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 present study deals with the effect of self -observation on EFL University students` achievement in conversation classes. The process of self-observation helps the teacher to understand one’s own actions and the reactions in the process of teaching. The sample of this study is EFL students in the third stage at the Department of English Language, morning studies, College of Education /Ibn-Rushd .The sample of the study consists of (84) students distributed on experimental group(A) includes (42) students, and (42) students as control group(B). In order to achieve the aim of the study ,and to gain a closer idea about the impact of reflective teaching technique(self-observation) on the students achievement in conversation classes, a chec

The aim of this study is to identify the effect of enabling the effectiveness of the work of the audit committees in private commercial banks and to identify the extent of awareness of the importance of empowerment in the work of these committees, especially as it is known that these committees, especially the inspection committees that go to private banks and from various sources including committees of the Central Bank of Iraq Committees of the Securities Commission and finally committees of the external audit offices, through an analysis of the determinants of empowerment in the performance of the most important work of the audit committees, namely: supervising the process of preparing reports, supervising the system of intern

SUMMARY. – Absorption, flourescence, quantum yield and lifetime of rhodamine B in chloroform, methanol and dimethyl sulfoxide were measured. A comparison was done of these quantities with those for solid solutions, which are obtained by mixing constant volume proportions of dye at a concentration of 1×10–4M/l with different volume proportions from the concentrated solution of polymer in chloroform and dimethyl sulfoxide. The results showed that the addition of polymer to liquid concentrated solutions (1×10–4M/l) of rhodamine B dye from expecting, which leads to development of active medium for laser dye at high concentration, increase the spectra shift toward high energies, and the luminescence quantum yield but decreasing radiative

This paper aims to study the fractional differential systems arising in warm plasma, which exhibits traveling wave-type solutions. Time-fractional Korteweg-De Vries (KdV) and time-fractional Kawahara equations are used to analyze cold collision-free plasma, which exhibits magnet-acoustic waves and shock wave formation respectively. The decomposition method is used to solve the proposed equations. Also, the convergence and uniqueness of the obtained solution are discussed. To illuminate the effectiveness of the presented method, the solutions of these equations are obtained and compared with the exact solution. Furthermore, solutions are obtained for different values of time-fractional order and represented graphically.

Polyhydroxyalkanoates (PHAs) have gained much attention as biodegradable polymers, many efforts are being made to minimize the cost of PHAs by finding cheap carbon source depending on the type of microorganism and fermentation conditions. The aims of this study were to evaluate the effects of different glucose concentrations and other important conditions on the PHA production by Bacillus cereus isolated from soil. Polyhydroxyalkanoates PHAs accumulated by soil microorganisms were examined by screening the isolated bacteria using Sudan B Black and Nile Blue staining process. A Gram positive strain was identified using the 16s rRNA gene, deposited in the NCBI GenBank sequence database. Different growth conditions (favorite glucose concentrat

The study aims to identify the colleges women in the USA where he was browsing the Internet for five universities and sixty-two women's college located these colleges in 25 states only three general and other civil 51% supported by the churches and religious associations of various began its founding in Alqrnn eighteenth and continued in the nineteenth and twentieth and to provide an opportunity for women to complete higher education, while most men's colleges opened their doors to the admission of women and turned it on coeducation

The term "semantic exchange" was popularized in Arabic, especially in derivatives, grammatical structures, etc., but it came under different names or terms, including deviation, deviation, transition, displacement, tooth breach, replacement, attention, etc. In the rooting of this term through its study in language and terminology, and among linguists, grammar and others, we have reached a number of results, including The existence of a harmonization between the lexical and idiomatic meaning of the term exchange, and the phenomenon of semantic exchange is a form of expansion in language, and that the first language scientists They had turned to this And studied under Cairo for different names, as noted above.

This study aims to know how and what is the media processing presented by the television talk shows for the religious extremism topics in terms of topics, hosted personalities, and ways to address this global phenomenon.

The study is based on descriptive research, and the researcher used the analytical-survey method, analyzing the episodes of (Awkar Al Dhalam) T.V Show which was presented on Al-Iraqiya News Channel, and (Islam Hur) T.V Show which was presented on Al-Hurra in 2019 with 25 episodes from each Show, The sample and research community was chosen with the intent to cover the research problem and its

The study reached several conclusions, including:

• The various dialogs in the episo