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.
Background: Dental implant is one of the most important options for teeth replacement. In two stage implant surgery, a few options could be used for uncovering implants, scalpel and laser are both considered as effective methods for this purpose. The Aim of the study: To compare soft tissue laser and scalpel for exposing implant in 2nd stage surgery in terms of the need for anesthesia, duration of procedure and pain level assessment at day 1 and day 7 post operatively using visual analogue scale . Materials and methods: Ten patients who received bilateral implants participated after healing period completed, gingival depth over each implant was recorded and then implant(s) were exposed by either scalpel or laser with determination for th
... Show MoreThe growing demand for optical fibers is due to their superior the ability to transmit information with high efficiency and minimal loss across extensive distances. In this study, four optical fibers with core radii ranging from (2.05-5.05) μm, and with a numerical aperture of 0.1624 were analyzed. The modal properties of these fibers were calculated at a wavelength of 1030 nm using the RP Fiber Calculator software (free version 2025). Furthermore, the impact of increasing the core radius on these properties was examined. The results showed that multimode fibers are formed when the core radius is much larger than the wavelength used. In contrast, single-mode fiber is obtained when th
A revolution called information revolution has recently invaded the world. It is Currently considered one of the most important properties of development to the countries of the world The criteria provided by computers such as accuracy, speed, time saving Storage and restore have led them to be widely used in economy, industry, agriculture, communications, etc., as well as being the major finder of reengineering the operations of innovation. The use of computers in the preparation of budgets will lead to achieve accuracy. Since, the operation draws upon the statistic and quantity estimations about budget items, the computerized balance sheet may save time and effort of preparing mathematical equations annually. According to the problem o
... Show MoreA comparison of double informative and non- informative priors assumed for the parameter of Rayleigh distribution is considered. Three different sets of double priors are included, for a single unknown parameter of Rayleigh distribution. We have assumed three double priors: the square root inverted gamma (SRIG) - the natural conjugate family of priors distribution, the square root inverted gamma – the non-informative distribution, and the natural conjugate family of priors - the non-informative distribution as double priors .The data is generating form three cases from Rayleigh distribution for different samples sizes (small, medium, and large). And Bayes estimators for the parameter is derived under a squared erro
... Show MoreThe marketing logistic chain, as an integrated system aimed to balance the achievement of its main opposite objectives which represented in the access to the best service presented to the customer with lowest possible logistic costs especially the transportation costs, where encourages the researcher to choose the second objective as a field of this study in order to reduce the transportation costs in the final link of marketing logistic chain which related to delivering of fuel oil to the customer that falls within organizational responsibilities of the company under consideration (Oil Marketing Company) and also known in a brief name by (SOMO) through two methods, the first is by functioning quantative techniques by using trans
... Show MoreY Adnan, H Atiyah, IH Neamah…, International Development Planning Review, 2024
The research aims to shed light on the nature of the tax gap in the income tax by the method of direct deduction and its reflection on the financial objective of the tax, and to determine the reasons for this gap in the deduction between the tax due in accordance with the laws and instructions in force and the tax actually paid. The tax gap is a real problem that cannot be ignored for what it represents loss of financial revenues due to the state.
The research problem is represented in the existence of a gap between the tax due according to direct deduction instructions and the tax actually paid according to the financial statements, and to achieve the objectives of the research and test the hypotheses, t
... Show MoreFinding communities of connected individuals in complex networks is challenging, yet crucial for understanding different real-world societies and their interactions. Recently attention has turned to discover the dynamics of such communities. However, detecting accurate community structures that evolve over time adds additional challenges. Almost all the state-of-the-art algorithms are designed based on seemingly the same principle while treating the problem as a coupled optimization model to simultaneously identify community structures and their evolution over time. Unlike all these studies, the current work aims to individually consider this three measures, i.e. intra-community score, inter-community score, and evolution of community over
... Show MoreOn Saturday, May 13, 2023, a glorious day was engraved in the history of Al-Kindy College Medical Journal as it is the day of indexing the journal in the Scopus Database Journals. The journal has paced a strenuous journey to make that achievement.
The sustainable environmental neighborhoods is sustainable development of neighborhoods that include considerations related to transport, density, urban forms, and environmental buildings and especially those related to social and functional integration, and civil society participation, This standard, which did not attract the attention of specialists in the 1990s, has today become a center of attention for all those interested in urbanism and sustainability. The problem of the research is the existence of urban problems in residential neighborhoods that lead to lack of sustainability in the city, and the research aims to explain the role and importance of environmental sustainability