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.
Abstract: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
Background: 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 MoreThe 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
... Show MoreDespite the antiplaque effect of mouth-rinsing with a combination composed of miswak (Salvadora persica L.) and green tea (Camellia sinensis var. assamica) extracts, no data are available regarding its effect on gingival tissue at the molecular level. This pilot study aimed to assess the effect of oral rinsing with this combination on gingival crevicular fluid (GCF) flow and IL-1β levels. Ten subjects rinsed with either the combination, 0.12% chlorhexidine gluconate (CHX) or distilled water without toothbrushing for 4 days after receiving baseline polishing. GCF IL-1β concentration, influx, resting volume and plaque quantity were measured at baseline and after 4 days for each intervention. No significant differences in GCF flow or
... Show MoreABSTRACT : This research involves the synthesis of five to seven heterocyclic compounds starting with Schiff’s bases which derived from oxime as a starting material. 1.3-oxazepine derivatives were prepared from adding different anhydrides to the Schiff bases, tetrazole and thiazolidinone derivatives synthesized from add sodium azide and thioglycolic acid to the same Schiff’s bases as a five members ring. Pyrimidine derivatives were prepared after the reaction of the azomethine group with acetyl chloride and then urea and thiourea to synthesis on derivatives contain the six members ring. Another step included identified and confirmed these compounds by FT- IR, 1HNMR, TLC and 13CNMR finally, step included the assay of biological activity
... Show MoreThis study focuses on studying an oscillation of a second-order delay differential equation. Start work, the equation is introduced here with adequate provisions. All the previous is braced by theorems and examplesthat interpret the applicability and the firmness of the acquired provisions