• Education of Primary School Mathematics
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• 제27권4호
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• pp.435-462
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• 2024

This study aims to derive educational implications for fostering mathematical creativity in elementary students. To achieve this, proportional distribution problems were presented as multiple-solution tasks, and students' problem-solving processes were analyzed from the perspective of mathematical creativity. The study involved 100 sixth-grade elementary students who were given proportional distribution problems as multiple-solution tasks to analyze their problem-solving methods. The students were grouped based on teacher variables, and the groups were assessed in terms of fluency, originality, and flexibility in mathematical creativity. The characteristics of the collective solution spaces were identified by comparing the frequency of various problem-solving strategies and representation types. The study found that teachers significantly influence mathematical creativity within collective solution spaces. Depending on the teacher, differences in fluency and originality were observed. Collective solution spaces with less reliance on formulaic approaches and higher use of diverse representations scored higher in creativity. Conversely, heavy reliance on symbolic representations was associated with lower creativity. These findings highlight the importance of encouraging various problem-solving strategies and representations within collective solution spaces to foster creativity. The study confirms that teachers play a crucial role in fostering mathematical creativity. Differences in creativity between groups based on teacher variables indicate that teachers impact students' problem-solving approaches. Additionally, relying solely on symbolic representations does not naturally lead to mathematical creativity, underscoring the need to provide students with opportunities to explore diverse mathematical representations. Creating an educational environment that encourages students to experiment with various strategies and representations is essential for nurturing their creativity.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• 제26권5호
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• pp.218-223
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• 2014

Korea District heating corp. recently give an attention to combine the district heating and supply pipes as a two pipe system that are in the present system separated with room heating and warm water supply pipe, and the two pipe system is commonly applied for heating service in European countries. In the new two pipe system, only one heat source is supplied to a house and partitioned into room heating and warm water supply by household substation. So the effective distribution of supplied heat source in accordance to user intention is very important. This paper presents the development and performance test of three-way proportional control valve for a combined heat source system in district heating. The proposed valve is controlled to partition heat source into two different directions : hot water distributor for space heating and household substation for warm water supply in response to the pressure drops of tap water caused by the user. The performance investigation is shown within 3% of error compared to the theoretical model of the three-way proportional valve and its controllability is verified.

• Journal of Korea Water Resources Association
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• 제48권4호
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• pp.299-308
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• 2015

The aim of this study is that a theoretical formula for estimating the one-dimensional longitudinal dispersion coefficient is derived based on a transverse distribution equation for the depth averaged stream-wise velocity in open channel. In "Part I. Theoretical equation for stream-wise velocity" which is the former volume of this article, the velocity distribution equation is derived analytically based on the Shiono-Knight Method (SKM). And then incorporating the velocity distribution equation into a triple integral formula which was proposed by Fischer (1968), the one-dimensional longitudinal dispersion coefficient can be derived theoretically in "Part II. Longitudinal dispersion coefficient" which is the latter volume of this article. The proposed equations for the velocity distribution and the longitudinal dispersion coefficient are verified by using observed data set. As a result, the non-dimensional longitudinal dispersion coefficient is inversely proportional to square of the Manning's roughness coefficient and the non-dimensional transverse dispersion coefficient, and is directly proportional to square of the aspect ratio (channel width to depth).

• The Journal of Information Technology
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• 제8권1호
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• pp.43-50
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• 2005

Quantitative analysis for distribution of penetrating ultrasound in vivo is very important to determine the treatment region and method. In this paper, we constructed a simplified 2-D femoral region model that consists of skin-fat-muscle-bone layered system, and simulated the pressure distribution in the model in case of applying ultrasound using Finite Element Method(FEM). The ultrasound used in the simulation was assumed to be pulse wave and the pressure distribution was analyzed during only one period of pulse wave. In order to find the penetration depth, amplitude of pressure and sphere that ultrasound reaches in the model, we performed the simulation with varying the applied frequency, transducer size and amplitude of transducer's output. The result showed that applied frequency is inversely proportional to the penetration depth and amplitude of pressure but the amplitude of transducer's output is proportional to the amplitude of pressure in the model. Also, the sphere that ultrasound reaches was widened and the amplitude of pressure became larger as the transducer size became larger. This results were similar to that obtained from the previous model consisting of fat-muscle-bone layered system, but we observed that the pressure of ultrasound is decreased due to the decrements of pressure by the absorption coefficient of skin and the interference that depends on the reflection of ultrasound caused by the difference of acoustic impedance of skin and fat. Finally, we can infer that the model proposed in this study is closer to the realistic model than the previous ones. It shows that the results obtained from this study can be useful in designing the ultrasound treatment instrument or in setting up the treatment plan.

