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.

In this study Candida speices was diagnosed in 26 swab samples from patients with denture stomatitis , investigates the antagonism activity of Lactobacillus was investigated against the yeast of Candida albicans in vitro.Results revealed that The inhibition effect of Lactic Acid Bacteria against C.albicans was examined in solid medium, L.plantarum gave higher inhibition average 11mm followed by L.acidophillus with average 9 mm and, L.fermentum , L.casei with averages 7 mm. Whereas the filtrates, the highest inhibition zone were 20 and 16 mm by L. plantarum and L.acidophillus, respectively.

Many consumers of electric power have excesses in their electric power consumptions that exceed the permissible limit by the electrical power distribution stations, and then we proposed a validation approach that works intelligently by applying machine learning (ML) technology to teach electrical consumers how to properly consume without wasting energy expended. The validation approach is one of a large combination of intelligent processes related to energy consumption which is called the efficient energy consumption management (EECM) approaches, and it connected with the internet of things (IoT) technology to be linked to Google Firebase Cloud where a utility center used to check whether the consumption of the efficient energy is s

The molluscicidal effects of herbicide 2, 4-D were studied against tow species of freshwater snail Bulinus truncatus and Melanopsis nodosa by short term experiments. Calculated values of lethal concentrations (LC50 and LC100) were maid to two spices for different period of time 24hr, 48hr, 72hr and 96hr. The study had showed that the herbicide 2, 4-D was toxic against the tow species. The toxicity of the herbicide was low or unknown in low concentrations in the first period of exposure 24and 48hr to two spices but it increase gradually with increase period of exposure. The spice of B.truncatus was more tolerant than the M.nodosa. All the individual of M nodosa was death while in B.truncatus the complete death was not appear until finish the

Background: This study was performed to compare the marginal fit changes and facture resistance of metal ceramic crowns constructed from Ceramill Sintron metal coping veneered with three different porcelain veneering materials (Vita Master Koromikos VMK, Willi Geller Creation CC and GC initial MC), also to evaluate the influence of thermocycling on load at fracture. Materials and Methods: Master brass die was scanned ,then metal coping was designed and milled from Ceramill Sintron blank to get 60 metal copings, then divided randomly into three groups(20 sample), then veneered with porcelain: VITA, Creation or GC. The marginal gaps were measured before and after porcelain veneering then marginal fit changes was calculated. Fracture resist

In this research, Mn-doped TiO2 thin films were grown on glass, Si and OIT/glass substrates by R.F magnetron sputtering technique with thicknesses (250 nm) using TiO2:Mn target under Ar gas pressure and power of 100 Watt. Through the results of X-ray diffraction, the prepared thin films are of the polycrystallization type after the process of annealing at 600°C for two hour The average crystalline size were 145.32, 280.97 and 261.23 nm for (TiO2:Mn) thin film on glass, Si and OIT/glass substrates respectively, while the measured surface roughness is between 0.981nm and 1.14 nm. The fabricated (TiO2:Mn) thin film on glass sensors have high sensitivity for hydrogen( H2 reducing gas) compared to the sensitivity for hydrogen gas on Si and OIT/

 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:

We present a simple model of charge transfer current through sensitizer N3 molecule contact to TiO2 and ZnO semiconductors to calculate the charge transfer current. The model underlying depends on the fundamental parameters of the charge transfer reaction and it is based on the quantum transition theory approach. A transition energy, driving energy and potential barrier have been taken into account charge transfer current at N3 / TiO2 and N3 / ZnO devices with wide polarity solvents Acetic acid, 2-Methoxyethanol, 1-Butanol, Methyl alcohol, chloroform, N,N-Dimethylacetamide and Ethyl alcohol via the quantum donor-acceptor system.The effects of the transition energy and potential barrier are computed and discussion on charge transfer current.

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.

This study presented an endeavour to integrate the value chain activities with the Balanced Scorecard for a comprehensive evaluation of an organization’s strategic performance. It also demonstrated the connection and the integration of the activities of the value chain with the Balanced Scorecard. The financial measurement was linked with non-financial measurement by integrating these techniques to achieve an appropriate performance that supports all aspects of the organizational performance. Consequently, the research problem in this study emerged, which is due to the concentration of many organizations on the measurement of financial performance. Notably, the latter caused the decline of some organizations from the competitive market. T