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.
This new azo dye 7-(3-hydroxy-phenylazo)-quinoline-8-ol was subsequently used to prepare a series of complexes with the chlorides of Fe, Co, Zn, Ru, Rh and Cd. The compounds identified by 1H and 13C-NMR, FT-IR, UV-Vis, mass spectroscopy, as well as TGA, DSC, and C.H.N., conductivity, magnetic susceptibility, metal and chlorine content. The results showed that the ligand behaves in a trigonal behavior, and that the complexes gave tetrahedral, except for Fe, Ru and Rh octahedral was given, that all of them are non-electrolytes. The effectiveness of both the compounds in inhibiting free radicals was evaluated by the ability to act as an antioxidant was measured using DPPH as a free radical and gallic acid as a standard substance, the
... Show MoreFreshwater scarcity poses a global challenge, particularly in regions where conventional water resources are limited. Solar stills offer an economical, sustainable solution; however, their yield is limited. This study aims to evaluate a new tracking concentrated tilted tubular solar still equipped with a heat‐pipe TTSS‐HP. The novelty of the present work lies in four aspects: a novel trough U‐channel design that improves the interception of reflected solar radiation, a novel hexagonal glass cover design. A receiver formed of four‐sections, combined with a heat‐pipe and dual trough concentrators. Outdoor experiments are carried out in Baghdad, Iraq (33.27° N, 44.37° E),
Background: The COVID-19 virus outbreak had a massive effect on many parts of people's lives, as they were advised to quarantine and lockdown to prevent the virus from spreading, which had a big impact on people's mental health, anxiety, and stress. Many internal and external factors lead to stress. This negatively influences the body's homeostasis. As a result, stress may affect the body's capacity to use energy to defend against pathogens. Many recent investigations have found substantial links between human mental stress and the production of hormones, prohormones, and/or immunological chemicals. some of these researches have verified the link between stress and salivary cortisol levels. The aim of this study is to measure salivary corti
... Show MoreSolid‐waste management, particularly of aluminum (Al), is a challenge that is being confronted around the world. Therefore, it is valuable to explore methods that can minimize the exploitation of natural assets, such as recycling. In this study, using hazardous Al waste as the main electrodes in the electrocoagulation (EC) process for dye removal from wastewater was discussed. The EC process is considered to be one of the most efficient, promising, and cost‐effective ways of handling various toxic effluents. The effect of current density (10, 20, and 30 mA/cm2), electrolyte concentration (1 and 2 g/L), and initial concentration of Brilliant Blue dye (15 and 30 mg/L) on
A laboratory experiment was carried out at the College of Agriculture University of Baghdad in 2017. The aim was to improve the anatomical and physiological traits of broad bean seedling under salt stress by soaking it in salicylic acid. The concentrations of salicylic acid were 0, 10, and 20 mg L-1 and the electrical conductivity levels were 0, 3, and 6 dS m-1. The complete randomized design was used with four replications. The increasing of salicylic acid concentration up to 10 mg L-1 led to increasing the stem cortex thickness, stem vascular bundles thickness, and root cortex thickness significantly by (34.9,36.7,and 55 µm) respectively, while the treatment of 20 mg L-1 led to decreasing these traits by (28.2, 27.8, and 48.1 µm
... Show MoreThe aldol condensation of 2-acetylnaphthalene with 9-anthracene carboxaldehyde afforded α, β-unsaturated keton (1) . New heterocyclic compounds containing: cyclohexenone[2], indazole[3], pyrimidinethion [4], thiazolo fused pyrimidine[5], isoxazoline[6], substituted pyrazoline[7]a-d and pyrimidinone[8] rings system were synthesized from α, β-unsaturated keton[1]. Cyclization of [1] with ethylacetoacetate gave the mentioned heterocycle cyclohexanone [2]. The cyclo condensation of [2] with hydrazine gave the new indazole derivative [3]. furthermore, the reation of [1]with thiourea gives thiopyrmidine derivative [4]. The cyclo condensation of [4] with chloroacetic acid gave the fused rings [5]. Then reacted compound[1] with hydroxy
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