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.

In this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].

The simulation of passively Q-switching is four non – linear first order differential equations. The optimization of passively Q-switching simulation was carried out using the constrained Rosenbrock technique. The maximization option in this technique was utilized to the fourth equation as an objective function; the parameters, γa, γc and β as were dealt with as decision variables. A FORTRAN program was written to determine the optimum values of the decision variables through the simulation of the four coupled equations, for ruby laser Q–switched by Dy +2: CaF2.For different Dy +2:CaF2 molecules number, the values of decision variables was predicted using our written program. The relaxation time of Dy +2: CaF2, used with ruby was

<span lang="EN-US">The need for robotics systems has become an urgent necessity in various fields, especially in video surveillance and live broadcasting systems. The main goal of this work is to design and implement a rover robotic monitoring system based on raspberry pi 4 model B to control this overall system and display a live video by using a webcam (USB camera) as well as using you only look once algorithm-version five (YOLOv5) to detect, recognize and display objects in real-time. This deep learning algorithm is highly accurate and fast and is implemented by Python, OpenCV, PyTorch codes and the Context Object Detection Task (COCO) 2020 dataset. This robot can move in all directions and in different places especially in

The present study has examined the spatiotemporal varieties of the demographics of the Shatt Al-Arab River fishes and their relation to some ecological components. The aim is to forecast these groups in the unexplored parts of the waterway with an emphasis on environmental indices of diversity. Three sites in the river were selected as an observation and study of these species, which lasted from March 2019 to February 2020, the study dealt with factors affecting fishes, as Water Temperature (WT), Dissolved Oxygen (DO), Potential Hydrogen Ion (pH), Salinity (Sal), and Transparency (Tra). Gill nets, cast nets, hooks, and hand nets were adopted to collecting fish. The results indicated that the fish population comprises 60 species represent

  The paper reports the influence of the thickness on the some optical properties of Fe2O3 thin films,which were prepared by chemical Spray  pyrolysis technique on glass substrate heated to 400Ëšc.The thickness of thin films (250,280,350)nm were measured by using weighting method. The optical properties include the absorbance and reflectance spectra,extinction coefficient,and real and imaginary part of the dielectric constant.The result  showed that the optical constant(k,εr,εi)decreased with the increase of the thickness.