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

The fluctuation properties of energy spectrum, electromagnetic transition intensities and electromagnetic moments in nucleus are investigated with realistic shell model calculations. We find that the spectral fluctuations of are consistent with the Gaussian orthogonal ensemble of random matrices. Besides, we observe a transition from an order to chaos when the excitation energy is increased and a clear quantum signature of the breaking of chaoticity when the single-particle energies are increased. The distributions of the transition intensities and of the electromagnetic moments are well described by a Porter-Thomas distribution. The statistics of electromagnetic transition intensities clearly deviate from a Porter-Thomas distribution (i

Recently a large number of extensive studies have amassed that describe the removal of dyes from water and wastewater using natural adsorbents and modified materials. Methyl orange dye is found in wastewater streams from various industries that include textiles, plastics, printing and paper among other sources. This article reviews methyl orange adsorption onto natural and modified materials. Despite many techniques available, adsorption stands out for efficient water and wastewater treatment for its ease of operation, flexibility and large-scale removal of colorants. It also has a significant potential for regeneration recovery and recycling of adsorbents in comparison to other water treatment methods. The adsorbents described herein were

In this paper, customers’ expectations are continually shifting due to the business environment’s growing competition and substantial changes. As a result, organisations no longer viewed it as a static objective but as an ever-evolving aim. From this vantage point, the research has explored the accounting literature in search of novel approaches to addressing the strategic dimensions of quality, cost and time. Getting them to respond positively to the customer’s requests also requires recognising their needs and controlling their impact on these dimensions. With the removal of operations that do not contribute any value to the product’s value chain and a reduction in manufacturing costs through continuous improvement, the ou

This research will cover different aspects of estimating process of construction work in a desert area. The inherent difficulties which accompany the cost estimating of the construction works in desert environment in a developing country, will stem from the limited information available, resources scarcity, low level of skilled workers, the prevailing severe weather conditions and many others, which definitely don't provide a fair, reliable and accurate estimation. This study tries to present unit price to estimate the cost in preliminary phase of a project.  Estimations are supported by developing mathematical equations based on the historical data of maintenance, new construction of managerial and school projects.

In this research we study a variance component model, Which is the one of the most important models widely used in the analysis of the data, this model is one type of a multilevel models, and it is considered as linear models , there are three types of linear variance component models ,Fixed effect of linear variance component model, Random effect of linear variance component model and Mixed effect of linear variance component model . In this paper we will examine the model of mixed effect of linear variance component model with one –way random effect ,and the mixed model is a mixture of fixed effect and random effect in the same model, where it contains the parameter (μ) and treatment effect (τ_i ) which  has

Background: Thermocycling simulates the temperature dynamics in the oral environment. This in vitro study done to measure and compare the effect of thermocycling on the shear bond strength of stainless steel and sapphire brackets bonded to human enamel teeth using light cured orthodontic adhesive and debonded at various time, and to measure adhesive remnant index after debonding. Materials and Methods: one-hundred-twenty extracted upper first premolars for orthodontic reason were used in this study; depending on weather thermocycled or not, the sample was divided into two main groups, then within each group 30 teeth were used for stainless-steel brackets (Bionic®) and for sapphire brackets (Pure®). Both groups were subdivided into three