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.

Biologically active natural compounds are molecules produced by plants or plant-related microbes, such as endophytes. Many of these metabolites have a wide range of antimicrobial activities and other pharmaceutical properties. This study aimed to evaluate (in vitro) the antifungal activities of the secondary metabolites obtained from Paecilomyces sp. against the pathogenic fungus Rhizoctonia solani. The endophytic fungus Paecilomyces was isolated from Moringa oleifera leaves and cultured on potato dextrose broth for the production of the fungal metabolites. The activity of Paecilomyces filtrate against the radial growth of Rhizoctonia solani was tested by mixing the filtrate with potato dextrose agar medium at concentrations of 15%,

Effect of [Cu/In] ratio on the optical properties of CuInS2 thin films prepared by chemical spray pyrolysis on glass slides at 300oC was studied. The optical characteristics of the prepared thin films have been investigated using UV-VIS spectrophotometer in the wavelength range (300-1100 nm). The films have a direct allow electronic transition with optical energy gap (Eg) decreased from 1.51 eV to 1.30 eV with increasing of [Cu/In] ratio and as well as we notice that films have different behavior when annealed the films in the temperature 100oC (1h,2h), 200oC (1h,2h) for [Cu/In]=1.4 . Also the extinction coefficient (k), refractive index (n) and the real and imaginary dielectric constants (ε1, ε2) have been investigated

Purpose: clarify the integrative relationship of strategic leadership skills and effective management and the role of those skills combined or individually in achieving effective management.

Research design: The researchers used the quantitative method by surveying a class sample from the heads of the executive departments in a group of Iraqi private banks, consisting of (106) individuals according to the (VUCA Prime) methodology for effective management and the ten skills model for Johansen. The questionnaire was analyzed using a model of the structural equation.

Findings: The most prominent results of the research were the presence of a weak ro

The present study aimed at identifying the effectiveness of Macaton method in improving some sensory and cognitive skills in autistic children. In order to achieve the aims of the study, the researcher used the experimental method. The present study sample was (10) children whose ages ranged between (7-10) years and were diagnosed medically with autism disorder. The researcher randomly selected the sample and divided it into two groups: the first group consisted of (5) children representing the experimental group, and (5) children representing the control group after extracting the equivalence between the two groups in terms of age, intelligence, economic and social level and the degree of communication. The program was implemented for t

In this study, silver nanoparticles (AgNPs) were synthesized using a cold plasma technique and a plasma jet. They were then used to explore how photothermal treatment may be used to treat lung cancer (A549) and normal cells (REF) <i>in vitro</i>. The anti-proliferative activity of these nanoparticles was studied after A549 cells were treated with (AgNPs) at various concentrations (100&#37;, 50&#37;, or 25&#37;) and exposure times (6 or 8 min) of laser after 1 h or 24 h from exposed AgNPs. The highest growth inhibition for cancer cells is (75&#37;) at (AgNPs) concentration (100&#37;) and the period of exposure to the laser is (8 min). Particle size for the prepared samples varied according to the diameter o

      In this paper, the researcher suggested using the Genetic algorithm method to estimate the parameters of the Wiener degradation process,  where it is based on the Wiener process in order to estimate the reliability of high-efficiency products, due to the difficulty of estimating the reliability of them using traditional techniques that depend only on the failure times of products. Monte Carlo simulation has been applied for the purpose of proving the efficiency of the proposed method in estimating parameters; it was compared with the method of the maximum likelihood estimation. The results were that the Genetic algorithm method is the best based on the AMSE comparison criterion, then the reliab

This research is concerned with the study of the projective plane over a finite field . The main purpose is finding partitions of the projective line PG( ) and the projective plane PG( ) , in addition to embedding PG(1, ) into PG( ) and PG( ) into PG( ). Clearly, the orbits of PG( ) are found, along with the cross-ratio for each orbit. As for PG( ), 13 partitions were found on PG( ) each partition being classified in terms of the degree of its arc, length, its own code, as well as its error correcting. The last main aim is to classify the group actions on PG( ).