• Bulletin of the Korean Mathematical Society
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• 제55권3호
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• pp.679-698
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• 2018

In this paper, with optimal normalized constants, the asymptotic expansions of the distribution and density of the normalized maxima from generalized Maxwell distribution are derived. For the distributional expansion, it shows that the convergence rate of the normalized maxima to the Gumbel extreme value distribution is proportional to 1/ log n. For the density expansion, on the one hand, the main result is applied to establish the convergence rate of the density of extreme to its limit. On the other hand, the main result is applied to obtain the asymptotic expansion of the moment of maximum.

• Steel and Composite Structures
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• 제25권4호
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• pp.473-484
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• 2017

In this study a seismic retrofit scheme for a building structure was presented using steel plate slit dampers. The energy dissipation capacity of the slit damper used in the retrofit was verified by cyclic loading test. Genetic algorithm was applied to find out the optimum locations of the slit dampers satisfying the target displacement. The seismic retrofit of the model structure using the slit dampers was compared with the retrofit with enlarging shear walls. A simple damper distribution method was proposed using the capacity spectrum method along with the damper distribution pattern proportional to the inter-story drifts. The validity of the simple story-wise damper distribution procedure was verified by comparing the results of genetic algorithm. It was observed that the capacity-spectrum method combined with the simple damper distribution pattern leaded to satisfactory story-wise distribution of dampers compatible with the optimum solution obtained from genetic algorithm.

• Communications of the Korean Mathematical Society
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• 제14권3호
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• pp.627-633
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• 1999

Let the given distribution $\pi$ have a log-concave density which is proportional to exp(-V(x)) on $R^d$. We consider a Markov chain induced by the method Gibbs sampling having $\pi$ as its in-variant distribution and prove geometric ergodicity and the functional central limit theorem for the process.

• The Korean Journal of Applied Statistics
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• 제25권2호
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• pp.279-291
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• 2012

When fitting a Cox proportional hazards model with missing covariates, it is inefficient to exclude observations with missing values in the analysis. Furthermore, if the missing-data mechanism is not Missing Completely At Random(MCAR), it may lead to biased parameter estimation. Many approaches have been suggested to handle the Cox proportional hazards model when covariates are sometimes missing, but they are based on the selection model. This paper suggest an approach to handle Cox proportional hazards model with missing covariates by using the pattern-mixture model (Little, 1993). The pattern-mixture model is expressed by the joint distribution of survival time and the missing-data mechanism. In the pattern-mixture model, many models can be considered by setting up various restrictions, and different results under various restrictions indicate the sensitivity of the model due to missing covariates. A simulation study was conducted to show the sensitivity of parameter estimation under different restrictions in a pattern-mixture model. The proposed approach was also applied to mouse leukemia data.

• Journal of Korean Society for Quality Management
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• 제25권1호
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• pp.182-192
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• 1997

The well-known standard normal distribution has been used within the limit of standard variable value of u=3.59. However, the probability values above the limit are not given in the literature. In this study, a probability computation program for standard normal distribution to u=5.99 with the proportional normal distribution a, pp.oximation suggested by Abramowitz and Stegun, Hastings is developed. The new standard normal distribution table developed by the program is presented and will be of help to estimate of probability values for testing and estimation of process mean value, lot acceptable probability, defective percentage of PPM unit of an out-of specification limit, process capability, test power of control charts, probability and statistics.

• Applied Chemistry for Engineering
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• 제9권3호
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• pp.364-371
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• 1998

A theoretical model of particle agglomeration was developed to investigate the adhesive force between contiguous coal particles in CWM agglomerate. While heating bituminous coal to about $400^{\circ}C$ or above, the transient occurrence of plastic behavior of coal particles can be observed. The adhesive force in the process of agglomeration of coal particles was found to be proportional to the duration of plasticity of the particles. In the research, how the heating rate and the particle size distribution of CWM fuel influenced the formation of the agglomerate in CWM fuel at the heat-up stage was investigated by the model of particle agglomeration. Simulation program used to this experiment was RKG method and was programmed by Fortran. It was represented that by the model of particle agglomeration, the adhesive force in the process of the particle agglomeration in CWM fuel was inversely proportional to the heating rate but proportional to particle size.