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 work, we focused on studying 1,4-naphthoquinones and their derivatives, and knowing the methods of preparing them using different auxiliary agents and forming derivatives containing heterocyclic rings, active groups and saturated rings containing heterogeneous elements . In addition, due to their strong antibacterial, antifungal and anticancer activity, 1,4-naphthoquinone compounds biological importance and are considered a source of various pharmaceutical compounds.
In this research, the semiparametric Bayesian method is compared with the classical method to estimate reliability function of three systems : k-out of-n system, series system, and parallel system. Each system consists of three components, the first one represents the composite parametric in which failure times distributed as exponential, whereas the second and the third components are nonparametric ones in which reliability estimations depend on Kernel method using two methods to estimate bandwidth parameter h method and Kaplan-Meier method. To indicate a better method for system reliability function estimation, it has be
... Show MoreIt is an established fact that substantial amounts of oil usually remain in a reservoir after primary and secondary processes. Therefore; there is an ongoing effort to sweep that remaining oil. Field optimization includes many techniques. Horizontal wells are one of the most motivating factors for field optimization. The selection of new horizontal wells must be accompanied with the right selection of the well locations. However, modeling horizontal well locations by a trial and error method is a time consuming method. Therefore; a method of Artificial Neural Network (ANN) has been employed which helps to predict the optimum performance via proposed new wells locations by incorporatin
This research involves studying the influence of increasing the
number of Gaussian points and the style of their distribution, on a circular exit pupil, on the numerical calculations accuracy of the point spread function for an ideal optical system and another system having focus error of (0.25 A. and 0.5 A. )
It was shown that the accuracy of the results depends on the type of
distributing points on the exit pupil. Also, the accuracy increases with the increase of the number of points (N) and the increase of aberrations which requires on increas (N).
Maximum values of one particle radial electronic density distribution has been calculated by using Hartree-Fock (HF)wave function with data published by[A. Sarsa et al. Atomic Data and Nuclear Data Tables 88 (2004) 163–202] for K and L shells for some Be-like ions. The Results confirm that there is a linear behavior restricted the increasing of maximum points of one particle radial electronic density distribution for K and L shells throughout some Be-like ions. This linear behavior can be described by using the nth term formula of arithmetic sequence, that can be used to calculate the maximum radial electronic density distribution for any ion within Be like ions for Z<20.
This research aimed to definite Blending learning (BL) technique, and to know the impact of its use onacademic achievement in Biology course of second class students in secondary special schools in Omdurman Locality and attitudes towards it, to achieve this; researcher adopted the experimental method. The sample was selected of (41) students, chosen from Atabiyah school, were divided into two equals groups: one experimental group reached (26) students studied by using the BL technique, and the second control group (25) students have been taught in the traditional method.
Data has collected by using two tools: achievement test and a questionnaire for measuring the attitudes towards Blend
... Show MoreNew derivatives of thiosemicarbazide were synthesized by reaction of different aromatic aldehydes and ketones with thiosemicarbazide to give schiff-bases 1(a-d) . schiff-bases have been used for synthesized the thioimidazolidine 2(a-d) by reaction of schiff-bases with ethyl chloroacetatein in presence of anhydrous sodium acetate that transformed part of it in to Beta-lactam 3(a-b) compounds with phenyl acetic acid and thionyl chloride , The compounds 4(a-b) came from the reactor of 4-bromobenzaldehyde with compounds 2(a-b) , as well as reaction of compounds 2(b-d) with methyl iodide and anhydrous potassium carbonate to give 5 (b-d) , then added hydrazine hydrate formed 6(b-d) , then
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One and two-dimensional hydraulic models simulations are important to specify the hydraulic characteristics of unsteady flow in Al-Gharraf River in order to define the locations that facing problems and suggesting the necessary treatments. The reach in the present study is 58200m long and lies between Kut and Hai Cities. Both numerical models were simulated using HEC-RAS software, 5.0.4, with flow rates ranging from 100 to 350 m3/s. Multi-scenarios of gates openings of Hai Regulator were applied. While the openings of Al-Gharraf Head Regulator were ranged between 60cm to fully opened. The suitable manning roughness for the unsteady state was
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