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.
رضًٍ ْزا انجذث رذضٛش ٔرشخٛض انهٛكبَذ انجذٚذ [KL [: - رفبػم ٍي ذضشًان K [4-{N-(5-methylisoxazol-3-yl) sulfamyl} phenyl carbamodithioate] عهفبيٛثٕكغبصٔل يغ ثُبئٙ كجشٚزٛذ انكبسثٌٕ ثٕجٕد ْٛذسٔكغٛذ انجٕربعٕٛو رذذ انزظؼٛذ االسجبػٙ ) نًذح اسثغ عبػبد ( ٔثئعزؼًبل انًٛثبَٕل كًزٚت نُٛزج انهٛكبَذ انًزكٕس اَفب رى رشخٛض انهٛكبَذ انًذضش ثبعزؼًبل طٛف االشؼخ رذذ انذًشاء ، ً طٛف االشؼخ فٕق انجُفغجٛخ - انًشئٛخ ، طٛف انشٍَٛ انُٕ٘ٔ انًغُبطٛغٙ نهجشٔرٌٕ أنهكبس
... Show MoreZeolite Y nanoparticles were synthesized by sol - gel method. Dffirent samples using two silica sources were prepared.
Sodium metasilicate (Na2SiO3) (48% silica) and silicic acid silica (H2SiO3) (75% silica) were employed as silica
source and aluminum nitrate (Al(NO3)3.9H2O) was the aluminum source with tetrapropylammonium hydroxide
(TPAOH) as templating agent.
The synihesized-samples were characterized by X-ray diffraction, showed the requirement of diffirent aging time for
complete crystallization to be achieved. Transmission Electronic Microscope (TEM) images, showed the particles were
in the same range of 30 - 75 nm. FT-IR spectroscory, showed the synthesized samples having the zeolite Y crystal
properties. The i
In this study, poly4-(nicotinamido)-4-oxo-2-butenoic acid (PNOE) was prepared by the electro polymerization of 4-(nicotinamido)-4-oxo-2-butenoic acid (NOE) monomer on a 316 stainless steel (St.St) which acts as an anticorrosion coating. Fourier transforms infrared (FTIR), atomic force microscopy (AFM), scanning electron microscopy (SEM), and cyclic voltammetry were used to diagnose the structure and the properties of the prepared polymer layer. The corrosion behavior of the uncoated and coated 316 St.St were evaluated by using an electro chemical polarization technique in 0.2 M hydrochloric acid solution as a corrosive medium at a temperature range of 293 to 323 K. Nano materials, such as nano ZnO and graphene were added in di
... Show MoreIn this study, SnO2 nanoparticles were prepared from cost-low tin chloride (SnCl2.2H2O) and ethanol by adding ammonia solution by the sol-gel method, which is one of the lowest-cost and simplest techniques. The SnO2 nanoparticles were dried in a drying oven at a temperature of 70°C for 7 hours. After that, it burned in an oven at a temperature of 200°C for 24 hours. The structure, material, morphological, and optical properties of the synthesized SnO2 in nanoparticle sizes are studied utilizing X-ray diffraction. The Scherrer expression was used to compute nanoparticle sizes according to X-ray diffraction, and the results needed to be scrutinized more closely. The micro-strain indicates the broadening of diffraction peaks for nano
... Show MoreThe optical properties for the components CuIn(SexTe1-x)2 thin films with both values of selenium content (x) [0.4 and 0.6] are studied. The films have been prepared by the vacuum thermal evaporation method with thickness of (250±5nm) on glass substrates. From the transmittance and absorbance spectra within the range of wavelength (400-900)nm, we determined the forbidden optical energy gap (Egopt) and the constant (B). From the studyingthe relation between absorption coefficient (α) photon energy, we determined the tails width inside the energy gap.
The results showed that the optical transition is direct; we also found that the optical energy gap increases with annealing temperature and selenium content (x). However, the width of l
Applications of superconductor compounds were considered as modern and important topics, especially these which are exposures to one of the nuclear radiation kinds. So, we gone to investigate the influence of fast neutrons irradiation on electrical and structural characteristics of HgxSb1-xBa2Ca2Cu3O8+δ superconducting compound at (x = 0.7) in ratio. The superconducting specimens were synthesized using solid state technique. Specimens were exposure to the nuclear radiation using fast neutrons with doses (0, 9.06 x1010, 15.3 x 1010 and 18.17 x 1010) n/cm2 respectively. Electrical and X-ray diffraction properties of superconductor specimens before and after irradiation were investigated under standard conditions. Results of X-ray diffraction
... Show MoreThe present research was conducted to reduce the sulfur content of Iraqi heavy naphtha by adsorption using different metals oxides over Y-Zeolite. The Y-Zeolite was synthesized by a sol-gel technique. The average size of zeolite was 92.39 nm, surface area 558 m2/g, and pore volume 0.231 cm3/g. The metals of nickel, zinc, and copper were dispersed by an impregnation method to prepare Ni/HY, Zn/HY, Cu/HY, and Ni + Zn /HY catalysts for desulfurization. The adsorptive desulfurization was carried out in a batch mode at different operating conditions such as mixing time (10,15,30,60, and 600 min) and catalyst dosage (0.2,0.4,0.6,0.8,1, and 1.2 g). The most of the sulfur compounds were removed at 10 min for all catalyst ty
... Show MoreA new ligand [ 2-chloro-N- (1,5-dimethyl-3-oxo-2-phenyl-2,3-dihydro -1H-pyrazol- 4-ylcarbamothioyl)acetamide](L) was synthesized by reacting the Chloro acetyl isothiocyanate with 4-aminoantipyrine,The ligand was characterized by(C HNS) elemental microanalysis and the spectral measurements including Uv-Vis ,IR ,1H and13C NMR spectra, some transition metals complex of this ligand were prepared and characterized by Uv-Vis, FT-IR spectra, conductivity measurements, magnetic susceptibility and atomic absorption. From the obtained results the molecular formula of all prepared complexes were [M(L)2(H2O)2]Cl2 (M+2 =Mn, Co, Ni, Cu, Zn, Cd and Hg),the proposed geometrical structure for all complexes were octahedral.