• Communications of Mathematical Education
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• v.9
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• pp.283-297
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• 1999

수학에서는 컴퓨터를 활용해야 하고, 사회생활에서는 수학을 활용해야 한다. 이런 의미에서 엑셀을 수업 시간에 활용하는 것이 필요하다. 수학II의 일차변환을 엑셀을 어떻게 활용할 수 있는 가를 제시한다. 일차변환의 응용으로서, 이동을 포함시킨 아핀변환을 이용하여 프랙탈을 생성하는 방법을 찾아본다. 프랙탈을 생성하기 위해서는 IFS(Iterated Function System)에 의해 수 만번의 합성변환을 필요하므로 소프트웨어가 필수적이다. 여기서는 Fanstic Fractals 프로그램을 이용하여 직관적으로 얻은 그림에서 변환 행렬의 값을 구하여, 엑셀에서 두 가지 방법으로 분석하였다.

• Communications of Mathematical Education
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• v.19 no.2 s.22
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• pp.379-388
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• 2005

일차변환은 선형대수에서 가장 중요한 개념 중 하나이다. 그럼에도 많은 학생들에게서 나타나는 이 개념에 대한 오류는 무엇이며 또 어디에 근거하는가? 이 논문은 효과적인 선형대수 교수학습 연구의 일부로, 주어진 여러 함수 중에서 일차변환인 것을 찾는 과정 중에 나타난 학생들의 오류와 그 근거를 알아보았다. 본 연구 결과는 선형대수 학습에 어려움을 겪는 학생들에게 보다 효율적인 교수디자인 설계를 위한 기초 자료의 의미를 갖는다.

• 전기의세계
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• v.9
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• pp.18-22
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• 1962

지수선로는 특히 microwave공학에서 Impedance 변환용으로 널리 사용되고 있으나 그 Impedance 함수 또는 반사계수의 표시식의 복잡성으로 인하여 이 선로의 특성연구, 설계에 있어서 적지 않은 계산의 곤란이 따른다. 따라서 이의 도식해법이 환영된다. 본논문에서 우리는 지수선로의 Impedance함수를 일차변환하면 보통의 균일선로에 대한 것과 유사한 표시식이 얻어짐에 착안하여 복소수의 일차변환을 대표하는 W-평면과 Smith chart 또는 직교 Impedance diagram을 병용하던지 W-평면을 직교 Impedance diagram에 중첩시키던지 또는 Smith chart의 constant-r constant-x도의 label를 고쳐서 사용하던지 하여 지수선로의 문제를 도식으로 해결하는 방법을 모색하였다. 또 같은 착안으로부터 지수선로의 집중정수 등가회로가 흥미있게 구해짐을 부수적으로 지적하였다.

• Journal of Educational Research in Mathematics
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• v.14 no.1
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• pp.39-69
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• 2004

This paper investigates the teaching and learning of Linear function relating functional contexts and suggests the improved methods of representation-shift through this analysis. The methods emphasize the link between students' preacquired knowledge of mathematical representations and the way of using those. This methods are explanatory teaching, teaching and teaming based on modelling perspectives or tasks (interpretation, prediction, translation and scaling). We categorize the 8th grade middle school students' errors on the linear function relating real contexts and make a comparative study of the error-remedial effects and the teaching and teaming methods. We present the results of a study in which representation-shift methods based on modelling perspectives and tasks are more effective in terms of flexible connection of representations and error remediation. Also, We describe how students used modelling perspective-taking to explain and justify their conceptual models, to assess the quality of their models and to make connection to other mathematical representation during the problem solving focusing on the students' self-diagnosis.

• The Mathematical Education
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• v.47 no.4
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• pp.437-445
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• 2008

On the basis of the meaning and general process of geometric proof through transformation concept and understanding the geometric properties of linear transformation, this study showed that the centroid of geometrical figure and certain properties of a parabola and an ellipse in school mathematics can be explained as a conservative properties through linear transformation. From an educational perspective, this is a good example of showing the process of how several existing individual knowledge can be reorganized by a mathematical concept. Considering the fact that mathematical usefulness of linear transformation can be revealed through an invariable and conservation concept, further discussion is necessary on whether the linear transformation map included in the former curriculum have missed its point.

