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.
A new Macrocyclic Schiff base ligand Bis[4-hydroxy(1,2-ethylene-dioxidebenzylidene) pheylenediamine] [H2L] and its complexes with (Co(II) , Ni(II) , Cu(II) , Zn(II) and Cd(II)) are reported . The ligand was prepared in two steps,in the first step a solution of (o-phenylene diamine) in methanol react under reflux with (2,4-dihydroxybenzylaldeyed) to give an (intermediatecompound) [Bis-1,2 (2,4-dihydroxybenzylediene)pheylinediamine] which react in the second step with (1,2- dichloro ethane) giving the mentioned ligand.Then the complexes were synthesis of adding of corresponding metal salts to the solution of the ligand in methanol under reflux with 1:1 metal to ligand ratio. On the basis of, molar conductance, I.R., UV-Vis, chloride content a
... Show MoreThe aim of this work covers the synthesis and characterization of the new tertra dentate ligand (H4L) containing (N and O) as donor set atoms kind (N2O2) where: H4L=Bis-1,2 (2,4- dihydroxybenzylediene phylinediamine . The preparation of ligand contains reaction 2, 4 - Dihydroxy benzaldehyde and o-phenylene diamine . Schiff base was reacted with some metal ions in the presence of methanol to give the complexes in the general formula [M (H2L)] where: MII = Co, Ni, Cu, Zn, Cd. All compounds were characterized by spectroscopic methods I.R , U.V.-Vis, metal content and molar conductivity measurements, showed that the complexes are non-electrolyte. The proposed geometry for all of the proposed complexes was a tetrahedral while Ni complex was squa
... Show Moresynthesis, Composition, Spectral, Geometry and Antibacterial Applications ofMn(||),Ni(||),Co(||),Cu(||) and Hg(||) schiff Base complexes of N2O2 mixed donor with 1,10-phenanthroline
A novel Schiff base ligand [N1-benzylidenebenezene-1,2-diamine(L) = C20H16N2] was prepared through intensification of benzaldehyde (C6H5CHO) and O- amino aniline O-C6H4(NH2)2 in ethanol with 8-Hydroxyquinoline (8HQ) . Formed compounds were acquired of 1:1:2 molar proportion reactions for metal ions and ligands (L) and 2(8HQ) during reaction for MCl2 .nH2O salt products complexes conformable into the forms [M(L)(8HQ)2] ,where M = Mn(II),Co(II) and Ni(II). Whole the compounds were identified during the basis of their; FT-IR and U.V spectrum, melting point, molar conduct, identify of the percentage from the metal at the complexes via flame (AAS), C, H and N content of the Schiff base (L) and metal complexes were analysis and magnetic susceptib
... Show MoreIn this study, poly4-(nicotinamido)-4-oxo-2-butenoic acid (PNOE) was prepared by the electro polymerization of 4-(nicotinamido)-4-oxo-2-butenoic acid (NOE) monomer on a 316 stainless steel (St.St) which acts as an anticorrosion coating. Fourier transforms infrared (FTIR), atomic force microscopy (AFM), scanning electron microscopy (SEM), and cyclic voltammetry were used to diagnose the structure and the properties of the prepared polymer layer. The corrosion behavior of the uncoated and coated 316 St.St were evaluated by using an electro chemical polarization technique in 0.2 M hydrochloric acid solution as a corrosive medium at a temperature range of 293 to 323 K. Nano materials, such as nano ZnO and graphene were added in di
... Show MoreAim: The reduction in the amount of marginal bone is the most important demand for the long term success of dental implants. This prospective clinical study was aimed to investigate the marginal bone loss of early loaded SLActive implants with different dimensions and surgical approaches. Materials and methods Fifteen patients aged from 18 to 60 years were divided into 2 groups (flapped and flapless approach) that underwent delayed implant placement protocol with SLActive implants. The marginal bone level was estimated by cone-beam computed tomography during three different periods: preoperatively, 8 weeks after surgery and 24 weeks after loading of the prosthesis. Results: The mean value of marginal bone level was not significantly chan
... Show MoreСтатья посвящена возможности использования в обучении русскому языку как иностранному лингвоориентированной методики для арабских студентов. Обосновывается термин «лингвоориентированная методика», предложенный В. Н. Вагнер, и на основе положений заявленной методики проводится сопоставление изучаемого (русского) языка с родным (арабским) языком обучающихся.