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.
The objective of the research is to identify the effect of the five-finger strategy on the holistic thinking of chemistry students in the second intermediate grade, where the sample consisted of 60 female students in a second classfrom one of the intermediate schools in Baghdad city, divided into two groups: control and experimental. The experimental design was based on the partial control; the scientific course was defined in the third and fourth chapters of the science book of the second intermediate grade.The two research tools were prepared: the attainment test with the scientific course and the holistic thinking scale paragraph (36) of multiple-choice pre- and posttest. The results showed a statistically significant difference between
... Show MoreEducation is considered the corner stone of all nations development. It is the principal way for the development of human sources and the most achievements of the age due to the knowledge of these resources .
As its active role which accounting departments implement in Iraq universities , (public and private) through their teaching programs , they aim to supply labour-market with qualified cadre graduated as accountants auditors , tax auditors , financial analysts , ac
... Show MoreA series of batch demulsification runs were carried out to evaluate the final emulsified water content of emulsion samples after the exposure to microwave. An experimental study was conducted to evaluate the effects of a set of operating variables on the demulsification performance. Several microwave irradiation demulsification runs were carried out at different irradiation powers (700, 800, and 900 watt), using water-in-oil emulsion samples containing different water contents (20-80%, 30-70%, and 50-50%) and salt contents (10000, 20000, and 30000 ppm). It was found that the best separation efficiency was obtained at 900watt, 50% water content and 160 s of irradiation time. Experimental results showed that microwave radiation method can
... Show MoreFolktales are increasingly recognized as potent enablers in evoking the ’genius loci’ of cities and sustaining their cultural identity. ’The Thousand and One Nights’ represents the most remarkable and memorable cross-cultural folktales, related to the Middle Eastern region in general, and the city of Baghdad in particular. Very limited research has been conducted on its impact on architecture and urban development. The current article aims to develop a conceptual framework for the notion of ’imageability’, by which to explore the spatial characteristics and the physical and spiritual attributes of the depicted architecture and urban spaces of selected tales. Based on a conducted narrative-analysis approach, the article introduce
... Show MoreInfrastructure projects take a long time, are complex, multidisciplinary, use different materials and products, and have high risk. These characteristics affect the process of supplying materials. The current paper studies the ability to improve the supply chain process and decrease its cost by identifying the factors that affect it. These factors are used as variables in the mathematical model, which is working under uncertain conditions when the consumption rate of materials is not constant. The information used in this model is obtained from Building Information Modeling (BIM) and Geographical Information System (GIS) techniques and the genetic algorithm is utilized to determine the optimal supplier and the quantities of supplies
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We have presented the distribution of the exponentiated expanded power function (EEPF) with four parameters, where this distribution was created by the exponentiated expanded method created by the scientist Gupta to expand the exponential distribution by adding a new shape parameter to the cumulative function of the distribution, resulting in a new distribution, and this method is characterized by obtaining a distribution that belongs for the exponential family. We also obtained a function of survival rate and failure rate for this distribution, where some mathematical properties were derived, then we used the method of maximum likelihood (ML) and method least squares developed (LSD)
... Show MoreIn this paper, a mathematical model was built for the supply chain to reduce production, inventory, and transportation in Baghdad Company for Soft Drink. The linear programming method was used to solve this mathematical model. We reduced the cost of production by reduced the daily work hours, the company do not need the overtime hours to work at the same levels of production, and the costs of storage in the company's warehouses and agents' stores have been reduced by making use of the stock correctly, which guarantees reducing costs and preserving products from damage. The units transferred from the company were equal to the units demanded by the agents. The company's mathematical model also achieved profits by (84,663,769) by re
... Show MoreAn experimental and theoretical analysis was conducted for simulation of open circuit cross flow heat
exchanger dynamics during flow reduction transient in their secondary loops. Finite difference
mathematical model was prepared to cover the heat transfer mechanism between the hot water in the
primary circuit and the cold water in the secondary circuit during transient course. This model takes under
consideration the effect of water heat up in the secondary circuit due to step reduction of its flow on the
physical and thermal properties linked to the parameters that are used for calculation of heat transfer
coefficients on both sides of their tubes. Computer program was prepared for calculation purposes which
cover a
This work, deals with Kumaraswamy distribution. Kumaraswamy (1976, 1978) showed well known probability distribution functions such as the normal, beta and log-normal but in (1980) Kumaraswamy developed a more general probability density function for double bounded random processes, which is known as Kumaraswamy’s distribution. Classical maximum likelihood and Bayes methods estimator are used to estimate the unknown shape parameter (b). Reliability function are obtained using symmetric loss functions by using three types of informative priors two single priors and one double prior. In addition, a comparison is made for the performance of these estimators with respect to the numerical solution which are found using expansion method. The
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