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.
The main objective and primary concern to every investor not only to achieve a greater return on his or her investments, but also to create the largest possible value of these investments the, researchers and those interested in the field of investment and financial analysis try to develop standards for performance valuation is guided through the  
... Show MoreNumerous integral and local electron density’s topological parameters of significant metal-metal and metal-ligand bonding interactions in a trinuclear tetrahydrido cluster [(Cp* Ir) (Cp Ru)2 (μ3-H) (μ-H)3]1 (Cp = η5 -C5Me5), (Cp* = η5 -C5Me4Et) were calculated and interpreted by using the quantum theory of atoms in molecules (QTAIM). The properties of bond critical points such as the delocalization indices δ (A, B), the electron density ρ(r), the local kinetic energy density G(r), the Laplacian of the electron density ∇2ρ(r), the local energy density
... Show MoreThe research to knows some biomechanics variables in different spots with and without players in basketball youth players and analysis by using destructive method in surfing study and the research were applied for jump shoot from one of basketball players in ( middle , left , right ) in side zone and out of zone also from three point shoot with and without defense and we depend on successful shoot on analyze .The results and conclusions that center of weight of the player on standby on high and knee angel and hips were more wide also the two angle of wrist , elbow on start of shooting be more wide with defender more than without defender .the maximum high center of weight and shooting angle and ball entrance being less degree with defender
... Show MoreThis paper investigates an effective computational method (ECM) based on the standard polynomials used to solve some nonlinear initial and boundary value problems appeared in engineering and applied sciences. Moreover, the effective computational methods in this paper were improved by suitable orthogonal base functions, especially the Chebyshev, Bernoulli, and Laguerre polynomials, to obtain novel approximate solutions for some nonlinear problems. These base functions enable the nonlinear problem to be effectively converted into a nonlinear algebraic system of equations, which are then solved using Mathematica®12. The improved effective computational methods (I-ECMs) have been implemented to solve three applications involving nonli
... Show MoreThis research aims to test the ability of glass waste powder to adsorb cadmium from aqueous solutions. The glass wastes were collected from the Glass Manufacturing Factory in Ramadi. The effect of concentration and reaction time on sorption was tested through a series of laboratory experiments. Four Cd concentrations (20, 40, 60, and 80) as each concentration was tested ten times for 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50 min. Solid (glass wastes) to liquid was 2g to 30ml was fixed in each experiment where the total volume of the solution was 30ml. The pH, total dissolved salts and electrical conductivity were measured at 30ºC. The equilibrium concentration was determined at 25 minutes, thereafter it was noted that the sorption
... Show MoreMany writers and scientists hardly differentiate between the two instruments of use
(If) and (if) to convergence in the meaning, as they perform the meaning of the penalty and condition, as the answer relates to his condition, but when linguistic meditation we find a great difference in use in terms of meaning, so this research came to reveal these meanings and was extrapolated applied in Surat al-Maidah By counting the verses in which (if) and (if) the cops were given and looking at their contexts, the connotation of the cops in most places was within the context of probability, which is the origin of its use, given in twenty places of Surat al-Ma'idah, and it had multiple connotations according to the contexts of the verses received
In this research, some probability characteristics functions (probability density, characteristic, correlation and spectral density) are derived depending upon the smallest variance of the exact solution of supposing stochastic non-linear Fredholm integral equation of the second kind found by Adomian decomposition method (A.D.M)
The aim of this work covers the synthesis and characterization of the new tertra dentate ligand (H4L) containing (N and O) as donor set atoms kind (N2O2) where: H4L=Bis-1,2 (2,4- dihydroxybenzylediene phylinediamine . The preparation of ligand contains reaction 2, 4 - Dihydroxy benzaldehyde and o-phenylene diamine . Schiff base was reacted with some metal ions in the presence of methanol to give the complexes in the general formula [M (H2L)] where: MII = Co, Ni, Cu, Zn, Cd. All compounds were characterized by spectroscopic methods I.R , U.V.-Vis, metal content and molar conductivity measurements, showed that the complexes are non-electrolyte. The proposed geometry for all of the proposed complexes was a tetrahedral while Ni complex was squa
... Show Morebstract The aim of this work covers the synthesis and characterization of the new tertra dentate ligand (H4L) containing (N and O) as donor set atoms kind (N2O2) where: H4L=Bis-1,2 (2,4- dihydroxybenzylediene phylinediamine . The preparation of ligand contains reaction 2, 4 - Dihydroxy benzaldehyde and o-phenylene diamine . Schiff base was reacted with some metal ions in the presence of methanol to give the complexes in the general formula [M (H2L)] where: MII = Co, Ni, Cu, Zn, Cd. All compounds were characterized by spectroscopic methods I.R , U.V.-Vis, metal content and molar conductivity measurements, showed that the complexes are non-electrolyte. The proposed geometry for all of the proposed complexes was a tetrahedral while Ni complex
... Show MoreIn this study, an unknown force function dependent on the space in the wave equation is investigated. Numerically wave equation splitting in two parts, part one using the finite-difference method (FDM). Part two using separating variables method. This is the continuation and changing technique for solving inverse problem part in (1,2). Instead, the boundary element method (BEM) in (1,2), the finite-difference method (FDM) has applied. Boundary data are in the role of overdetermination data. The second part of the problem is inverse and ill-posed, since small errors in the extra boundary data cause errors in the force solution. Zeroth order of Tikhonov regularization, and several parameters of regularization are employed to decrease error
... Show More