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.

The influence of fiber orientation and water absorption on fatigue crack growth resistance for cold cure acrylic (PMMA) reinforced by chopped and woven -glass-fibers were investigated. A weight of 2 g for chopped fibers and the same weight for woven -glass-fibers (one layer) were used to prepare samples. Some of these samples would storage in dry condition; the others were immersed in water for 15 days. Fatigue test was carried out. The results shows that, for PMMA, the initial bending stress for dry specimen was 3.392 N/cm2 and the number of cycles were 1364, the initial bending stress for wet samples was 4.20 N/cm2, and the number of cycles was 2411. The samples would cut in two pieces because of the cracks would propagated fast during

Proxy-based sliding mode control PSMC is an improved version of PID control that combines the features of PID and sliding mode control SMC with continuously dynamic behaviour. However, the stability of the control architecture maybe not well addressed. Consequently, this work is focused on modification of the original version of the proxy-based sliding mode control PSMC by adding an adaptive approximation compensator AAC term for vibration control of an Euler-Bernoulli beam. The role of the AAC term is to compensate for unmodelled dynamics and make the stability proof more easily. The stability of the proposed control algorithm is systematically proved using Lyapunov theory. Multi-modal equation of motion is derived using the Galerkin metho

Soil improvement has developed as a realistic solution for enhancing soil properties so that structures can be constructed to meet project engineering requirements due to the limited availability of construction land in urban centers. The jet grouting method for soil improvement is a novel geotechnical alternative for problematic soils for which conventional foundation designs cannot provide acceptable and lasting solutions. The paper's methodology was based on constructing pile models using a low-pressure injection laboratory setup built and made locally to simulate the operation of field equipment. The setup design was based on previous research that systematically conducted unconfined compression testing (U.C.Ts.). Th

The aim of this research is to develop qualitative workouts based on certain sensory perceptions for the development of offensive basketball abilities and to determine their impact on female pupils. Several findings, based on the au-thor's extensive expertise instructing basketball materials and our closeness to the sample, revealed deficits in some sensory perceptions “in the game of basketball”, which impair the accuracy of passing the ball to the best team-mate. It also affects the pace of dribbling and the difficulty of selecting the op-timal moment and distance to fire. Therefore, the researcher designs qualita-tive activities based on many sensory experiences, including distance, speed, force, and direction shift. In addition, the

In this research, Artificial Neural Networks (ANNs) technique was applied in an attempt to predict the water levels and some of the water quality parameters at Tigris River in Wasit Government for five different sites. These predictions are useful in the planning, management, evaluation of the water resources in the area. Spatial data along a river system or area at different locations in a catchment area usually have missing measurements, hence an accurate prediction. model to fill these missing values is essential.
The selected sites for water quality data prediction were Sewera, Numania , Kut u/s, Kut d/s, Garaf observation sites. In these five sites models were built for prediction of the water level and water quality parameters.

The current research discusses “The impact of the critical factors for the transfer of knowledge on opportunities and strategic success ", the attention have been increased on knowledge transfer and strategic success subjects because on being one of the important and contemporary issues, which have a significant impact on the existence of organizations and its future. The research aims to identify the critical factors for knowledge transfer in private high education environment which enables (the college community surveyed) to achieve strategic success, also the research sought to answer questions related to research problem by testing a number of major and minor hypothes in impact, in order to test the hypotheses I used a fiel

A metal mandrel was designed for manufacturing the cathodes of high power electron tube ( Tetrode ) used in broadcasting transmitting tubes type TH558 and CQS200.The cathodes were manufactured in the present work from thoriated tungsten wires ( 2? ThO2- W) with different diameters .These cathodes were carbonized in sequences of processes to determine the carbonization parameters (temperature, pressure, time, current and voltage).Then the carbonized cathodes dimension were accurately measured to determine the deviation due to the high temperature distortion effect at about 1800°C .the distorted cathodes due to the carbonization process was treated when it was subjected inside the vacuum chamber and heat treated again .The carbonized cat

The solution gas-oil ratio is an important measurement in reservoir engineering calculations. The correlations are used when experimental PVT data from particular field are missing. Additional advantages of the correlations are saving of cost and time.
This paper proposes a correlation to calculate the solution gas -oil ratio at pressures below bubble point pressure. It was obtained by multiple linear regression analysis of PVT data collected from many Iraqi fields.
In this study, the solution gas-oil ratio was taken as a function of bubble point pressure, stock tank oil gravity, reservoir pressure, reservoir temperature and relative gas density.
The construction of the new correlation is depending on thirty seven PVT reports th