• Bulletin of the Korean Space Science Society
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• 2010.04a
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• pp.28.1-28.1
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• 2010

이 연구에서는 기존 선형 상대운동방정식에 차등중력, 주위성의 이심율, J2 섭동 등의 비선형항을 추가하여 보다 정확한 상대운동방정식을 만든 후 섭동이론을 적용하여 위성편대 연료최적화 재배치 문제에 대한 근사 해석해를 구하고자 한다. 먼저, 비선형 섭동항을 테일러 급수를 이용하여 2차항까지 전개한 후, 이를 기존 선형상대운동방정식에 추가하여 새로운 비선형 상대운동방정식을 만든다. 이 때 사용된 선형상대운동방정식은 힐스 방정식으로 주위성의 궤도가 일반적인 타원이고 위성 간 상대거리가 충분히 가깝다고 가정한다. 최적화 조건으로부터 상태벡터와 라그랑지 곱수로 이루어진 연립 미분방정식이 만들어 지는데, 이 식은 힐스 방정식에 기인한 선형부분과 2차 비선형항에 기인한 섭동부분으로 나뉜다. 이 때, 이 연립미분방정식의 해는 선형부분의 해와 섭동으로 인한 변화량의 합으로 근사할 수 있으며 그 변화량은 섭동이론을 적용하여 얻을 수 있다. 이와 같이 얻어진 해는 여러 섭동의 비선형항을 2차까지 포함한 상대운동방정식을 사용했기 때문에, 기존 선형상대운동방정식을 사용하여 구한 최적해 보다 더 정확한 결과를 얻을 것이라 예상한다.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.13 no.1
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• pp.139-146
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• 2003

In this paper we demonstrate a cryptanalysis of the stream cipher LILI-128. Our approach to analysis on LILI-128 is to solve an overdefined system of multivariate equations. The LILI-128 keystream generato $r^{[8]}$ is a LFSR-based synchronous stream cipher with 128 bit key. This cipher consists of two parts, “CLOCK CONTROL”, pan and “DATA GENERATION”, part. We focus on the “DATA GENERATION”part. This part uses the function $f_d$. that satisfies the third order of correlation immunity, high nonlinearity and balancedness. But, this function does not have highly nonlinear order(i.e. high degree in its algebraic normal form). We use this property of the function $f_d$. We reduced the problem of recovering the secret key of LILI-128 to the problem of solving a largely overdefined system of multivariate equations of degree K=6. In our best version of the XL-based cryptanalysis we have the parameter D=7. Our fastest cryptanalysis of LILI-128 requires $2^{110.7}$ CPU clocks. This complexity can be achieved using only $2^{26.3}$ keystream bits.

• 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.

• Journal for History of Mathematics
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• v.23 no.1
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• pp.25-40
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• 2010

We first seek a principle of cognitive development processes by reviewing and summarizing Piaget's cognitive development theory, constructivism and Dubinsky's APOS theory, and also the epistemology on logics of 墨子 and 荀子. We investigate Chapter 8 方程 on the theory of systems of linear equations, of the Nine Chapters, one of the oldest ancient Asian mathematical books, from the viewpoint of our principle of cognitive development processes. We conclude the educational value of the chapter and the value of the research on Asian ancient mathematical works and heritages.

• Proceedings of the KIPE Conference
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• 2014.07a
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• pp.361-362
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• 2014

본 논문은 PV cell의 전기적 등가회로에 대하여 테브난-노턴 분석방법을 통하여 3개의 대표적인 운전점에서 I-V 특성곡선의 접선의 기울기를 $R_s$와 $R_{sh}$ 및 $R_{MPP}$에 관련되는 값으로써 정량적으로 구하는 방법을 제시한다. 이 값들은 PV cell의 전류방정식에서 파생되는 4원 1차 연립방정식의 경계조건은 만족함으로써 전기적 등가회로의 4가지 요소에 대한 값을 구할 수 있는 길이 열린다. 제안된 방법은 제조사가 datasheet에서 특성을 보장하는 초기 PV cell 제품에 대한 I-V 특성뿐만 아니라, 열화가 진행된 PV cell의 실제적인 I-V 특성을 정확히 시뮬레이션 할 수 있다는 장점이 있다.

