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 molluscicidal effects of herbicide 2, 4-D were studied against tow species of freshwater snail Bulinus truncatus and Melanopsis nodosa by short term experiments. Calculated values of lethal concentrations (LC50 and LC100) were maid to two spices for different period of time 24hr, 48hr, 72hr and 96hr. The study had showed that the herbicide 2, 4-D was toxic against the tow species. The toxicity of the herbicide was low or unknown in low concentrations in the first period of exposure 24and 48hr to two spices but it increase gradually with increase period of exposure. The spice of B.truncatus was more tolerant than the M.nodosa. All the individual of M nodosa was death while in B.truncatus the complete death was not appear until finish the

Background: This study was performed to compare the marginal fit changes and facture resistance of metal ceramic crowns constructed from Ceramill Sintron metal coping veneered with three different porcelain veneering materials (Vita Master Koromikos VMK, Willi Geller Creation CC and GC initial MC), also to evaluate the influence of thermocycling on load at fracture. Materials and Methods: Master brass die was scanned ,then metal coping was designed and milled from Ceramill Sintron blank to get 60 metal copings, then divided randomly into three groups(20 sample), then veneered with porcelain: VITA, Creation or GC. The marginal gaps were measured before and after porcelain veneering then marginal fit changes was calculated. Fracture resist

Transition metal complexes of Co(II), Ni(II), Cu(II), and Zn(II) with 2-(4-antipyrine azo)-4-nitroaniline derived from 4-aminoantipyrine and 4-nitroaniline were synthesized. Characterization of these compounds has been done on the basis of elemental analysis, electronic data, FT-IR, UV-Vis and 1HNMR, as well as magnetic susceptibility and conductivity measurements. The nature of the complexes formed were studied following the mole ratio and continuous variation methods, Beer's law obeyed over a concentration range (1×10-4 - 3×10-4 M). High molar absorbtivity of the complex solutions were observed. From the analytical data, the stoichiometry of the complexes has been found to be 1:2 (metal:ligand). On the basis of physicochemical data octa

In this research, Mn-doped TiO2 thin films were grown on glass, Si and OIT/glass substrates by R.F magnetron sputtering technique with thicknesses (250 nm) using TiO2:Mn target under Ar gas pressure and power of 100 Watt. Through the results of X-ray diffraction, the prepared thin films are of the polycrystallization type after the process of annealing at 600°C for two hour The average crystalline size were 145.32, 280.97 and 261.23 nm for (TiO2:Mn) thin film on glass, Si and OIT/glass substrates respectively, while the measured surface roughness is between 0.981nm and 1.14 nm. The fabricated (TiO2:Mn) thin film on glass sensors have high sensitivity for hydrogen( H2 reducing gas) compared to the sensitivity for hydrogen gas on Si and OIT/

We present a simple model of charge transfer current through sensitizer N3 molecule contact to TiO2 and ZnO semiconductors to calculate the charge transfer current. The model underlying depends on the fundamental parameters of the charge transfer reaction and it is based on the quantum transition theory approach. A transition energy, driving energy and potential barrier have been taken into account charge transfer current at N3 / TiO2 and N3 / ZnO devices with wide polarity solvents Acetic acid, 2-Methoxyethanol, 1-Butanol, Methyl alcohol, chloroform, N,N-Dimethylacetamide and Ethyl alcohol via the quantum donor-acceptor system.The effects of the transition energy and potential barrier are computed and discussion on charge transfer current.

In this paper, a new third kind Chebyshev wavelets operational matrix of derivative is presented, then the operational matrix of derivative is applied for solving optimal control problems using, third kind Chebyshev wavelets expansions. The proposed method consists of reducing the linear system of optimal control problem into a system of algebraic equations, by expanding the state variables, as a series in terms of third kind Chebyshev wavelets with unknown coefficients. Example to illustrate the effectiveness of the method has been presented.

The influence of pre- shot peening and welding parameters on mechanical and metallurgical properties of dissimilar and similar aluminum alloys AA2024-T3 and AA6061-T6 joints using friction stir welding have been studied. In this work, numbers of plates were equipped from sheet alloys in dimensions (150*50*6) mm then some of them were exposed to shot peening process before friction stir welding using steel ball having diameter 1.25 mm for period of 15 minutes. FSW joints were manufactured from plates at three welding speeds (28, 40, 56 mm/min) and welding speed 40mm/min was chosen at a rotating speed of 1400 rpm for welding the dissimilar pre- shot plates. Tow joints were made at rotational speed of 1000 rpm and welding speed of 40m/min f

A field experiment was conducted during winter season of 2021 at a research station of college of agricultural engineering sciences, university of Baghdad to determine the response of active fertility percentage and seed yield and its components of faba bean (Vicia faba L. cv. Aguadulce) to distance between plants and spraying of nano and traditional boron. A Randomized Complete Block Design according to split-plots arrangement was used at three replicates. The main plots were three distances between plants (25, 35 and 45 cm), while the sub plots including spraying of distilled water only (control treatment), spraying of boron at a 100 mg L-1 and spraying of nano boron at two concentrations (10 and 15 mg L-1). The results showed that the 25