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 .

Background: Colorectal cancer (CRC) is a major killer, and nonalcoholic fatty liver disease (NAFLD) affects almost one-quarter of the global population. The aim of the study is to Investigate the correlation between nonalcoholic fatty liver disease (NAFLD) and an increased risk of colorectal cancer (CRC), as well as the relationship between liver function enzymes and specific serum biomarkers in CRC patients with NAFLD. Methods: A case-control study involving 60 participants was conducted from February to August 2022. The patients with colon cancer were examined at Baghdad Medical City's Al-Amal Hospital for Radiation and Nuclear Medicine and Oncology Teaching Hospital, and blood samples were taken. Thirty patients with NAFLD who ha

Poetry occupied the Arabs in a unique position, especially in the era; ignorant, Umayyad and Abbasid, in addition to its literary and aesthetic dimensions, it is at the forefront of tools and media at the time. The poet appointed society and poetry Diwan Arabs records their exploits and virtues and their valor in the wars... The Prophet Muhammad () realized the importance of poetry, so he took advantage of him in the libel for his Islamic call. In the Umayyad and Abbasid states, poetry had a clear role in social, literary and political life, as the ruling authority used its influence on many poets to be media to support its political theory, by praising the Caliph and his aides, and exposing those who dissented and opposing them. The

Objective: Comprehending microbial diversity and antibiotic resistance patterns is essential for efficient treatment protocols. This study sought to determine the incidence of bacterial and fungal pathogens responsible for burn and wound infections and their antibiotic susceptibility profiles. Methods: This cross-sectional study involved 140 patients with burn or wound infections. Sterile swabs and pus aspiration were employed to collect samples, which were subsequently processed using standard microbiological procedures. Antibiotic resistance was determined using the Kirby-Bauer disc diffusion method, following Clinical and Laboratory Standards Institute (CLSI) guidelines. Data was analysed using IBM SPSS version 25.0, and the Chi-

Permanent deformation, fatigue and thermal cracking are the three typical distresses of flexible pavement. Using hydrated lime (HL) into the conventional limestone mineral additive has been widely practiced, including in Europe, to improve the mechanical properties of hot mix asphalt (HMA) concrete and as the result the durability of the constructed pavement. Large number of experimental studies have been reported to find the optimum addition of HL for the improvement on HMA concrete mechanical properties, moisture susceptibility and fatigue resistance. Pavement in service is under complex thermomechanical stress-strain conditions due to coupled atmospheric and surrounding environment temperature variation and the traffic loading. To predic

The research aims to know the traits or characteristics of woman in terms of her external
appearance, motives for her behavior, feelings, mood and ability.
It, moreover, seeks woman’s relationship with others as it is presented by the Iraqi
satirical television show “ State of Melon “.
The researcher adopted for that survey approach using the method of content analysis
to study the research sample represented by “ State of Melon “ show which was
exposed through the screen of a group of channels:
“Hona Baghdad Satellite Channel, then Asia Satellite Channel, Dijla Satellite Channel,
and UTV Satellite Channel.”For this, the researcher used Margaret Gallagher’s Model to analyze the image of
woman in

Topology and its applications occupy the interest of many researching centers in the advanced world. From this point of view and because the near open sets play a very important role in general topology and they are now the research topics of many topologists worldwide and its sets doesn’t enter in fibrewise topology yet. Therefore, we use some of the near open sets to be model for introduce results and new spaces in fibrewise topological spaces. Also, there is a very important role of closure operators in constructing a topological spaces, so we introduce a new closure operators on the power set of vertices on graphs and conclusion theorems and new spaces from it. Furthermore, we discuss the relationships of connectedness between some ty