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

This study presented an endeavour to integrate the value chain activities with the Balanced Scorecard for a comprehensive evaluation of an organization’s strategic performance. It also demonstrated the connection and the integration of the activities of the value chain with the Balanced Scorecard. The financial measurement was linked with non-financial measurement by integrating these techniques to achieve an appropriate performance that supports all aspects of the organizational performance. Consequently, the research problem in this study emerged, which is due to the concentration of many organizations on the measurement of financial performance. Notably, the latter caused the decline of some organizations from the competitive market. T

In this study, the adsorption of Zn (NO3)2 is carried out by using surfaces of malvaparviflora. The validity of the adsorption is evaluated by using atomic absorption Spectrophotometry through determination the amount of adsorbed Zn (NO3)2. Various parameters such as PH, adsorbent weight and contact time are studied in terms of their effect on the reaction progress. Furthermore, Lagergren’s equation is used to determine adsorption kinetics. It is observed that high removal of Zn (NO3)2 is obtained at PH=2. High removal of Zn (NO3)2 is at the time equivalent of 60 min and reaches equilibrium,where 0.25gm is the best weight of adsorbant . For kinetics the reaction onto malvaparviflora follows pseudo first order Lagergren’s equation.

The biochar prepared from sawdust raw material was applied in this study for the treatment of wastewater polluted with methyl orange dye. The effect of pH (2-11), initial concertation (50-250 mg/L) and time were studied. The isotherm of Langmuir, Frendluch and temkin models studied. The Langmuir model was the best to explain the adsorption process, maximum uptake was 136.67 mg/g at 25C^o of methyl orange dye. Equilibrium reached after four hours of contact for most adsorbents.The values of thermodynamic parameters ∆G were negative at various temperatures, so the process spontaneous, while ∆H values were 16683 j/mol and ∆S values was 60.82 j/mol.k.

The analysis and efficiency of phenol extraction from the industrial water using different solvents, were investigated. To our knowledge, the experimental information available in the literature for liquid-liquid equilibria of ternary mixtures containing the pair phenol-water is limited. Therefore the purpose of the present investigation is to generate the data for the water-phenol with different solvents to aid the correlation of liquid-liquid equilibria, including phase diagrams, distribution coefficients of phenol, tie-lines data and selectivity of the solvents for the aqueous phenol system.

                The ternary equilibrium diagrams and tie-lines

   In this study, the circulating fluidized bed was used to remove the Tetracycline from wastewater utilizing a pistachio shell coated with ZnO nanoparticles. Several parameters including, Tetracycline solution flowrate, initial static bed height, Tetracycline initial concentration and airflow rate were systematically examined to show their effect on the breakthrough curve and the required time to reach the adsorption capacity and thus draw the fully saturated curve of the adsorbent. Results showed that using ZnO nanoparticles will increase the adsorbent surface area and pores and as a result the adsorption increased, also the required time for adsorbent saturation increased and thus the removal efficiency may be achieved at mi

This study aims to test ceramic waste's capacity to remove nickel from aqueous solutions through adsorption. Ceramic wastes were collected from the Refractories Manufacturing Plant in Ramadi. Through a series of lab tests, the reaction time (5, 10, 15, 20, 25, 30, 35, 40, 45, and 50 minutes, and Ni concentrations (20, 40, 60, and 80) were tested using ceramic wastes with a solid to liquid ratio of 2g/30ml. At a temperature of 30ºC, the pH, total dissolved solids (TDS), and electrical conductivity (EC) were all measured. The equilibrium time was set at 30 min. Thereafter, the sorption (%) somewhat increased positively with the Ni concentration. Freundlich's equation showed that the adsorption intensity is 1.1827 and the Freundlich c

Cadmium is one of the heavy metal found in the wastewater of many industries. The electrocoagulation offers many advantages for the removal of cadmium over other methods. So the removal of cadmium from wastewater by using electrocoagulation was studied to investigate the effect of operating parameters on the removal efficiency. The studied parameters were the initial pH, initial concentration, and applied voltage. The study experiments were conducted in a batch reactor with  with two pairs of aluminum electrodes with dimension  and 2mm in thick with 1.5 cm space between them. The optimum removal was obtained at pH =7, initial concentration = 50 mg/L, and applied voltage = 20 V and it was 90%.

The exploitation of obsolete recyclable resources including paper waste has the advantages of saving resources and environment protection. This study has been conducted to study utilizing paper waste to adsorb phenol which is one of the harmful organic compound byproducts deposited in the environment. The influence of different agitation methods, pH of the solution (3-11), initial phenol concentration (30-120ppm), adsorbent dose (0.5-2.5 g) and contact time (30-150 min) were studied. The highest phenol removal efficiency obtained was 86% with an adsorption capacity of 5.1 mg /g at optimization conditions (pH of 9, initial phenol concentration of 30 mg/L, an adsorbent dose of 2 g and contact time of 120min and at room temperature).

This is a research in which I studied the opinions of Arab scholars, in their studies
For (what) and (whatever) the two conditionals and their indication of time, and its name
B (time in (what) and (whatever) the two conditions), and I mentioned their opinions in it
This issue was discussed and discussed, and in this study it relied on the sources of the Arabic language.
Especially the books of grammar, interpretation, and the opinions of the scholars of the principles of jurisprudence are mentioned,
I also mentioned the opinion of the scholars of jurisprudence, and how they likened (whatever) to (everything).
In its indication of repetition, and as long as it indicates repetition, it indicates
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