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.
Exposure of reinforced concrete buildings to an accidental fire may result in cracking and loss in the bearing capacity of their major components, columns, beams, and slabs. It is a challenge for structural engineers to develop efficient retrofitting techniques that enable RC slabs to restore their structural integrity, after being exposed to intense fires for a long period of time. Experimental
investigation was carried out on twenty one slab specimens made of self compacting concrete, eighteen of them are retrofitted with CFRP sheets after burning and loading till failure while three of them (which represent control specimens) are retrofitted with CFRP sheet after loading till failure without burning. All slabs had been tested in a
A simple reverse-phase high performance liquid chromatographic method for the simultaneous analysis (separation and quantification) of furosemide (FURO), carbamazepine (CARB), diazepam (DIAZ) and carvedilol (CARV) has been developed and validated. The method was carried out on a NUCLEODUR® 100-5 C18ec column (250 x 4.6 mm, i. d.5μm), with a mobile phase comprising of acetonitrile: deionized water (50: 50 v/v, pH adjusted to 3.6 ±0.05 with acetic acid) at a flow rate 1.5 mL.min-1 and the quantification was achieved at 226 nm. The retention times of FURO, CARB, DIAZ and CARV were found to be 1.90 min, 2.79 min, 5.39 min and 9.56 min respectively. The method was validated in terms of linearity, accuracy, precision, limit of detection and li
... Show MoreThis research was carried out at University of Baghdad - College of Agricultural Engineering Sciences during the fall season of 2020 and spring season of 2021 in order to evaluate the effect of organic fertilizer and the foliar application of boron on the growth and yield of industrial potatoes (Solanum tuberosum L.). Using factorial experiment (5*4) within Randomized Complete Block Design with three replicates, the organic fertilizer (palm fronds peat) was applied at four levels (0, 12, 24, and 36 ton ha-1) in addition to the treatment of the recommended of chemical fertilizer. The foliar application of Boron was applied at four concentrations which were 0, 100, 150 and 200 mg (H3Bo3). L-1. The results Revealed a significant incr
... Show MorePareto distribution is used in many economic, financial and social applications. This distribution is used for the study of income and wealth and the study of settlement in cities and villages and the study of the sizes of oil wells as well as in the field of communication through the speed of downloading files from the Internet according to their sizes. This distribution is used in mechanical engineering as one of the distributions of models of failure, stress and durability. Given the practical importance of this distribution on the one hand, and the scarcity of sources and statistical research that deal with it, this research touched on some statistical characteristics such as derivation of its mathematical function , probability density
... Show MoreGingival crevicular fluid (GCF) may reflect the events associated with orthodontic tooth movement. Attempts have been conducted to identify biomarkers reflecting optimum orthodontic force, unwanted sequallea (i.e. root resorption) and accelerated tooth movement. The aim of the present study is to find out a standardized GCF collection, storage and total protein extraction method from apparently healthy gingival sites with orthodontics that is compatible with further high-throughput proteomics. Eighteen patients who required extractions of both maxillary first premolars were recruited in this study. These teeth were randomly assigned to either heavy (225g) or light force (25g), and their site specific GCF was collected at baseline and aft
... Show MoreIn this paper, the Decomposition method was used to find approximation solutions for a system of linear Fredholm integral equations of the second kind. In this method the solution of a functional equations is considered as the sum of an infinite series usually converging to the solution, and Adomian decomposition method for solving linear and nonlinear integral equations. Finally, numerical examples are prepared to illustrate these considerations.
The research aims to estimate missing values using covariance analysis method Coons way to the variable response or dependent variable that represents the main character studied in a type of multi-factor designs experiments called split block-design (SBED) so as to increase the accuracy of the analysis results and the accuracy of statistical tests based on this type of designs. as it was noted in the theoretical aspect to the design of dissident sectors and statistical analysis have to analyze the variation in the experience of experiment )SBED) and the use of covariance way coons analysis according to two methods to estimate the missing value, either in the practical side of it has been implemented field experiment wheat crop in
... Show MoreThiazoles are heterocyclic nitrogenous compounds, which were given a great attention due to their antibacterial effect, antihypertensive, stimulating glucose absorption (like antibiotics), acts as cytoprotective agent. The present work is conducted to evaluate the degree of antibacterial activity on the growth activity of Escherichia Coli (E.Coli) and Pseudomonas aeruginosa (P. aeruginosa) by incubation with 2-methyl-4-(3,4 dihydroxy phenyl)-Thiazole compound (MDHPT). Optical density (O.B) was measured by turbidmetric method, any increase in O.D would represent the increase in the bacterial growth .The results showed that there was a 75.7 % inhibition when using 190.4 ïg/ml (MDHPT) solution and 64.3% was obtained when using concentr
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