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 Problem

The fuzzy assignment models (FAMs) have been explored by various literature to access classical values, which are more precise in our real-life accomplishment. The novelty of this paper contributed positively to a unique application of pentagonal fuzzy numbers for the evaluation of FAMs. The new method namely Pascal's triangle graded mean (PT-GM) has presented a new algorithm in accessing the critical path to solve the assignment problems (AP) based on the fuzzy objective function of minimising total cost. The results obtained have been compared to the existing methods such as, the centroid formula (CF) and centroid formula integration (CFI). It has been demonstrated that operational efficiency of this conducted method is exquisitely develo

In our article, three iterative methods are performed to solve the nonlinear differential equations that represent the straight and radial fins affected by thermal conductivity. The iterative methods are the Daftardar-Jafari method namely (DJM), Temimi-Ansari method namely (TAM) and Banach contraction method namely (BCM) to get the approximate solutions. For comparison purposes, the numerical solutions were further achieved by using the fourth Runge-Kutta (RK4) method, Euler method and previous analytical methods that available in the literature. Moreover, the convergence of the proposed methods was discussed and proved. In addition, the maximum error remainder values are also evaluated which indicates that the propo

This paper considers approximate solution of the hyperbolic one-dimensional wave equation with nonlocal mixed boundary conditions by improved methods based on the assumption that the solution is a double power series based on orthogonal polynomials, such as Bernstein, Legendre, and Chebyshev. The solution is ultimately compared with the original method that is based on standard polynomials by calculating the absolute error to verify the validity and accuracy of the performance.

The optimum conditions for production of fibrinolytic protease from an edible mushroom Pleurotus ostreatus grown on the solid medium , Sus medium, composed of Sus wastes (produced from extracted medicinal plant Glycyrrhiza glabra) were determined. Addition of 5% of Soya bean seeds meal in Sus medium recorded a maximum fibrinolytic protease activity resulting in 7.7 units / ml. The optimum moisture content of Sus medium supplemented with 5% Soya bean seeds meal was 60% resulting in 7.2 units / ml.Pleurotus ostreatus produced a maximum fibrinolytic protease activity when the spawn rate,pH of medium and incubation temperature were 2,6 and 30°C, respectively. The maximum fibrinolytic protease activity was 7.6 units / ml when incubat

The degradation and mineralization of 4-chlorophenol (4-CP) by advanced oxidation processes (AOPs) was investigated in this work, using both of UV/H2O2 and photo-Fenton UV/H2O2/Fe+3 systems.The reaction was influenced by the input concentration of H2O2, the amount of the iron catalyst, the type of iron salt, the pH and the concentration of 4-CP. A colored solution of benzoquinon can be observed through the first 5 minutes of irradiation time for UV/H2O2 system when low concentration (0.01mol/L) of H2O2 was used. The colored solution of benzoquinon could also be observed through the first 5 minutes for the UV/H2O2/Fe+3 system at high
concentration (100ppm) of 4-CP. The results have shown that adding Fe+3 to the UV/H2O2 system enhanced

This study aimed to assess the efficiency of Nerium oleander in removing three different metals (Cd, Cu, and Ni) from simulated wastewater using horizontal subsurface flow constructed wetland (HSSF-CW) system. The HSSF-CW pilot scale was operated at two hydraulic retention times (HRTs) of 4 and 7 days, filled with a substrate layer of sand and gravel. The results indicated that the HSSF-CW had high removal efficiency of Cd and Cu. A higher HRT (7 days) resulted in greater removal efficiency reaching up to (99.3% Cd, 99.5% Cu, 86.3% Ni) compared to 4 days. The substrate played a significant role in removal of metals due to adsorption and precipitation. The N. oleander plant also showed a good tolerance to the uptake of Cd, Cu, and Ni ions fr