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.

 Summary

    I wanted to address this topic because of creedal purposes importance,and its r le in regulating lives of individuals and society, and to talk about purposes of Almighty's saying:{It is easy for me},to simplify its meanings for general educated person to obtain the believe of the Creator’s power and his oneness.

Therefore,this research came,whichincludes:an introduction and topics, first :concept of creedal objectives and their divisions,second: creedal purposes in Almighty’s saying:{It is easy for me},and conclusion:in where most important results were included:

In this paper, a new third kind Chebyshev wavelets operational matrix of derivative is presented, then the operational matrix of derivative is applied for solving optimal control problems using, third kind Chebyshev wavelets expansions. The proposed method consists of reducing the linear system of optimal control problem into a system of algebraic equations, by expanding the state variables, as a series in terms of third kind Chebyshev wavelets with unknown coefficients. Example to illustrate the effectiveness of the method has been presented.

From a large number of bacterial samples collected from different hospital in Iraq in central  health laboratory ,only ten isolates were identified primary as Vibrio. A number of  morphology and biochemical test were carried out to complete this identification that showed all bacterial isolates were related to Vibrio cholerae .In this study  all Vibrio isolates were investigated for Bio typing and the result showed that all (10) isolate were related to (Eltor biotypes) .Also, the susceptibility test towards eight antibiotics were carried  out .

Results shows that  ciprofloxacin , Norfloxacin, Erythromycin, Ampicillin,  ceftriaxone  and Amikacin were the most effective

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

Industrial dyes are major pollutants in wastewater and river water with an initial visible concentration of 1 mg/L. Recent studies have shown the possibility of using polyphenol oxidase in catalytic biological treatment due to its ability to oxidize a large number of dyes and pollutants in wastewater and the flexibility to work in wide ranges of temperature, pH and salinity. It is easy availability as well as the low economic cost resulting from its use in biological treatments, this enzyme polyphenol oxidase was used. The findings in this study showed that the extraction of polyphenol oxidase (PPO) from potato peel was homogenized with potassium phosphate buffer (0.1 M, pH 7) at a ratio of 1:10 (weight: volume) for two min. The res

      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

A rapid and sensitive method for analysis of amino acid hydrolysates of nigella sativa L seed has been developed using O-phthaldialehyde(OPA ) as a pre-column derivatizing agent. OPA reagents in the presence of mercaptoethanol react rapidly with primary amino acids ( less than 60 sec.) to form isindole derivatives which easily separated with good selectivity on ODS column. Resolution of amino acid derivatives is carried out with a methanol gradient in 0.01 maqueous sodium acetate. pH 7.1 . The quantitation of amino acid derivatives is reproducible within an average relative deviation of + 1.4% the linearity for most amino acids were more than 0.9993 with detection limit of 0.2 ppm. 15 amino acid were detected in the analysis of

Ten isolates of Klebsiella pneumoniae, seven isolates of Pseudomonas aeruginosa and nine isolates of Staphylococcus aureus, were obtained from 100 urine samples collected from Baghdad hospitals. All isolates were identified biochemically and confirmed by using VITEK 2 and were then tested for their susceptibility towards 6 antibiotics and for phenolic extracts of Thymus vulgaris and Cinnamomum cassia. All bacteria were greatly affected by T. vulgaris, especially K. pneumoniae. Viable count was performed, it was noted that the number of bacterial cells reduced from 1×108 CFU to 1.2× 103, 2×105 and 1.8×106CFU of K. pneumoniae, P. aeruginosa and S. aureus respectively. While C. cassiahad a slight effect on them. K. pneumoniae isola

Films of pure Poly (methyl methacrylate) (PMMA) doped by potassium iodide (KI) salt with percentages (1%) at different thickness prepared by casting method at room temperature. In order to study the effect of increasing thickness on optical properties, transmission and absorption spectra have been record for five different thicknesses(80,140,210,250,320)µm. The study has been extended to include the changes in the band gap energies, refractive index, extinction coefficient and absorption coefficient with thickness.