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.

Conservation of Concept among Children: Semantic Study

Worldwide attention is being focused on  nanocrystalline  zeolites  and they are replacing conventional ones due to their pronounced potential in many fields. In this study, NaY zeolite has been prepared hydrothermally using sol –gel method and modified to the proton type by ion –exchange process. Characterization is made using X-ray diffraction (XRD), thermogravimetric analysis (TGA),  Fourier transform infrared spectroscopy (FTIR),  Atomic force microscopy (AFM), Brunauer –Emmet- Teller (BET) nitrogen adsorption method, Ammonia Temperature programmed desorption (NH₃-TPD) and Scanning electron microscopy( SEM).  The effect of aging time, silica to alumina ratio is studied and the results sh

Praise be to Allaah.
My research has included the following: The field of application of semantics when fundamentalists are the book and the Sunnah. Imam Ibn Hajar agreed with the majority of fundamentalists that what is meant from the year (one word denotes one side on two things onwards), and agreed that the significance of the year specific to the rest of its members is not a definite and definite formulas of the public has the singular known as (the) Astragharism, and the plural known as ( The nationality stating that dumping, pluralism is defined as (add), and nakra, if it occurs in the context of the condition, denial and prohibition, the names of the condition, the connected names, and the word (all - all). And the year in whic

Increasing interest in planning at the level of government units as a means to manage the physical and human resources, direct and invest in areas that would include an increase in the economies of the general government units that are part of the general economics of the state.The research problem lies in the introduction of the factors influencing the ongoing expenses that adversely affect the financial planning process at the level of the Ministry of Health Planning, which affects the quality of services provided to citizens, so I sought the researchers to study the reality of financial planning in some of the Ministry of Health and health departments through the analysis of current budgets and diagnose deviations in the implementatio

The variables of quantitative and qualitative Population role in the economic development process and it was said the human center of development and population is the goal of development and its tool , and Iraq suffers from problems in the economic growth and the standard of living and development in general, and if I want him evolution and development sectors must pay for these demographic changes especially , to study and that invest Pmaasb in the interest of the man
The study of the demographic situation in Iraq and at the provincial level to track paths demographic change and its impact on the entry of Iraq to the demographic window due to the change in the age structure of the population and how to use them and invested well in

A new Differential Evolution (ARDE) algorithm is introduced that automatically adapt a repository of DE strategies and parameters adaptation schemes of the mutation factor and the crossover rate to avoid the problems of stagnation and make DE responds to a wide range of function characteristics at different stages of the evolution. ARDE algorithm makes use of JADE strategy and the MDE_pBX parameters adaptive schemes as frameworks. Then a new adaptive procedure called adaptive repository (AR) has been developed to select the appropriate combinations of the JADE strategies and the parameter control schemes of the MDE_pBX to generate the next population based on their fitness values. Experimental results have been presented to confirm the reli