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.

Academic achievement is a professional standard for measuring student levels in the first stages. Therefore, any indication of the level of achievement makes us in an attempt to employ students in evening schools. The researcher has developed a closed questionnaire of (36) paragraphs. A total of (164) male and (24) female students were chosen from evening schools. The result of this research revealed that the number of students was a reason for the low level of their achievement, the lack of laboratories, educational methods, and techniques of the most prominent problems confirmed by students in these schools. In addition, to support educational institutions with their necessary needs. The most important conclusion in this research is th

Molar conductivity of different concentrations of thymine and adenosine in water , sodium acetate and ammonium chloride solution at different temperatures , 283. 15-323.15 K has been determined from direct conductivity measurements , examination of aqueous mixture of thymine and adenosine with Onsager equation reveal deviation from linearity at high concentration .This deviation was explained in term of molecular interaction . Ostwald dilution law also examined with the above mixtures lead to calculation of limiting molar conductivities and dissociation constants of both nucleic acid in water , sodium acetate and ammonium chloride. The agreement between the values obtained for Onsager equa

     In this research, silver nanoparticles (AgNPs) were manufactured using aqueous extract of mushroom Pleurotus ostreatus. Anticancer potential of AgNPs was investigated versus human breast cancer cell line (MCF-7). Cytotoxic response was assessed by MTT assay. AgNPs showed inhibition effect at the following concentrations 12.5, 25, 50, 100 and 200 µg/ml versus MCF-7 cell line, and all treatments had a positive result. The MCF-7 cells were inhibited up to 85.14 % at the concentration 200 μg/ml of AgNPs which reduced cells viability to 14.86%, while 12.5 μg/ml of AgNPs caused 24.23% cells inhibition with reduction of cells viability to 75.77%.

This research overcomes traditional training methodologies, which struggle to incorporate multidirectional movement patterns representative most game-play scenarios. We used a controlled experimental design (n = 24) with subjects presented in an experimental group, which underwent a structured agility and reaction-based training program, and a control group, which continued with conventional basketball training programs. Motor response speed, defensive movement efficiency, and agility were all measured using standardized physical performance tests and compared before and after an eight-week training period. All three-performance metrics for the experimental group showed statistically significant improvement as further evidence for

The federal state is usually based on a number of regions because it is based on the multiplicity of political entities. The federal experiments were based on the existence of two or more regions and each federal system has its own peculiarities. Administrative authority between the federal government and local elected bodies of local people of absolute relative independence does not threaten the entity of the state according to the Constitution and the law and on a regional or reformer basis and exercise its powers within the legal scope prescribed The relationship between the federal authority and the Kurdistan region is the first level of the relationship on the real level, especially since no other region in Iraq has been formed exce

Big data analysis is essential for modern applications in areas such as healthcare, assistive technology, intelligent transportation, environment and climate monitoring. Traditional algorithms in data mining and machine learning do not scale well with data size. Mining and learning from big data need time and memory efficient techniques, albeit the cost of possible loss in accuracy. We have developed a data aggregation structure to summarize data with large number of instances and data generated from multiple data sources. Data are aggregated at multiple resolutions and resolution provides a trade-off between efficiency and accuracy. The structure is built once, updated incrementally, and serves as a common data input for multiple mining an