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.
Small ring heterocycles containing nitrogen and sulfur have been under investigation for a long time because of their important medicinal properties. Among the wide range of heterocycles explored to develop pharmaceutically important molecules, thiadiazoles had played an important role in medicinal chemistry. A survey of literature had shown that compounds having thiadiazole nucleus possess a broad range of biological activities such as anti-inflammatory (1), antibacterial (2), and antifungal activities (3). Thiazine-4-one and their derivatives are import classes of compounds in organic and medicinal chemistry. The thiazine-4-one ring system is a core structure in various synthetic pharmaceutical agents, displaying a broad spectrum of biolo
... Show MoreFour new copolymers were synthesized from reaction of bis acid monomer 3-((4-carboxyphenyl) diazenyl)-5-chloro-2-hydroxybenzoic acid with five diacidhydrazide in presence of poly phosphoric acid. The resulted monomers and copolymers have been characterized by FT-IR, 1H-NMR, 13C-NMR spectroscopy as well as EIMs technique. The number averages of molecular weights of the copolymers are between 4822 and 9144, and their polydispersity indexes are between 1.02 and 2.15. All the copolymers show good thermal stability with the temperatures higher than 305.86 C when losing 10% weight under nitrogen. The cyclic voltammetry (CV) measurement and the electrochemical band gaps (Eg) of these copolymers are found below 2.00 ev.
In this work involved prepared of several new 1-cyclopentene-1,2-dicarboxylimide linked to oxadiazole and benzothiazole moiety were synthesized by two steps: The first step 2-amino-substituted-1,3,4-oxadiazoles and substituted-2-aminobenzothiazole were reaction with 1-cyclopentene-1,2-dicarboxyl anhydride producing N-( 5- substituted-1,3,4-oxadiazole-2-yl)-1-cyclopentene-1,2-dicarboxyl amic acids and N-(Substitutedbenzothiazole-2-yl)-1-cyclopentene-1,2-dicarboxyl amic acids which in turn were dehydrated in the second step via fusion method to afford he desirable N-(5-substituted-1,3,4-oxadiazole-2-yl)-1-cyclopentene-1,2-dicarboxylimides and N-(Substituted benzothiazole-2-yl)1-cyclopentene-1,2-dicarboxylimides respectively. Struct
... Show MoreNewly acid hydrazide was synthesized from ethyl 2-(2,3-dimethoxyphenoxy) acetate (2), which is cyclized to the corresponding 4-amino-1,2,4-triazole (3). Five newly azo derivatives (4a-e) were synthesized from this 1,2,4-triazole by converting the amine group to diazonium salt then reacted with various substituent phenol,as well three newly imine derivatives (5a-c) were synthesized from reacting the amine group of compound (3) with three aryl aldehyde. The thermal electro conductivity of these compounds was tested at 30, 50, 75 and 100 áµ’C. compound 4a showed interesting electro conductivity at 75áµ’C as well 5a at 75áµ’C while 5b showed significant conductivity at 100 áµ’C
Background: Lateral sinus augmentation and simultaneous insertion of dental implants is a highlypredictable procedure and associated with high rate of implants success.Aims: To evaluate implant stability changes following maxillary sinus augmentation utilizing deproteinizedbovine bone alone or mixed with platelet-rich fibrin.Materials and Methods: A total of 34 lateral sinus augmentation procedures were performed and 50 dentalimplants simultaneously installed. The lateral sinus augmentation cases were allocated randomly into 3groups: Group A comprised 13 procedures and 21 dental implants utilizing solely deproteinized bovine bone.Group B involved 10 cases and 16 dental implants using deproteinized bovine bone mixed with leukocyteand
... Show MoreIn this work, a series of new Nucleoside analogues (D-galactopyranose linked to oxepanebenzimidazole moiety) was synthesized via multisteps synthesis. The first step involved preparation of two benzimidazoles 2-styrylbenzimidazole and 2-(phenyl ethynyl) benzimidazole via reaction of phenylenediamine with cinnamic acid or ?-phenyl propiolic acid. Electrophilic addition of the prepared benzimidazoles by three anhydrides in the second step afforded (4-6) and (14-16) which in turn were treated with 1,2,3,4-di-O-isopropylidene galactopyranose in the third step to afford a series of the desirable protected nucleoside analogues (7-9) ,(17-19)which after hydrolysis in methanolic sodium methoxidein the fourth step afforded the free nucleoside analog
... Show MoreThe analysis of Iraqi light oil (light naphtha) by capillary gas chromatography- mass spectrometry (GC-MS) was performed by the injection of whole naphtha sample without use of solvents. Qualitative analysis and the identification of the hydrocarbon constituents of light naphtha was performed and comparison had been done with American light oil (light naphtha). The obtained results showed a major difference between the two-light naphtha.
In this work, multilayer nanostructures were prepared from two metal oxide thin films by dc reactive magnetron sputtering technique. These metal oxide were nickel oxide (NiO) and titanium dioxide (TiO2). The prepared nanostructures showed high structural purity as confirmed by the spectroscopic and structural characterization tests, mainly FTIR, XRD and EDX. This feature may be attributed to the fine control of operation parameters of dc reactive magnetron sputtering system as well as the preparation conditions using the same system. The nanostructures prepared in this work can be successfully used for the fabrication of nanodevices for photonics and optoelectronics requiring highly-pure nanomaterials.