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.
In this paper, the dynamic behaviour of the stage-structure prey-predator fractional-order derivative system is considered and discussed. In this model, the Crowley–Martin functional response describes the interaction between mature preys with a predator. e existence, uniqueness, non-negativity, and the boundedness of solutions are proved. All possible equilibrium points of this system are investigated. e sucient conditions of local stability of equilibrium points for the considered system are determined. Finally, numerical simulation results are carried out to conrm the theoretical results.
New Fe(II),Co(II),Ni(II),Cu(II) and Zn(II) Schiff base complexes which have the molar ratio 2:1 metal to ligand of the general formula [M2( L) X4] (where L=bis(2-methyl furfuraldene)-4-4`-methylene bis(cyclo-hexylamine) ) were prepared by the reaction of the metal salts with the ligand of Schiff base derived from the condensation of 2:1 molar ratio of 2-acetyl furan and 4-4`-methylene bis (cyclohexylamine). The complexes were characterized by elemental analysis using atomic absorption spectrophotometer ,molar conductance measurements, infrared, electronic spectra,and magnetic susceptibility measurement. These studies revealed binuclear omplexes. The metal(II) ion in these complexes have four coordination sites giving the most ex
... Show MoreThis paper includes the synthesis of some new nucleoside analogues starting with 2-substituted benzimidazole derivative (7-9), that synthesized by condensation of O-phenylenediamine with p-chloro benzaldehyde and two substituted benzoic acid , which on nucleophilic substitution with propargyl bromide gave a new N-substituted compounds (10-12). D-Fructose and D-galactose were chosen as a sugar moiety which were protected, brominated and azotated to give azido sugars (5) and (6), then they were subjected to 1,3-dipolar cycloaddition reaction with N-substuted compounds afforded bloked nucleoside analoges (13-16), which after hydrolysis gave our target the free nucleoside analogues (17-20). All prepared compounds were identified by FT-IR
... Show MoreThis paper develops the work of Mary Florence et.al. on centralizer of semiprime semirings and presents reverse centralizer of semirings with several propositions and lemmas. Also introduces the notion of dependent element and free actions on semirings with some results of free action of centralizer and reverse centralizer on semiprime semirings and some another mappings.
The current research seeks to identify mono-multi Vision and its relation to the psychological rebellion and personality traits of university students. To achieve this aim, the researcher has followed all the procedures of the descriptive correlational approach, as it is the closest approach to the objectives of the current research. The researcher has determined his research community for Baghdad University students for the academic year 2019-2020. As for the research sample, it was chosen by the random stratified method with a sample of (500) male and female students. In order to collect data from the research sample, the researcher adopted a mono-multi-dimensional scale
(Othman, 2007), the researcher designed a psychological r
... Show More4-((2-hydroxy-3,5-dinitrophenyl)diazenyl)-1,5-dimethyl-2-phenyl-1H-pyrazol-3(2H)-one was produced through the reaction of diazonium salt from 4-amino antipyrine with 2,4-dinitrophenol. This ligand is examined by (UV-Vis, FTIR,1H,13CNMR, and LC-Mass) spectral techniques and micro elemental analysis (C.H.N.O). Co(II), Ni(II), Cu(II), and Zn(II) complexes were also performed and depicted. Metal chelates were distinguished by utilizing flame atomic absorption, infrared analysis, and elemental, visible, as well as ultraviolet spectroscopy, in addition to conductivity and magnetic quantification. Methods of mole ratio and continuous contrast have been studied to determine the nature of the compounds. Beer's law was followed throughout a co
... Show MoreAdsorption of lead ions from wastewater by native agricultural waste, precisely tea waste. After the activation and carbonization of tea waste, there was a substantial improvement in surface area and other physical characteristics which include density, bulk density, and porosity. FTIR analysis indicates that the functional groups in tea waste adsorbent are aromatic and carboxylic. It can be concluded that the tea waste could be a good sorbent for the removal of Lead ions from wastewater. Different dosages of the adsorbents were used in the batch studies. A random series of experiments indicated a removal degree efficiency of lead reaching (95 %) at 5 ppm optimum concentration, with adsorbents R2 =97.75% for tea. Three mo
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