• Journal for History of Mathematics
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• v.32 no.6
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• pp.281-299
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• 2019

Mathematical problem solving has become a major concern in school mathematics, and methods to enhance children's mathematical problem solving abilities have been the main topics in many mathematics education researches. In addition to previous researches about problem solving, the development of a mathematical problem solving method that enables children to establish mathematical concepts through problem solving, to discover formalized principles associated with concepts, and to apply them to real world situations needs. For this purpose, I examined the necessity of problem solving education and reviewed mathematical problem solving researches and problem solving models for giving the theoretical backgrounds. This study suggested the problem solving approach based on the intuitive and the formal inquiry which are the basis of mathematical discovery and inquiry process. And it is developed to keep the balance and complement of the conceptual understanding and the procedural understanding respectively. In addition, it consisted of problem posing to apply the mathematical principles in the application stage.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.65 no.6
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• pp.979-986
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• 2016

At present, electric power industry around the world are being gradually changed to a new paradigm, such as electrical energy storage system, the wireless power transmission. Demand for ESS, the core technology of the new paradigm, has been growing worldwide. However, it is essential to estimate the optimal capacity of ESS facilities for frequency regulation because the benefit would be saturated in accordance with the investment moment and the increase of total invested capacity of ESS facilities. Hence, in this paper, the annual optimal mathematical investment model is proposed to estimate the optimal capacity and to establish investment plan of ESS facility for frequency regulation. The optimal mathematical investment model is newly established for each season, because the construction period is short and the operation effect for the load by seasons is different unlike previous the mathematical investment model. Additionally, the marginal operating cost is found by new mathematical operation model considering no-load cost and start-up cost as step functions improving the previous mathematical operation model. ESS optimal capacity is established by use value in use iterative methods. In this case, ESS facilities cost is used in terms of the value of the beginning of the year.

• Journal of Educational Research in Mathematics
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• v.26 no.1
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• pp.47-62
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• 2016

Cultivating mathematical creativity is one of the aims in the recently revised mathematics curricular. However, there have been lack of researches on how to nurture mathematical creativity for ordinary students. Perspective of Realistic Mathematics Education(RME), which pursues education of creative person as the ultimate goal of mathematics education, could be useful for developing principles and methods for cultivating mathematical creativity. This study reanalyzes RME from the points of view in mathematical creativity education. Major findings are followed. First, students should have opportunities for mathematical creation through mathematization, while seeking and creating certainty. Second, it is vital to begin with realistic contexts to guarantee mathematical creation by students, in which students can imagine or think. Third, students can create mathematics in realistic contexts by modelling. Fourth, students create the meaning of 'model of(MO)', which models the given context, the meaning of 'model for(MF)', which models formal mathematics. Then, students create MOs and MFs that are equivalent to the intial MO and MF given by textbook or teacher. Flexibility, fluency, and novelty could be employed to evaluate the MOs and the MFs created by students. Fifth, cultivation of mathematical creativity can be supported from development of local instructional theories by thought experiment, its application, and reflection. In conclusion, to employ the education model of cultivating mathematical creativity by RME drawn in this study could be reasonable when design mathematics lessons as well as mathematics curriculum to include mathematical creativity as one of goals.

• Education of Primary School Mathematics
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• v.15 no.2
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• pp.107-134
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• 2012

The purpose of this study is to investigate the effectiveness of two teaching methods of word problems, one based on mathematical modeling learning(ML) and the other on traditional learning(TL). Additionally, the influence of mathematical modeling learning in word problem solving behavior, application ability of real world experiences in word problem solving and the beliefs of word problem solving will be examined. The results of this study were as follows: First, as to word problem solving behavior, there was a significant difference between the two groups. This mean that the ML was effective for word problem solving behavior. Second, all of the students in the ML group and the TL group had a strong tendency to exclude real world knowledge and sense-making when solving word problems during the pre-test. but A significant difference appeared between the two groups during post-test. classroom culture improvement efforts. Third, mathematical modeling learning(ML) was effective for improvement of traditional beliefs about word problems. Fourth, mathematical modeling learning(ML) exerted more influence on mathematically strong and average students and a positive effect to mathematically weak students. High and average-level students tended to benefit from mathematical modeling learning(ML) more than their low-level peers. This difference was caused by less involvement from low-level students in group assignments and whole-class discussions. While using the mathematical modeling learning method, elementary students were able to build various models about problem situations, justify, and elaborate models by discussions and comparisons from each other. This proves that elementary students could participate in mathematical modeling activities via word problems, it results form the use of more authentic tasks, small group activities and whole-class discussions, exclusion of teacher's direct intervention, and classroom culture improvement efforts. The conclusions drawn from the results obtained in this study are as follows: First, mathematical modeling learning(ML) can become an effective method, guiding word problem solving behavior from the direct translation approach(DTA) based on numbers and key words without understanding about problem situations to the meaningful based approach(MBA) building rich models for problem situations. Second, mathematical modeling learning(ML) will contribute attitudes considering real world situations in solving word problems. Mathematical modeling activities for word problems can help elementary students to understand relations between word problems and the real world. It will be also help them to develop the ability to look at the real world mathematically. Third, mathematical modeling learning(ML) will contribute to the development of positive beliefs for mathematics and word problem solving. Word problem teaching focused on just mathematical operations can't develop proper beliefs for mathematics and word problem solving. Mathematical modeling learning(ML) for word problems provide elementary students the opportunity to understand the real world mathematically, and it increases students' modeling abilities. Futhermore, it is a very useful method of reforming the current problems of word problem teaching and learning. Therefore, word problems in school mathematics should be replaced by more authentic ones and modeling activities should be introduced early in elementary school eduction, which would help change the perceptions about word problem teaching.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.36 no.2
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• pp.145-151
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• 2012

