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 .

           Satire is genre of the literary arts that has always been the source of human interest. Because  it is difficult to accept direct criticism, Satire appears as a literary tool in which vices, follies, abuses and shortcomings are held up to ridicule, with the intent of shaming individuals, corporations, government, or society itself into improvement. A satirical critic usually employs irony to attain this goal. Although satire is usually meant to be humorous, its greater purpose is often profitable social criticism, using wit to draw at

The research aims at constructing a Scale of Kindness phenomenon among university female students and elicit criteria to it, It also recognizes the differences in kindness levels among female students according to variables (specialization, academic grade, social status, and the age). The sample consists of 534 female students who were selected randomly. The two researchers rely on experience and the results of questionnaire, The questionnaire is given to 130 female university students from different colleges as well as their acquaintance with literary works witch dealt with kindness , The scale consists of 39 items , It has psychometric characteristics (Validity and Reliability) . The criterion (Z) is extracted from it and throu

The interests toward developing accurate automatic face emotion recognition methodologies are growing vastly, and it is still one of an ever growing research field in the region of computer vision, artificial intelligent and automation. However, there is a challenge to build an automated system which equals human ability to recognize facial emotion because of the lack of an effective facial feature descriptor and the difficulty of choosing proper classification method. In this paper, a geometric based feature vector has been proposed. For the classification purpose, three different types of classification methods are tested: statistical, artificial neural network (NN) and Support Vector Machine (SVM). A modified K-Means clustering algorithm

Accurate computation of the roughness coefficient is important in the studies of open channel flow. To measure and identify the hydraulic characteristics of the flow system, the model simulation is necessary to study and get the results of the hydraulic properties to specify Manning coefficient of the Euphrates River. In this study, the reach is extended along the Euphrates River from Haditha Dam to Ramadi Barrage with a distance of 169km. The HEC-RAS model was implemented to simulate the flow within the study reach. The geometry of the river was represented by more than two hundred cross-sections surveyed in 2013 and 2021. The model was calibrated using some observed discharges at the Heet gage station for records of th

Abstract :

          Researchers have great interest in studying the black box models this thesis has been focused in the study one of the black box models , a ARMAX model which is one of the important models and can be accessed through a number of special cases which models (AR , MA , ARMA, ARX) , which combines method of the time series that depend on historical data and and regression method as explanatory variables addition to that past errors , ARMAX model importance has appeared in many areas of application that direct contact with our daily lives , it consists of constructing ARMAX model several traditional stages of the process , a iden

There is a great deal of systems dealing with image processing that are being used and developed on a daily basis. Those systems need the deployment of some basic operations such as detecting the Regions of Interest and matching those regions, in addition to the description of their properties. Those operations play a significant role in decision making which is necessary for the next operations depending on the assigned task. In order to accomplish those tasks, various algorithms have been introduced throughout years. One of the most popular algorithms is the Scale Invariant Feature Transform (SIFT). The efficiency of this algorithm is its performance in the process of detection and property description, and that is due to the fact that

Metronidazole therapy is recommended in the treatment of giardiasis,athough some clinical reports mention the resistance to this drug from many pathogens. Many studies were applied to show the effect of probiotic to prevent or to heal diseases of gastrointestine, but only few is known about probiotic activity against infections of protozoa. This study aims to evaluate the efficiency of Bifidobacterium against infection with Giardia lamblia   in experimental mice. It was found that daily application of viable Bifidobacterium cells with a single dose (0.1ml∕mice∕day) significantly reduced the shedding of Giardia lamblia parasite cysts in feces, and infection completely disappeared at the da

With the vast usage of network services, Security became an important issue for all network types. Various techniques emerged to grant network security; among them is Network Intrusion Detection System (NIDS). Many extant NIDSs actively work against various intrusions, but there are still a number of performance issues including high false alarm rates, and numerous undetected attacks. To keep up with these attacks, some of the academic researchers turned towards machine learning (ML) techniques to create software that automatically predict intrusive and abnormal traffic, another approach is to utilize ML algorithms in enhancing Traditional NIDSs which is a more feasible solution since they are widely spread. To upgrade t