The  present study  deals  with successive  stages  of  productive

operations happened to produce a production within each stage befo re it  moves to the next one. ll cou ld  be deduced that this study is an extension  to what bas  been mentioned  in (1 ) .ln  (I),  the  optimum distribution of  di!Terent jobs of  workers and  machines  in  the productive operations has been st ud ied whi le the study  invol ves the optimum schedule for the succession of these operations presuming that thay have already been distributed on machines and workers (2).A mathematical form has been put for this study to define the "Object.ive Function "

Zygapophyseal joints (or facet joints), are a plane synovial joint which located between the articular facet processes of the vertebral arch which is freely guided movable joints. Ten dried vertebrae were used for the lumbar region and taking (L₄) as a sample to reveal stress pathways across the joints by using ANSYS program under different loading conditions which used Finite Elements Analysis model. Results obtained from the ANSYS program are important in understanding the boundary conditions for load analysis and the points of stress concentration which explained from the anatomical point of view and linked to muscle and ligament attachments. This model used as a computational tool to joint biomechanics and to prosthetic im

In this paper, a theoretical analysis of optimum bed thickness operates under mass transfer control for realizing a high efficiency and reaction conversion of an electrochemical reactor has been made based on flowthrough porous electrode (FTPE) configuration. Many models have been used to represent the optimum bed thickness by taking a look into previous works concerned and collecting all related information, data, and models. The parameters that affect the optimum bed thickness have been visualized and reviewed, and almost all of them have been examined by experimental data from different sources and based on the various models. It has been found that the increase in electrolyte flow rate, concentration, limiting current density, and sp

This study was conducted to evaluate the efficacy of 6 isolates of Pseudomonas fluorescens and Trichoderma harzianum and there combination against Fusarium tomato wilt disease caused by Fusarium oxysporum F.sp. Lycopersisi under green house condition .The isolates of bacteria (B3) and Trichoderma (T1) were found to be highly effective in reducing the disease incidence to 13.3% , 21% respectively , compared to control treatment (40%).Furthermore, disease severity was reduced to 28 and 30% respectively in comparison to control (90%) .Colonization of the roots (cfu /g fresh root weight )by the two isolates whether alon or together was extremely high . The combination treatment had a high ability in reducing disease incidenece and sev

The purpose of this research paper is to present the second-order homogeneous complex differential equation   , where   , which is defined on the certain complex domain depends on solution behavior. In order to demonstrate  the relationship between the solution of the second-order of the complex differential equation and its coefficient of function, by studying the solution in certain cases: a meromorphic function, a coefficient of function, and if the solution is considered to be a transformation with another complex solution. In addition, the solution has been provided as a power series with some  applications.

In This paper generalized spline method and Caputo differential operator is applied to solve linear fractional integro-differential equations of the second kind. Comparison of the applied method with exact solutions reveals that the method is tremendously effective.

This paper studies a novel technique based on the use of two effective methods like modified Laplace- variational method (MLVIM) and a new Variational method (MVIM)to solve PDEs with variable coefficients. The current modification for the (MLVIM) is based on coupling of the Variational method (VIM) and Laplace- method (LT). In our proposal there is no need to calculate Lagrange multiplier. We applied Laplace method to the problem .Furthermore, the nonlinear terms for this problem is solved using homotopy method (HPM). Some examples are taken to compare results between two methods and to verify the reliability of our present methods.

       In the present paper, by making use of the new generalized operator, some results of third order differential subordination and differential superordination consequence for analytic functions are obtained. Also, some sandwich-type theorems are presented.

Several previous investigations and studies utilized silica fume (SF) or (micro silica) particles as supplementary cementitious material added as a substitute to cement-based mortars and their effect on the overall properties, especially on physical properties, strength properties, and mechanical properties. This study investigated the impact of the inclusion of silica fume (SF) particles on the residual compressive strengths and microstructure properties of cement-based mortars exposed to severe conditions of elevated temperatures. The prepared specimens were tested and subjected to 25, 250, 450, 600, and 900 °C. Their residual compressive strengths and microstructure were evaluated and compared with control samples (C