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.
Restoration of degraded lands by adoption of recommended conservation management practices can rehabilitate watersheds and lead to improving soil and water quality. The objective was to evaluate the effects of grass buffers (GBs), biomass crops (BCs), grass waterways (GWWs), agroforestry buffers (ABs), landscape positions, and distance from tree base for AB treatment on soil quality compared with row crop (RC) (corn [
Periodontitis is a chronic inflammation affecting the tooth-supporting periodontal tissues. It is diagnosed by measuring periodontal parameters. However, documenting this data takes effort and may not discover early periodontitis. Biomarkers may help diagnose and assess periodontitis. This study aimed to evaluate the potential diagnostic of the salivary tumor necrosis factor-α (TNF-α) and receptor-activator of nuclear factor ĸ-B-ligand (RANKL) in distinguishing between periodontitis and healthy periodontium.
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A series of novel hybrid molecules containing 1,3,4-oxadiazole and 1,3,4-thiadiazole moieties bearing an ibuprofen moiety were designed, synthesized, and evaluated for their in vitro antibacterial activity against Gram-positive and Gram-negative bacteria. A carboxylic acid compound with a 1,3,4-thiadiazole unit was synthesized via the coupling reaction of 5-(1-(4-isobutylphenyl) ethyl)-1,3,4-thiadiazol-2-amine with benzoic acid. This compound was then used as the starting material to make several new 1,3,4-oxadiazole derivatives through ring closure reactions, after first converting it to its ester (methyl 4-(5-(1-(4-isobutylphenyl)ethyl)-1,3,4-thiadiazol-2-yl) benzoate) and then to the acid hydrazide (4-(5-(1-(4-isobutylphenyl) eth
... Show MoreIn this paper, thermal performance of a zig-zig solar air heater (ZZSAH) with and without using steel wire mesh on the absorber plate of the collector is experimentally investigated. The experimental work includes four inclination angles of the collector 20o, 30o, 45o, and 60o and four air mass flow rates of 0.03, 0.04, 0.06, and 0.08 kg/s under varieties of operating conditions of a geographic location of Baghdad. New correlation equations of Nusselt number are obtained from experimental results for both types of collectors where the effect of varying of the inclination angle of collector taken into consideration in the experiment. The correlations show good agreement wi
... Show MoreIn this study, new oxazolidinone and thiazolidinone derivatives were synthesized through a three-step process. In the first step, o-aminothiophenol was reacted with p-aminobenzoic acid in hydrochloric acid to produce an amine containing a thiazole ring, achieving a product yield of 80%. The second step involves synthesizing Schiff bases (E1-E4) by reacting 4-(benzo[d]thiazol-2-yl)aniline with various aromatic aldehydes in the presence of glacial acetic acid. This reaction yields products of 76% to 90%. In the third step, the Schiff derivatives (E1-E4) are reacted with glycolic acid and thioglycolic acid to obtain the desired products. Oxazolidinone derivatives (N1-T1) were produced with rates ranging from 66% to 74%, while thiazolidin
... Show MoreBackground: University students in Iraq face rising obesity risk linked to physical inactivity, prolonged sedentary behavior, insufficient sleep, and academic stress. Longitudinal evidence examining the combined influence of these behaviors on weight status in Iraqi universities remains limited. Objective: This study examined six-month longitudinal associations of physical activity, sedentary behavior, sleep duration, and perceived stress with body mass index and percentage body fat among Iraqi university students. Methods: A prospective multi-behavioral study was conducted at six public universities in Iraq. Six hundred undergraduate students aged 18–25 years were followed monthly during one academic semester. Validated questionn
... Show MoreThin films ZrO2: MgO nanostructure have been synthesized by a radio frequency magnetron plasma sputtering technique at different ratios of MgO (0,6, 8 and 10)% percentage to be used as the gas sensor for nitrogen dioxide NO2. The samples were investigated by X-ray diffraction (XRD), atomic force microscopy (AFM), scanning electron microscopy (SEM), energy-dispersive X-ray (EDX) and sensing properties were also investigated. The average particle size of all prepared samples was found lower than 33.22nm and the structure was a monoclinic phase. The distribution of grain size was found lower than36.3 nm and uninformed particles on the surface. Finally, the data of sensing properties have been discussed, where the
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