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.
A new Schiff base (4-chlorophenyl)(phenyl methanimine (6R,7R)-3-methyl-8-oxo-7-(2-phenylpropanamido)-5-thia-1-azabicyclo[4.2.0]oct-2-ene-2-carboxylate=HL=C29H24ClN3O4S) has been synthesized from β-lactam antibiotic (cephalexin mono hydrate (CephH)=(C16H19N3O5S.H2O) and 4- chlorobenzophenone. Metal mixed ligand complexes of the Schiff base were prepared from chloride salt of Fe(II), Co(II), Ni(II), Cu(II), Zn(II) and Cd(II), in 50% (v/v) ethanol – water medium in aqueous ethanol(1:1) and Saccharin(C7H5NO3S) containing sodium hydroxide. Several physical tools in particular; IR, C:H:N , 1H NMR,13C NMR for ligand, melting point, molar conductance, magnetic moment. and determination of the percentage of the metal in the complexes by flame(AAS
... Show Morenew Schiff base 4-chlorophenyl)methanimine (6R,7R)-3-methyl-8-oxo-7-(2-phenylpropanamido)-5-thia-1-azabicyclo[4.2.0]oct-2-ene-2-carboxylate= (HL)= C23H20 ClN3O4S) has been synthesized from β-lactam antibiotic (cephalexin mono hydrate(CephH)=(C16H19N3O5S.H2O) and 4-chlorobenzaldehyde . Figure(1) Metal mixed ligand complexes of the Schiff base were prepared from chloride salt of Fe(II),Co(II),Ni(II),Cu(II),Zn(II) and Cd (II), in 50% (v/v) ethanol –water medium (SacH ) .in aqueous ethanol(1:1) containing and Saccharin(C7H5NO3S) = sodium hydroxide. Several physical tools in particular; IR, CHN, 1H NMR, 13C NMR for ligand and melting point molar conductance, magnetic moment. and determination the percentage of the metal in the complexes by fl
... Show MoreSolar hydrogen line emission has been observed at the frequency of 1.42 GHz (21 cm wavelength) with 3m radio telescope installed inside the University of Baghdad campus. Several measurements related to the sun have been conducted and computed from the radio telescope spectrometer. These measurements cover the solar brightness temperature, antenna temperature, solar radio flux, and the antenna gain of the radio telescope. The results demonstrate that the maximum antenna temperature, solar brightness temperature, and solar flux density are found to be 970 K, 49600K, and 70 SFU respectively. These results show perfect correlation with recent published studies.
The effect of the initial pressure upon the laminar flame speed, for a methane-air mixtures, has been detected paractically, for a wide range of equivalence ratio. In this work, a measurement system is designed in order to measure the laminar flame speed using a constant volume method with a thermocouples technique. The laminar burning velocity is measured, by using the density ratio method. The comparison of the present work results and the previous ones show good agreement between them. This indicates that the measurements and the calculations employed in the present work are successful and precise
This paper was conducted to identifying the body growth averages for the infants of the age (3-6) months and their relation with brest (natural ) or artificial feeding The results showed that the higher percentage was for the infants with the natural feeding in comparison with those of the artificial or mixed feeding. Also there was a clear increase in the average of the body growth for those with the natural feeding and such results were closer to the standard criterion. While the averages of body growth for those with the artificial or mixed feeding were low. In addition, it was clear that the averages of body growth of the i
... Show MoreExpanded use of antibiotics may increase the ability of pathogenic bacteria to develop antimicrobial resistance. Greater attention must be paid to applying more sustainable techniques for treating wastewater contaminated with antibiotics. Semiconductor photocatalytic processes have proven to be the most effective methods for the degradation of antibiotics. Thus, constructing durable and highly active photocatalytic hybrid materials for the photodegradation of antibiotic pollutants is challenging. Herein, FeTiO3/Fe-doped g-C3N4 (FTO/FCN) heterojunctions were designed with different FTO to FCN ratios by matching the energy level of semiconductors, thereby developing effective direct Z-type heterojunctions. The photodegradation behaviors of th
... Show MoreIn this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods i
... Show MoreIn this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods is
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