The necessary optimality conditions with Lagrange multipliers are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time and the final state are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.
A mathematical model constructed to study the combined effects of the concentration and the thermodiffusion on the nanoparticles of a Jeffrey fluid with a magnetic field effect the process of containing waves in a three-dimensional rectangular porous medium canal. Using the HPM to solve the nonlinear and coupled partial differential equations. Numerical results were obtained for temperature distribution, nanoparticles concentration, velocity, pressure rise, pressure gradient, friction force and stream function. Through the graphs, it was found that the velocity of fluid rises with the increase of a mean rate of volume flow and a magnetic parameter, while the velocity goes down with the increasing a Darcy number and lateral walls. Also, t
... Show MoreThe effects of T-shaped fins on the improvement of phase change materials (PCM) melting are numerically investigated in vertical triple-tube storage containment. The PCM is held in the middle pipe of a triple-pipe heat exchanger while the heat transfer fluid flows through the internal and external pipes. The dimension effects of the T-shaped fins on the melting process of the PCM are investigated to determine the optimum case. Results indicate that while using T-shaped fins improves the melting performance of the PCM, the improvement potential is mainly governed by the fin’s body rather than the head. Hence, the proposed T-shaped fin did not noticeably improve melting at the bottom of the PCM domain; additionally, a flat fin is ad
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The current research aims to examine the effectiveness of a training program for children with autism and their mothers based on the Picture Exchange Communication System to confront some basic disorders in a sample of children with autism. The study sample was (16) children with autism and their mothers in the different centers in Taif city and Tabuk city. The researcher used the quasi-experimental approach, in which two groups were employed: an experimental group and a control group. Children aged ranged from (6-9) years old. In addition, it was used the following tools: a list of estimation of basic disorders for a child with autism between (6-9) years, and a training program for children with autism
... Show MoreThis work studied the electrical and thermal surface conductivity enhancement of polymethylmethacrylate (PMMA) clouded by double-walled carbon nanotubes (DWCNTs) and multi-walled carbon nanotube (MWCNTs) by using pulsed Nd:YAG laser. Variable input factors are considered as the laser energy (or the relevant power), pulse duration and pulse repetition rate. Results indicated that the DWCNTs increased the PMMA’s surface electrical conductivity from 10-15 S/m to 0.813×103 S/m while the MWCNTs raised it to 0.14×103 S/m. Hence, the DWCNTs achieved an increase of almost 6 times than that for the MWCNTs. Moreover, the former increased the thermal conductivity of the surface by 8 times and the later by 5 times.
Weibull distribution is considered as one of the most widely distribution applied in real life, Its similar to normal distribution in the way of applications, it's also considered as one of the distributions that can applied in many fields such as industrial engineering to represent replaced and manufacturing time ,weather forecasting, and other scientific uses in reliability studies and survival function in medical and communication engineering fields.
In this paper, The scale parameter has been estimated for weibull distribution using Bayesian method based on Jeffery prior information as a first method , then enhanced by improving Jeffery prior information and then used as a se
... Show MoreThe avoidance strategy of prey to predation and the predation strategy for predators are important topics in evolutionary biology. Both prey and predators adjust their behaviors in order to obtain the maximal benefits and to raise their biomass for each. Therefore, this paper is aimed at studying the impact of prey’s fear and group defense against predation on the dynamics of the food-web model. Consequently, in this paper, a mathematical model that describes a tritrophic Leslie-Gower food-web system is formulated. Sokol-Howell type of function response is adapted to describe the predation process due to the prey’s group defensive capability. The effects of fear due to the predation process are considered in the first two levels
... Show MoreA new panel method had been developed to account for unsteady nonlinear subsonic flow. Two boundary conditions were used to solve the potential flow about complex configurations of airplanes. Dirichlet boundary condition and Neumann formulation are frequently applied to the configurations that have thick and thin surfaces respectively. Mixed boundary conditions were used in the present work to simulate the connection between thick fuselage and thin wing surfaces. The matrix of linear equations was solved every time step in a marching technique with Kelvin's theorem for the unsteady wake modeling. To make the method closer to the experimental data, a Nonlinear stripe theory which is based on a two-dimensional viscous-inviscid interac
... Show MoreControlling public expenditures is one of the main objectives of the public budget. The public budget often suffers from a deficit, whether in developed or developing countries, because expenditures are usually greater than the revenues generated. This requires the existence of financial rules that are adhered to by the government, which in turn leads to discipline. Fiscal policy leads to a reduction in the obligations incumbent on the government. Adhering to the financial rules would correct the course of fiscal policy in Iraq, with the need to direct oil revenues in the years of financial abundance when global oil prices rise to sovereign funds similar to other rentier countries, which contributes to maintaining the stabi
... Show MoreMixed-effects conditional logistic regression is evidently more effective in the study of qualitative differences in longitudinal pollution data as well as their implications on heterogeneous subgroups. This study seeks that conditional logistic regression is a robust evaluation method for environmental studies, thru the analysis of environment pollution as a function of oil production and environmental factors. Consequently, it has been established theoretically that the primary objective of model selection in this research is to identify the candidate model that is optimal for the conditional design. The candidate model should achieve generalizability, goodness-of-fit, parsimony and establish equilibrium between bias and variab
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