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.
Abstract The main purpose of the research is to clarify and investigate in details about Susan Glaspell’s role in shedding light on the predicament of women in American society in the early twentieth century showing how sense of the place played an important role in limiting the opportunities of female protagonists who try to escape the roles imposed upon them by society. Glaspell lived in the early twentieth century in the Midwest and tackled the important issues like: women's suffrage, birth control, socialism, union organizing when women were not able to vote or sit as a member on juries. Her Feminist cause is quite obvious through her works from her first one act play Suppressed Desire to the final three act play, Alison’s House. Th
... Show MoreIt is well known that petroleum refineries are considered the largest generator of oily sludge which may cause serious threats to the environment if disposed of without treatment. Throughout the present research, it can be said that a hybrid process including ultrasonic treatment coupled with froth floatation has been shown as a green efficient treatment of oily sludge waste from the bottom of crude oil tanks in Al-Daura refinery and able to get high yield of base oil recovery which is 65% at the optimum operating conditions (treatment time = 30 min, ultrasonic wave amplitude = 60 micron, and (solvent: oily sludge) ratio = 4). Experimental results showed that 83% of the solvent used was recovered meanwhile the main water
... Show MoreThe present study deals with the synthesis of four different azo-azomethine derivatives; this is done by two steps; the first step is diazotization of sulfonamides (sulfanilamide, sulfacetamide, sulfamethoxazole, and sulfadiazine) separately, followed by the second step; the coupling reaction of diazotized compounds with isatin bis-Schiff base named 3-((4-nitrobenzylidene) hydrazono)indolin-2-one. The later one (bis-Schiff base) was synthesized by the reaction of 3-hydrazono-indolin-2-one with p-nitrobenzaldehyde. The chemical structures of newly synthesized compounds were approved on the basis of their FTIR, 1H-NMR, and CHNS elemental analysis data results. The synthesized azo compounds were tested in vitro for their antimicrobial potentia
... Show MoreThe temperature control process of electric heating furnace (EHF) systems is a quite difficult and changeable task owing to non-linearity, time delay, time-varying parameters, and the harsh environment of the furnace. In this paper, a robust temperature control scheme for an EHF system is developed using an adaptive active disturbance rejection control (AADRC) technique with a continuous sliding-mode based component. First, a comprehensive dynamic model is established by using convection laws, in which the EHF systems can be characterized as an uncertain second order system. Second, an adaptive extended state observer (AESO) is utilized to estimate the states of the EHF system and total disturbances, in which the observer gains are updated
... Show MoreThe cost-effective removal of heavy metal ions represents a significant challenge in environmental science. In this study, we developed a straightforward and efficient reusable adsorbent by amalgamating chitosan and vermiculite (forming the CSVT composite), and comprehensively investigated its selective adsorption mechanism. Different techniques, such as Fourier-transform infrared spectroscopy (FTIR), zeta potential analysis, scanning electron microscopy (SEM), X-ray diffraction (XRD), and Brunauer, Emmett, Teller (BET) analysis were employed for this purpose. The prepared CSVT composite exhibited a larger surface area and higher mesoporosity increasing from 1.9 to 17.24 m2/g compared to pristine chitosan. The adsorption capabilities of the
... Show MoreDyes are extensively water-soluble and toxic chemicals. The disposing of wastewater rich with such chemicals has severely impacted surface water quality (rivers and lakes). In the current study, an anionic dye, methyl orange, were extracted from wastewater fluids using bulk liquid membranes supplemented with an anionic carrier (Aliquat 336 (QCI)). Parameters including solvent type (carbon tetrachloride and chloroform), membrane stirring speed (100-250 rpm), mixing speed of both phases (50-100 rpm), The feed pH (2-12) and implemented temperature (35-60 °C) were thoroughly analyzed to determine the effect of such variables on extraction effectiveness. Furthermore, the effect of methyl orange (10-50 ppm) in the feed stage and NaOH (0
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