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: The hybrid compounds hold promise for developing novel pharmaceuticals, potentially exhibiting greater activity, mainly against viruses and cancer diseases, than their components.

Objective: In this study, researchers explored the potential synergistic effects of hybrid molecules by designing and synthesizing a series of isatin-gallate hybrids, denoted as N’-(5-substituted-2-oxoindolin-3-ylidene)-3,4,5-trihydroxybenzohydrazide (3a–d).

Methods: Isatin-gallate hybrids (3a–d) were synthesized by reacting gallic hydrazide with each of the isatin analogs (2a–d). The structures of all produced comp

Biodiesel production from microalgae depends on the biomass and lipid production. Both biomass and lipid accumulation is controlled by several factors. The effect of various culture media (BG11, BBM, and Urea), nutrients stress [nitrogen (N), phosphorous (P), magnesium (Mg) and carbonate (CO₃)] and gamma (γ) radiation on the growth and lipid accumulation of   Dictyochloropsis splendida were investigated. The highest biomass and lipid yield of D. splendida were achieved on BG11 medium. Cultivation of D. splendida in a medium containing 3000 mg L⁻¹ N, or 160 mg L⁻¹ P, or 113 mg L⁻¹ Mg, or 20 mg L^-1 CO_3, led to enhanced growth rate. While u

Background: During acrylic resin processing, the mold must be separated from the surface of the gypsum to prevent liquid resin from penetrating into the gypsum, and water from the gypsum seeping into the acrylic resin. For many years, tin foil was the most acceptable separating medium, and because it's difficult to apply, a tin-foil substitute is used. In this study, olive oil is used as an alternative to tin foil separating medium for first time, and evaluating its effect as a separating medium on some mechanical properties such as (indentation hardness and transverse strength) of acrylic resins denture base comparing it with those processed using tin-foil and tin foil substitute such as (cold mold seal) separating medium. Materials and M

Some research reports that cognitive grammar (CG) theory has good contributions to teaching English as a foreign language. In this research, the researchers seek to apply this theory and its principles when teaching the simple present tense to Iraqi students who face difficulties in differentiating between the multiple usages of this tense. To achieve this objective, the researchers have conducted an experimental study on a group of 60 Iraqi students in the University of Baghdad, College of Education for Women. Langacker’s (2003) theory has been adopted in the analysis of the cognitive relations to understand the common and different connections of these usages of the simple present. The study has concluded that the cognitive grammar t

The Iraqi culture faced a set of challenges that can be diagnosed with the most prominent features as follows:

1. The dominance of authoritarian political systems which entails authoritarian regimes with the absence of contemporary political concepts of human rights.
2. The prevalence of non- informed cultural systems which have the shortage of capabilities that enable them to activate cultural elements in positive references, historical, or seclusion on itself and not be able to interact with the current active cultures.
3. Stagnant economic conditions have not had a decent life for individuals, or a certain level of well-being, as well as poor services and others.
4. Social life controlled by the prevai

The paper probes into minute identification of the data of the methods followed in the electronic newspapers that aim to promote terrorist organizations like Al Qaeda and ISIS to draw emotional empathy and sympathy with them.
The paper aims at identifying:
How emotional empathy was utilized by terrorists in E-newspapers.
How useful utilizing emotional empathy was in attracting supporters. The sample that is used in the paper is based on the opening articles of E-newspapers that propagate Al Qaeda and ISIS, e.g. (Sawtu el jihad) “The Sound of Fighting in the Name of God”, (Mua’skar el Battar wal Shamikha wal Khansaa) “Camps of Al Battar, Shamika, and Khansaa”, “Inspire” and (Thurwatu el Sanam, Dabiq, and Rumiyah)

The study aimed to investigate the employment of electronic supervision applications in developing the teaching performance of teachers in Oman. Based on the qualitative method and the study population consisted of all the teachers of the first cycle in the Governorate of Muscat. The study sample amounted to 24 female teachers. The interview was used as a tool for data collection. The study reached several results, including: There are difficulties in employing electronic supervision applications, which are weak network, density of curricula, lack of experience in applying technology, and the large number of tasks assigned to the teacher. These difficulties can also be overcome by strengthening the network, training teachers, reducing th

The research Concentrates on modern Variable in the organizations that is 6 sigma. The field study is two of Iraqi industrial organizations, The first is state company of …………… , the other is the state company of ……

The problem of the research determines some questions and hypotheses, The data was Collected by question air, which contains 5 dimensions and (10) critical Successful factories  . 

The sample contains (42) who Works in that organizations. The points out many conclusions. The main of it, there is significant differences among the two organizations Then The research concluded with a number of important recommendations serve it's objectives .