• Communications of Mathematical Education
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• v.35 no.1
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• pp.119-136
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• 2021

We performed the research and education programs using engineering tools such as Mathematica, Microsoft Excel and GeoGebra for the students in mathematics mentorship program of the institute of science education for the gifted. We used the engineering tools to solve the problems and found the rules by observing the solutions. Then we generalized the rules to theorems by proving the rules. Mathematica, the professional mathematical computation program, was used to calculate and find the length of the repeating portion of the repeating decimal. Microsoft Excel, the spreadsheet software, was used to investigate the Beatty sequences. Also GeoGebra, the dynamic geometric software, was used to investigate the Voronoi diagram and develop the Voronoi game. Using GeoGebra, we designed the Voronoi game plate for the game. In this program, using engineering tools improved the mathematical creativity and the logical thinking of the gifted students in mathematics mentorship program.

• Geotechnical Engineering
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• v.13 no.6
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• pp.147-164
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• 1997

This study has the assumption that scale effects in rock mass properties are atrributed to the discontinuous and inhomogeneous nature of rock masses. In order to escape the general equivalent material approach applied to the concept of representative volume element, this study presents the new method considering irregular i oink geometry and arbitrary numbers of i oink and arbitrary joint orientations. Based on the theoretical approach, this theory is applied to a real engineering project. Showing the property variations with size of rock mass element, various numerical experiments about scale effect are conducted. Particularly, to prove the adequacy of the verification process in scale effect with nomerical method, and to investigate the detailed source of scale effect, 4 models with increas ins number of joints are tested. On the basis of the experimental results, the test results of scale effects in 3-D rock mass are presented. From these experiments the effects of the mechanical properties of rock joints on the scale effects in rock mass strength and elastic constants are discussed. To verify the mechanism of scale effects in jointed rock mass, two models with different j oink geometries are studied.

• Education of Primary School Mathematics
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• v.11 no.2
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• pp.141-159
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• 2008

The purpose of this study id to delve into how elementary mathematics textbook deal with the quadrilaterals from a view of Didactic Transposition Theory. Concerning the instruction period and order, we have concluded the following: First, the instruction period and order of quadrilaterals were systemized when the system of Euclidian geometry was introduced, and have been modified a little bit since then, considering the psychological condition of students. Concerning the definition and presentation methods of quadrangles, we have concluded the following: First, starting from a mere introduction of shape, the definition have gradually formed academic system, as the requirements and systemicity were taken into consideration. Second, when presenting and introducing the definition, quadrilaterals were connected to real life. Concerning the contents and methods of instruction, we have concluded the following: First, the subject of learning has changed from textbook and teachers to students. Second, when presenting and introducing the definition, quadrilaterals were connected to real life. Third, when instructing the characteristics and inclusive relation, students could build up their knowledge by themselves, by questions and concrete operational activities. Fourth, constructions were aimed at understanding of the definition and characteristics of the figures, rather than at itself.

• Journal of Elementary Mathematics Education in Korea
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• v.11 no.2
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• pp.199-216
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• 2007

The purpose of the present study was to analyze the types of errors made by students in the figure domain at the stages of first and second semester of 4th grade in elementary school that include the definition and the properties of figure, to identify the causes of such errors, and to help the teaching of the 4th grade figure domain. When the trends of errors were analyzed for each question, the most common error was the wrong use of theorems or definitions, and its main causes were student's low level in geometry and limited concept images. Thus, it is necessary to make them have clear understanding of these concepts and terms and students need to do various activities suitable for their level in geometry. In addition, figure images presented in the mathematics textbooks and the mathematics practice book have limitations. Thus, figures of various positions and lengths should be presented and described accurately, and the books should be redesigned for various practical activities.

