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 .

Denture cleansing is an essential step that can stop cross‑contamination and adds to the health of the patient, denture durability, and the general quality of life. A disinfection technique must be practical and devoid of damaging effects on the material's properties used to construct the denture base. The main aim of this study is to evaluate the effect of three concentrations of electrolyzed water denture cleanser on heat cure acrylic and polyamide after immersion in electrolyzed water. The evaluation is based on their efficacy on surface hardness, wettability, and color stability compared with one submerged in distilled water as a control group. The method consists of eighty samples of heat-cured acrylic and polyamide material.

The language that consists of only twenty-eight letters, but it is so broad that we are unable to understand it from all sides and this expansion is mainly caused by imagination, so Arab imagination, whose language goes in all directions And as it always responds to our ears, ancient critics divide imagination into holistic and partial But the language is not limited to these parts only. Do we wonder, where is the structural method of wishing, hope, questions and other methods of all this? In this paper, we try to show the importance of the method of writing in moving imagination in an interactive way, and what is related to human feelings in most, if not all, of its methods By studying the poetry of the believers in the Ahl al-Bayt, pea

Hypertension is one of the main causes of heart disease; beta- blockers play a crucial role in the management of patients with essential hypertension. Bisoprolol is one of the widely used drugs for the treatment of hypertension. Bisoprolol tablets were prepared by two methods (direct and wet) using different proportion and types of diluents, different binder types and forms, then evaluated for, weight variation, hardness, friability, disintegration time and dissolution rate. The results were compared with a reference Bisoprolol tablet.

Both methods of preparation wet and direct compression method gave good results, which are consistent with the requirements of British Pharmacopeia and United States Pharmacopeia. It was found that

A simple and novel method was developed by combination of dispersive liquid-liquid microextraction with UV spectrophotometry for the preconcentartion and determination of trace amount of malathion. The presented method is based on using a small volume of ethylenechloride as the extraction solvent was dissolved in ethanol as the dispersive solvent, then the binary solution was rapidly injected by a syringe into the water sample containing malathion. The important parameters, such the type and volume of extraction solvent and disperser solvent, the effect of extraction time and rate, the effect of salt addition and reaction conditions were studied. At the optimum conditions, the calibration graph was linear in the range of 2-100 ng mL-1 of ma

Huge efforts are being made to control the spread and impacts of the coronavirus pandemic using vaccines. However, willingness to be vaccinated depends on factors beyond the availability of vaccines. The aim of this study was three-folded: to assess children’s rates of COVID-19 Vaccination as reported by parents, to explore parents’ attitudes towards children’s COVID-19 vaccination, and to examine the factors associated with parents’ hesitancy towards children’s vaccination in several countries in the Eastern Mediterranean Region (EMR).

the mental image is so important in human life as one of the major standers for his trends and behavior, and as the human nature requires to interest in things based on how much it’s close to and how much it effects on his interest, So the neighborhood countries was one  of the topics that occupied the attention of the Iraqi individual and pushed him to form perceptions of them based on the cultural heritage and the historical relations of Iraq with these countries as well as the actions of neighboring countries on Iraq and the resulting effects on the course of events. the mental image is so important in human life as one of the major standers for his trends and behavior, and as the human nature requires to interest in things bas

Summary: The study focused on the role of the educational counselor in schools, as an integral part of the educational system that faces multiple challenges and difficulties. In this context, the counselor’s role becomes crucial in attempting to reduce or eliminate such difficulties, in addition to guiding students in an appropriate manner. Methodes: The study employed a descriptive field approach, using interviews and direct observation as tools to examine the actual role performed by school counselors. Results: The study concluded with several key findings, most notably the numerous challenges faced by counselors, including students’ negative behaviors, school dropouts, and the limited administrative support for counselors’ work. Fu

Human beings have an innate and natural aim to achieve their self-interests and to show their ability to overcome challenges in a better way, therefore the move towards self determination is expressed by intrinsic motivation. The desire of absorbing in this task is to enjoy the task in it self and benefitting from it such a motivation is the desire rooted in human nature to judge and choose in which individual is conscious in his self, abilities and adequacy that help him in control the different  situations of life passed by him. His choices and actions are voluntary  and non-restricted to intervention or external control because control is inner and subjective, while his behavior is self-regulated with the feeling of

The present paper attempts to establish a distinction between Exochomus negripennis (Er.) and E. quadripustulatus L., depending on the characters of femoral line, male genitalia and spermatheca.