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 importance of the present work falls on the pitting corrosion behavior investigation of 304 SS and 316 SS alloys in 3.5 wt% of aqueous solution bearing with chloride and bromide anion at different solutions temperature range starting from (20-50)oC due to the pitting corrosion tremendous effect on the economic, safety and materials loss due to leakage. The impact of solution temperatures on the pitting corrosion resistance at 3.5wt% (NaCl and NaBr) solutions for the 304 SS and 316 SS has been investigated utilizing the cyclic polarization techniques at the potential range -400 to1000 mV vs. SCE at 40 mV/sec scan rate followed by the surface characterization employing Scanning Electron&nbs
... Show MoreTitanium oxide nanoparticles-modified smectite (SMC-nTiO2) as a low-cost adsorbent was investigated for the removal of Rhodamine B (RhB) from aqueous solutions. The adsorbents (SMC and SMC-nTiO2) were characterized by scanning electron microscopy, Fourier transforms infrared spectroscopy, and energy-dispersive X-ray spectroscopy. The effects of various parameters like contact time, adsorbent weight, pH, and temperatures were examined. Three kinetic equations (pseudo-first-order (PFO), pseudo-second-order (PSO), and intra-particle diffusion) were used to evaluate the experimental kinetic of the data and the results showed that the adsorption process is in line with the PSO kinetic model. Adsorption equilibrium isotherms were modeled using La
... Show MoreRemoval of heavy metals from waste water has received a great deal of attention. The compare Cr
(VI) adsorption characteristics removing from wastewater by using thermally modified and non-modified
eggshells were examined
New metal ion complexes were synthesized with the general formula; K[PtLCl4], [ReLCl4] and K[ML(Cl)2] where M = Pd(II), Cd(II), Zn(II) and Hg(II), from the Azo ligand (HL) [2-Hydroxy-3-((5-mercapto-1,3,4-thiadiazol-2-yl)diazenyl)-1-naphth aldehyde] (HL) the ligand was synthesized from (2-hydroxy-1-naphthaldehyde) and (5-amino-1,3,4-thiadiazole-2-thiol). The ligand and its metal complexes are characterized by phisco- chemical spectroscopic techniques (FT.IR, UV-Vis and Mass spectra, elemental analysis, molar conductivity, Atomic Absorption, Chloride contain and magnetic susceptibility). The spectral data suggest that the (HL) behaves as a bidentate ligand in all complexes. These studies revealed tetrahedral geometries for all metal complexes
... Show More