Evaluation of the heart work is starting to emerge as a new diagnostic tool for arterial diseases. The aim of this study is to develop a mathematical model for the estimation of heart work utilizing the pulse waves between two points of a vessel. In order to calculate heart work, medical data such as blood pressure waveforms (which are measured using a cuff) are utilized. The heart work is calculated by employing the modified Windkessel model together with the viscosity models of Casson or Herschel-Bulkely (H-B). The results indicate that the compliance values at the proximal and distal locations differ for the Casson and H-B models.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.16 no.4
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• pp.87-92
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• 2007

The full automation welding has not yet been achieved partly because the mathematical model for the process parameters of a given welding task is not fully understood and quantified. Several mathematical models to control welding quality, productivity, microstructure and weld properties in arc welding processes have been studied. However, it is not an easy task to apply them to the various practical situations because the relationship between the process parameters and the bead geometry is non-linear and also they are usually dependent on the specific experimental results. Practically, it is difficult, but important to know how to establish a mathematical model that can predict the result of the actual welding process and how to select the optimum welding condition under a certain constraint. In this paper, an attempt has been made to develop an neural network model to predict the weld top-bead height as a function of key process parameters in the welding. and to compare the developed models using three different training algorithms in order to select an adequate neural network model for prediction of top-bead height.

• Smart Structures and Systems
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• v.18 no.5
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• pp.931-953
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• 2016

In this paper, the effects of mass eccentricity of superstructure as well as stiffness eccentricity of isolators on the amplification of seismic responses of base-isolated structures are investigated by using mathematical near-fault pulse models. Superstructures with 3, 6 and 9 stories and aspect ratios equal to 1, 2 and 3 are mounted on a reasonable variety of Triple Concave Friction Pendulum (TCFP) bearings considering different period and damping ratio. Three-dimensional linear superstructure mounted on nonlinear isolators are subjected to simplified pulses including fling step and forward directivity while various pulse period ($T_p$) and Peak Ground Velocity (PGV) amounts as two crucial parameters of these pulses are scrutinized. Maximum isolator displacement and base shear as well as peak superstructure acceleration and drift are selected as the main engineering demand parameters. The results indicate that the torsional intensification of different demand parameters caused by superstructure mass eccentricity is more significant than isolator stiffness eccentricity. The torsion due to mass eccentricity has intensified the base shear of asymmetric 6-story model 2.55 times comparing to symmetric one. In similar circumstances, the isolator displacement and roof acceleration are increased 49 and 116 percent respectively in the presence of mass eccentricity. Furthermore, it is demonstrated that torsional effects of mass eccentricity can force the drift to reach the allowable limit of ASCE 7 standard in the presence of forward directivity pulses.

• Journal of Korea Water Resources Association
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• v.31 no.5
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• pp.613-620
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• 1998

Field and laboratory studies of the near field behavior of the San Francisco ocean outfall were reported. The data sets cover broad ranges of discharge conditions and oceanic conditions, and are associated with a typical type of outfall discharges with multiport diffusers. The laboratory data sets were obtained in density-stratified towing tanks to replicate the field tests. Model studies of wastefield behavior using these data sets were predicted by the mathematical models UM, UDKHDEN, RSB, and CORMIX2 for minimum dilution, the height to top of wastefield, and wastefield thickness. In this paper, the results are discussed and compared measurements with mathematical model predictions. The hydraulic model studies reproduced the major features observed in the field. It also afforded considerable insight into the mechanics of mixing of multiport risers which could have been obtained neither from the field test nor the mathematical models.

• Journal of Biosystems Engineering
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• v.10 no.2
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• pp.36-46
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• 1985

This study was intended to develop the mathematical model of the head-fed type threshing unit. As the first step, the physical model of the threshing phenomena was considered to consist of four separate processes as 1) detachment process of grains, 2) movement of grains between the cylinder and concave, 3) grain penetration through stems of bundle, and 4) grain passing through concave. The mathematical and computer models were developed based on the physical models. Threshing experiments were performed and determined the distribution of grain accumulation along the cylinder shaft by varying the moisture content of grains, feeding rate, and cylinder speed. It was found that the model developed coincided very well with the experimental results for the varied operational conditions. Greater concentration of grains passing through concave toward the thresher inlet was equally true for the model and experiment work for the threshing of grains with higher moisture content and with higher cylinder-speed. The model could be used for obtaining the optimized design or for optimizing the performance of the head-fed type threshing unit if term as to power requirement for threshing may be additionally included in the developed model.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.40 no.12
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• pp.1055-1062
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• 2012

In this paper, the mathematical models and control algorithm of a thrust control valve were described as a precedent study on the design of thrust control algorithm for a liquid rocket engine (LRE). Numerical simulations were performed using a simplified simulation system of an LRE and the developed mathematical models were validated by comparison with the experimental results. Through these research, basic data were acquired for the development of a thrust control algorithm for a LRE.