• Journal of the Korean School Mathematics Society
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• v.20 no.2
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• pp.119-139
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• 2017

The construction in the ancient Greek era had more meanings than a construction in the present education. Based on this fact, this study examines the meaning of the current textbook. In contrast, we have extracted the meaning of the constructions in Euclid Elements. In addition, we have been thinking about what benefits can come up if the meaning of the construction in Euclid Elements was reflected in current education, and suggested a way to exploit that advantage. As results, it was confirmed that the construction in the current textbook was merely a means for introducing and understanding the congruent conditions of the triangle. On the other hand, the construction had four meanings in Euclid Elements; Abstract activities that have been validated by the postulates, a mean of demonstrating the existence of figures and obtaining validity for the introduction of auxiliary lines, refraining from intervening in the argument except for the introduction of auxiliary lines, a mean of dealing with numbers and algebra. Finally we discussed the advantages of using the constructions as a means of ensuring the validity of the introduction of the auxiliary line to the argument. And we proposed a viewpoint of construction by intervention of virtual tools for auxiliary lines which can not be constructed with Euclid tool.

• Structural Engineering and Mechanics
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• v.27 no.6
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• pp.713-739
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• 2007

Nowadays computers can perform symbolic computations in addition to mere number crunching operations for which they were originally designed. Symbolic computation opens up exciting possibilities in Structural Mechanics and engineering. Classical areas have been increasingly neglected due to the advent of computers as well as general purpose finite element software. But now, classical analysis has reemerged as an attractive computer option due to the capabilities of symbolic computation. The repetitive cycles of simultaneous - equation sets required by the finite element technique can be eliminated by solving a single set in symbolic form, thus generating a truly closed-form solution. This consequently saves in data preparation, storage and execution time. The power of Symbolic computation is demonstrated by six examples by applying symbolic computation 1) to solve coupled shear wall 2) to generate beam element matrices 3) to find the natural frequency of a shear frame using transfer matrix method 4) to find the stresses of a plate subjected to in-plane loading using Levy's approach 5) to draw the influence surface for deflection of an isotropic plate simply supported on all sides 6) to get dynamic equilibrium equations from Lagrange equation. This paper also presents yet another computationally efficient and accurate numerical method which is based on the concept of derivative of a function expressed as a weighted linear sum of the function values at all the mesh points. Again this method is applied to solve the problems of 1) coupled shear wall 2) lateral buckling of thin-walled beams due to moment gradient 3) buckling of a column and 4) static and buckling analysis of circular plates of uniform or non-uniform thickness. The numerical results obtained are compared with those available in existing literature in order to verify their accuracy.

• The Journal of Korean Association of Computer Education
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• v.20 no.4
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• pp.77-84
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• 2017

This paper proposes a tool that can be used as a logical expression simplification tool that can be used for deepening learning of logic circuits and further utilized as a design automation tool for optimizing semiconductor parts. The simplification method of logical expressions proposed in this paper is to find common subexpressions existing in various logical expressions and reduce the repetitive use. Finally, the goal is to minimize the number of literals used in all logical expressions. These previous studies failed to produce a common subexpression embedded in the logical expressions because they only use division principle. The proposed method uses cubes with a Hamming distance of 3 to find the common subexpression embedded between logical expressions. Experiments using benchmark circuits show that the proposed method reduces the number of literals by as much as 47% when comparing simplifications with other methods.

• Journal of the Korea Society of Computer and Information
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• v.15 no.11
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• pp.215-224
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• 2010

Most chronic diseases are complex diseases which are caused by interactions of several genes. Studies on finding SNPs and gene-gene interactions involved in the development of complex diseases can contribute to prevention and treatment of the diseases. Previous studies mostly concentrate on finding only the set of SNPs involved. In this study we suggest a way to see how these SNPs interact using boolean expressions. The proposed method consists of two stages. In the first stage we find the set of SNPs involved in the development of diseases using mutual information based on entropy. In the second stage we find the highest accuracy boolean expression that consists of the SNP set obtained in the first stage. We experimented with clinical data to demonstrate the effectiveness of the proposed method. We also compared the differences between our method and the previous results on the SNP associations studies.

• Journal of the Korea Society of Computer and Information
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• v.16 no.12
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• pp.139-155
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• 2011

In recent years, parents of students and government have been taking a growing interest in education for the gifted students and there are many research reports about the gifted education. Most of the reports, however, focuses on the conceptional feature of the gifted education program such as organization, operation, management, evaluation, etc,. In other words, there are very few researches on instructional materials for gifted students even though the materials is a critical factor for successful education programs. So, this paper introduces a lecture notes used in a personal education for gifted students to contribute in developing education contents in computer science area. The instructional materials titled as "The Necessity and Application of Matrix in Computer Science" is based on linear equation to usher the students into creative problem recognition and groping for solutions. Also, the instructional materials is useful for students to understand the tight mathematics-computer science relationship and the basic concept of liner algebra.

