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 .

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 paper discusses the Sums of Squares of “m” consecutive Woodall Numbers. These discussions are made from the definition of Woodall numbers. Also learn the comparability of Woodall numbers and other special numbers. An attempt to communicate the formula for the sums of squares of ‘m’ Woodall numbers and its matrix form are discussed. Further, this study expresses some more correlations between Woodall numbers and other special numbers.

 According to the circumstances experienced by our country which led to Occurrence of many crises that are the most important crisis is gaining fuel therefore , the theory of queue ( waiting line ) had been used to solve this crisis and as the relevance of this issue indirect and essential role in daily life  .

This research aims to conduct a study of the distribution of gasoline station in (both sides AL – kharkh and AL Rusafa, for the purpose of reducing wasting time and services time through the criteria of the theory of queues and work to improve the efficiency of these stations by the other hand. we are working to reduce the cost of station and increase profits by reducing the active serv

The 3D electro-Fenton technique is, due to its high efficiency, one of the technologies suggested to eliminate organic pollutants in wastewater. The type of particle electrode used in the 3D electro-Fenton process is one of the most crucial variables because of its effect on the formation of reactive species and the source of iron ions. The electrolytic cell in the current study consisted of graphite as an anode, carbon fiber (CF) modified with graphene as a cathode, and iron foam particles as a third electrode. A response surface methodology (RSM) approach was used to optimize the 3D electro-Fenton process. The RSM results revealed that the quadratic model has a high R2 of 99.05 %. At 4 g L-1 iron foam particles, time of 5 h, and

Reading is one of the essential components of the English language. Countries that use English as a second language (ESL) sometimes have difficulties in reading and comprehension. According to many researches, mother tongue has proved some interferences with learning a second language. This study investigated the results of reading difficulties of young second language learners in terms of accuracy, comprehension, and rate using the Neale Analysis of Reading Ability test. The study was carried out in one of the High Schools for Boys in Hyderabad, India and included Grade five, aged 10-12 years. In order to understand the reading difficulties of English as a second language, a qualitative approach was employed. Interview, reading tes

This research examines the factors which influence pedestrian's walking speed in Baghdad. the variations in walking speed of pedestrians are related to pedestrian characteristics such as gender, age group, and clothing traditions. Using the established methodology, the counts of pedestrians were performed using manual and video counting. The case study was performed in two streets located in a highly crowded commercial zone at the city center of Baghdad: Al-Karada Dakhel and Al- Sina’a Street. Data were subjected to statistical analysis using IBM SPSS Statistics 19 software. It has been found that Iraqi pedestrians walk slower than other pedestrians in the developed countries or in the region with minimum walking speed of 29.85 m/min.

Achieving high achievement in the sport of fencing requires thinking, awareness and visual tracking, as visual tracking is one of the important visual abilities that a fencing player needs and is considered one of the special visual abilities as it contributes and helps in the correct motor, mental and mental performance and gives the fencing the ability to perfect and accomplished performance in training and competition. Where the research problem lies in the weak skill performance of the fencing players as a result of the weakness in possessing visual and mental abilities. The two researchers used the experimental method in a controlled manner (experimental and control groups) with a pre and post-test. The research community was identifie

يهدف البحث الى التعرف على تأثير تمرينات خاصة لتطوير القوة الانفجارية والقوة المميزة بالسرعة والتحمل اللاهوائي للاعبي كرة القدم ، واستخدمت الباحثتان المنهج التجريبي باستخدام القياس القبلي البعدي لمجموعتين احداهما تجريبية والأخري ضابطة ، واختيرت عينة البحث عمديا من الناشئين في أكاديمية سبانيول الاسبانية في العراق والبالغ عددهم 16 لاعباً . واستخدمت الاختبارات البدنية كوسائل وأدوات لجمع البيانات ومن أهم