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.
Today we are witnessing huge scientific and technical progress so we need more skills and methods of thinking that needs to be acquired by the teacher, as the importance of computers in education there are many teachers suffering of the difficulty in teaching for pupils . researchers tried to find a good suitable way with the technological interests for now which represent by computer design software and the introduction of enrichment activities in the curriculum because it is one of a contemporary trends for the development of the Arabic language with various levels of education and knowing if this program has negative or positive impact.
So 
... Show MoreIn this paper, the exact solutions of the Schlömilch’s integral equation and its linear and non-linear generalized formulas with application are solved by using two efficient iterative methods. The Schlömilch’s integral equations have many applications in atmospheric, terrestrial physics and ionospheric problems. They describe the density profile of electrons from the ionospheric for awry occurrence of the quasi-transverse approximations. The paper aims to discuss these issues.
First, the authors apply a regularization meth
In this paper, new approach based on coupled Laplace transformation with decomposition method is proposed to solve type of partial differential equation. Then it’s used to find the accurate solution for heat equation with initial conditions. Four examples introduced to illustrate the accuracy, efficiency of suggested method. The practical results show the importance of suggested method for solve differential equations with high accuracy and easy implemented.
Simulated annealing (SA) has been an effective means that can address difficulties related to optimization problems. is now a common discipline for research with several productive applications such as production planning. Due to the fact that aggregate production planning (APP) is one of the most considerable problems in production planning, in this paper, we present multi-objective linear programming model for APP and optimized by . During the course of optimizing for the APP problem, it uncovered that the capability of was inadequate and its performance was substandard, particularly for a sizable controlled problem with many decision variables and plenty of constraints. Since this algorithm works sequentially then the current state wi
... Show MoreResponse of cross-ply plates subjected to transient load is obtained using five variables refined plate theory, and four variables plate theory. Equations of motion are derived through the principleof virtual work. Navier series used for simply supported laminated plates. The results of this work are presented for different parameters, such as the ply number, thickness, and modulus ratio with mechanical load (sinusoidal and step pulses), which are compared with those obtained using high-order shear plate theory. Five variables of refined plate theory give results that are considerably different from the four variables of refined plate theory and higher-order theory. The obtained results from the four variables theory have the same behavior
... Show Moreلطالما كان انتظار الملأ للخلاص والتي ترتبط بشكل اساسي بال "منتظر" او ال "مخلص" جزءا من الوعي الجمعي الذي تطور ليكون مرتبطا بالنمط البدائي والذي بدوره أصبح مرآةً تنعكس على اساسها فرص الانسان نحو النجاة. في مسرح القرن العشرين, لم تنفك فكرة الانتظار ان ترتبط بمسرحية صاموئيل بيكيت العبثية " في انتظار غودو" كونها مثالا رمزيا بالرغم من انه تجسيد شخصية "غودو" وقعت تحت وطأة الكثير من عمليات التحوير والتغيير في اطاره
... Show MoreThe tax base is one of the bases of the technical organizing of taxes, and that a good selection of the tax base effects the outcome of the tax and its fairness, and with the expansion of the tax range results a dangerous phenomenon called tax evasion, which became threaten the economies of countries and this phenomenon prevents the achievement of the state to its economic, political and social objectives which seeks to resolve this phenomenon and identifying all human and material potential and realize the real reasons that lie behind it. The researcher found that tax authorities are weak in terms of it the technical material and financial abilities, the analysis of data show that then is a significant reve
... Show MoreSource of energy and protein Field crops considered an important needed for human
beings Due of this fact increases should appear in the quantities of their production in order to
meet the needs of continuous increasing in the population of the glope year after year ;
otherwise, an increase in the gap between the amount of production and consumption will
occur .
This study aims to reveal the geographical distribution of the potato crop in the district
of Abu – Ghraib. For this purpose, a study conducted about the cultivated areas, production
and crop yields per Dunam for period of 7 years lasted from 2005-2011.
The study shows that potato is one of the most important field crops that are grown in
the Abu –
Crude oil is one of the most important sources of energy in the world. To extract its multiple components, we need oil refineries. Refineries consist of multiple parts, including heat exchangers, furnaces, and others. It is known that one of the initial operations in the refineries is the process of gradually raising the temperature of crude oil to 370 degrees centigrade or higher. Hence, in this investigation the focus is on the furnaces and the corrosion in their tubes. The investigation was accomplished by reading the thickness of the tubes for the period from 2008 to 2020 with a test in every two year, had passed from their introduction into the work. Where the thickness of more than one point was measured on each tube in the sa
... Show More