• Korean Chemical Engineering Research
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• v.53 no.4
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• pp.489-495
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• 2015

A fundamental mathematical model for mass transfer processes has been used to understand the air pollution control process in biotrickling filtration and to evaluate the mass transfer coefficients of gas/liquid (trickling liquid), gas/solid (biomass) and liquid/solid based upon experimental results and mathematical model calculations for selected operating conditions. The mass transfer models for the utilization of the steady-state mass balance for gas/liquid, and dynamic mass balance model for gas/solid & liquid/solid in biotrickling filters were established and discussed. The mass transfer model considered the reactor to comprise finite sections, for each of which dynamic mass balances for gas/solid and liquid/solid system were solved by numerical analysis code (numerical iteration). To determine the mass transfer coefficients ($K_La$) of gas/liquid, gas/solid & liquid/solid in a biotrickling filter, the calculation results based upon mass balance equation was optimized to coincide with the experimental results for the selected operating conditions. Finally, this study contributed the development of experimental methods and discussed the mathematical model to determine the mass transfer coefficients in a biotrickling filtration for air pollution control.

• The Mathematical Education
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• v.59 no.4
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• pp.405-420
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• 2020

There have been mixed reports about the idea of utilization of resources developed from one discipline across disciplinary areas. Grounded with the argument that critical thinking is not domain-specific (Mulnix, 2012; Vaughn, 2005), we developed a theoretical model of intellectual resources (IR) that students develop and use when learning and doing mathematics and science. The theoretical model shows that there are two parallel epistemic practices students engage in science and mathematics - searching for reasons and giving reasons (Bailin, 2002; 2007; Mulnix, 2012). Applying Confirmatory Factor Analysis and Structural Equation Model to the data of 9,300 fourth grade students' responses to standardized science and mathematics assessments, we verified the theoretical model empirically. Empirically, the theoretical model is verified in that fourth graders do use the two epistemic practices, and the development of parallel practices in science impacts the development of the two practices in mathematics: A fourth grader's ability to search for reasons in science affects his or her ability to search for reasons in mathematics, and the ability to give reasons in science affects the same ability use in mathematics. The findings indicate that educators need to open ideas of sharing development of epistemic practices across disciplines because students who developed intellectual resources can utilize these in other settings.

• Journal of Aerospace System Engineering
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• v.11 no.5
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• pp.6-12
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• 2017

This paper deals with mathematical modeling of a 75-ton open-cycle Liquid Propellant Rocket Engine (LPRE) and the steady state simulation based on a nominal operating point. Each component of open-cycle LPRE may be classified into seven major categories using thermodynamics and dynamics characteristics. To simplify the simulation model of LPRE in this paper, we used four govern equations with assuming no heat transfer process. We confirmed the mathematical model of LPRE by using the error ratio and comparing the experiment data and simulation data in steady state, and checked the stability with the linearized model. Finally, we demonstrated the simulation model as compared to the transient response of experimental data.

• East Asian mathematical journal
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• v.28 no.2
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• pp.135-158
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• 2012

The ideals of the rings of integers are used to induce rational number system as operators(=group homomorphisms). We modify this inducing method to be effective in teaching rational numbers in secondary school. Indeed, this modification provides a nice model for explaining the equality property to define addition and multiplication of rational numbers. Also this will give some explicit ideas for students to understand the concept of 'field' efficiently comparing with the integer number system.

• East Asian mathematical journal
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• v.26 no.4
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• pp.487-507
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• 2010

We study mathematization of natural thinking and some materials developed in geometric construction of regular n-polygons. This mathematization provides a nice model for illustrating interesting approaches to trigonometric functions and trigonometric ratios as well as their inter-connections. Thereby, results of this paper will provide the procedure of the development for these concepts in natural way, which will be helpful for understanding background knowledges.

• The Mathematical Education
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• v.42 no.4
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• pp.561-577
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• 2003

Because statistical concepts are important parts in school mathematics, mathematics teachers have trained by special education model. In this study, a desirable direction of curriculum on probability and statistics at pre-service for mathematics teacher is considered. We proposed four subjects as Exploration and Analysis of Data for Mathematics Teacher, Probability and Statistics I, II for Mathematics Teacher and Statistical Software for Mathematics, and suggested the constituents and something being kept in mind for each subject.

• Proceedings of the KIEE Conference
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• 2006.11a
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• pp.46-48
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• 2006

WASP which is used to plan generation expansion has disadvantages that can't manage environmental factors and regional supply-demand planning. But with the effectuation of the United Nations Framework Convention on Climate Change (UNFCCC) and Kyoto Protocol, it is expected that reducing greenhouse gases affects power system in its long-term generation expansion planning. Therefore national countermeasures is needed. This paper formulates a mathematical model considering CO2 emission constraints and Emission Trading that will be enforced. This model is based on the ORIRES which was made by ESI, Russia and manages generation expansion planning. And this mathematical model is verified by studying a case system.

• Journal of Drive and Control
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• v.18 no.4
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• pp.59-64
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• 2021

In this paper, a mathematical pressure dynamics model for a variable thrust solid propulsion system with an electric actuator was derived from the mass conservation of gas. To solve the problem induced by modeling uncertainties in the propellant model and the dead zone of the actuator, a nonlinear pressure controller combined with a nonlinear disturbance observer was designed using a mathematical model of the system. The simulation results showed that the proposed pressure controller could reduce tracking errors compared to another conventional nonlinear controller even in situations where input disturbances were present.

• Honam Mathematical Journal
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• v.43 no.4
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• pp.717-739
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• 2021

We used blood data to predict obesity by complementing the BMI risk, because some blood factors are significantly associated with obesity. For the sampling method, a two-step stratified colony sampling method was used based on sixteen blood factors collected by the Korea National Health and Nutrition Examination Survey(KNHANES). We identify the number of effective blood data of obesity in the final model as 6 ~ 8 factors that differ somewhat depending on age and gender. Also, the coefficient of determination that represents the predictive power of obesity in the regression model is the highest for both men and women of aged 19 and in their 20s and 30s, and the predictive power decreases with increasing age.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.695-708
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• 2024

In this paper we present a non-standard finite difference method for solving a fractional decay model. The proposed NSFDM is constructed by incorporating a non-standard denominator function, resulting in an explicit numerical scheme as easy as the conventional Euler method, but it provides very accurate solutions and has unconditional stability. Two examples from the literature are presented to demonstrate the performance of the proposed numerical scheme, which is compared to three methods from the literature. It is found that the method's estimated errors are extremely minimal, such as within the machine precision.