• Journal for History of Mathematics
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• v.23 no.4
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• pp.83-100
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• 2010

This paper is to raise several questions in teaching the Graph and Linear Transformation complied with the Mathematics Amended Curriculum announced in 2006 Aug. and then to formulate a plan accordingly. For this, we'll take a good look at the prior studies on the Graph and Linear Transformation after the announcement of the 7th School Curriculum along with the changes in their contents through the process of curriculum. Then we'll check over learning factors of the Graph and Linear Transformation in all 27 kinds of the authorized textbooks - 'Mathematics I', 'Applications of Mathematics', and 'Geometry and Vectors' - and 27 kinds of exercise books issued on 2009. By this, we put measures which improve understanding and apply correctly to the Graph and Linear Transformation in the Mathematics Amended Curriculum to high school teachers.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.16 no.1
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• pp.85-91
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• 2002

Generally when the orthogonal functions are used in system analysis, the time consuming processes of high order matrix inversion for finding the Kronecker products and the truncation errors are occurred. In this paper, a method for the system analysis of bilinear systems via fast walsh transform is devised. This method requires neither the inversion of large matrices nor the cumbersome procedures for finding Kronecker products. Thus, both the computing time and required memory size can be significantly reduced.

• Journal of the Korean Institute of Telematics and Electronics
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• v.19 no.3
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• pp.1-4
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• 1982

The purpose of this paper is to find and compare efficient and "statistically accurate" algorithms for linear systems with bandlimited random inputs. Using the previously investigated truncated expansions[2], a new state-transition algorithm is derived. With statistical error criteria (mean-square error), comparative study on the Performances has been done for the first and second-order linear system models. The results show that a new bandlimited state-transition algorithm works better than any commonly used algorithms (e. g., first-order state-transition method or Z-transform method).

• Journal of Biomedical Engineering Research
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• v.23 no.5
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• pp.351-364
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• 2002

Conventional 3D ultrasound imaging using mechanical ID arrays suffers from poor elevation resolution due to the limited depth-of-focus (DOF). On the other hand, 3D imaging systems using 2D phased arrays have a large number of active channels and hence require a very expensive and bulky beamforming hardware. To overcome these limitations, a new real-time volumetric imaging method using curved 2-D arrays is presented, in which a small subaperture, consisting of 256 elements, moves across the array surface to scan a volume of interest. For this purpose, a 2-D curved array is designed which consists of 90$\times$46 elements with 1.5λ inter-element spacing and has the same view angles along both the lateral and elevation directions as those of a commercial mechanical 1-D array. In the proposed method, transmit and receive subapertures are constructed by cutting the four corners of a rectangular aperture to obtain a required image qualify with a small number of active channels. In addition the receive subaperture size is increased by using a sparse array scheme that uses every other elements in both directions. To suppress the grating lobes elevated due to the increase in clement spacing, fold-over array scheme is adopted in transmit, which doubles the effective size of a transmit aperture in each direction. Computer simulation results show that the proposed method can provide almost the same and greatly improved resolutions in the lateral and elevation directions, respectively compared with the conventional 3D imaging with a mechanical 1-D array.

• Magazine of the Korean Society of Agricultural Engineers
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• v.36 no.4
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• pp.64-72
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• 1994

설계홍수량의 유도를 위해 일차적으로 극치계열인 금강, 영산강 및 석진강 수개 3개 유역의 연최고치계열을 중심으로 하여 SMEMAX법, 역변환(Power Transformation) 및 2단계역변환(Two step Power Transformation, TSPT)법에 의해 척도분포의 정규화를 위한 변환법의 효율성 검정과 설계홍수량의 유도 및 비교분석을 수행한 결과 SMEMAX 법과 Power 변환법에서는 정규분포화를 왜곡도계수의 영으로의 접근 시도는 가능하나 소설도, 3으로의 조건을 충족시킬 수 없었던 반면 2단계역변환법에서는 소설도, 3에 매우 근접된 결과를 가져오므로서 척도분포의 정규화를 기할 수 있었고 각각의 변환법에 유도된 설계홍수량간의 비교분석에서는 SMEMAX 및 Power 변환법에 비해 2단계역변환방법에 의한 설계 홍수량이 재현기간 10년 이상 실측치에 보다 접근된 좋은 결과를 나타내었다.