• Communications of Mathematical Education
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• v.29 no.4
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• pp.661-685
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• 2015

This study is to search for a program of professional development of mathematics teachers on the viewpoint of content knowledge of mathematics. To do this, we select algebraic subject as content knowledge for solution of polynomials and develop material for group study based on selected subject. We supply the developed material to teachers and discuss the possibility of application and the acceptability of it. For discussion, we collect data through tests and questionnaire. Through analysing the data, we obtain the positive result.

• Proceedings of the Korean Nuclear Society Conference
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• 1998.05a
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• pp.93-98
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• 1998

PEN(1)(다항식전개 노달) 해법을 육방형 노심의 과도상태 해석과 Adjoint flux(수반 중성자속)해법에 응용하여 여러가지 Benchmark문제들(3)(4)(5)을 풀고 그 결과를 다른 수치기법 결과와 비교·분석하였다. 2차원 육방형 대형중수로 과도상태 Benchmark문제(5)를 다항식전개 노달해법에 의한 과도상태 해석·검증의 대상으로 삼았으며 그 기준 계산치로서 FX2-TH 코드의 계산결과를 사용하였다 대형중수로 노심의 과도상태 해석 결과, 기준해와 비교해 집합체 낙하시작 3초 후에 집합체가 낙하한 위치에서 Normalized Flux 오차가 0.5% 이내, 집합체가 낙하하지 않은 위치에서 Normalized Flux 오차가 1% 이내의 정확한 결과를 보였다. Adjoint flux 해의 검증을 위해서는 VENTURE 코드(2)의 계산 결과를 기준해로 하였으며, 계산능 검증을 위해 사용된 대부분 의 Benchmark 문제들에서 작은 오차를 보였으나 반사체가 포함된 IAEA 문제에서는 큰 오차를 보였다.

• Journal of the KSME
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• v.26 no.5
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• pp.389-393
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• 1986

고유치는 여러 공학문제에서 중요하다. 예를들어 비행기의 안전성은 어떤 행렬(matrix)의 고유 치에 의해서 결정된다. 보의 고유진동수는 실제로 행렬의 고유치이다. 좌굴(buckling) 해석도 행렬의 고유치를 구하는 문제이다. 고유치는 여러 수학적인 문제의 해석에서도 자연히 발생한다. 상수계수 일계연립상미분방정식의 해는 그 계수행렬의 고유치로 구할 수 있다. 또한 행렬의 제곱의 수렬 $A,{\;}A^{2},{\;}A^{3},{\;}{\cdots}$의 거동은 A의 고유치로서 가장 쉽게 해석할 수 있다. 이러한 수렬은 연립일차방정식(비선형)의 반복해에서 발생한다. 따라서 이 강좌에서는 행렬의 고유치를 수치적으로 구하는 문제에 대하여 고찰 하고자 한다. 실 또는 보소수 .lambda.가 행렬 B의 고유치라 함은 영이 아닌 벡터 y가 존재하여 $By={\lambda}y$ 가 성립할 때이다. 여기서 벡터 y를 고유치 ${\lambda}$에 속하는 B의 고유벡터라 한다. 윗식은 또 $(B-{\lambda}I)y=0$의 형으로도 써 줄 수 있다. 행렬의 고유치를 수치적으로 구하는 방법에는 여러 가지 방법이 있으나 그 중에서 효과있는 Danilevskii 방법을 소개 하고자 한다. 이 Danilevskii 방법에 의하여 특 성다항식(Characteristic polynomial)을 얻을 수 있고 이 다항식의 근을 얻는 방법 중에 Bairstow 방법 (또는 Hitchcock 방법)이 있는데 이에 대하여 아울러 고찰하고자 한다.

• Journal of Educational Research in Mathematics
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• v.13 no.4
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• pp.429-446
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• 2003

Gu-il-jip is a mathematical book of Chosun dynasty in the 18c. It consists of nine chapters including more than 473 problems and their solutions. Analyzing the problems and their solutions, we can appreciate the mathematical researches by the professional mathematicians of Chosun. Especially, it is worth noting the followings: - units for measuring and decimal notations - $\pi$, area of circle, volume of sphere - naming the powers - counting rods - excess and deficit: calculation technique for excess-deficit relations among quantities - rectangular arrays: calculation technique for simultaneous linear equations - 'Thien Yuan' notation: method for representing equations - 'Khai Fang': algorithm for numerical solution of quadratic, cubic and higher equations Based on these analyses, some pedagogical applications are proposed.

