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

In this work, a comparative analysis for the behavior and pattern of the variations of the IF2 and T Ionospheric indices was conducted for the minimum and maximum years of solar cycles 23 and 24. Also, the correlative relationship between the two ionospheric indices was examined for the seasonal periods spanning from August 1996 to November 2008 for solar cycle 23 and from December 2008 to November 2019 for solar cycle 24. Statistical calculations were performed to compare predicted values with observed values for the selected indices during the tested timeframes. The study's findings revealed that the behavior of the examined indices exhibited almost similar variations throughout the studied timeframe. The seasonal variations were

This investigation integrates experimental and numerical approaches to study a novel solar air heater aimed at achieving an efficient design for a solar collector suitable for drying applications under the meteorological conditions of Iraq. The importance of this investigation stems from the lack of optimal exploitation of solar energy reaching the solar collector, primarily attributable to elevated thermal losses despite numerous designs employed in such solar systems. Consequently, enhancing the thermal performance of solar collectors, particularly those employed in crop drying applications, stands as a crucial focal point for researchers within this domain. Two identical double-pass solar air heaters were designed and constructed for

Research aims to shed light on the concept of corporate failures , display and analysis the most distinctive models used to predicting corporate failure; with suggesting  a model to reveal the probabilities of corporate failures which including internal and external financial and non-financial indicators, A tested is made for the research objectivity and its indicators weight and by a  number of academics professionals experts, in addition to  financial analysts  and have concluded a set of conclusions ,  the most distinctive of them that failure is not considered a sudden phenomena for the company and its stakeholders , it is an Event passes through numerous stages; each have their symptoms that lead eve

The present work establishes and validates HILIC strategies simple, accurate, exact and precise in pure form and inpharmaceutical dosage for separating and determining theophylline. These methods are developed on HILIC theophyllineseparation in columns ZIC2 and ZIC3. The eluent was prepared by mixing buffer (20% sodium acetate-40 mM, pH 5.5), 80%acetonitrile. The flow rate is 0.8 mL/min, with gradient elution and UV detection at 270 nm. In the ZIC2 and ZIC3 columns oftheophylline determining, the concentration range was 0.01-4μg.ml-1. The lower limit of detection and quantification fortheophylline were determined as 0.130, 0.190 μg.ml-1 and accuracy were 99.70%, 99.58% on ZIC2 and ZIC3, respectively. TheHILIC methods developed and validat

Each phenomenon contains several variables. Studying these variables, we find mathematical formula to get the joint distribution and the copula that are a useful and good tool to find the amount of correlation, where the survival function was used to measure the relationship of age with the level of cretonne in the remaining blood of the person. The Spss program was also used to extract the influencing variables from a group of variables using factor analysis and then using the Clayton copula function that is used to find the shared binary distributions using multivariate distributions, where the bivariate distribution was calculated, and then the survival function value was calculated for a sample size (50) drawn from Yarmouk Ho

The question of estimation took a great interest in some engineering, statistical applications, various applied, human sciences, the methods provided by it helped to identify and accurately the many random processes.

In this paper, methods were used through which the reliability function, risk function, and estimation of the distribution parameters were used, and the methods are (Moment Method, Maximum Likelihood Method), where an experimental study was conducted using a simulation method for the purpose of comparing the methods to show which of these methods are competent in practical application This is based on the observations generated from the Rayleigh logarithmic distribution (RL) with sample sizes