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 research aimed to identify the extent to which the media offices in the ministries depend on the website of the Iraqi Council of Ministers as a source of information. Such goal includes a set of sub-goals: Knowing the reasons for media offices' reliance on the information provided by the Cabinet's website; and revealing the benefit derived from relying on the Cabinet's website.

The researcher used the survey method to screen and comprehend the extent to which the media offices in the ministries depend on the website of the Iraqi Council of Ministers as a source of information.

The mechanism of comprehensive account of the limits of research wa

The study aimed to reveal the extent of the first intermediate grade science curriculum focus on the national values, health, environmental, economic values, in the light of the education policy in the Kingdom of Saudi Arabia, in addition to present a proposed vision to strengthen it in the science curriculum for the first intermediate grade. The study was applied to the two books student and the two books of activity on the first-second semesters for the academic year 1441 AH. To analyze the curriculum content, the study used a verified card prepared by the researchers and a criterion for interpreting percentages. The study reached the following results: environmental values ranked first with a concentration of (43%), i.e. with an avera

The purpose of this study is to measure the levels of quality control for some crude oil products in Iraqi refineries, and how they are close to the international standards, through the application of statistical methods in quality control of oil products in Iraqi refineries. Where the answers of the study sample were applied to a group of Iraqi refinery employees (Al-Dora refinery, Al-Nasiriyah refinery, and Al-Basra refinery) on the principles of quality management control, and according to the different personal characteristics (gender, age, academic qualification, number of years of experience, job level). In order to achieve the objectives of the study, a questionnaire that included (12) items, in order to collect preliminary inform

In this paper, the deterministic and the stochastic models are proposed to study the interaction of the Coronavirus (COVID-19) with host cells inside the human body. In the deterministic model, the value of the basic reproduction number   determines the persistence or extinction of the COVID-19. If   , one infected cell will transmit the virus to less than one cell, as a result,  the person carrying the Coronavirus will get rid of the disease .If   the infected cell  will be able to infect  all  cells that contain ACE receptors. The stochastic model proves that if  are sufficiently large then maybe  give  us ultimate disease extinction although ,  and this  facts also proved by computer simulation.

Abstract:
The aim of the present research is to evaluate the child’s nutritional
method (2-5 years old) which is based on his resistance of the food highly rich
with nutritional elements and his acceptance of the food of a low nutritional
value in addition to his having forbidden food with other mates and making
use of all mates when having food, in establishing the sound social values and
affection since child hood. The required statistical equation have been used
by the researcher namely (Z test).
The sample of the present study consists of (26) children who were selected
intentionally and randomly from the kindergartens of Al-Bayaa region and the
college of Education for women. The questionnaires were d

The aim of this study to identity using Daniel's model and Driver’s model in learning a kinetic chain on the uneven bars in the artistic gymnastics for female students. The researchers used the experimental method to design equivalent groups with a preand post-test, and the research community was identified with the students of the third stage in the college for the academic year 2020-2021 .The subject was, (3) class were randomly selected, so (30) students distributed into (3) groups). has been conducted pretesting after implementation of the curriculum for (4) weeks and used the statistical bag of social sciences(SPSS)to process the results of the research and a set of conclusions was reached, the most important of which is t

ABSTRACT

Learning vocabulary is a challenging task for female English as a foreign language (EFL) students. Thus, improving students’ knowledge of vocabulary is critical if they are to make progress in learning a new language. The current study aimed at exploring the vocabulary learning strategies used by EFL students at Northern Border University (NBU). It also aimed to identify the mechanisms applied by EFL students at NBU University to learn vocabulary. It also aimed at evaluating the approaches adopted by EFL female students at Northern Border University (NBU) to learn a language. The study adopted the descriptive-analytical method. Two research instruments were developed to collect data namely, a survey qu

STAG proteins, which are part of the cohesin complex and encoded by the STAG genes, are known as Irr1/Scc3 in yeast and as SA/STAG/stromalin in mammals. There are more variants as there are alternate splice sites, maybe three open reading frames (ORFs) code for three main proteins, including: SA1 (STAG1), SA2 (STAG2) and SA3 (STAG3). The cohesin protein complex has various essential roles in eukaryotic cell biology. This study compared the expression of the STAG1 gene in four different breast cancer cell lines, including: MCF-7, T-47D, MDA-MB-468, and MDA-MB-231 and normal breast tissue. RNA was extracted from these cell lines and mRNA was converted to cDNA, and then expression of the STAG1 gene was quantified by three sets of specific prim

PKE Sharquie MD, PDPAA Noaimi MD, DDV, FDSM Al-Ogaily MD, IOSR Journal of Dental and Medical Sciences (IOSR-JDMS), 2015