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 novel series of mixed-ligand complexes of the type, [ML 1 (L 2 ) 3 ]Cl x [M = Cr(III), Fe(III), Co(II),Ni(II), Cu(II), Cd(II) and Hg(II), n = 2, 3], was synthesized using Schiffbase (HL 1 ) as main ligand, nicotinamide (L 2 ) as secondary ligand, and the corresponding metal ions in 1:3:1 molar ratio. The main ligand, HL 1 was prepared by the interaction of ampicillin drug and 4-chlorobenzophenone. The synthesized mixed ligand complexes were characterized by elemental analysis, UV-Vis, FT-IR, 1 H-NMR, 13 C-NMR and TG/DTG studies. In the mixed-ligand complexes, the Schiffbase ligand, HL 1 showed coordination to the central metal ion in tridentate manner via azomethine nitrogen, β-lactam ring oxygen and deprotonated carboxylic oxy- gen atom
... Show MoreAromatic Schiff-bases are known to have antibacterial activity, but most of these compounds are sparingly soluble in water. The present work describes the synthesis of new Schiff-bases derived from branched aminosugars. Treatment of 3-Amino-3-Cyano-3-Deoxy-1,2:5,6-Di-O-Isopropylene-α-D-Allofuranose (1) with the aldehydes (2) under reflux in methanol afforded the Schiff-bases (3) in good yields. The new Schiff-bases were in accord with their NMR, IR spectral data and elemental analysis.
A novel Schiff base ligand (DBC) synthesized from 4-chlorobenzoic acid, along with its Cu (II) and Co (II) complexes, was prepared and characterized using FT-IR, 1H and 13C-NMR, UV-Vis spectroscopy, as well as magnetic and conductivity measurements. Based on this, a tetrahedral structure of [M(DBC)Cl2] was proposed for the complexes. Antioxidant activity of the compounds was assessed and compared to ascorbic acid, revealing that the copper complex exhibited superior antioxidant properties compared to the cobalt complex and the ligand. Furthermore, the antibiofilm potential of the copper and cobalt complexes was assessed against five clinically relevant bacterial species (P.aeruginosa, E.coli, K.pneumoniae, S.aureus and S.typhi) usin
... Show MoreTo prepare a new ligand, many compounds were used to synthesize Schiff-Mannich base, such as isatin, Para chloro Aniline, 2-mercaptobenzimidazole and indole. The resulting compound 1-((2-((1H-indol-1-ylthio)-1H-benzo[d]imidazol1-yl)methyl)-3-(4-chlorophenylimino)indolin-2-one (L). (L) was used to create a series of metal ion complexes with Co (II), Ni (II), Cu (II), Pd (II), Pt (IV), and Au (III). C.H.N.S., FTIR, mass spectra UV-ViS, 1H-NMR, 13CNMR, magnetic moment, and molar conductivity were used to characterize all of these compounds. Except for the palladium(II) and gold(III) complexes, all of the produced complexes had an octahedral geometry, according to the data. The antibacterial activity of the produced compounds was tested by usin
... Show MoreThe ligand 2-[1-(1H-indol-3-yl)ethylimino) methyl]naphthalene-1-ol, derived from 1-hydroxy-2-naphthaldehyde and 2-(1H-indol-3-yl)ethylamine, was used to produce a new sequence of metal ions complexes. Thus ligand reactions with NiCl2.6H2O, PdCl2, FeCl3.6H2O and H2PtCl6.6H2O were sequentially made to collect mono-nuclear Ni(II), Pd(II), Fe (III), and Pt(IV). (IR or FTIR), Ultraviolet Reflective (UV–visible), Mass Spectra analysis, Bohr-magnetic (B.M.), metal content, chloride content and molar conductivity have been the defining features of the composites. The Fe(III) and Pt(IV) complexes have octahedral geometries, while the Ni(II) complex has tetra
... Show MoreThe design of coordination compounds with solvent-responsive optical properties remains a central challenge in molecular photonics. Here, we describe the synthesis and full characterisation of a symmetrical tetradentate diamine ligand, 3,3′-((1,2-phenylenebis(azanediyl))- bis(methanylylidene))bis(pentane-2,4-dione) (H₂L), and its neutral square-planar complexes [M(L)] (M(II) = Co, Ni, Cu). The Cu(II) complex crystallised as [Cu(L)]⋅0.5 (pyrazine), adopting a nearly square-planar geometry (τ₄ = 0.06) in the solid state, as confirmed by single-crystal X-ray diffraction. In DMSO solution, UV–Vis spectra revealed reversible axial coordination of two solvent molecules, driving a transformation to a distorted octahedral geometry. Struc
... Show MoreThe 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
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