A computational investigation is carried out to describe the behaviour of reflected electrons upon a charged insulator sample and producing mirror effect images. A theoretical expression for the scanning electron path equation is derived concerning Rutherford scattering and some electrostatic aspects. The importance of the derived formula come from its correlation among some of the most important parameters that controls the mirror effect phenomena. These parameters, in fact, are the trapped charges, incident angle and the scanning potential which investigated by considering its influences on the incident electrons. A pervious experimental operation requirements are adopted for operating the introduced expression. However, the obtained r

This work was conducted to study the extraction of eucalyptus oil from natural plants (Eucalyptus camadulensis leaves) by organic solvents. the effects of the main operating parameters were studied; type of solvent (n-hexane and ethanol), time to reach equilibrium, the temperature (45°C to 65°C) for n-hexane and (45°C to 75°C) for ethanol, solvent to solid ratio (5:1 to 8:1 (v/w)), agitation speed (0 to 900 rpm) and the particle size (0.5 to 2.5 cm) of fresh leaves to find the best processing conditions for the achieving maximum oil yield. The concentration of eucalyptus oil in solvent was measured by using UV-spectrophotometer. The results (for n-hexane) showed that the agitation speed of 900 rpm, temperature 65°C with solvent to soli

The interplay of predation, competition between species and harvesting is one of the most critical aspects of the environment. This paper involves exploring the dynamics of four species' interactions. The system includes two competitive prey and two predators; the first prey is preyed on by the first predator, with the former representing an additional food source for the latter. While the second prey is not exposed to predation but rather is exposed to the harvest. The existence of possible equilibria is found. Conditions of local and global stability for the equilibria are derived. To corroborate our findings, we constructed time series to illustrate the existence and the stability of equilibria numerically by varying the different values

In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R³ is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

Mathematical Subject Classificat

Background: Passive smoking and dental caries affect the integrity of the health of individuals and both of them affected by sociodemographic characteristics of those individuals. This research aimed to investigate the severity of dental caries in relation to salivary magnesium and zinc of stimulated whole saliva of a group of 10 years passive smokers in comparison with normal subjects. Materials and methods: the study group included 40 subjects (20boys and 20 girls), with an age of 10 years of passive smokers determined by a questionnaire. The control group included 40 normal subjects of the same gender and age of the study group. The diagnosis and recording of dental caries was measured by (D1-4MFS & d1-4mfs) index according to the criter