics was studied. The effects of gate dielectrics thickness on the device performance were investigated. The thickness of the two gate dielectric materials was in the range of 100-200nm to maintain a large current density and stable performance. MATLAB simulation demonstrated for model simulation results in terms of output and transfer characteristics for drain current and the transconductance. The layer thickness of 200nm may result in gate leakage current points to the requirement of optimizing the t

This study appears GIS techniqueand remote sensing data are matching with the field observation to identify the structural features such as fault segments in the urban area such as the Merawa and Shaqlawa Cities. The use of different types of data such as fault systems, drainage patterns (previously mapped), lineament, and lithological contacts with spatial resolution of 30m was combined through a process of integration and index overlay modeling technique for producing the susceptibility map of fault segments in the study area. GIS spatial overlay technique was used to determine the spatial relationships of all the criteria (factors) and subcriteria (classes) within layers (maps) to classify and map the potential ar

This paper presents the electrical behavior of the top contact/ bottom gate of an organic field-effect transistor (OFET) utilizing Pentacene as a semiconductor layer with two distinctive gate dielectric materials Polyvinylpyrrolidone (PVP) and Zirconium oxide (ZrO2) were chosen. The influence of the monolayer and bilayer gates insulator on OFET performance was investigated. MATLAB software was used to simulate and determine the electrical characteristics of a device. The output and transfer characteristics were studied for ZrO2, PVP and ZrO2/PVP as an organic gate insulator layer. Both characteristics show a high drain current at the gate dielectric ZrO2/PVP equal to -0.0031A and -0.0015A for output and transfer characteristics respectively

 The current paper studied the concept of right n-derivation satisfying certified conditions on semigroup ideals of near-rings and some related properties. Interesting results have been reached, the most prominent of which are the following: Let M be a 3-prime left near-ring and A_1,A_2,…,A_n are nonzero semigroup ideals of M, if d is a right n-derivation of M satisfies on of the following conditions,
d(u_1,u_2,…,(u_j,v_j ),…,u_n )=0 ∀ 〖 u〗_1 〖ϵA〗_1 ,u_2 〖ϵA〗_2,…,u_j,v_j ϵ A_j,…,〖u_n ϵA〗_u;
d((u_1,v_1 ),(u_2,v_2 ),…,(u_j,v_j ),…,(u_n,v_n ))=0 ∀u_1,v_1 〖ϵA〗_1,u_2,v_2 〖ϵA〗_2,…,u_j,v_j ϵ A_j,…,〖u_n,v_n ϵA〗_u ;
d((u_1,v_1 ),(u_2,v_2 ),…,(u_j,v_j ),…,(u_n,v_n ))=(u_

In this paper investigate the influences of dissolved CO₂/H₂S gases, crude oil velocity and temperature on the rate of corrosion of crude oil transmission pipelines of Maysan oil fields southern Iraq. The Potentiostatic corrosion test technique was conducted into two types of carbon steel pipeline (materials API 5L X60 and API 5L X80). The computer software ECE electronic corrosion engineer was used to predict the influences of CO₂ partial pressure, the composition of crude oil, flow velocity of crude oil and percentage of material elements of carbon steel on the rate of corrosion. As a result, the carbon steel API 5L X80 indicates good and appropriate resistance to corrosion compared to carbon steel API