The investigation of determining solutions for the Diophantine equation over the Gaussian integer ring for the specific case of is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.
حضر الليكاند (L) 1-فنيل-3-بردين-2-يل مثيل-ثايويوريا من تفاعل 2-أمينو مثيل بردين مع فنيل ايزوثايوسيانيت وبنسبة 1: 1 وشخص الليكاند بواسطة التحليل الدقيق للعناصر (C, H, N), الأشعة تحت الحمراء، الأشعة فوق البنفسجية–المرئية وطيف الرنين النووي المغناطيسي كما حضرت وشخصت معقدات أملاح بعض ايونات العناصر الثنائية التكافؤ (Co, Ni, Cu, Cd and Hg). استخدمت تقنية الأشعة تحت الحمراء، الأشعه فوق البنفسجية-المرئية, التوصيلية الكهربائية و الا
... Show MoreA series of lanthanide metal (???) complexes have been prepared from the new azo ligand, 3-(1-methyl-2-benzimidazolylazo)-Tyrosine (MBT). The structural feature were confirmed on the basis of their elemental analysis, metal content, molar conductance, magnetic measurement, FTIR, 1 HNMR and UV-Vis spectra studies. The isolated complexes were found to have a mole ratio (1:2) (metal:ligand) stoichiometry with the general formula [Ln(MBT)2]Cl (Ln(???) = La, Ce, Pr, Nd, Sm, Eu and Gd). The chelates were found to have octahedral structures. The FTIR spectra shows that the ligand (MBT) is coordinated to lanthanide ions as a N, N, O-tridentate anion via benzimidazole nitrogen, azo nitrogen and oxygen of hydroxyl after deprotonation. Com
... Show MoreWriting in English is one of the essential factors for successful EFL learning .Iraqi students at the preparatory schools encounter problems when using their background knowledge in handling subskills of writing(Burhan,2013:164).Therefore, this study aims to investigate the 4thyear preparatory school students’ problems in English composition writing, and find solutions to these pro
... Show MoreBackground: Removal of bacteria from the pulp system by instrumentation of an infected root canal, will be significantly reduced the number of bacteria, but it is well documented that instrumentation alone can-not clean and kill all bacteria found on the root canal walls. Antibacterial irrigants are needed to kill the remaining microorganisms. The aims of this study was to assess antibacterial effect of titanium tetrafluoride (TiF4) solution and brewing green tea against root canal bacteria and to compare with sodium hypochlorite and normal saline through microbiological and molecular studies. Materials and methods: Microbiological study was carried out to determine the concentration of titanium tetrafluoride and brewing green tea at which
... Show MoreComplexes of 1-phenyl-3-(2(-5-(phenyl amino)-1,3,4-thiadiazole-2-yl)phenyl) thiourea have been prepared and characteizedby elemental analysis, Ff-[R, and u.v./ visible spectra moreover,determination of metal content M%o by flame atomic absorptionspectroscopy, molar conductance in DMSO solution and magneticmoments (peffl.The result showed that the ligand (L) was coordinated to Mn+2, Ni+2,Ct+2,2n+2,Cd+2, and Hg+2 ions through the nitrogen atoms and sulpheratoms.From the result obtained, rhe following general formula [MLCl2] hasbeen given for the prepared complexes with an octahedral geometryaround the metal ions for all complexes.where M= Mn+2, Ni+2, cu+2, zn+2, cd+2, and Hg+2 l= l-phenyl-3-(2-(5-(phenyl amino
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