• Korean Chemical Engineering Research
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• v.51 no.6
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• pp.655-660
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• 2013

In this review, I present the configuration behaviors of various Janus particles at fluid-fluid interfaces. As a model system, Janus spheres, Janus ellipsoids, and Janus dumbbells are selected to investigate the effect of shape, size, and wettability on their configurations. In particular cases, Janus ellipsoids can adopt two distinct configurations (i.e., upright and tilted configurations) due to the presence of two energy minima in the attachment energy profile. On the contrary, a single energy minimum is found in the case of Janus dumbbells such that they adopt either the upright or tilted configuration. Interestingly, the geometric and chemical asymmetry and anisotropy in the characteristic properties of Janus dumbbells lead to an intermediate state in which the particles can rotate freely in a certain range of orientation angles.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.10
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• pp.1910-1924
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• 1994

Curved 3D objects represented by range data contain large amounts of information compared with planar objects, but do not have distinct features for matching to those of object models. This makes it difficult to represent and identify a general 3D curved object. This paper introduces a new view-point independent approach to recognizing general 3D curved objects using range data. Our approach makes use of the relative geometric differences between particular points on the object surface and some model points. The model points are prespecified arbitrarily and keeping the task in mind so that the following task can be easily described using the model points. Our approach has several advantages. Since model points are specified arbitrarily and task dependently, further processing can be reduced in application by locating the model points at places which are useful for further operations in the task. The knowledge base is simple with less storage requirement. And, it is easy to compensate the uncertainties of positions estimation caused by noise and quantization error.

• Journal of the Korean Society for Nondestructive Testing
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• v.18 no.2
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• pp.112-120
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• 1998

A nondestructive evaluation technique was developed for the quantitative determination of the reinforcement volume fractions in particulate reinforced metal matrix composites. The proposed technique employed a composite micromechanics which accounts for the microstructure of the composite medium together with the measurement of anisotropic electrical conductivity. When the measured conductivity was coupled with the theoretically predicted conductivity, the unknown reinforcement volume fraction was calculated. An analytical model based on the Mori-Tanaka method was described which relates the NDE signatures to the composite microstructure. The volume fractions were calculated using eddy current measurements made on a wide range of silicon carbide particulate ($SiC_p$) reinforced aluminum (Al) matrix composites. The calculated $SiC_p$ volume fractions were in good agreement with the measured volume fractions in the range of 0-30%. The technique was also found to be effective in estimating the total volume percentage of reinforcement and intermetallic compound formed during the processing stage.

• The Journal of Engineering Geology
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• v.27 no.3
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• pp.267-274
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• 2017

Behavior of rock mass depend on the mechanical properties of intact rock and geometrical property of discontinuity distributed in rock mass. In case of rock slope, particularly, location of slope failure surface and behavior after failure are changed due to discontinuities. In this study, two 3D slope stability analysis methods were developed for two different failure types which are circular failure and planar failure, considering that failure type of rock slope is dependent on scale of discontinuity which was then applied to real rock slope to review the applicability. In case of circular failure, stable condition was maintained in natural dry condition, which however became unstable when the moisture content of the surface was increased by rainfall. In case of planar failure, rock slope become more unstable comparing to dry condition which is attributable to decrease in friction angle of discontinuity surface due to rainfall. Viewing analysis result above, analysis method proved to have well incorporated the phenomenon occurred on real slope from the analysis result, demonstrating its applicability to reviewing the slope stability as well as to maintaining the slope.

• Journal of the Korean Society of Hazard Mitigation
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• v.7 no.5
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• pp.61-71
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• 2007

Navier's and Finite element solutions based on the first-order shear deformation theory are presented for the analysis of through-thickness functionally graded plates and shells. The functionally graded materials are considered: a sigmoid function is utilized for the mechanical properties through the thickness of the isotropic structure which varies smoothly through the plate and shell thickness. The formulation of a nonlinear 9-node Element-based Lagrangian shell element is presented for the geometrically nonlinear analysis. Natural-coordinate-based strains are used in present shell element. Numerical results of the linear and nonlinear analysis are presented to show the effect of the different top/bottom elastic modulus, loading conditions, aspect ratios and side-to-thickness ratios on the mechanical behaviors. Besides, the result according to the variation of the power-law index of isotropic functionally graded structures is investigated.

• Journal of the Korean Chemical Society
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• v.54 no.4
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• pp.387-394
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• 2010

The theoretical calculations for $B_nH_n$, $B_nH_{n+1}$, $B_nH_{n+2}$ (n = 3-6) have been considered at the B3LYP level of theory with the 6-311G$^*$ basis set. The optimized geometries, harmonic vibrational frequencies, and binding energies are evaluated to elucidate the thermodynamic stability and spectroscopic properties. The harmonic vibrational frequencies for the molecules considered in this study show all real numbers implying true minima and the binding energies are corrected using zero-point vibrational energies (ZPVE). The binding energies and average energies due to increasing of BH monomer are predicted.