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 .

     The research aimed to identify the extent to which the media offices in the ministries depend on the website of the Iraqi Council of Ministers as a source of information. Such goal includes a set of sub-goals: Knowing the reasons for media offices' reliance on the information provided by the Cabinet's website; and revealing the benefit derived from relying on the Cabinet's website.

The researcher used the survey method to screen and comprehend the extent to which the media offices in the ministries depend on the website of the Iraqi Council of Ministers as a source of information.

The mechanism of comprehensive account of the limits of research wa

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 major aim of this research is study the effect of the type of lightweight aggregate (Porcelinite and Thermostone), type and ratio of the pozzolanic material(SF and HRM) and the use of different ratios of w/cm ratio(0.32 and 0.35) on the properties of SCLWC in the fresh and hardened state. SF and HRM are used in three percentage 5%,10%, and 15% as a partial replacement by weight of
cement for all types of SCLWC. The requirements of self-compatibility for SCC are fulfilled by using the high performance superplasticizer (G51) at 1.2liter per 100 kg of cement. The values of air dry density and compressive strength at age of 28 days within the limits of structural lightweight concrete. The air dry density and compressive strength at a

The ligand [Potassium (E)-(4-(((2-((1-(3-aminophenyl) ethylidene) amino)-4-oxo-1, 4-dihydropteridin-6-yl) methyl) amino) benzoyl)-L-glutamate] was prepared from the condensation reaction of folic acid with (3-aminoacetophenone) through Schiff reaction to give a new Schiff base ligand [H2L]. The ligand [H2L] was characterized by elemental analysis CHN, atomic absorption (AA),(FT-IR),(UV-Vis), TLC, ES mass (for spectroscopes), molar conductance, and melting point. The new Schiff base ligand [H2L], reacts with Mn (II), Co (II), Ni (II), Cu (II), Cr (III) and Cd (II) metal ions and (2-aminophenol),(metal: derivative ligand: 2-aminophenol) to give a series of new mixed complexes in the general formula:-K3 [M2 (HL)(HA) 2],(where M= Mn (II) and Cd

A new Schiff base [1-((2-(1H-indol-3-yl)ethylimino)methyl)naphthalene-2-ol] (HL) has been synthesized by condensing (2-hydroxy-1-naphthaldehyde) with (2-(1H-indol-3-yl)ethylamine). In turn, its transition metal complexes were prepared having the general formula; [Pt(IV)Cl2(L)2], [Re(V)Cl2(L)2]Cl and [Pd(L)2], 2K[M(II)Cl2(L)2] where M(II) = Co, Ni, Cu] are reported. Ligand as well as metal complexes are characterized by spectroscopic techniques such as FT-IR, UV-visible, 13C & 1H NMR, mass, elemental analysis. The results suggested that the ligand behaves like a bidentate ligand for all the synthesized complexes. On the other hand, theoretical studies of the ligand as well its metal complexes were conducted at gas phase using Hyp

Industrial dyes are major pollutants in wastewater and river water with an initial visible concentration of 1 mg/L. Recent studies have shown the possibility of using polyphenol oxidase in catalytic biological treatment due to its ability to oxidize a large number of dyes and pollutants in wastewater and the flexibility to work in wide ranges of temperature, pH and salinity. It is easy availability as well as the low economic cost resulting from its use in biological treatments, this enzyme polyphenol oxidase was used. The findings in this study showed that the extraction of polyphenol oxidase (PPO) from potato peel was homogenized with potassium phosphate buffer (0.1 M, pH 7) at a ratio of 1:10 (weight: volume) for two min. The res

A new simple and sensitive spectrophotometric method for the determination of trace amount of Co(II) in the ethanol absolute solution have been developed. The method is based on the reaction of Co(II) with ethyl cyano(2-methyl carboxylate phenyl azo acetate) (ECA) in acid medium of hydrochloric acid (0.1 M) givining maximum absorbance at ((λmax = 656 nm). Beer's law is obeyed over the concentration range (5-60) (μg / ml) with molar absorptivity of (1.5263 × 103 L mol-1 cm-1) and correlation coefficient (0.9995). The precision (RSD% ˂ 1%). The stoichiometry of complex was confirmed by Job's method which indicated the ratio of metal to reagent is (2:1). The studied effect of interference elements Zn(II), Cu(II), Na(I), K(I), Ca(II) and Mg

A rapid high performance liquid chromatography method for the determination of sphinganine (Sa) and sphingosine (So) in urine samples by employing a silica-based monolithic column is described. The samples were first extracted using ethyl acetate and derivatized using ortho-phthaldialdehyde in the presence of 2-mercaptoethanol. C20 sphinganine was used as internal standard. Under the optimized conditions, separation was achieved using a mixture of methanol:water (93:7, v/v), column temperature at 30°C, flow rate of 1 mL min−1, and an injection volume of 10 μL. Good linearity was obtained for Sa and So over the concentration range 20–500 ng mL−1(correlation coefficients ≥0.9978). The detection limits were 0.45 ng mL−1 for Sa and