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 .

Purpose: The present study seeks to examine various history stages in which undergone by the concept of scenarios, and development of this concept to integration with the strategic management practices:
Methodology: The current study relied on a literature review and approach in providing total picture of different stages undergone by this concept.
The main results: the scenarios did not reach maturity in their quest for integration with strategic management, and still need a great effort for the maturation of this thought in the framework of strategic management, and through it can contribute in creating important knowledge evolution.
Originality and value: providing a contemporary model linking the roots of this concept and cu

       unacceptable social behaviors, particularly withdrawal behavior that appears in children with autism represent a major problem hindering the process of communication with those around them and therefore the process of mergence  with them be difficult.

     The withdrawal causes a real affect deficit for children with autism limits the possibility of development of their intellectual and mental growth due to their solitude and the weakness of their focus in the acquisition of pedagogical skills and lack the necessary social skills to maintain the relations of friendship and enjoyment of them.

      withdrawal children fail to participate

Since the beginning of the second decade of the twenty-first century, Saudi Arabia tried to pursue an open foreign policy towards many countries in the Horn of Africa, especially with Ethiopia and Somalia, due to the geostrategic qualities that these two countries possess.Despite the development of Saudi foreign policy towards Ethiopia and Somalia, it was soon affected by the tension after the events that the Gulf states went through, that is, the Qatari crisis with Saudi Arabia,especially after most of the countries of the Horn of Africa adhered to a policy of neutrality towards the Gulf-Gulf crisis.

Thus it is expected that despite the geographical proximity and the historical, economic and political relations between Saudi Ara

This study reports the fabrication of tin oxide (SnO₂) thin films using pulsed laser deposition (PLD). The effect of ⁶⁰Co (300, 900, and 1200 Gy) gamma radiation on the structural, morphological, and optical features is systematically demonstrated using X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM), atomic force microscopy (AFM), and ultraviolet-visible light analysis (UV-Vis), respectively In XRD tests, the size of the crystallites decreased from 45.5 to 40.8 nm for the control samples and from 1200 Gy to 60Co for the irradiated samples. Using FESEM analysis, the particle diameter revealed a similar trend to that attained using XRD; in particular, the average diameters were 93.8 and

Ephedra alata. is a plant that widely available around the world and long used in folk medicine as a natural medication, was employed in the current work to prepare extracts rich in alkaloids and to test their cytotoxic potential. Alkaloids-rich and crude extracts of E.alata were compared to pure ephedrine medication for mitosis on Allium cepa. test system. Alkaloids and crude aqueous extracts of A. cepa root tips were examined for a total of five hours at five different concentrations compared to ephedrine standard. Mitotic index, phase index, and chromosomal aberration as part of the study. IC50 values of 35 mg/ml were found for each extract, indicating a sub-lethal influence on cell viability. (Toxic and sublethal effects are thought to

The placenta is an organ between the mother and fetus necessary for fetal growth and development. Gestational diabetes mellitus (DM) is the most frequent metabolic condition detected during pregnancy. It is characterized as hyperglycemia of various severity with onset or first detection during pregnancy that does not clearly describe any form of preexisting diabetes. Urotensin II (UII), a pluripotent vasoactive peptide, is important in developing insulin resistance. This study aimed to determine the level of Urotensin II(UII) in placenta and in the serum of diabetic and nondiabetic women. Methods The blood and placenta tissue collected from 50 ladies had been enrolled in this research ( 25 females with uncomplicated), (25 women with gestati