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 research aims to predict the value of the maximum daily loss that the fixed-return securities portfolio may suffer in Qatar National Bank - Syria, and for this purpose data were collected for risk factors that affect the value of the portfolio represented by the time structure of interest rates in the United States of America over the extended period Between 2017 and 2018, in addition to data related to the composition of the bonds portfolio of Qatar National Bank of Syria in 2017, And then employing Monte Carlo simulation models to predict the maximum loss that may be exposed to this portfolio in the future. The results of the Monte Carlo simulation showed the possibility of decreasing the value at risk in the future due to the dec

Robot manipulator is a multi-input multi-output system with high complex nonlinear dynamics, requiring an advanced controller in order to track a specific trajectory. In this work, forward and inverse kinematics are presented based on Denavit Hartenberg notation to convert the end effector planned path from cartesian space to joint space and vice versa where a cubic spline interpolation is used for trajectory segments to ensure the continuity in velocity and acceleration.  Also, the derived mathematical dynamic model is based on Eular Lagrange energy method to contain the effect of friction and disturbance torques beside the inertia and Coriolis effect. Two types of controller are applied ; the nonlinear computed torque control (CTC

The aim of this study is to investigate the role of prodigiosin on P. aeruginosa' s biofilm genes involved in the pathogenicity and persistency of the bacteria; Materials and methods: Gram negative bacterial isolates were taken from burn and wounds specimen obtained from some of Baghdad hospitals. Forty six isolates were identified as Pseudomonas aeruginosa and four isolates as Serratia marcescens by using biochemical tests and VITEK 2 compact system. Susceptibility test was performed for all P. aeruginosa isolates, the results showed that 100% were resistant to Amikacin and 98% were sensitive to Meropenem. Resistant isolates were tested for biofilm formation; the strong and moderate isolates (17) were detected by PCR for AlgD gene

Anastatica hierochuntica is believed to be very useful in Arab countries for treating various health disorders. The aqueous extract of Anastatica hierochuntica was investigated for its effects on hormones in mice females. the aqueous extract of plant at a dose level of 100mg/1mL showed significant increase (p<0.05) on levels of hormones LH, FSH, PRL level and PRO level. Clomid treated group showd significant increase in LH, FSH, and PRL while there was non-significant increase in PRO. From the above results, it is concluded for the first time that aqueous Anastatica hierchuntica extract offers significant effect of LH, FSH, PRL, and PRO in this mice females scompared with control.

The primary aim of this study was to find out the effect of a training program on the development of physical abilities in football goalkeepers. The current study was conducted on goalkeepers of the Academy of Espanyol Sports Club in the premises of Haifa Sports Club Stadium. The study was completed by the researchers within the timeline of May 2021 to August 2021. A total of 7 goalkeepers falling within the age group of 15-17 years were recruited as the sample participants for the study. Out of 7 goalkeepers, 5 goalkeepers were included in the primary experiment and 2 of them were excluded. The training program applied had a positive effect on the development of physical abilities in the football goalkeepers of the sa

The accelerating effect of 1,4- phenylenediamine (PDA) additions in 1M hydrochloric acid solution at temperature rang (20-60) C° has been studied by weight losses measurement during ranging time (1-260) h and by following the pb2+ concentration in solution after several times by using Atomic absorption spectroscopy (AAS) . The volume of hydrogen gas involving was followed also in presence and absence of (PDA) in the corrosive solution .Accelerating enhanced by adding (NaCl , NaBr , NaI ) was also investigated.

Background: Apicoectomy and retrograde filling is indicated when conventional endodontic treatment is impossible or failed to achieve apical seal. The aim of this study was to evaluate the effect of ER: YAG laser on apical microleakage. Materials and Methods: Sixty extracted single-rooted teeth were used in this study. The roots were divided into six groups. Group 1: apicoectomy by fissure bur, and apical cavities prepared by round bur, then cavities were filled with MTA. Group 2: the roots preparations and fillings were the same as group 1, then the apical areas were treated by Er:YAG Laser. Group 3: apicoectomy by fissure bur, and apical cavities prepared by ultrasound retrotip and cavities were filled with MTA. Group 4: the roots prepara

This study included collecting of 150 specimens of the Iraqi Bird Bulbule Pycnonotus lecuotis mesoptamiae (Pycnotidae , Passeriformes), from the 1st of November 2004 to 30th of October 2005 in the city of Baghdad and its suburbs, in concern of identifying the internal parasite of the digestive tract of these birds and studying the diseases resulted from the infection. The study showed that the bird Bulbule is Parasitized by Four types of Cestodes ,two of them are recorded in this kind of bird in Iraq for the first time ,Paradicranotinae anormalis and Haploparaxis sp. , and the other two are Raillietina tetragona and Allohymenolepsis sp. ,and by two types of Pin Worm(Trematode) that are identified for the first time in the Bird Bulb

This study aimed to identify the political factors influencing the performance of specialized journalists in Iraqi electronic newspapers. The significance of the study stems from the role of communication in newspapers that have established themselves in reality due to their wide dissemination, multiple uses, expanding freedom base, and the current diversity in perspectives. These newspapers highlight and publish societal issues of concern. The importance of these newspapers is associated with their creators who face various factors affecting their value and performance, whether positively or negatively. In light of this, the political factor was identified as the primary driver for other influencing factors. The