The dimensions of bubbles were measured in a stirrer tank electrochemical reactor, where the analysis of the bubble size distribution has a substantial impact on the flow dynamics. The high-speed camera and image processing methods were used to obtain a reliable photo. The influence of varied air flow rates (0.3; 0.5; 1 l/min) on BSD was thoroughly investigated. Two types of distributors (cubic and circular) were examined, and the impact of various airflow rates on BSD was investigated in detail. The results showed that the bubbles for the two distributors were between 0.5 and 4.5 mm. For both distributors at each airflow, the Sauter mean diameter for the bubbles was calculated. According to the results, as the flow rate raised, the bubb

      This study aims to classify the critical points of functions with 4 variables and 8 parameters, we found the caustic for the certain function with the spreading of the critical points. Finally, as an application, we found the bifurcation solutions for the equation of sixth order with boundary conditions using the Lyapunov-Schmidt method in the variational case.

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

The purpose of this study is to investigate the histopathological response of dentinopulpal
response of human teeth to the Er: YAG laser cavity preparation in comparison with the conventional
class I cavity preparation. Thirty five sound human upper and lower first premolar teeth which were
needed to be extracted for orthodontic purposes were used in the study. Regarding to the method of
cavity preparation, the teeth were grouped into three groups; Group1; Control group which consists of
seven sound teeth without cavity preparation, Group2; Conventional cavity preparation group and group
3; Er: YAG laser cavity preparation group. Each of Group2 and3 consists of fourteen teeth that is
subdivided into: A. 7teeth that e

New complexes of Al(III) such as [Al (Ura) (Phen) (OH2) Cl ] Cl. 2H2O, [Al(Ura)2(OA)(OH2)Cl].H2O and [Al(Ura)3Cl3]H2O type, where (Ura)=Uracil, (Phen)= 1,10-Phenanthroline monohydrate and (OA)= Oxalic acid dihydrate, were prepared. The elemental microanalysis, FT.IR, electronic spectra, and magnetic susceptibility as well as the conductivity measurements are characterized. For isolated three complexes for six coordinated of Al(III) are proposed with molecular formulas that depend on the nature of (Ura), (Phen) and (OA) present. The suggested molecular structure into all complexes for aluminum ion is octahedral geometries .The antibacterial efficacy was examined from metal salt (AlCl3), ligands and metal complexes into the pathogenic bacteri

المتغير العشوائي X  له توزيع أسي اذا كان له دالة احتمالية الكثافة بالشكل:

عندما  ، هذه هي الحالة الخاصة لتوزيع كاما.

غالباً جداً ولسبب معقول تأخذ . الحالة الخاصة لـ (1) التي نحصل عليها تسمى بالتوزيع الاسي لمعلمة واحدة.

اذا كانت  ، ، التوزيع في هذه الحالة يسمى التوزيع الاسي القياسي

اما بالنسب

The aim of this study is to investigate the feasibility of underground storage of gas in Um El-Radhuma formation /Ratawi field. This formation is an aquifer consisting of a high permeable dolomitebeds overlain by impermeable anhydrite bed of Rus formation. Interactive petrophysics (IP), Petrel REand Eclipse 100 softwares were used to conduct a well log interpretation, build a reservoir simulationmodel and predict the reservoir behavior during storage respectively. A black oil, three dimensionaland two phase fluid model has been used. The results showed that the upper part of Um El-Radhumaformation is suitable for underground gas storage, because of the seal of its cap rock and capability ofreserving gas in the reservoir. It was foun

In this paper, 3D simulation of the global coronal magnetic field, which use observed line of sight component of the photosphere magnetic field from (MDI/SOHO) was carried out using potential field model. The obtained results, improved the theoretical models of the coronal magnetic field, which represent a suitable lower boundary conditions (Bx, By, Bz) at the base of the linear force-free and nonlinear force free models, provides a less computationally expensive method than other models. Generally, very high speed computer and special configuration is needed to solve such problem as well as the problem of viewing the streamline of the magnetic field. For high accuracy special mathematical treatment was adopted to solve the computation comp

        In the last years, the self-balancing platform has become one of the most common candidates to use in many applications such as flight, biomedical fields, industry. This paper introduced the simulated model of a proposed self-balancing platform that described the self–balancing attitude in (X-axis, Y-axis, or both axis) under the influence of road disturbance. To simulate the self-balanced platform's performance during the tilt, an integration between Solidworks, Simscape, and Simulink toolboxes in MATLAB was used. The platform's dynamic model was drawn in SolidWorks and exported as a STEP file used in the Simscape Multibody environment. The system is controlled using the proportional-integral-derivative (PID) co