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 .

Al-Yusifia river was assessed at three sampling stations with study period from Autumn 2010 to the end of Summer 2011. The present investigation was carried out on diversity of fungi and bacteria from Al-Yusifia river, Baghdad city. During the study, a total of 12 fungal genus and 6 bacterial genus were isolated during the year seasons. The dominant fungus at the three stations were Penicillium sp., then Rhizopus and Trichophyton   megninii while the dominant bacteria was Escherichia coli and Klebsiella sp.

            The higher

This paper proposes a new approach to model and analyze erect posture, based on a spherical inverted pendulum which is used to mimic the body posture. The pendulum oscillates in two directions, [Formula: see text] and [Formula: see text], from which the mathematical model was derived and two torque components in oscillation directions were introduced. They are estimated using stabilometric data acquired by a foot pressure mapping system. The model was quantitatively investigated using data from 19 participants, who were first were classified into three groups, according to the foot arch-index. Stabilometric data were then collected and fed into the model to estimate the torque’s components. The components were statistically proce

Praise be to God, Lord of the worlds, and peace and blessings be upon our master Muhammad, and upon his family and companions as a whole. Now, the research deals with the grammatical issues mentioned in the Book of Al-Zahir in the meanings of people's words to Abu Bakr Al-Anbari (d. 328 AH). Two parts of the book have more than one edition, it was printed by the Iraqi Ministry of Culture and Information Beirut in 1979 AD, and the Al-Resala Foundation issued the second edition in 1992 AD The third edition was printed in Dar Al-Bashaer in Damascus in the year 2003 AD and it was the reliance on the research and the grammatical issues were arranged on topics that are: interrogation - Deletion, exclusion, marbling, call and Wallace Relief and

There are many animal models for polycystic ovary (PCO); using exogenous testosterone enanthate is one of the methods of induction of these models. However, induction of insulin resistance should also be studied in the modeling technics. Therefore, the present study aims to investigate the expression of insulin receptor substrate (Irs)-2 mRNA in the liver tissue of rat PCO model. Nineteen Wistar rats were divided into three groups; (1) PCO modeling group (N =7) received daily 1.0 mg/100g testosterone enanthate solved in olive oil along with free access dextrose water 5%, (2) vehicle group (N =6), which handled like the PCO group, but did not receive testosterone enanthate, (3) control group (N =6) with standard care. Al

Dora petroleum refinery waste water is the one of the important source of pollution by priority pollutant aromatic compound discharged to Tigris river in Iraq. the station has waste water treatment unit contains many treatment subunits The most important sub units is :skimmer units ,physiochemical unit ,daf unit, biological unit. The aim of research project is to study the ability of unit to remove the priority pollutant aromatic compound and follow up these compounds in river to study ability of river to self removal. A solid phase extraction (SPE) followed by high performance liquid chromatography-ultra violet (HPLC-UV) technique is depicted for the quantitative estimation of benzidines and phenols. Experimental studies were performed to

Abstract

Electrical magnate  was designed and constructed,  the optimum Magnetic flux  and the effect of time on the physical properties of the alkaline (magnetic water) produced from the bottled drinking water [the total dissolved solids (TDS) or the electrical conductivity, and pH] were studied, to simulate ZamZam water in Mekka Saudi Arabia. Also, the efficiency of magnetic field from this designed electrical magnate in decreasing the TDS of sea water (of 1500 ppm NaCl Content), to convert it to water suitable for irrigation (TDS<1000 ppm) was investigated in this work.The results show that the magnetic flux from our designed electrical magnate in the range of (0.013- 0.08) Tesla and 30 minut

The research topic was chosen as a result of the importance of human resource in business organizations in general and the industrial process in particular. Without the human resource, business organizations cannot continue and achieve success and excellence, and the research problem has been diagnosed in the lack of sales of General Cement Company’s northern products, despite their distinctiveness, standing, and reputation in The market and its products with standard specifications, and through this problem, the following questions were raised:                                                    &nbs

Aims to find out the (Extent of mathematics teachers' appreciation of the mathematical problem `multiple solutions) Research sample consisted of (100) mathematics teachers distributed on the General Directorates of Education in Baghdad (Rusafa 1/2/3) and (Karkh 1/2/ 3) There was two research approach which are: The first - two different answers of students to the same issue where teachers must assess each answer and explain which one the teacher will accept and why? The second - Different solutions of students' to the same issue, including wrong answers , Teachers should correct the answers and give them final grades (0-10). Descriptive and analytical Approch was used in this research methodology And zero hypotheses, which are as f

The aim of the research is to find out the methods of employing the : Infographics in the news sites due to the different communicative roles of the : Infographics . To achieve the research objective, the researcher used the survey method: the method of analyzing the content to analyze the : Infographics material from the selected sample of the news sites. What was said ? And how was it said? Through the design of a content analysis form that includes a number of studied analysis Infographics of the study.