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 Problem

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The research deals with the statement of the importance of unanimous in Islamic Sharia in terms of being the third source of Islamic legislation after the Holy Qur’an and the Sunnah of the Prophet, and the extent of interest of the scholars of interpretation in it, and those who took great interest in mentioning what was agreed upon in every site that necessitated mentioning its issues within, or mentioning an event that has encountered an unanimous, and in various sciences, to extract and extrapolate Sharia rules when these rules are lost in the texts, because it is based on them and derived from them. Among these distinguished scholars is Muhammad bin Jarir al-Tabari. Besides, the research discusses in

Diversity has become one of the required phenomena to be available within public organizations, in light of the changes taking place in the global and international environment and in various fields. Therefore, it was imperative to study the impact of this phenomenon in various institutions, especially public ones, in most developing countries, including Iraq. The current research aims to analyze the relationship between The demographic diversity and institutional effectiveness of a sample of workers in public institutions included (500) respondents. The questionnaires were distributed to them randomly. Diversity is considered an independent variable and institutional effectiveness a dependent variable. The researcher used interview tools a

A seasonal study of periphytic algae attached to the surface of river boats was conducted in Tigris river in Al Aadhamiya site for the period from October 2016 to May 2017. A total of 107 taxa of periphytic algae were identified belonging to the four classes of algae. The periphytic algae community dominated by Bacillariophyceae was (60.7%) followed by Chlorophyceae (20.5%) and Cyanophyceae (17.7%) Chrysophyceae was constituted (0.9%) of the total number. During the whole period of study filamentous taxa such as Oscillatoria amphibian, Phormidium spp., Spirulinagigantean, Cladophoreglomerata and Melosira roeseana remained the dominant colonizer which may be reflect the ability of this species to grow multiplies under different environmental

Since the Internet has been more widely used and more people have access to multimedia content, copyright hacking, and piracy have risen. By the use of watermarking techniques, security, asset protection, and authentication have all been made possible. In this paper, a comparison between fragile and robust watermarking techniques has been presented to benefit them in recent studies to increase the level of security of critical media. A new technique has been suggested when adding an embedded value (129) to each pixel of the cover image and representing it as a key to thwart the attacker, increase security, rise imperceptibility, and make the system faster in detecting the tamper from unauthorized users. Using the two watermarking ty

Abstract- Asymptomatic or clinically silent kidney stones are possibly serious because, in their expected passage, they may cause infection, obstruction and renal impairment. The purpose of this study was to determine the prevalence of silent kidney stones in a sample of Baghdad population and consider how this value could affect the justification for a screening system. To our best knowledge, this is the first study of its kind conducted in Iraq. We investigated 714 consecutive patients who sustained an abdominal ultrasound at our hospital with further kidney screening. All these patients did not have clinical signs and symptoms of nephrolithiasis. Age, sex, the indication for ultrasound, the size, side, and the number of the disco