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 .

This study synthesized nanocomposite photocatalyst materials from a mixture of Cu₂O nanoparticles, ZnO nanoparticles, and graphene oxide (GO) through coprecipitation and hydrothermal methods. This study aims to determine the optimum composition of Cu₂O/ZnO/GO nanocomposites in degrading methylene blue. The nanocomposite was synthesized in two steps:  1  the synthesis of Cu₂O and ZnO nanoparticles through the coprecipitation method and the preparation of GO through the modified Hummer method.  2  The preparation of Cu₂O and ZnO nanoparticles mixtures with GO through the hydrothermal method to form Cu₂O/ZnO/GO nanocomposites. The adsorption-photocatalysis process of methylene blue

This research aims to investigate the effect of four types of nanomaterial on the Marshall properties and durability of warm mix asphalt (WMA). These types are; nano silica(NS), nano carbonate calcium (NCC), nano clay(NC), and nanoplatelets (NP). For each type of Nanomaterial, three contents are tried as following; NS(1%, 3%, and 5%), NCC(2%, 4%, and 6%), NC(3%, 5%, and 7%), and NP (2%, 4%, and 6%) by weight of asphalt cement. Following Marhsall mix design method, the optimum asphalt cement content is determined, thereafter the optimum dosage for each nanomaterial is obtained based on the highest Marshall stability value. The durability of the control mix (no nanomaterial) and modified mixtures have been compared based on moisture damage, r

The objective of the study was to identify the effectiveness of a training program based on the employment of the educational portal in the development of the skills of the administrative body in the basic education schools in Dhofar Governorate. To achieve the goal, a training program was designed that includes the skills of the educational portal to be met by the administrative body and measuring its effectiveness. A questionnaire to identify training needs, and a notecard to evaluate performance. The study sample consisted of (70) individuals of the administrative staff. The researchers used the descriptive-analytical method to identify the training needs, design and build the training program and the experimental method for applying

Objective(s): To determine the impact of instructional intervention program upon psychological health status for
women who undergo chemotherapy after mastectomy
Methodology: The sample consisted of (100) women, (50) considered as study group, and another (50) the control
group. A pre test was done for both groups (study and control), and then the study samples were exposed to an
instructional intervention and three-dimensional post tests and the length of time between each test 21 days in
the Institute and Hospital of Radiation and Nuclear Medicine. The questionnaire composed of three parts, first,
demographic information; include (age, educational level, type of family, occupation, marital status, and adequacy
of mo

Friction stir spot welding (FSSW) is a relatively new welding process that may have significant advantages compared to the fusion processes as follows joining of conventionally non-fusion weldable alloys, reduced distortion and improved mechanical properties of weldable alloys joints due to the pure solidstate joining of metals. In this paper, a three-dimensional model based on finite element analysis is used to study the thermal history in the spot-welding of aluminum alloy 2024. The model take place the thermomechanical property on the process of the welded metals. The thermal history and the evolution results with numerical model at the measured point in the friction stirred spot weld have a good matching, then the prediction of the t

Objectives: To assess nurses-midwives' knowledge about pain management during labor before and after implementation of educational program and to determine the effectiveness of educational program on nurses-midwives' knowledge about pain management during labor in Baghdad Maternity Hospitals.

Methodology: A quasi-experimental design has been conducted during the period of (February 27^th 2019 through 2^nd June 2019) on non-probability sample (purposive) consists of (44 Nurses/midwives') who are work in delivery room, the sample was exposed to pretest, educational program, posttest. The study was conducted in three Directories, (Baghdad Teaching Hospital) at medical city health

Objective(s):        The study aims to evaluate the information of the elderly about personal hygiene , and to find out the relationship between residents of geriatric-care homes knowledge and their demographic characteristics .

Methodology:      A quasi-experimental design study is conducted at geriatric home  in Al Cyelakh  Geriatric Care Home. The study was started at between November 20, 2021, and March 1, 2023. randomly sample of (30) elderly  in geriatric home were studied . Data were collected throughout the utilization of the adopted questionnaire and interview technique. The questionnaire was consists of (40) items related to concerned personal hygiene geriatrics persons, t

This study suggests using the recycled plastic waste to prepare the polymer matrix composite (PMCs) to use in different applications. Composite materials were prepared by mixing the polyester resin (UP) with plastic waste, two types of plastic waste were used in this work included polyethylene-terephthalate (PET) and Polyvinyl chloride (PVC) with varies weight fractions (0, 5, 10, 15, 20 and 25 %) added as a filler in flakes form. Charpy impact test was performed on the prepared samples to calculate the values of impact strength (I.S). Flexural and hardness tests were carried out to calculate the values of flexural strength and hardness. Acoustic insulation and optical microscope tests were carried out. In general, it is found that UP/PV

Objective: To assess the effect of education program on psychological and social changes of secondary school teachers with menopause.

Method: A quasi-experimental design is carried out with the application of a pre- post –test for menopause secondary school teacher's bio-psychosocial changes. Non-probability sample consists of (60 female teachers) (40) teachers from Al- Rusafa first Education Directorate secondary schools, and (20) teachers from Al- Karkh third Education Directorate secondary schools. The sample was exposed to pretest, educational program, and posttest. Data were collected through the utilization of the study instrument (the questionnaire) and application of bio-psychosocial ed