In this paper, a discretization of a three-dimensional fractional-order prey-predator model has been investigated with Holling type III functional response. All its fixed points are determined; also, their local stability is investigated. We extend the discretized system to an optimal control problem to get the optimal harvesting amount. For this, the discrete-time Pontryagin’s maximum principle is used. Finally, numerical simulation results are given to confirm the theoretical outputs as well as to solve the optimality problem.
In this paper, a procedure to establish the different performance measures in terms of crisp value is proposed for two classes of arrivals and multiple channel queueing models, where both arrival and service rate are fuzzy numbers. The main idea is to convert the arrival rates and service rates under fuzzy queues into crisp queues by using graded mean integration approach, which can be represented as median rule number. Hence, we apply the crisp values obtained to establish the performance measure of conventional multiple queueing models. This procedure has shown its effectiveness when incorporated with many types of membership functions in solving queuing problems. Two numerical illustrations are presented to determine the validity of the
... Show MoreCerebellum is the most important and critical part of the central nervous system, cerebellum is very sensitive to the abnormal changes during the embryological development in its histological structure, the exposure to any infection during embryogenesis produce abnormalities in the cerebellum and behavioral of offspring. In this study we tried to study the ontogenesis of the cerebellum in the embryos of the albino rats and detection the effect of the AgNPs on the ontogenesis of the rat cerebellum after exposure of AgNPs during pregnancy. we used 60 female pregnant rats divided in to three group, each contain 20 female, (G1) treated with 2mg/kg /day suspension of silver nanoparticles (Ag NPs) (G2) treated with 20mg/kg/day AgNPs from first da
... Show MoreNew simple and sensitive spectrophotometric methods for the determination of paracetamol in aqueous medium were developed. The first method is based on coupling of paracetamol with p-amino-2-hydroxy sodium benzoate (AHB) in the presence of sodium periodate, as oxidizing agent, to form a brownish-orange compound which shows a λmax at 470 nm. The molar absorptivity (εmax) of the colored product was found to be (3371) l. mole1. cm-1 and Sandel’s index 0.0449 μg. cm-2. The method follows Beer’s law in the concentration range of 12.5-500.0 μg of paracetamol in a final volume of 25 ml (0.5-20.0) μg. ml-1 with relative standard deviation percent (RSD%) ranged between 0.26-4.71% and accuracy, expressed by recovery percent, 95-106% for five
... Show More(Thimma) in Arabic means compact, and immunity. (People of Thimma) are the free non-Muslim people under Muslim rule. This includes Heavenly Religions people, i. e., Christian and Jews).
They have been called (People of Thimma) because they had paid (Jizyah: tribute) so they became safe for their souls, honor, properties at the custody of Muslims.
Islamic law had posed (Jizyah: tribute) upon the Jews and Christians who were living under Muslim rule as a reaction of not embracing Islam Faith against securing their rights and freedom.
Freedoms secured by Islam for the (People of Thimma) had been many, including the right of faith, not coercing them to be Muslim, the right to live, to possess properties, protect and secure them, the