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 derivatives of Schiff bases connected with 5H-thiazolo[3,4-b][1,3,4]thiadiazole ring 5a-c were prepared via many reactions starting by treating 1,4-phenylene diamine 1 with chloroacetylchloride to prepared compound 2, then reaction with p-hydroxybenzaldehyde to synthesize compound 3 then, this was reacted with thioglycolic acid and thiosemicarazide to giveN,N-(1.4-phenylene)bis(2-(4-(2-amino-5Hthiazolo[4,3-b][1,3,4]thiadiazol-5-yl)phenoxy)acetamide) 4. Compound 4 was treated with different aromatic aldehydes to give a new derivatives of Schiff bases containing 5H-thiazolo[3,4-b][1,3,4]thiadiazole ring 5a-c. The synthesized compounds were characterized using FTIR spectrophotometer and 1H NMR spectroscopy and the biological activity of
... Show MoreThis research was aimed to study the exposure of Razzazah Lake to major hydrological changes in recent years as a result of natural climatic changes and drought, high evaporation in lake due to stop discharge from Habbaniyah Lake by Al- majera channel. During 2019, we collected surface water samples at three locations, and three samples from groundwater, in addition one samples from each location Imam Ali Drop and Sewage water of Karbala. The Results show that the heavy isotopes in lake and groundwater well are enriched during the warm period, and depleted during the cold period. Chemically, The dominant cations and anions in Al-Razzaza lake water are mainly of in Order Ca > Na > Mg and Cl>SO4 and the water
... Show MoreWhile conservative access preparations could increase fracture resistance of endodontically treated teeth, it may influence the shape of the prepared root canal. The aim of this study was to compare the prepared canal transportation and centering ability after continuous rotation or reciprocation instrumentation in teeth accessed through traditional or conservative endodontic cavities by using cone-beam computed tomography (CBCT).
Forty extracted intact, matured, and 2-rooted human maxillary first premolars were selected for this
The research includes preparation of a new Schiff base from the condensation of sulfonic acid with 2-phthalaldehyde by dissolving (0.2 g, 0.346 mmole) of the ligand (L) in (10 ml) of absolute ethanol, then 0.06 g of potassium hydroxide (KOH) dissolved in 10 ml of distilled water added to it and reacting the product with some binary metal salts (Mn, Co, Ni, Cu, Cd, Zn, Pt, Hg). The biological study was conducted against two types of gram-positive and gram-negative bacteria, Staphylococcus. aureus and Escherichia coli, and the fungus Candida albicans was also used. All the prepared complexes showed higher activity against bacteria and fungi than the ligand for the free Schiff base. The total antioxidant content of the ligand and the c
... Show MoreRelease of industrial effluents comprising dyes in water bodies is one of the foremost causes of water pollution. Therefore, the proper and proficient treatment of these dyes contaminated left-over material before their release is crucial. Herein, an eco-friendly biological macromolecule Gum-Acacia (GA) integrated Fe3O4 nanoparticles composite hydrogel was manufactured via co-precipitation technique for effective adsorption of Congo red (CR) dye existing in water bodies. The as-prepared magnetic GA/Fe3O4 composite hydrogel was characterized by FTIR, XRD, EDX, VSM, SEM, and BET techniques. These studies discovered the fruitful fabrication of biodegradable magnetic GA/Fe3O4 composite hydrogel possessing porous structure with large surface are
... Show MoreAn experiment was conducted in pots under field conditions during fall seasons of 2017 and 2018. This study aimed to improve a weak growth of seedlings under salt stress in sorghum. Three factors were studied. 1st factor was three cultivars (Inqath, Rabeh, and Buhoth70). 2nd factor was seed priming (primed and unprimed seed). Seed were primed by soaking for 12 hours in a solution containing 300 + 70 mg L−1 of gibberellic (GA3) and salicylic (SA) acids, respectively. 3rd factor was irrigation with saline water (6, 9 and 12 dS m−1) resulting from dissolving sodium chloride in distilled water in addition to control treatment (distilled water). Randomized complete block design was used with four replications. In both seasons: the results sh
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