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.
In this paper, the Azzallini’s method used to find a weighted distribution derived from the standard Pareto distribution of type I (SPDTI) by inserting the shape parameter (θ) resulting from the above method to cover the period (0, 1] which was neglected by the standard distribution. Thus, the proposed distribution is a modification to the Pareto distribution of the first type, where the probability of the random variable lies within the period The properties of the modified weighted Pareto distribution of the type I (MWPDTI) as the probability density function ,cumulative distribution function, Reliability function , Moment and the hazard function are found. The behaviour of probability density function for MWPDTI distrib
... Show MoreN, N′- bis[4-hydroxy phenyl] pyromillitdiimide [II] was prepared from the corresponding diamic acid , which was transfered to its new ester by the reaction with chloroethyl acetate [III ], [III] was used to prepare the novel hydrazide derivative [IV] , which was allowed to react with several aldehydes to yield the hydrazones [V – IX]. All the new compounds were synthesized , and characterized by their melting points .HNMR for some of them1FTIR,C,H,N analysis and ,
Anodic electrodeposition was used to synthesize a composite electrode of nanostructured manganese dioxide/carbon fiber (CF) galvanostatically. Different characterization results of the nanostructured MnO2 were obtained by varying the H2SO4 concentration and the current density. Field emission scanning electron microscopy, X‐ray diffraction, and atomic force microscopy were utilized to characterize the prepared composite electrodes. The best conditions were: 0.3 mA cm−2 current density and 0.64 M H2SO4 concentration. The electrosorption performance of the MnO
The research acquires its importance by motivating the behavioural side of the employees to apply modern technology in the work, because of its great importance in increasing the efficiency of employees’ performance and excellence. The research was based on two main hypotheses to show the relationship and impact between the variables through the adoption of a questionnaire to collect data and information related to the research, which consisted of (50) people from administrators working at different levels, based on personal interviews and field visits to collect research data. The data collection process was subjected to statistical analysis using the statistical program (SPSS) (Statistical package for social science) to reach
... Show MoreA method for Approximated evaluation of linear functional differential equations is described. where a function approximation as a linear combination of a set of orthogonal basis functions which are chebyshev functions .The coefficients of the approximation are determined by (least square and Galerkin’s) methods. The property of chebyshev polynomials leads to good results , which are demonstrated with examples.
Transport is a problem and one of the most important mathematical methods that help in making the right decision for the transfer of goods from sources of supply to demand centers and the lowest possible costs, In this research, the mathematical model of the three-dimensional transport problem in which the transport of goods is not homogeneous was constructed. The simplex programming method was used to solve the problem of transporting the three food products (rice, oil, paste) from warehouses to the student areas in Baghdad, This model proved its efficiency in reducing the total transport costs of the three products. After the model was solved in (Winqsb) program, the results showed that the total cost of transportation is (269,
... Show MoreA total of 28 birds were examined to investigate about the distribution of the nematode Hadjelia truncata among some members of the avian family Columbidae in Al-Diwaniya Province, Central Iraq. The percentages of the infection rate with this nematode were 27.27, 37.5, 14.28 and 0 in Columba livia, C. palumbis, Streptopelia decaocto, and S. turtur respectively. Reporting Hadjelia truncata from Streptopelia decaocto constitutes a new host record.