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.
Abstract Physical requirements are an important priority for the development of football gymnastics coaches because the nature of performance is interconnected and interconnected in terms of the player's duties in the match. In the gameplay situations, the player must perform the skill with strength and speed coupled with accuracy and the reactions of the colleague and competitor alike, which represents the normal reality of the football gymnasium Skilled exercises are one of the most suitable technical side exercises as they are built according to the components of the skill requirements of the game and the nature of its performance, which appear on the gro
... Show MoreThe house flies Musca domestica )Diptera:musidae) are the primary carrier of many pathogens such as cholera, typhoid, anthrax, and others. The use of chemical pesticides as a basic method of control leads to many problems at the environmental and health level. The use of safe alternatives to chemical pesticides has become an urgent necessity. The research aims to find biological alternatives that are environment-friendly and non-pathogenic to humans in controlling house flies through the possibility of extracting and diagnosing some secondary metabolites produced by the fungus Metarhizium anisopliae and testing their effects on the second larval stage of house flies using different treatment methods that include
... Show MoreIn this paper, the problem of resource allocation at Al-Raji Company for soft drinks and juices was studied. The company produces several types of tasks to produce juices and soft drinks, which need machines to accomplish these tasks, as it has 6 machines that want to allocate to 4 different tasks to accomplish these tasks. The machines assigned to each task are subject to failure, as these machines are repaired to participate again in the production process. From past records of the company, the probability of failure machines at each task was calculated depending on company data information. Also, the time required for each machine to complete each task was recorded. The aim of this paper is to determine the minimum expected ti
... Show MoreUnderstanding energy metabolism and intracellular energy transmission requires knowledge of the function and structure of the mitochondria. Issues with mitochondrial morphology, structure, and function are the most prevalent symptoms. They can damage organs such as the heart, brain, and muscle due to a variety of factors, such as oxidative damage, incorrect metabolism of energy, or genetic conditions. The control of cell metabolism and physiology depends on functional connections between mitochondrial and biological surroundings. Therefore, it is essential to research mitochondria in situ or in vivo without isolating them from their surrounding biological environment. Finding and spotting abnormal alterations in mitochondria is the
... Show MoreIraqi insurance market need to develop products and to find new insurance policies to cover the damages of the violence and political commotions dangers and to meet the needs of the proposers.
The global insurance companies recently issued such policies to pay the losses wich caused by the violent political acts of vandalism suffered by the property and investments wich estimated billions of dollars.
... Show MoreFusarium pseudograminearum and Fusarium graminearum commonly cause crown rot (FCR) and head blight (FHB) in wheat, respectively. Disease infection and spread can be reduced by the deployment of resistant cultivars or through management practices that limit inoculum load. Plants deficient in micronutrients, including zinc, tend to be more susceptible to many diseases. On the other hands, and zinc deficiency in cereals is widespread in Australian soils. Zinc deficiency may have particular relevance to crown rot, the most important and damaging Fusarium disease of wheat and barley in Australia. Four wheat genotypes; Batavia, Sunco and two lines from the International Maize and Wheat Improvement Center (CIMMYT) were tested for response
... Show MoreSuffer most of the facilities of the high cost of inventory , which affects the high cost of the product and thus affects many administrative decisions , as well as suffer the facilities of the systems developed by the provisions of inventory control , and this problem is exacerbated in the construction sector where the inventory in the form of Construction spin of the Year for another it becomes difficult to control the cost effectively , and is the research problem in question follows: What are the implications of the use of the system in time inventory accounting system for the contracting company does kills Alrkaah to the provisions of the cost of inventory and what is the optimal approach to inventory control ? Find assumed
... Show MoreThe new, standard molecular biologic system for duplicating DNA enzymatically devoid of employing a living organism, like E. coli or yeast, represents polymerases chain reaction (PCR). This technology allows an exponential intensification of a minor quantity of DNA molecule several times. Analysis can be straightforward with more DNA available. A thermal heat cycler performs a polymerization chain reaction that involves repeated cycles of heating and cooling the reactant tubes at the desired temperature for each reaction step. A heated deck is positioned on the upper reaction tube to avoid evaporating the reaction mixture (normally volumes range from 15 to 100 l per tube), or an oil layer can be placed on a reaction mixture su
... Show MoreThe new, standard molecular biologic system for duplicating DNA enzymatically devoid of employing a living organism, like E. coli or yeast, represents polymerases chain reaction (PCR). This technology allows an exponential intensification of a minor quantity of DNA molecule several times. Analysis can be straightforward with more DNA available.
A thermal heat cycler performs a polymerization chain reaction that involves repeated cycles of heating and cooling the reactant tubes at the desired temperature for each reaction step. A heated deck is positioned on the upper reaction tube to avoid evaporating the reaction mixture (normally volumes range from 15 to 100 l per tube), or an oil layer can be placed on a reaction mixture surfa
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