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.

     This work includes the synthesis of new ester compounds containing two 1,3,4-oxadiazole rings, 15a-c and 16a-c. This was done over seven steps, starting with p-acetamido-phenol 1 and 2-mercaptobenzoimidazole 2. The structure of the products was determined using FT-IR, 1H NMR, and mass spectroscopy. The evaluation of the antimicrobial activities of some prepared compounds was achieved against four types of bacteria (two types of gram-positive bacteria; Staphylococcus aureus and Bacillus subtilis, and two types of gram-negative bacteria, Pseudomonas aeruginosa and E. Coli), as well as against one types of fungus (C. albino). The results show moderate activit against the study bacteria, and the theoretical analysis of the toxi

Indexes of topological play a crucial role in mathematical chemistry and network theory, providing valuable insights into the structural properties of graphs. In this study, we investigate the Resize graph of G2(3), a significant algebraic structure arising from the exceptional Lie group (G2) over the finite field F3. We compute several well-known topological indices, including the Zagreb indices, Wiener index, and Randić index, to analyze the graph's connectivity and complexity. Our results reveal intricate relationships between the algebraic structure of G2(3) and its graphical properties, offering a deeper understanding of its combinatorial and spectral characteristics. These findings contribute to the broader study of algebraic graph t

A successful synthesis of mesoporous Santa Barbara amorphous (SBA-15) with nanoparticle size was attempted using prepared sodium silicate from Iraqi high silica sand. EO20PO70EO20 copolymer was used as a template at highly acidic conditions (pH < 2). The effect of crystallization temperature of (100, 110, 120, and 130 0C), and crystallization time of (24, 48, 72, and 120 h) on surface properties was studied. The experiments were characterized using XRD, FTIR, AFM, BET, and FESEM. The XRD and FTIR tests represent amorphous SBA-15 without any impurities. Decreasing average particle size distribution increased the surface area, and decreased the porosity (pore volume, and pore size) in all experiments. The texture properties were su

The performance analyses of 15 kWp (kW peak) Grid -Tied solar PV system (that considered first of its type) implemented at the Training and Energy Research Center Subsidiary of Iraqi Ministry of Electricity in Baghdad city has been achieved. The system consists of 72 modules arranged in 6 strings were each string contains 12 modules connected in series to increase the voltage output while these strings connected in parallel to increase the current output. According to the observed duration, the reference daily yields, array daily yields and final daily yields of this system were (5.9, 4.56, 4.4) kWh/kWp/day respectively. The energy yield was 1585 kWh/kWp/year while the annual total solar irradiation received by solar array system was 198

A general velocity profile for a laminar flow over a flat plate with zero incidence is obtained by employing a new boundary condition to the other available boundary conditions. The general velocity profile is mathematically simple and nearest to the exact solution. Also other related values, boundary layer thickness, displacement thickness, momentum thickness and coefficient of friction are nearest to the exact solution compared with other corresponding values for other researchers.

A general velocity profile for a laminar flow over a flat plate with zero incidence is obtained by employing a new boundary condition to the other available boundary conditions. The general velocity profile is mathematically simple and nearest to the exact solution. Also other related values, boundary layer thickness, displacement thickness, momentum thickness and coefficient of friction are nearest to the exact solution compared with other corresponding values for other researchers.

The aims of research is to identify the role of strategic human resource management Practices in organizational performance improvement in the Baghdad soft drinks company, as well as the implications of the results for both managers and practitioners.

In order to achieve the objectives of the research, the researcher designed questionnaire included (40) items to collect the initial data from the research sample consisting of (53) Single. In light of that has been collecting and analyzing data and test hypotheses using the statistical package for Social Sciences (SPSS21), and use a number of statistical methods to achieve the goal of the research, including the means, standard deviations and simple correla

     This research aims to shed light on the reality of the process of rehabilitation of human resources for the implementation of electronic management practice in the ministry, and availability requirements of the application of electronic management and diagnosis of the most important stages and steps that can be followed in the process of transition towards electronic management to keep abreast of developments in the field of information technology, has been the application of this research in the Ministry of science and technology on a group of heads of departments and directors of the people in the departments of the Ministry through the use of case study method, which includes cohabitation field intervi