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 work aims to study forward osmosis process using different kinds of draw solutions and membranes. Three types of draw solutions (sodium chloride, sodium formate, and sodium acetate) were used in forward osmosis process to evaluate their effectiveness with respect to water flux and reverse salt flux. Experiments conducted in a laboratory-scale forward osmosis (FO) unit in cross flow flat sheet membrane cell. Three types of membranes (Thin film composite (TFC), Cellulose acetate (CA), and Cellulose triacetate (CTA)) were used to determine the water flux under osmotic pressure as a driving force. The effect of temperature, draw solution concentration, feed and draw solution flow rate, and membrane types, were studied with
... Show MoreAn efficient combination of Adomian Decomposition iterative technique coupled Elzaki transformation (ETADM) for solving Telegraph equation and Riccati non-linear differential equation (RNDE) is introduced in a novel way to get an accurate analytical solution. An elegant combination of the Elzaki transform, the series expansion method, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has
... Show MorePMMA (Poly methyl methacrylate) is considered one of the most commonly used materials in denture base fabrication due to its ideal properties. Although, a major problem with this resin is the frequent fractures due to heavy chewing forces which lead to early crack and fracture in clinical use. The addition of nanoparticles as filler performed in this study to enhance its selected mechanical properties. The Nano-additive effect investigated in normal circumstances and under a different temperature during water exposure. First, tests applied on the prepared samples at room temperature and then after exposure to water bath at (20, 40, 60) C° respectively. SEM, PSD, EDX were utilized for samples evaluation in this study. Flexural
... Show MoreBackground: Tooth decay is still one of most common diseases of childhood, child’s primary teeth are important even though they aretemporary. This study was conducted to assess the physiochemical characteristic of saliva among caries experience preschool children and compared them with caries free matching in age and gender. Then an evaluation was done about these salivary characteristics to dental caries and evaluated the relation of body mass index to dental caries and to salivary variables. Materials and method: After examination 360 children aged 4-5 years of both gender. Caries-experiences was recorded according to dmfs index by (World Health Organization criteria 1987) during pilot study children with caries experience was di
... Show MoreAbstract:In this paper, some probability characteristics functions (moments, variances,convariance, and spectral density functions) are found depending upon the smallestvariance of the solution of some stochastic Fredholm integral equation contains as aknown function, the sine wave function
The interactions of drug amoxicillin with maltose or galactose solutions with a variation of temperature have been discussed by taking in the volumetric and viscometric procedures. Physical properties [densities (ρ) and viscosities (η)] of amoxicillin (AMOX) aqueous solutions and aqueous solutions of two type saccharides (maltose and galactose 0.05m) have been measured at T = (298.15, 303.15 and 308.15) K under atmospheric pressure. The apparent molar volume (ϕv cm3mole-1) has been evaluated from density data and fitted to a Redlich-Mayer equation. The empirical parameters of the Mayer-Redlich equation and apparent molar volume at infinite dilution ذv were explicated in terms of interactions from type solute-solvent and solute
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