• Communications of the Korean Mathematical Society
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• v.24 no.4
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• pp.501-508
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• 2009

This paper presents a new representation algorithm which computes the representation for elements of a free group generated by two linear fractional transformations and also the justification of the algorithm in order to show how it operates correctly and efficiently according to inputs.

• Journal of Elementary Mathematics Education in Korea
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• v.16 no.3
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• pp.427-450
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• 2012

Using representations is essential for students to organize their thinking, to solve problems and to communicate each other. Students express information or situations suggested by problems easily and organize and infer them systematically using representations. Also, teachers are able to comprehend students' levels of understanding and thinking process better through them, and influence their representations. This study was conducted to understand mathematical representations of students uprightly and to seek implications for proper teaching of representations, by analyzing representations of students in mathematical problem solving process and the transformation process of representation via interactions.

• Journal of the Korean Graphic Arts Communication Society
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• v.25 no.1
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• pp.11-26
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• 2007

In this paper, an experiment was done where the input device used the linear multiple regression and the sRGB color space to perform a color transformation. The output device used the GOG, GOGO and sRGB for the color transformation. After the input device underwent a color transformation, a $3\;{\times}\;20\;size$ matrix was used in a linear multiple regression and the scanner's color representation of scanner was better than a digital still camera's color representation. When using the sRGB color space, the original copy and the output copy had a color difference of 11. Therefore it was more efficient to use the linear multiple regression method than using the sRGB color space. After the input device underwent a color transformation, the additivity of the LCD monitor's R, G and B signal value improved and therefore the error in the linear formula transformation decreased. From this change, the LCD monitor with the GOG model applied to the color transformation became better than LCD monitors with other models applied to the color transformation. Also, the color difference varied more than 11 from the original target in CRT and LCD monitors when a sRGB color transformation was done in restricted conditions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.2 s.173
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• pp.489-495
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• 2000

Stress and strain in continuum mechanics have a mathematical form of the second order tensor. it is well-known that the usefulness of tensor components could be explained in a relation with coordin ates system transformation and Mohr's circle could be easily used to make a coordinate system transformation of tensors. However, Mohr's circle is applied mainly to plane problems and its use to three dimensional cases is limitedly employed. In this paper, we propose a matrix and dyadic representation of stress and strain tensors which could equivalently replace the graphical representation of second order tensors. The use of the proposed representation might provide a valuable means for the educational respects as well as research view point.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.3 no.3
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• pp.39-44
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• 2010

In this paper, we addressed a face transform scheme with age-progressing based on vector representation. Proposed approach utilized a vector modeling as well as morphing so as to improve not only a reliability but also a consistency. For the more, some elements of texture change owing to the face shape are defined and some parameters with respect to the internal and external environments are also considered. To testify the proposed approach, estimation of similarity is performed with qualitative manner by using experimental output, and finally resulted in satisfactory for face shape transformation aged from sixty to fourteen.

• Journal of the Korean Society for Precision Engineering
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• v.13 no.6
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• pp.78-89
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• 1996

Every mechanical component is fabricated with the variations in its size and shape, and the allowable range of the variation is specified by the tolerance in the design stage. Geometric tolerances specify the size or the thickness of each shape entity itself or its relative position and orientation with respect to datums. Since the range of shape variation can be represented by the variation of the coordinate system attached to the shape, the transformation matrix of the coordinate system would mathematically express the range of shape variation if the interval numbers are inserted for the elements of the transformation matrix. For the shape entity specified by the geometric tolerance with reference to datums, its range of variation can be also derived by propagating the transformation matrices composed of interval numbers. The propagation depends upon the order of precedence of datums.

• Journal of the Korean School Mathematics Society
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• v.17 no.4
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• pp.507-539
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• 2014

The algebra is an important tool influencing on a mathematics in general. To make good use of the algebra, it is necessary to transfer from a given situation to a proper algebraic representation. But some research in related to algebraic word problems have reported the difficulty changing to a proper algebraic representation. Our study have focused on transformation and elaboration of algebraic representation. We investigated in detail the responses and perceptions of 29 Grade 7 students while transforming to algebraic representation, only concentrating on the literature expression form the problematic situations given. Most of students showed difficulties in transforming both descriptive and geometric problems to algebraic representation. 10% of them responded wrong answers except only a problem. Four of them were interviewed individually to show their thinking and find the factor influencing on a positive elaboration. As results, we could find some characteristics of their thinking including the misconception that regard the problem finding a functional formula because there are the variables x and y in the problematic situation. In addition, we could find the their fixation which student have to set up the equation. Furthermore we could check that making student explain own algebraic representation was able to become the factor influencing on a positive elaboration. From these, we also discussed about several didactical implications.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.605-614
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• 2008

In this paper, we find the matrix representation of multi-degree reduction by $L_{\infty}$ of $B{\acute{e}}zier$ curves with constraints of endpoints continuity. Using the basis transformation between Chebyshev polynomials and Bernstein polynomials we can derive the matrix representation of multi-degree reduction of $B{\acute{e}}zier$ with respect to $L_{\infty}$ norm.

• Korean Journal of Optics and Photonics
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• v.5 no.1
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• pp.25-30
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• 1994

We derive a set of formuale which show one-to-one correspondence between the the unitary Jones matrices of transparent anisotropic media and the rotational transformations on the Poincare sphere. By using the formuale one can determine the vectorial representation of the rotational transformation on the Poincare sphere which specifies the direction of the axis and the angle of the rotation in terms of the three parameters specific to the corresponding unitary Jones matrix, and conversely the the three parameters of the uniatry Jones matrix in terms of the vectorial representation of the corresponding rotational transformation on the Poincare sphere. To understand the polarization transmission characteristics of an optical system consisting of transparent linear anisotropic media, start with the Jones calculus to get the unitary Jones matrix for the whole system and then convert it to a rotational transformation on the Poincare sphere, from which we can intuitively understand the effect of the optical system on the polarization state of the light passing through the system.

• The Korean Journal of Applied Statistics
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• v.31 no.6
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• pp.707-719
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• 2018

Various time series representation methods have been proposed for efficient time series clustering and classification. Lin et al. (DMKD, 15, 107-144, 2007) proposed a symbolic aggregate approximation (SAX) method based on symbolic representations after approximating the original time series using piecewise local mean. The performance of SAX therefore depends heavily on how well the piecewise local averages approximate original time series features. SAX equally divides the entire series into an arbitrary number of segments; however, it is not sufficient to capture key features from complex, large-scale time series data. Therefore, this paper considers data-adaptive local constant approximation of the time series using the unbalanced Haar wavelet transformation. The proposed method is shown to outperforms SAX in many real-world data applications.