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.

Researches in the field of evaluation of industrial products emotionally are internationally new and non-existing in the Arabic speaking countries, which is considered the crux of the problem in the current research, in addition to the need of the designers and design students to know how to measure the emotional responses for the industrial product in order to get benefit from them in their designs. The research objective is to get a tool that uses emojis in measuring the emotional responses for the products. The researcher designed an emotional verbal wheel and emojis wheel. The sample of the research consisted of (7) chairs different in design and use, and the respondents were (89) students. The most important results are:
1- Desi

Market share is a major indication of business success. Understanding the impact of numerous economic factors on market share is critical to a company’s success. In this study, we examine the market shares of two manufacturers in a duopoly economy and present an optimal pricing approach for increasing a company’s market share. We create two numerical models based on ordinary differential equations to investigate market success. The first model takes into account quantity demand and investment in R&D, whereas the second model investigates a more realistic relationship between quantity demand and pricing.

In this paper Hermite interpolation method is used for solving linear and non-linear second order singular multi point boundary value problems with nonlocal condition. The approximate solution is found in the form of a rapidly convergent polynomial. We discuss behavior of the solution in the neighborhood of the singularity point which appears to perform satisfactorily for singular problems. The examples to demonstrate the applicability and efficiency of the method have been given.

This study is dedicated to solving multicollinearity problem for the general linear model by using Ridge regression method. The basic formulation of this method and suggested forms for Ridge parameter is applied to the Gross Domestic Product data in Iraq. This data has normal distribution. The best linear regression model is obtained after solving multicollinearity problem with the suggesting of 10 k value.

Fiber-to-the-Home (FTTH) has long been recognized as a technology that provides future proof bandwidth [1], but has generally been too expensive to implement on a wide scale. However, reductions in the cost of electro-optic components and improvements in the handling of fiber optics now make FTTH a cost effective solution in many situations. The transition to FTTH in the access network is also a benefit for both consumers and service providers because it opens up the near limitless capacity of the core long-haul network to the local user. In this paper individual passive optical components, transceivers, and fibers has been put together to form a complete FTTH network. Then the implementation of the under construction Baghdad/Al

     One technique used to prepare nanoparticles material is Pulsed Laser Ablation in Liquid (PLAL), Silver Oxide nanoparticles (AgO) were prepared by using  this technique, where silver target was submerged in ultra-pure water (UPW)  at room temperature after that Nd:Yag laser which characteristics by 1064 nm wavelength, Q-switched, and 6ns pulse duration was used to irradiated silver target. This preparation method was used to study the effects of laser irradiation on Nanoparticles synthesized by used varying laser pulse energy 1000 mJ, 500 mJ, and 100 mJ, with 500 pulses each time on the particle size. Nanoparticles are characterized using XRD, SEM, AFM, and UV-Visible spectroscopy. All the structural peaks determined by the XRD