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.
The reaction of [Benzoyl hydrazine] with [Diphenyl mono oxime] and Glacial acetic acid was carried out in methanol gave a new tridentate ligand [Benzoic acid (2- hydroxyimino- 1, 2-diphyneylethylidene) - hydrazide]. This ligand was reacted with some metal ions (Fe(II), Co(II), Ni(II), and Cu(II)) in methanol with (1:1) metal : ligand ratio to give a series of new complexes of the general formula [M(L)Cl2.H2O], where M= Fe(11), Co(11), Ni(11) and Cu(11) . All compounds were characterized by spectroscopic methods (I.R, UV-Vis), elemental microanalysis (C.H.N), atomic absorption, magnetic susceptibility, and conductivity measurements. From the obtained data the proposed molecular structures were suggested for the complexes of Fe (II), Co (II)
... Show MoreAnew Schiff base (NaHL) has been prepared from the reaction between the salt of amino acid glycine with 2-hydroxy naphthaldehyde. By tridentate Schiff base of (ONO), donors were characterized by using U.V and spectrophotometer techniques. Complexes of Co(II) Ni(II) Cu(II) and Zn(II) ion with the ligand have been prepared, these complexes were identified by infrared, electronic spectral data, elemental analysis, magnetic moments, and molar conductivity measurements. It is concluded from the elemental analysis that all the complexes have (1:2) [metal:ligand] molar ratios, octahedral, with the exception to Zn(II) complex which have (1:1)[metal:ligand] molar ratio.
... Show MoreThe reaction of [Benzoyl hydrazine] with [Diphenyl mono oxime] and Glacial acetic acid was carried out in methanol gave a new tridentate ligand [Benzoic acid (2-hydroxyimino- 1, 2-diphyneylethylidene) - hydrazide]. This ligand was reacted with some metal ions (Fe(II), Co(II), Ni(II), and Cu(II)) in methanol with (1:1) metal : ligand ratio to give a series of new complexes of the general formula [M(L)Cl2.H2O], where M= Fe(11), Co(11), Ni(11) and Cu(11). All compounds were characterized by spectroscopic methods (I.R, UV-Vis), elemental microanalysis (C.H.N), atomic absorption, magnetic susceptibility, and conductivity measurements. From the obtained data the proposed molecular structures were suggested for the complexes of Fe
... Show Moreحضرت معقدات كل من الفنادايل, الخارصين, النحاس والكادميوم بتكافؤهم الثنائي والذهب بتكافؤه الثلاثي بأستخدام صبغة ازوجديدة (6،4،2-ثلاثي هيدروكسي-3-((3-هيدروكسي فنيل) ثنائي زينيل ) فنيل ) ايثان-1-اون المحضرة من ملح الديازونيوم مع ٦,٤,٢- ثلاثي هيدروكسي اسيتوفينون بعد عزل (E)-1-(2,4,6-trihydroxy-3-((3-hydroxyphenyl)diazenyl)phenyl)ethan-1-one تم تشخيصها بواسطة الطرق الطيفية المتاحة والتقنيات التشخيصية لكل من التحليل الدقيق للعناصرواطياف كل من ال
... Show MoreMixed ligands reaction of [2-[(3-hydroxyphenyl)diazinyl]-1,2-benzothiazol-3(2H)-one-1,1-dioxide] (H2L, primary ligand) and bipyridyl (secondary ligand) with salts of Cr(III), Mn(II), Fe(III), Co(II) and Ni(II) was performed. A series of air-stable complexes with distinctive octahedral moieties was created by equal molar ratio (1:1:1). The formation of these compounds was verified using detecting analysis techniques incorporating mass spectra, which validated the achieved geometries. Fourier transform infrared (FTIR) analysis demonstrated how the ligands (H2L and bipyridyl) are chelated as tridentate (ONO) and bidentate (NN) groups, respectively and the coordination with the metal ions. Thermal decomposition studies using pyrolysis (
... Show MoreThis study aimed to fabricate a curcumin@platinum nanohybrid (CUR@Pt NPs) through a green tea–based synthesis method and to evaluate its various functions, including antioxidant, burn-healing, and selective anticancer activities against PANC-1 pancreatic cancer cells. Green tea polyphenols served as natural reducing and stabilizing agents, facilitating an eco-friendly, single-step manufacturing process. Physicochemical characterization confirmed successful nanohybrid formation: a CUR@Pt band appeared at 457 nm in the UV–Vis spectrum, XRD displayed crystalline platinum peaks at 2θ = 46.9°, and 67.0°, matching the (200), and (220) planes, respectively, and TEM images showed well-dispersed spherical nanoparticles with an average siz
... Show MoreFour Co(II), (C1); Ni(II), (C2); Cu(II), (C3) and Zn(II), (C4) chelates have been synthesized with 1-(4-((2-amino- 5‑methoxy)diazenyl)phenyl)ethanone ligand (L). The produced compounds have been identified by using spectral studies, elemental analysis (C.H.N.O), conductivity and magnetic properties. The produced metal chelates were studied using molar ratio as well as sequences contrast types. Rate of concentration (1 ×10 4 - 3 ×10 4 Mol/L) sequence Beer’s law. Compound solutions have been noticed height molar absorptivity. The free of ligand and metal chelates had been applied as disperse dyes on cotton fabrics. Furthermore, the antibacterial activity of the produced compounds against various bacteria had been investigated. F
... Show MoreCompound 4-(((6-amino-7H-[1,2,4]triazolo[3,4-b][1,3,4]thiadiazin-3-yl)methoxy)methyl)- 2,6-dimethoxyphenol (6) was synthesized by multi steps. The corresponding acetonitrile thioalkyl (7) was cyclized by refluxing with acetic acid to afford 4-(((6-amino-7H-[1,2,4]triazolo[3,4- b][1,3,4]thiadiazin-3-yl)methoxy)methyl)-2,6-dimethoxyphenol (8). Two new series of 4-(((6-(3- (4-aryl)thioureido)-7H-[1,2,4]triazolo[3,4-b][1,3,4] thiadiazin-3-yl)methoxy)methyl)-2,6- dimethoxyphenol (9a-c) and of 4-(((6-(substitutedbenzamido)7H-[1,2,4]triazolo[3,4- b][1,3,4]thiadiazin-3-yl)methoxy)methyl)-2,6-dimethoxyphenol (10a-c) were synthesized as new derivatives for fused 1,2,4-trizaole-thiadiazine(8). The antioxidants of newly compounds were evaluated by DPPH
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