Markov chains are an application of stochastic models in operation research, helping the analysis and optimization of processes with random events and transitions. The method that will be deployed to obtain the transient solution to a Markov chain problem is an important part of this process. The present paper introduces a novel Ordinary Differential Equation (ODE) approach to solve the Markov chain problem. The probability distribution of a continuous-time Markov chain with an infinitesimal generator at a given time is considered, which is a resulting solution of the Chapman-Kolmogorov differential equation. This study presents a one-step second-derivative method with better accuracy in solving the first-order Initial Value Problems (IVPs) compared to other approaches found in the literature, which is verified by the obtained solutions. The determination of the transient solutions for Markov chains is presented using the proposed method. The results show better accuracy in solving the transient distribution in Markov chains, which implies that there is an improved assurance in adopting this approach in future studies of the Markov chain modeling process for predicting future events based on the current state of a process. Future studies on Markov chain modeling could adopt the introduced method to predict future events based on the current state of a process.
In this work we used the environmentally friendly method to prepared ZrO2 nanoparticles utilizing the extract of Thyms plant In basic medium and at pH 12, the ZrO2 NPs was characterized by different techniques such as FTIR, ultraviolet visible, Atomic force microscope, Scanning Electron Microscopy, X-ray diffraction and Energy dispersive X-ray. The average crystalline size was calculated using the Debye Scherres equation in value 7.65 nm. Atomic force microscope results showed the size values for ZrO2 NPs were 45.11nm, and there are several distortions due to the presence of some large sizes. Atomic force microscope results showed the typical size values for ZrO2 NPs were 45.11 nm, and there are several distortions due to the presence of so
... Show MoreUsing a mathematical model to simulate the interaction between prey and predator was suggested and researched. It was believed that the model would entail predator cannibalism and constant refuge in the predator population, while the prey population would experience predation fear and need for a predator-dependent refuge. This study aimed to examine the proposed model's long-term behavior and explore the effects of the model's key parameters. The model's solution was demonstrated to be limited and positive. All potential equilibrium points' existence and stability were tested. When possible, the appropriate Lyapunov function was utilized to demonstrate the equilibrium points' overall stability. The system's persistence requirements were spe
... Show MoreThis article presents the results of an experimental investigation of using carbon fiber–reinforced polymer sheets to enhance the behavior of reinforced concrete deep beams with large web openings in shear spans. A set of 18 specimens were fabricated and tested up to a failure to evaluate the structural performance in terms of cracking, deformation, and load-carrying capacity. All tested specimens were with 1500-mm length, 500-mm cross-sectional deep, and 150-mm wide. Parameters that studied were opening size, opening location, and the strengthening factor. Two deep beams were implemented as control specimens without opening and without strengthening. Eight deep beams were fabricated with openings but without strengthening, while
... Show MoreThere is an interesting potential for the use of GFRP-pultruded profiles in hybrid GFRP-concrete structural elements, either for new constructions or for the rehabilitation of existing structures. This paper provides experimental and numerical investigations on the flexural performance of reinforced concrete (RC) specimens composite with encased pultruded GFRP I-sections. Five simply supported composite beams were tested in this experimental program to investigate the static flexural behavior of encased GFRP beams with high-strength concrete. Besides, the effect of using shear studs to improve the composite interaction between the GFRP beam and concrete as well as the effect of web stiffeners of GFRP were explored. Encasing the GFRP
... Show MoreIn this study, the potential of adsorption of amoxicillin antibiotic (AMOX) from aqueous solutions using prepared activated carbon (AC) was studied. The used AC was prepared from an inexpensive and available precursor (sunflower seed hulls (SSH)) and activated by potassium hydroxide (KOH). The prepared AC was examined for its ability to remove AMOX from aqueous contaminated solutions and characterized with the aid of N2 -adsorption/desorption isotherm Brunauer–Emmett– Teller, scanning electron microscopy, energy-dispersive X-ray spectroscopy and Fourier-transform infrared. Zeta potential of the prepared activated carbon from sunflower seed hulls (SSHAC) were studied in relation to AMOX adsorption. The physical and chemical propert
... Show MoreIn the present study, the effectiveness of a procedure of electrocoagulation for removing chemical oxygen demand (COD) from the wastewater of petroleum refinery has been evaluated. Aluminum and stainless steel electrodes were used as a sacrificial anode and cathode respectively. The effect of current density (4-20mAcm−2), pH (3-11), and NaCl concentration (0-4g/l) on efficiency of removal of chemical oxygen demand was investigated. The results have shown that increasing of current density led to increase the efficiency of COD removal while increasing NaCl concentration resulted in decreasing of COD removal efficiency. Effect of pH was found to be lowering COD re