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 .

A program in Visual Basic language was designed to predict the type of radio storm that emitted from Jupiter at specific Local Time (LT) from two different Iraqi locations (Baghdad and Basra), such storms result from the Central Meridian Longitude (CML) of system ??? for Jupiter and phase of Io’s satellite (?Io). Some of these storms are related to position of Io (Io- A,B,C,D) and others are unrelated (non-Io-A,B,C,D) to its position. The input parameters for this program were user specified by determining the observer’s location (longitude), year, month and day. The output program results in form of tables provides the observer with information about the date and the LT of beginning and end of each type of emitted storm. Two Io-storm r

Five Saccharomyces cerevisiae isolated from the ability of chitinase production from the isolates were studied. Quantitative screening appeared that Saccharomyces cerevisiae S4 was the highest chitinase producer specific activity 1.9 unit/mg protein. The yeast was culture in liquid and solid state fermentation media (SSF). Different plant obstanases were used for (SSF) with the chitine, while liquid media contained chitine with the diffrented nitrogen source. The favorable condition for chitinase producers were incubated at 30 ºC at pH 6 and 1% colloidal chitine.

تُعبّرُ الصُّورةُ الحسَّيةُ في شعرِ ابن دُنَينير الموصليِّ^([i]) في بنيتها عن تجربةِ الشاعرِ الوجدانيةِ والذهنيةِ, وأفكارهِ ومشاعرِهِ؛ فيصوغُ بها مَفهومًا جديدًا للواقعِ الماديِّ والمعنويِّ، الذي يتسمُ بالوضوحِ أولاً، وبالقرْبِ من الذهنِ ثانيًا، للربْطِ بين الحواسِّ الإنسانيةِ والمعاني الذهنيةِ، لِتُقَدِّمَ الصُّورةُ الحسيَّةُ إلى ((المتلقي صُورًا مرئيةً، يُعادُ تشكيلُها سياق

Abraham son of Izra, the poet, the philosopher, the grammarian, and the Turah exegesis, is considered one of the famous poets in the era of Islamic reign in Spain which is called the "Golden Era". He was taught all types of teaching which was rich in Jewish literary products. He learned Arabic and studied Arabic language and literature. He travelled a lot, and made tours within Spanish places, and even reached the North of Africa. He preferred living with Muslim rulers in the south of Spain, like the rest of the Jews who emigrated from the north of Spain to the South in search for freedom and to participate in higher positions of the Islamic Palace. He was influenced by Arabic culture, and even translated "Th

The study of the laptop computer table is one of the important studies at the present time due to the importance of electronic computers that are used in work sites and homes for very long hours, so one of the most important basics of caring for the comfort of the user lies in the design of the laptop table in different shapes and sizes and multiple functions in addition to calculating the measurements of the human body and the extent Its compatibility with the design and measurements of laptop computer tables by taking into account the calculations and measurements of the dimensions of the user's body of all ages and their consistency and use with the general measurements of the tables and the importance of research comes through the es

 Education is a process of learning and education at the same time. As the conditions of modern life necessitate every person to keep learning, education has become a necessity to meet life needs. The society today is concerned with the educational process and aims to live up the expectations. Since education is an integral part of education and its means, it has become as a mean to achieve its purposes. The educational environment was a traditional environment limited to specific inputs, possibilities and stimulus of both teacher and student. Due to the latest advancement, the educational environment has been expanded to become a rich, with strong connections. It has expanded to encompass the entire global environment. The current