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.

Present study was conducted in order to assess Slabiaat water quality by measuring some physical and chemical factors of river water, the study included a choice of three stations along of Slabiaat River in Samawa city, water samples collected a monthly during the period from September 2013 August 2014. The study involved measuring the Air & water temperatures, pH, Electrical conductivity, Total dissolved solids, Dissolved oxygen, Total hardness, calcium hardness, magnesium, turbidity, and some types of bacteria in River water. The study results showed that the values of air & water temperatures have ranged between (20.1-36.6)?C , (10-21.8) in Slabiaat River, respectively . pH values ranged between (6.6-8.7). Electrical conductivity in

The researchers have recently noticed the interest in the problem of overweight and how to find solutions to it until it is now at the forefront in terms of innovating various and different methods and treatment methods, and the interest in developing health fitness is one of the most important requirements of physical activity for the trainees, which led to the multiplicity of sports activities that promote the health aspect For the individual, in addition to the aesthetic aspect, the problem lies in not adopting training programs according to codified scientific foundations aiming, in addition to reducing weight, to raise the general health level of the trainee participating in fitness institutes, as the trainers do not follow the

The purpose of this paper is to preparing preventive exercises supported by collagen supplements and vitamin D for handball players, and identify the effect of preventive physical exercises supported by collagen supplements and vitamin D on some physical and skill abilities of handball players. The researchers used the experimental method and designed two groups, one experimental and the other control, with both pre- and post-tests, to suit the nature of the research. The research community was selected from handball players (specialized school players), numbering (14), and they were divided into two groups, each group numbering (7) players. One of the most important results reached by the researcher is that: The exercises prepared by the r

The primary aim of this study was to find out the effect of a training program on the development of physical abilities in football goalkeepers. The current study was conducted on goalkeepers of the Academy of Espanyol Sports Club in the premises of Haifa Sports Club Stadium. The study was completed by the researchers within the timeline of May 2021 to August 2021. A total of 7 goalkeepers falling within the age group of 15-17 years were recruited as the sample participants for the study. Out of 7 goalkeepers, 5 goalkeepers were included in the primary experiment and 2 of them were excluded. The training program applied had a positive effect on the development of physical abilities in the football goalkeepers of the sa

This survey investigates the thermal evaporation of Ag2Se on glass substrates at various thermal annealing temperatures (300, 348, 398, and 448) °K. To ascertain the effect of annealing temperature on the structural, surface morphology, and optical properties of Ag2Se films, investigations and research were carried out. The crystal structure of the film was described by Xray diffraction and other methods.The physical structure and characteristics of the Ag2Se thin films were examined using X-ray and atomic force microscopy (AFM) based techniques. The Ag2Se films surface morphology was examined by AFM techniques; the investigation gave average diameter, surface roughness, and grain size mutation values with increasing annealing temperature