• Korean Journal of Optics and Photonics
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• v.20 no.2
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• pp.110-117
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• 2009

This work introduces the uncertainty evaluation formulation on color measurement of light sources and display devices, such as CIE 1931 (x, y) chromaticity, CIE 1960 (u, v) chromaticity, correlated color temperature, and distribution temperature. All the mentioned quantities are reduced from spectral data in the visible range, for which uncertainties are strongly correlated between different wavelengths. Using matrix algebra we have formulated the uncertainty propagation from the SI- traceable spectral irradiance standard to the individual color related measurement quantities taking the correlation between wavelengths into account. As a result, we have demonstrated uncertainty evaluation examples of 3 types of light sources: CIE illuminant A, LED white light, and LCD white light. This method can be applied to any other quantities based on spectral measurement such as solar irradiance, material color measurement, etc.

• Journal for History of Mathematics
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• v.22 no.3
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• pp.187-206
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• 2009

On this study, the historical flow of the notation was briefly examined and the direction of mathematical investigation activity of the content of notation by analogy was explored and teaching learning materials were developed. Diverse mathematical facts were investigated on the basis of decimal system and binary system which are learned in middle school. First, the way of progressing analytic activity with algebraic material was examined. Second, on the basis of the notation which are learned in the first grade of middle school, the definition of the scale of a -notation, -a -notation, $\frac{1}{a}$notation, $\sqrt{a}$-notation was extended by analogy. The result of this study will be expected to establish the curriculum of mathematics and provide teaching and learning with the meaningful current events.

• Journal of Korea Spatial Information System Society
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• v.4 no.1 s.7
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• pp.5-14
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• 2002

The generalization of geospatial data is an important way in deriving a new database from an original one. The generalization of a geospatial object changes not only its geometric and aspatial attributes but also results in propagation to other objects along their relationship. We call it generalization propagation of geospatial databases. Without proper handling of the propagation, it brings about an inconsistent database or loss of semantics. Nevertheless, previous studies in the generalization have focused on the derivation of an object by isolating it from others. And they have proposed a set of generalization operators, which were intended to change the geometric and aspatial attributes of an object. In this paper we extend the definition of generalization operators to cover the propagation from an object to others. In order to capture the propagation, we discover a set of rules or constraints that must be taken into account during generalization procedure. Each generalization operator with constraints is expressed in relational algebra and it can be converted to SQL statements with ease. A prototype system was developed to verify the correctness of extended operators.

• Journal of Korea Spatial Information System Society
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• v.4 no.1 s.7
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• pp.39-46
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• 2002

In distributed spatial database systems, users nay issue a query that joins two relations stored at different sites. The sheer volume and complexity of spatial data bring out expensive CPU and I/O costs during the spatial join processing. This paper shows a new spatial join method which joins two spatial relation in a parallel way. Firstly, the initial join operation is divided into two distinct ones by partitioning one of two participating relations based on the region. This two join operations are assigned to each sites and executed simultaneously. Finally, each intermediate result sets from the two join operations are merged to an ultimate result set. This method reduces the number of spatial objects participating in the spatial operations. It also reduces the scope and the number of scanning spatial indices. And it does not materialize the temporary results by implementing the join algebra operators using the iterator. The performance test shows that this join method can lead to efficient use in terms of buffer and disk by narrowing down the joining region and decreasing the number of spatial objects.

• Journal of Educational Research in Mathematics
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• v.15 no.4
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• pp.505-522
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• 2005

In this article we studied the role of spreadsheet in teaching function and modeling activity by some examples and students' activity performed by the six 10th graders. We especially focused the role of spreadsheet in understanding of various kinds of functions and the families of functions, and in the explanation of the given modeling problem situations. The functions of automatic copy, graphic and the cell reference of spreadsheet can be used to make students observe the causes and effects of changes of the various kind of mathematical representations of functions such as algebraic formulas, tables and graphs. Especially those functions give students a chance to identify family of functions by changing the parameters and this may lead them to the discovery of mathematical facts. In modeling activities they play a key role in the stages of the analysis of the model, explanation of the results of model and conjecture of the real world situations. As well as they make students find the rules underlying in the real world by making spreadsheet as simulation environments, which are almost impossible to make in paper and pencil environments, and give them a chance to justify their findings using mathematics.