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.

This paper aims to find new analytical closed-forms to the  solutions of the nonhomogeneous functional differential equations of the n^th order with finite and constants delays and various initial delay conditions in terms of elementary functions using Laplace transform method. As well as, the definition of dynamical systems for ordinary differential equations is used to introduce the definition of dynamical systems for delay differential equations which contain multiple delays with a discussion of their dynamical properties: The exponential stability and strong stability

In this work, a local sunflower husk (SFH) was used as a natural surface for removing Basic Green-4 (BG4) dye, as a watersoluble pollutant. The effect of initial concentration, contact time, the mass of surface of the dye with the SFH as well as the medium temperature was studied. The application of Langmuir, Freundlich isotherms on the collected data of the adsorption process found to harmonize to Freundlich equation more than that of Langmuir. However, the adsorbed mass of BG4 dye showed a direct increase with the increase of SFH mass and equilibrium was achieved within a 60min window. The interaction of BG4 with SFH surface was spontaneous and exothermic. The empirical kinetic outcomes at ambient temperatures were applied to pseudo 1st a

In this study, the photodegradation of Congo red dye (CR) in aqueous solution was investigated using Au-Pd/TiO₂ as photocatalyst. The concentration of dye, dosage of photocatalyst, amount of H₂O₂, pH of the medium and temperature were examined to find the optimum values of these parameters. It has been found that 28 ppm was the best dye concentration. The optimum amount of photocatalyst was 0.09 g/75 mL of dye solution when the degradation percent was ~ 96 % after irradiation time of 12 hours, while the best amount of hydrogen peroxide was 7μl/75 mL of dye solution at degradation percent ~97 % after irradiation time of 10 hours, whereas pH 5 was the best value to carry out the reaction at the highest deg

For this research, the utilisation of electrocoagulation (EC) toremove theciprofloxacin (CIP) and levofloxacin (LVX) from aqueous solutions was examined. The effective removal efficiencies are 93.47% for CIP and 88.00% for LVX, under optimum conditions. The adsorption isotherm models with suitable mechanisms were applied to determine the elimination of CIP and LVX utilizingtheEC method. Thefindingsshowed the adsorption of CIP and LVX on iron hydroxide flocs followed the Sips isotherm, with correlation coefficient values (R2) of 0.939 and 0.937. Threekinetic models were reviewed to determine the accurate CIP and LVX elimination methods using the EC method. The results showed that itfittedfor the second-order model, which indicated that the c

There is no doubt that Agricultural Policy is the main responsible for the degrading in Agricultural sector in Iraq during the period 2003-2013, and that was very clear from magnitude of indicators because of little sharing of each of agricultural product in GDP because it was (9.38%) in average during the study period and the annual changing of it was negative (-5.82%), and there is increasing in deficit of trade balance in Agriculture during the study period about (4185.73) million US$, and the percentage of agricultural exports from total exports was (0.14%) in average only. The foreign trade policy in Agricultural products also cannot determine map of Revealed Comparative Advantage (RCA) of Agricultural products and crops. The study sh

Abstract

This study cares for the economic living conditions in Mosul City. Its importance lies in the critical period that has been covered
(2002-2007), which was dominated by far–reaching events at political economic and social levels. Among the main results that have been revealed are the following: the rate of economic growth in the City has been the lowest among major urban centers in Iraq. Besides, real income per capita in the City has stayed stagnant during the period of the study. However, the inequality in distribution of income has decreased. The main bulk of the city's population rely on their income from wages and salari