• Journal of Korean Society of Steel Construction
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• v.13 no.6
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• pp.703-713
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• 2001

Derivation procedures of exact dynamic stiffness matrices of thin-walled straight beams subjected to eccentrically axial forces are rigorously presented for the spatial free vibration analysis. An exact dynamic stiffness matrix is established from governing equations for a uniform beam element with nonsymmetric thin-walled cross section. First this numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. Thus, the displacement functions of displacement parameters are exactly derived and finally exact stiffness matrices are determined using element force-displacement relationships. The natural frequencies of nonsymmetric thin-walled straight beams are evaluated and compared with analytical solutions or results by thin-walled beam element using the cubic Hermitian polynomials and ABAQU's shell elements in order to demonstrate the validity of this study.

• Korean Journal of Optics and Photonics
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• v.18 no.1
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• pp.19-23
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• 2007

We derived analytically the generalized curvature linear equation useful in the initial optical design of a two-mirror system with finite object distance, including an infinite object distance from paraxial ray tracing and Seidel third order aberration theory for coma coefficient. These aberration coefficients for finite object distance were described by the curvature, the inter-mirror distance, and the effective focal length. The analytical equations were solved by using a computer with a numerical analysis method. Two useful linear relationships, determined by the generalized curvature linear equations relating the curvatures of the two mirrors, for the cancellation of each aberration were shown in the numerical solutions satisfying the nearly zero condition ($<10^{-10}$) for each aberration coefficient. These equations can be utilized easily and efficiently at the step of initial optical design of a two-mirror system with finite object distance.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 1999.10a
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• pp.28-28
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• 1999

본 연구에서는 가스 발생기에서 발생되는 고온, 고압의 가스를 이용하여 유도탄을 수직 발사하는 사출 시스템에 대해 해석적 연구를 수행하였다. 사출 시스템에 의한 수직발사 방식은 발사관내에 설치된 가스 발생기에 의해 생성된 가스가 사출 실린더의 피스톤을 구동시켜, 피스톤에 연결된 유도탄을 요구되는 높이로 사출 시킨 후 유도탄이 점화되는 발사방식이다. 이러한 발사방식은 유도탄 자체의 부스터 발사방식에 비해 유도탄의 화염에 의한 영향이 적다. 현재 사출 시스템은 가스발생기, 가스 튜브, 사출 실린더와 피스톤으로 구성되어있다. 본 논문은 가스 발생기에서 사출 실린더까지의 내부 유동장을 일차원적으로 모델링하였고, 가스발생기, 가스튜브, 실런더 내의 유동과 열전달 과정 및 유도탄의 동적거동에 대한 미분방정식을 연립하여 4th-order Runge-Kutta 방법으로 계산하였다. 또한 가스튜브와 사출 실린더의 열전달 손실에 대하여 1차원 비정상 열전도 방정식의 수치적 계산을 통해 에너지 손실을 계산하였다. 특히 해석에 사용된 작동유체인 추진제 가스의 열학적 상태량은 온도 함수의 5차 다항식으로 표현하여 사용하였다. 이론적인 해석을 통해 사출 장치 시스템의 성능 요구조건과 신뢰성을 만족시키기 위한 가스발생기의 추진제 그레인 및 사출 시스템 설 계 조건을 도출하였다.

• Journal of Korean Society of Steel Construction
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• v.14 no.4
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• pp.509-518
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• 2002

In order to perform the spatial buckling and static analysis of the nonsymmetric thin-walled beam-column element, improved exact static stiffness matrices were evaluated using equilibrium equation and force-deformation relationships. This numerical technique was obtained using a generalized linear eigenvalue problem, by introducing 14 displacement parameters and system of linear algebraic equations with complex matrices. Unlike the evaluation of dynamic stiffness matrices, some zero eigenvalues were included. Thus, displacement parameters related to these zero eigenvalues were assumed as polynomials, with their exact distributions determined using the identity condition. The exact displacement functions corresponding to three loadingcases for initial stress-resultants were then derived, by consistently combining zero and nonzero eigenvalues and corresponding eigenvectors. Finally, exact static stiffness matrices were determined by applying member force-displacement relationships to these displacement functions. The buckling loads and displacement of thin-walled beam were evaluated and compared with analytic solutions and results using ABAQUS' shell element or straight beam element.

• Korean Journal of Optics and Photonics
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• v.4 no.3
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• pp.243-251
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• 1993

We have derived Gaussian bracket expressions of aplanatic and achromatic conditions and obtained the numerical solutions for each of two modules of the telephoto type telescope objective free from the Seidel first order spherical aberration, coma, and longitudinal chromatic aberration. The system which is for use in sighting a target is optimized within the resolution of eyes. The objective lens satisfying the aplanatic and achromatic condition has f/8.5 with the half field angle 0.$3^{\circ}$, and the telephoto ratio is 0.839 with the focal length of 30 cm.