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: As human history is implicated in landscape or the natural history, it can be stated that the origins of the Caribbean writers' conflict, in general, are the colonial history of West India. That history which tells the story behind not only their fragmented identity, but also the problems connected to their language as well. Building on the arguments of the prominent Postcolonial ecoccritics such as Elizabeth DeLoughrey, George Handley, Helen Tiffin, and Graham Huggan, this research analyzes selected poems by Derek Walcott's which are bounded in his volume, Collected Poems. It shows how the Caribbean history has been erased due to the brutality of colonization offering landscape as a reliable source which has recorded that history

The applications of herbal medicine have recently acquired growing interest in range of the prophylaxis and treatment of diseases. Olibanum has been used since ancient eras and several reports studied the pharmacological characteristics of boswellic acid, particularly their effect on the inflammatory response, analgesic properties, and anti-arthritic activity mostly in cell lines, but new approaches include animal models to assess these natural derivatives effects taking into consideration of being safer than synthetic preparations.  The impact of olibanum oil on several parameters was studied in rats during this study. These included white blood cell (WBC) count, lactate dehydrogenase (LDH), and C reactive protein (CRP), as well a

The removal of congo red (CR) is a critical issue in contemporary textile industry wastewater treatment. The current study introduces a combined electrochemical process of electrocoagulation (EC) and electro-oxidation (EO) to address the elimination of this dye. Moreover, it discusses the formation of a triple composite of Co, Mn, and Ni oxides by depositing fixed salt ratios (1:1:1) of these oxides in an electrolysis cell at a constant current density of 25 mA/cm2. The deposition ended within 3 hours at room temperature. X-ray diffractometer (XRD), field emission scanning electron microscopy (FESEM), atomic force microscopy (AFM), and energy dispersive X-ray (EDX) characterized the structural and surface morphology of the multi-oxide sedim

This study involved the effect of the aqueous extracts of two plants, Origanum vulgare L.(1), Trigonella Foenum Graecum L. (Fenugreek) seeds(2) on the growth of cancer cell lines. Rhabdomyo sarcomas (RD) of human cell line and female intestine cells of Albino mice (L20B) in vitro System. These extracts were compared with the known anticancer drug Cis-platinum(Cis-Pt) as a positive control. The phytochemical tests were used for screening the active compounds in plants. The inhibition activity assay was used as a parameter of the cytotoxic effect of these extracts. Cancer cell lines were treated with four concentrations of Cis-platin, 31.25, 62.5, 125 and 250 ?g/ml for 72 hour exposure time. The same concentrations were used for the other ext

In this work, solid random gain media were fabricated from laser dye solutions containing nanoparticles as scattering centers. Two different rhodamine dyes (123 and 6G) were used to host the highly-pure titanium dioxide nanoparticles to form the random gain media. The spectroscopic characteristics (mainly fluorescence) of these media were determined and studied. These random gain media showed laser emission in the visible region of electromagnetic spectrum. Fluorescence characteristics can be controlled to few nanometers by adjusting the characteristics of the host and nanoparticles as well as the preparation conditions of the samples. Emission of narrow linewidth (3nm) and high intensity in the visible region (533-537nm) was obtained.

A new copolymer (MFA) was prepared from condensation of melamine (M) with p- methyl – anisole (A) in the presence of condensation agent like 37% (w/v) of formaldehyde. The new copolymer was characterized by elemental, IR and HNMR spectra. The chelating ion-exchange property of this polymer was studied for methylene blue dye in aqueous solution in 100-200ppm concentrations. The adsorption study was carried out over a wide range of pH, shaking time and in media of various kinetic parameters models. Thermal parameters like enthalpy, entropy and Gibbs free energy of adsorption process of methylene blue on surface of MFA resin were determined on the basis of kinetic parameters at different temperatures. To describe the equilibrium of adsorp

In this work, solid random gain media were fabricated from laser dye solutions containing nanoparticles as scattering centers. Two different rhodamine dyes (123 and 6G) were used to host the highly-pure titanium dioxide nanoparticles to form the random gain media. The spectroscopic characteristics (mainly fluorescence) of these media were determined and studied. These random gain media showed laser emission in the visible region of electromagnetic spectrum. Fluorescence characteristics can be controlled to few nanometers by adjusting the characteristics of the host and nanoparticles as well as the preparation conditions of the samples. Emission of narrow linewidth (3nm) and high intensity in the visible region (533-537nm) was obtained.