• Nuclear Engineering and Technology
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• v.22 no.4
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• pp.359-370
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• 1990

This study concerns with comparing low-dimensional reactor kinetics methods with a three-dimensional kinetics method to be used for safety analysis of light water reactors in order to suggest means of preparing input parameters required for low-dimensional methods. For this purpose a one-dimensional finite difference two-group diffusion theory code ODTRAN and a third-order Hermit polynomial-based point kinetics code POTRAN are developed and used to obtain low-dimensional solutions to the LRA-BWR kinetics benchmark problem. The results are compared with a three-dimensional modified Borresen's coarse-mesh solution of the kinetics problem by CMSNACK code. Through this comparison some simple but practical means of preparing input parameters of low-dimensional kinetics analysis methods are suggested.

• Journal of the Institute of Convergence Signal Processing
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• v.12 no.3
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• pp.163-168
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• 2011

In this paper, we proposed non-linear gamma curve algorithm for gamma correction. The previous non-linear gamma curve algorithm is generated by the least square polynomial using the Gauss-Jordan inverse matrix. However, the previous algorithm has some weak points. When calculating coefficients using inverse matrix of higher degree, occurred truncation errors. Also, only if input sample points are existed regular interval on 10-bit scale, the least square polynomial is accurately works. To compensate weak-points, we calculated accurate coefficients of polynomial using eigenvalue and orthogonal value of mat11x from singular value decomposition (SVD) and QR decomposition of vandemond matrix. Also, we used input data part segmentation, then we performed polynomial curve fitting and merged curve fitting results. When compared the previous method and proposed method using the mean square error (MSE) and the standard deviation (STD), the proposed segmented polynomial curve fitting is highly accuracy that MSE under the least significant bit (LSB) error range is approximately $10^{-9}$ and STD is about $10^{-5}$.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.13 no.9
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• pp.937-946
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• 2002

In this paper, we present a stable solution of the transient electromagnetic scattering from the conducting objects. This method does not utilize the conventional marching-on in time (MOT) solution. Instead we solve the time domain integral equation by expressing the transient behavior of the induced current in terms of weighted Laguerre polynomials. By using this basis functions for the temporal variation, the time derivative in the integral equation can be handled analytically. Since these temporal basis functions converge to zero as time progresses, the transient response of the induced current does not have a late time oscillation. To show the validity of the proposed method, we solve a time domain electric feld integral equation and compare the results of MOT, Mie solution, and the inverse discrete Fourier transform (IDFT) of the solution obtained in the frequency domain.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.17 no.3
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• pp.257-264
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• 1999

The lens distortions were corrected directly using the high-order polynomial which was offered in camera calibration data for the forward transformation and the root of Newton-Raphson's $2\times{2}$ nonlinear system for the backward transformation. The 0.04~0.08 pixels increase in accuracy was indicated through the use of direct correction of lens distortions instead of least square methods of commercial software. The least square adjustment method of high-order polynomial requires many control points which has a same weight. But this suggested method which is unnecessary to determine control points was developed and applied. The algorithm showed improved efficacy.

• Journal of the Society of Naval Architects of Korea
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• v.30 no.1
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• pp.125-133
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• 1993

Most studies on the vibration analysis of a beam-column with ends elastically restrained and various intermediate constraints have been based on the Euler beam theory, which is inadequate for beam-columns of low slenderness ratios. In this paper, analytical methods for vibration and dynamic sensitivity of a Timoshenko beam-column with ends elastically restrained and various intermediate constraints are presented. Firstly, an exact solution method is shown. Since the exact method requires considerable computational effort, a Rayleigh-Ritz analysis is also investigated. In the latter two kinds of trial functions are examined for comparisions : eigenfunctions of the base system(the system without intermediate constraints) and polynomials having properties corresponding to the eigenfunctions of the base system. The results of some numerical Investigations show that the Rayleigh-Ritz analysis using the characteristic polynomials is competitive with the exact solutions in accuracy, and that it is much more efficient in computations than using the eigenfunctions of the base system, especially in the dynamic sensitivity analysis. In addition, the prediction of the changes of natural frequencies due to the changes of design variables based on the first order sensitivity is in good agreements with that by the ordinary reanalysis as long as the changes of design variables are moderate.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.16 no.2
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• pp.211-221
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• 2018

Nodal transport methods are proposed for solving the simplified even-parity neutron transport (SEP) equation. These new methods are attributed to the success of existing nodal diffusion methods such as the Polynomial Expansion Nodal and the Analytic Function Expansion Nodal Methods, which are known to be very effective for solving the neutron diffusion equation. Numerical results show that the simplified even-parity transport equation is a valid approximation to the transport equation and that the two nodal methods developed in this study also work for the SEP transport equation, without conflict. Since accuracy of methods is easily increased by adding node unknowns, the proposed methods will be effective for coarse mesh calculation and this will also lead to computation efficiency.