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 synthesis of ligands with N2S2 donor sets that include imine, an amide, thioether, thiolate moieties and their metal complexes were achieved. The new Schiff-base ligands; N-(2-((2,4-diphenyl-3-azabicyclo[3.3.1]nonan-9-ylidene)amino)ethyl)-2-((2-mercaptoethyl)thio)-acetamide (H2L1) and N-(2-((2,4-di-p-tolyl-3-azabicyclo[3.3.1]nonan-9-ylidene)amino)ethyl)-2-((2-mercaptoethyl)thio) acetamide (H2L2) were obtained from the reaction of amine precursors with 1,4-dithian-2-one in the presence of triethylamine as a base in the CHCl3 medium. Complexes of the general formula K2<
novel spectrofluorimetric flow injection analysis (FIA) method was developed for the selective quantification of ascorbic acid via fluorescence quenching of serotonin hydrochloride. The system employs a custom-designed photometric array comprising 16 irradiation sources arranged in a dual-axis matrix—eight aligned horizontally and eight orthogonally, enabling multi-angle excitation and enhanced spectral resolution. Fluorescence signals were captured using a twin-pair solar cell detector, offering high sensitivity and minimal optical interference. The method exhibited a linear calibration range of 0.1–30 limit of detection (LOD) of 0.025 μ μ g/mL with a correlation coefficient (r mol /L, equivalent to 4.403 * 10 4 μ 2 ) of 0.9966, a g
... Show MoreThe ligand 4-amino-N-(5-methylisoxazole-3-yl)-benzene-sulfonamide(L1) (as a chelating ligand) was treated with Pd(II),Pt (IV) and Au(III) ions in alcoholic medium in order to prepare a series of new metal complexes. Mixed ligand complexes of this primary ligand were prepared in alcoholic medium in presence of the co-ligand 4,4'-dimethyl-2,2'-bipyridyl(L2) with Cu(II) ,Pd(II) and Au(III) ions. The complexes were characterized in solid state using flame atomic absorption, elemental analysis C.H.N.S, FT-IR, UV-Vis Spectroscopy, conductivity and magnetic susceptibility measurements. The nature of some complexes formed in ethanolic solution has been studied following the molar ratio method, also stability constant was studied and the complexes f
... 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 MoreThe search involve the synthesis of some new 1,3-oxazepine and 1,3-diazepine derivatives were synthesized from Schiff base. The Schiff base (VIII) prepared from reaction of aldehyde (IV) derived from L-ascorbic acid with aromatic amine ([2-(4- nitrophenyl)-5-(4-aminophenyl)-1,3,4-oxadiazole] (VII). Oxazepine compounds (IX-XI) were synthesized from the cyclic condensation of Schiff base (VIII) with (maleic, phthalic and 3-nitrophthalic) anhydride, compounds (IX-XI) that were reacted with p-methoxyaniline to give diazepine derivatives (XII-XIV). The structures of the new synthesized compounds have been confirmed by physical properties and spectroscopy measurements such as FTIR, and some of them by 1 H-NMR, 13 CNMR, Mass, and evaluated
... Show MoreSYNTHESIS AND CHARACTERISATION OF NEWCo(II), Zn(II) AND Cd(II) COMPLEXES DERIVED FROM OXADIAZOLE LIGAND AND 1,10-PHENANTHROLINE AS Co-LIGAND
synthesis, Composition, Spectral, Geometry and Antibacterial Applications ofMn(||),Ni(||),Co(||),Cu(||) and Hg(||) schiff Base complexes of N2O2 mixed donor with 1,10-phenanthroline
Background: The present study aimed to assess the distribution, prevalence, severity of malocclusion in Baghdad governorate in relation to gender and residency Materials and Methods: A multi-stage stratified sampling technique was used in this investigation to make the sample a representative of target population. The sample consisted of 2700 (1349 males and 1351 females) intermediate school students aged 13 years representing 3% of the total target population. A questionnaire was used to determine the perception of occlusion and orthodontic treatment demand of the students and the assessment procedures for occlusal features by direct intraoral measurement using veriner and an instrument to measure the rotated and displaced teeth. Results a
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