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.
This research was to determine the effect of rare earth metal (REM) on the as-cast microstructure of Mg-4Al alloy. The rare earth metal used here is Lanthanum to produce Mg-4Al-1.5La alloy. The microstructure was characterized by optical microscopy. The phases of this alloy were identified by X-ray diffraction. The microstructure of Mg-4Al consists of α-Mg and grain boundaries with precipitated phase particles. With the addition of Lanthanum, three distinct phases were identified in the X-ray diffraction patterns of the as cast Mg-4Al-1.5La: Mg, Al11La3, Al4La. The Mg17Al12 phase was not detected. The addition of Lanthanium increases the hardness and dec
... Show MoreThis paper aims to find new analytical closed-forms to the solutions of the nonhomogeneous functional differential equations of the nth order with finite and constants delays and various initial delay conditions in terms of elementary functions using Laplace transform method. As well as, the definition of dynamical systems for ordinary differential equations is used to introduce the definition of dynamical systems for delay differential equations which contain multiple delays with a discussion of their dynamical properties: The exponential stability and strong stability
A study carried out to prepare Hg1-xCdxTe compound and to see the effect on increasing the percentage of x on the compound structure by using x-ray diffraction and atomic absorption for 0
In this work, a local sunflower husk (SFH) was used as a natural surface for removing Basic Green-4 (BG4) dye, as a watersoluble pollutant. The effect of initial concentration, contact time, the mass of surface of the dye with the SFH as well as the medium temperature was studied. The application of Langmuir, Freundlich isotherms on the collected data of the adsorption process found to harmonize to Freundlich equation more than that of Langmuir. However, the adsorbed mass of BG4 dye showed a direct increase with the increase of SFH mass and equilibrium was achieved within a 60min window. The interaction of BG4 with SFH surface was spontaneous and exothermic. The empirical kinetic outcomes at ambient temperatures were applied to pseudo 1st a
... Show MoreComplexes of 1-phenyl-3-(2(-5-(phenyl amino)-1,3,4- thiadiazole-2-yl)phenyl) thiourea have been prepared and characteized by elemental analysis, Ff-[R, and u.v./ visible spectra moreover, determination of metal content M%o by flame atomic absorption spectroscopy, molar conductance in DMSO solution and magnetic moments (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 sulpher atoms. From the result obtained, rhe following general formula [MLClz] has been given for the prepared complexes with an octahedral geometry around the metal ions for all complexes. where M= Mn*2, Ni*2, cu*2, zn*z, cd*z, and Hg*2 l= l-phenyl-3-(2-(5-(phenyl amino)-1, 3,
... Show MoreA new ligand [N-(3-acetylphenylcarbamothioyl)-4-chlorobenzamide] (CAD) was synthesized by reaction of 4-Chlorobenzoyl isothiocyanate with 3-amino acetophenone, The ligand was characterized by elemental micro analysis C.H.N. S., FT-IR, UV-Vis and 1H,13C- NMR spectra, some transition metals complexes of this ligand were prepared and characterized by FT-IR, UV-Vis spectra, conductivity measurements, magnetic susceptibility and atomic absorption, From obtained results the molecular formula of all prepared complexes were [M(CAD)2(H2O)2]Cl2 (M+2 =Mn, Co, Ni, Cu, Zn, Cd and Hg),the proposed geometrical structure for all complexes were octahedral.
A new ligand [N-(3-acetylphenylcarbamothioyl)-4-chlorobenzamide] (CAD) was synthesized by reaction of 4-Chlorobenzoyl isothiocyanate with 3-amino acetophenone, The ligand was characterized by elemental micro analysis C.H.N. S., FT-IR, UV-Vis and 1H,13C- NMR spectra, some transition metals complexes of this ligand were prepared and characterized by FT-IR, UV-Vis spectra, conductivity measurements, magnetic susceptibility and atomic absorption, From obtained results the molecular formula of all prepared complexes were [M(CAD)2(H2O)2]Cl2 (M+2 =Mn, Co, Ni, Cu, Zn, Cd and Hg),the proposed geometrical structure for all complexes were octahedral
ABSTRACT: Oxadiazole ring is a heterocyclic molecule with an oxygen and two nitrogen atoms spread throughout its five-membered structure. There are four different isomers that have been discovered, Because of their wide applications in a range of sectors, including medications . Some of these biological activity are; anticonvulsant capacity, anticancer as well, antibacterial, antiviral, antifungal, antimalarial, antitubercular, anti-asthmatic, antidepressant, antidiabetic, antioxidant, antiparkinsonian, analgesic and anti-inflammatory, are just some of the therapeutic uses that have drawn attention to drug candidates containing an oxadiazole moiety. This review, we will examine the various methods of oxadiazole synthesis. The mo
... Show MoreIn this work, we construct the projectively distinct (k, n)-arcs in PG (3, 4) over Galois field GF (4), where k 5, and we found that the complete (k, n)-arcs, where 3 n 21, moreover we prove geometrically that the maximum complete (k, n)-arc in PG (3, 4) is (85, 21)-arc. A (k, n)-arcs is a set of k points no n+ 1 of which are collinear. A (k, n)-arcs is complete if it is not contained in a (k+ 1, n)-arcs
In this paper, series of new complexes of Manganese(II), Cobalt(II), Nickel (II) Cupper(II) Zinc(II), Cadmium(II) and Mercury (II) are prepared from the new ligand [2-(3-benzoylthioureido)-3-(-4- hydroxyphenyl) propanoic acid (BHP) derived from tyrosine and benzoylisothiocyanate .Chemical structures are obtained from their 1 H, 13CNMR spectra (for BHP), elemental microanalyses, molar conductance, FTIR, UV–Vis, magnetic susceptibility in addition to TGA/DTG and DSC analysis, the suggested geometry for all complexes was tetrahedral. The biological activity of BHP and its complexes has been extensively studied against two bacterial species Staphylococcus aurous (G+) and Escherichia coli (G-) by agar-well diffusion technique, where Mn(II), Co
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