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 .

Abstract

The study aims to identify the common fears of preschool children and their relationship to the approaches to parental treatment in South Al Batinah Governorate from their mother’s point of view. Total of (466) mothers were selected as the study sample. The researcher used the scale of common fear and the scale of parental treatment approaches. The results of the study have shown that the most common fear among the study sample was (the fear of darkness) in the first level with a rate of 75.03%, and in the second level came the item (my child is afraid to sleep alone) by 72.74%, in the third level came to the item (fear of seeing insects) with a rate of 67.59%, and the last one was (the fear of rain) w

Learning education in the Islamic legacy vision considers a completed The Islamic learning education took its bases from origins of Quran and honored prophet Suna , and stressed on education child a good education and providing him with principles of religion and semantic moral values and Messenger (peace on him) considers the higher example for man in his moral, behavior and goodness and witness on this Higher God said

(you had in God Messenger a good leadership for those were requesting God and last day and mentioned God a lot). Al- Ahzab Surah :21. learning education converts man from religion to another and from culture to another and teacher left his signs on the generation if he accept or refuse.

This article explores the role of talk shows in setting the public's agenda regarding political mobilization in Iraq. The researcher designed a questionnaire that contains both closed and open-ended questions to allow respondents to express their opinions more freely.

 The researcher chose a phased purposive sample consisting of 294 respondents. The data was then subjected to analysis and verification using the Statistical Package for the Social Sciences (SPSS).

Background: Polymethylmethacrylate (PMMA) is the most ‎commonly used m‏aterial in denture construction. This material is ‎far from ideal in fulfilling the‎ mechanical requirements, like low impact and transverse strength and poor thermal conductivity are present in this material. The purpose of this study was to study the effect of addition a composite which include 1%wt silanized silicone dioxide nano fillers (SiO2) and 1wt% oxygen plasma treated polypropylene fiber (PP) on some properties of heat cured acrylic resin denture base material (PMMA). Materials and methods: One hund‏red (100) prepared specimens were divided into five groups according to the tests, each group consisted of 20 specimens and t

          Graphite Coated Electrodes (GCE) based on molecularly imprinted polymers were fabricated for the selective potentiometric determination of Risperidone (Ris). The molecularly imprinted (MIP) and nonimprinted (NIP) polymers were synthesized by bulk polymerization using (Ris.) as a template, acrylic acid (AA) and acrylamide (AAm) as monomers, ethylene glycol dimethacrylate (EGDMA) as a cross-linker and benzoyl peroxide (BPO) as an initiator. The imprinted membranes and the non-imprinted membranes were prepared using dioctyl phthalate (DOP) and Dibutylphthalate (DBP) as plasticizers in PVC matrix. The membranes were coated on graphite electrodes. The MIP electrodes using

The research aims to examine the effect of KUD strategy on acquiring the grammatical concepts among intermediate school students. To achieve the research objective, the researcher adopted the null hypothesis in which there is no statistically significant difference at the level (0.05) between the average scores of students of the experimental group who study grammar base on the KUD strategy and the average scores of the control group who study the grammar through the traditional way of acquiring grammatical concepts. In a random manner, the researcher selected the research sample from one of Baghdad’s education schools in al Rusafa / 2, as the total number of students of the two groups reached (67) students. They were divided into (33)

This work describes the weathering effects (UV-Irradiation, and Rain) on the thermal conductivity of PS, PMMA, PS/PMMA blend for packaging application. The samples were prepared by cast method at different ratios (10, 30, 50, 70, and 90 %wt). It was seen that the thermal conductivity of PMMA (0.145 W/m.K), and for PS(0.095 W/m.K), which increases by PS ratio increase up to 50% PS/PMMA blend then decreased that was attributed to increase in miscibility of the blend involved. By UV-weathering, it was seen that thermal conductivity for PMMA increased with UV-weathering up to (30hr) then decreased, that was attributed to rigidity and defect formation, respectively. For 30%PS/PMMA, there results showed unsystematic decrease in thermal conduct

The purpose of this study is to evaluate the effect of hydrated lime addition methods as filler replacement on fatigue performance of Hot Mix Asphalt (HMA). Three types of addition methods of hydrated lime were introduced namely dry HL on dry aggregate and saturated surface aggregate above 3% and slurry HL on dry aggregate, ordinary Lime stone powder was reduced by three HL percentage (1.0, 2.0 and 3.0 %). The effect of different methods were investigated on the fatigue properties of HMA using, third-point flexural fatigue bending Test. Pneumatic Repeated Load System (PRLS) was carried out to establish the effect of hydrated lime on the fatigue failure criteria and to select the proper hydrated lime application methods on fatigue behavior o