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 field trial was conducted at Abu-Ghraib research station , Baghdad , Iraq . The objectives were to study the effect of nitrogen fertilizer and planting space on the performance of rape seed. A split-plot in a randomized complete of block design with three replications were used. Five levels of nitrogen fertilizer ( 120,160,200,240,280 Kg / ha ) were assigned to main plots, where as planting space in sub-plots. The result obtained confirmed that 280,240 kg / ha nitrogen maximized seed yield 1.830 , 1.773 ton/ha, oil yield,0.843,0.824 ton/ha .Results showed that planting space 30 cm produced the highest seed yield 1.90 ton / ha and oil yield , 0.884 ton / ha . Interactions between nitrogen fertilizer and p

A field trial was conducted at Abu-Ghraib research station , Baghdad , Iraq , during the autumn season of 2006. The objectives were to study the effect of nitrogen fertilizer and planting space on the performance of rape seed. A split-plot in a randomized complete of block design with three replications were used. Five levels of nitrogen fertilizer ( 120,160,200,240,280 Kg / ha ) were assigned to main plots, where as planting space in sub-plots. The result obtained confirmed that 280,240 kg / ha nitrogen maximized seed yield 1.830 , 1.773 ton/ha, oil yield,0.843,0.824 ton/ha .Results showed that planting space 30 cm produced the highest seed yield 1.90 ton / ha and oil yield , 0.884 ton / ha . Interactions be

The determiner phrase is a syntactic category that appears inside the noun phrase and makes it definite or indefinite or quantifies it. The present study has found wide parametric differences between the English and Arabic determiner phrases in terms of the inflectional features, the syntactic distribution of determiners and the word order of the determiner phrase itself. In English, the determiner phrase generally precedes the head noun or its premodifying adjectival phrase, with very few exceptions where some determiners may appear after the head noun. In Arabic, parts of the determiner phrase precede the head noun and parts of it must appear after the head noun or after its postmodifying adjectival phrase creating a discontinu

The present paper investigates the role of fear and predator dependent refuge in the prey-predator system. The system describes the interaction between prey and a stage structure of predator that incorporates Holling II functional response. The predator splits into two compartments immature (juvenile) and mature (adult). The mature predators can hunt and reproduce but this capability is not found in the immature predators, the immature depend on their parents. The growth rate of prey decreases due to the existence of mature predators. The existence, uniqueness, and boundedness of the solution of the system are investigated. Three equilibrium points of the system are determined. The local stability of the system is studied. The global stabil

     The ground state density distributions and electron scattering Coulomb form factors of Helium (4,6,8He) and Phosphorate (27,31P) isotopes are investigated in the framework of nuclear shell model. For stable (4He) and (31P) nuclei, the core and valence parts are studied through Harmonic-oscillator (HO) and Hulthen potentials. Correspondingly, for exotic (6,8He) and (27P) nuclei, the HO potential is applied to the core parts only, while the Hulthen potential is applied to valence parts. The parameters for HO and Hulthen are chosen to reproduce the available experimental size radii for all nuclei under study. Finally, the CO component of electron scattering charge form factors are also investigated. Unfortunately, there is no

This study presents determination of the paleostress magnitudes and orientation of Bekhme Structure in Shaqlawa area northeastern Iraq. Paleostress Analysis of slip-fault measurements is performed using Right dihedral, Lisle diagram and Mohr Circles methods. Depending on Mohr Circles, Bott law and vertical thickness, the magnitudes of the paleostress at the time of the tectonic activity were determined. Firstly, Georient Software was used to estimate the orientation of the paleostresses (σ1, σ2 and σ3). Secondly, using the rupture –friction law, taking into account depth of the overburden and the vertical stress (σv) was calculated to determine the magnitude of the paleostresses (σ1=4500 bars, σ2=1

This paper proposes a compact, plasmonic-based 4 × 4 nonblocking switch for optical networks. This device uses six 2 × 2 plasmonic Mach-Zehnder switch (MZS), whose arm waveguide is supported by a JRD1 polymer layer as a high electro-optic coefficient material. The 4 × 4 switch is designed in COMSOL environment for 1550 nm wavelength operation. The performance of the proposed switch outperforms those of conventional (nonplasmonic) counterparts. The designed switch yields a compact structure ( 500 × 70   µ m 2 ) having V π L = 12   V · µ m , 1.5 THz optical bandwidth, 7.7 dB insertion loss, and −26.5 dB crosstalk. The capability of the switch to route 8 × 40 Gbps WDM signal is demonstrated successfully.

In our article, three iterative methods are performed to solve the nonlinear differential equations that represent the straight and radial fins affected by thermal conductivity. The iterative methods are the Daftardar-Jafari method namely (DJM), Temimi-Ansari method namely (TAM) and Banach contraction method namely (BCM) to get the approximate solutions. For comparison purposes, the numerical solutions were further achieved by using the fourth Runge-Kutta (RK4) method, Euler method and previous analytical methods that available in the literature. Moreover, the convergence of the proposed methods was discussed and proved. In addition, the maximum error remainder values are also evaluated which indicates that the propo