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 .

Mixed ligand complexes of bivalent metal ions, viz; Co(II), Ni(II), Cu(II) and Zn(II) of the composition [M(A)2((PBu3)2]in(1:2:2)(M:A:(PBu3). molar ratio, (where A- Anthranilate ion ,(PBu3)= tributylphosphine. M= Co(II),Ni(II),Cu(II) and Zn(II). The prepared complexes were characterized using flame atomic absorption, by FT-IR, UV/visible spectra methods as well as magnetic susceptibility and conductivity measurements. The metal complexes were tested in vitro against three types of pathogenic bacteria microorganisms: (Staphylococcus, Klebsiella SPP .and Bacillas)to assess their antimicrobial properties. Results. The study shows that all complexes have octahedral geometry; in addition, it has high activity against tested bacteria. Based on th

Complexes of Co(II),Ni(II),Cu(II)and Zn(II) with mixed ligand of 4- aminoantipyrine (4-AAP) and tributylphosphine (PBu3) were prepared in aqueous ethanol with (1:2:2) (M:L:PBu3). The prepared complexes were characterized using flame atomic absorption, FT.IR and UV-Vis spectroscopic methods as well as magnetic susceptibility and conductivity measurements. In addition biological activity of the two ligands and their complexes against three selected type of bacteria were also examined. The general compositions of the complexes are found to be [M(4-AAP)2(PBu3)2] Cl2 . Where M= Co(II),Ni(II),Cu(II)and Zn(II). Some of the complexes exhibit good bacterial activities. From the obtained data the octahedral structures have suggested for all prepare

Mixed ligand complexes of bivalent metal ions, viz; Co(II), Ni(II), Cu(II) and Zn(II) of the composition [M(A)2((PBu3)2]in(1:2:2)(M:A:(PBu3). molar ratio, (where A- Anthranilate ion ,(PBu3)= tributylphosphine. M= Co(II),Ni(II),Cu(II) and Zn(II). The prepared complexes were characterized using flame atomic absorption, by FT-IR, UV/visible spectra methods as well as magnetic susceptibility and conductivity measurements. The metal complexes were tested in vitro against three types of pathogenic bacteria microorganisms: (Staphylococcus, Klebsiella SPP .and Bacillas)to assess their antimicrobial properties. Results. The study shows that all complexes have octahedral geometry; in addition, it has high activity against tested bacteria. Based on th

The synthesized ligand (3-(2-amino-5-(3,4,5-tri-methoxybenzyl)pyrimidin-4-ylamino)-5,5-dimethylcyclohex-2-enone] [H1L1] was characterized via fourier transform infrared spectroscopy (FTIR), 1H, 13C – NMR, Mass spectra, (CHN analysis), UV-vis spectroscopic approaches. Analytical and spectroscopic techniques like chloride content, micro-analysis, magnetic susceptibility UV-visible, conductance, and FTIR spectra were used to identify mixed ligand complexes. Its (ML13ph) mixed ligand complexes [M= Co (II), Ni (II), Cu (II), Zn (II), and Cd (II); (H1L1) = β-enaminone ligand=L1 and (3ph) =3-aminophenol= L2]. The results demonstrate that the complexes are produced with a molar ratio of M: L1:L2 (1:1:1). To generate the appropriate compl

The current work reports a new Schiff base [N1-benzylidenebenezene-1,2-diamine(L) = C20H16N2] has been synthesized from benzaldehyde (C6H5CHO) and O- aminoaniline (O-C6H4(NH2)2. Metal mixed ligand complexes of the Schiff base were prepared from chloride salts of Zn(II), Cd(II) and Hg(II) in ethanol and 8-hydroxyquinoline(8HQ)(C9H7NO) containing sodium hydroxide. All the complexes were characterized on the basis of their; FT-IR and U.V spectra, melting point, molar conductance, and determination of the percentage of the metal in the complexes by flame (AAS). In the all complexes, (8HQ) behaves as a bidentate ligand as primary ligand through –-OH phenolic group and –N groups of pyridine group. Also, the prepared ligand (L) was bidentate i

Introduction: Different surgical techniques used for closure of various oral defects. While each one of these techniques has its limitation; the buccal pad of fat used in last quarter of last century as pedicle or free graft in reconstruction of small to medium, congenital and acquired defects showed good potentials for success. The present study used the BPF as pedicled flap to reconstruct intra oral defects. The study aimed to evaluate of the success of buccal pad of fat pedicled flap in the reconstruction of intra oral defects. Outlining its indications, limitations and complications. Materials and Methods: The study included 19 patients (17 males and 2 females) with age range between (1- 70 years), all patients were treated with pedic

The stories of children in Iraq during the past two decades have received a number of important scientific studies. Despite tyranny of the historical study method on most of these studies, they have been and still are very important, because they have established a chronicle of this literary style that has been neglected and based not only on the academic level and serious in-depth university studies but also on the enclosed sight that doesn’t consider studied art as an innovation with its specificity and its typical technical components. While many of the public impressions and self-reflections contributed to the dominance of some of the provisions and concepts that were circulated as critical remarks and adopted by som

At the time when many important political events and evolutions took place, the cinema has been pretty active, and witnessed the historical events before and after the two world wars and the cold war. During the first half of the 20th century, the cinema had great interest from the major countries and their politicians, as well as the commercial turnout of large companies to invest in that field for the profits.  In the beginning of the 20th century, the major powers like the Soviet Union, the United States, Germany, Italy, England, and France started to compete in the development of their film industry and the investment of the new medium and the transformation of some famous works of fiction into films that perpetuate their cultur