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 .

Maximum likelihood estimation method, uniformly minimum variance unbiased estimation method and minimum mean square error estimation, as classical estimation procedures, are frequently used for parameter estimation in statistics, which assuming the parameter is constant , while Bayes method assuming the parameter is random variable and hence the Bayes estimator is an estimator which minimize the Bayes risk for each value the random observable and for square error lose function the Bayes estimator is the posterior mean. It is well known that the Bayesian estimation is hardly used as a parameter estimation technique due to some difficulties to finding a prior distribution.

The interest of this paper is that

Lorraine Hansberry’s A Raisin in the Sun (1959) appeared at the beginning of renewed political activity on the part of the blacks; it is a pamphlet about the dream of recognition of black people and the confusion of purposes and means to reach such recognition. It embodies ideas that have been uncommon on the Broadway stage in any period. Situations such as a black family moving into an all-white neighborhood were not familiar before this time; they were just beginning to emerge. In depicting this so realistically, Hansberry depends more on her personal experience as an African American embittered by social prejudices and discrimination. 

This study analyzes the features of historical and modern mosques in Jordan compared to that of Amman. The architecture of the Jordanian mosques reflects the images of great ancient empires and kingdoms of Europe and the Middle East. This has happened due to the geographical position of the country. From the studies of historians and archaeologists, comparative analysis of planning solutions, the use of plastics and decor of the facades of mosques, and the literature on the construction methods of the mosques allow us to conclude that age-old traditions have been preserved through the establishment of mosques in both the countries. Besides, the emergence of new features in constructing mosques has been observed. We find the influence of

It was Aristotle who first drew attention to the superior quality of literature to the other factual fields of knowledge. Contradicting his predecessor Plato on the issue of „truth,‟ Aristotle believed that „poetry is more philosophical and deserves more serious attention than history: for while poetry concerns itself with universal truths, history considers only particular facts.‟ (1) The critical attention to the disparity between the literary truth and the historical truth grew up throughout ages to flourish in the Renaissance and after with a bunch of distinctive views on this subject. Sir Philip Sidney (1554-1586), for example, found that literature does not offer a literal description of reality but rather a heightened vers

The extract of fig fruit has shown significant medical usefulness in various fields. The entrance of nanotechnology into the field of medicinal and pharmacology has shown remarkable advantages. Plants contain diverse molecules thatcan reduce metals, and provide a safe, eco-friendly approach for synthesizing nanoparticles. Iron oxide nanoparticles (IONPs) have been reported to possess an antimicrobial effect against some strains of bacteria and moulds. We have aimed to synthesize IONPs from fig fruit extract and investigate the influence of fig extract and IONPs in wound healing of mice. UV-Vis spectroscopy, X-ray diffraction (XRD), and field emission scanning electron microscopy were used to characterize the IONPs that were produced

The present study explores the solar-induced photocatalytic degradation of reactive red (RR) and reactive turquoise (RT) dyes in a single system using TiO2 immobilized in xanthan gum (TiO2/XG), synthesized using the sol–gel dip-coating technique for direct precipitation. SEM-EDX, XRD, FTIR, and UV–Vis were used to assess the characteristics of the resulting catalyst. Moreover, the effects of different operating parameters, specifically pH, dye concentration, TiO2/XG concentration, H2O2 concentration, and contact time, were also investigated in a batch photocatalytic reactor. The immobilized TiO2/XG catalyst showed a slight adsorption degradation efficiency and then improved the RR and RT dye degradation activity (92.5 and 90.8%

In this study, aluminum nanoparticles (Al NPs) were prepared using explosive strips method in double-distilled deionized water (DDDW), where the effect of five different currents (25, 50, 75, 100 and 125 A) on particle size and distribution was studied. Also, the explosive strips method was used to decorate zinc oxide particles with Al particles, where Al particles were prepared in suspended from zinc oxide with DDDW. Transmission electron microscopy (TEM), UV-visible absorption spectroscopy, and x-ray diffraction are used to characterize the nanoparticles. XRD pattern were examined for three samples of aluminum particles and DDDW prepared with three current values (25, 75 and 125 A) and three samples prepared with the same currents for zin

        In this study, Zinc oxide nanostructures were synthesized via a hydrothermal method by using zinc nitrate hexahydrate and sodium hydroxide as a precursor. Three different annealing temperatures were used to study their effect on ZnO NSs properties. The synthesized nanostructure was characterized by X-ray diffraction (XRD), field emission scanning electron microscopy (FESEM), Atomic force microscope (AFM), and Fourier Transform Infrared Spectroscopy (FTIR). Their optical properties were studied by using UV -visible spectroscopy. The XRD analysis confirms that all ZnO nanostructures have the hexagonal wurtzite structure with average crystallite size within the range of (30.59 - 34