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

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

In this work the interaction of plasma jet with water and hydrogen peroxide liquids used for assisted teeth bleaching by plasma jet had been study. A homemade plasma jet system was used. The plasma jet supply by 15 W electrical power generated by high voltage power supply of 9.6 kV peak to peak and frequency of 33 kHz .this power supply generate high electric field on electrodes that would be enough to ionize the argon gas. Some important agents were study such as the effect of the Ar gas flow rates on the length of the plasma jet, the influence of plasma jet on some properties of water and two hydrogen peroxide concentrations 25 % and 30 % like pH, conductivity and liquid temperature for different exposure time. The liquids temperature

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

Idiomatic expressions in Russian journalism make one important borrowed means for making a dialogue with the receiver's intellect in so far as it has the distinct feature of  having clarity and exactness of meaning. The meaning is seen as a shortcut for covering a series of concepts and details so as to arrive at the intended meaning. This is done by stimulating the reader by the use of certain clear idioms. The use of such idioms in a journalistic text is not for a linguistic purpose only, but it is a cultural and social phenomenon reflecting the type of current changes in the society and it aims at discoursing with the reader's mind. This paper is a practi

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

Heuristic approaches are traditionally applied to find the optimal size and optimal location of Flexible AC Transmission Systems (FACTS) devices in power systems. Genetic Algorithm (GA) technique has been applied to solve power engineering optimization problems giving better results than classical methods. This paper shows the application of GA for optimal sizing and allocation of a Static Compensator (STATCOM) in a power system. STATCOM devices used to increase transmission systems capacity and enhance voltage stability by regulate the voltages at its terminal by controlling the amount of reactive power injected into or absorbed from the power system. IEEE 5-bus standard system is used as an example to illustrate the te