• 대한수학회지
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• 제36권2호
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• pp.267-298
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• 1999

A geometric construction of an exact algebraic formula for graded partition functions, of which a special one is the classical unrestricted partition function p(n), from a diophantine point of view is presented. Moreover, the involved process allows us to compute the value of a graded partition function in an inductive manner with a geometrically built-in self-error-checking ability at each step for correctness of the computed values of the partition function under consideration.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.317-324
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• 2008

This paper shows the degree of simultaneous neural network approximation for a target function in $C^r$[-1, 1] and its first derivative. We use the Jackson's theorem for differentiable functions to get a degree of approximation to a target function by algebraic polynomials and trigonometric polynomials. We also make use of the de La Vall$\grave{e}$e Poussin sum to get an approximation order by algebraic polynomials to the derivative of a target function. By showing that the divided difference with a generalized translation network can be arbitrarily closed to algebraic polynomials on [-1, 1], we obtain the degree of simultaneous approximation.

• 대한수학회지
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• 제40권3호
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• pp.447-460
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• 2003

In this paper we study the non-degenerate n-connected canonical domains with n>1 related to the conjecture of S. Bell in [4]. They are connected to the algebraic property of the Bergman kernel and the Szego kernel. We characterize the non-degenerate doubly connected canonical domains.

• 한국수학교육학회지시리즈A:수학교육
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• 제58권1호
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• pp.79-99
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• 2019

This study is a study to collect information about 'Limitations of functions' related learning. Especially, this study was conducted on three students who can find answers by algebraic procedure in the process of extreme problem solving. Students have had the experience of converting from their algebraic procedures to graphical expressions. This shows how they reflect on their algebraic procedures. This study is a study that observes these parts. To accomplish this, twelfth were teaching experiment in three high school students. And we analyzed the contents related to the research topic of this study. Through this, students showed the difference of expressions in the method of finding limits by using algebraic interpretation methods and graphs. In addition, we examined the connectivity of the limitations of functions problem solving process of functions using algebraic procedures and graphs in the process of converting algebraic expressions to graph expressions. This study is a study of how students construct limit concepts. As in this study, it is meaningful to accumulate practical information about students' limit conceptual composition. We hope that this study will help students to study limit concept development process for students who have no limit learning experience in the future.

• East Asian mathematical journal
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• 제17권2호
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• pp.339-348
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• 2001

• Kyungpook Mathematical Journal
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• 제56권4호
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• pp.1141-1160
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• 2016

In this paper, a symbolic algorithm for solving a regular initial value problem (IVP) for a system of linear differential-algebraic equations (DAEs) with constant coeffcients has been presented. Algebra of integro-differential operators is employed to express the given system of DAEs. We compute a canonical form of the given system which produces another simple equivalent system. Algorithm includes computing the matrix Green's operator and the vector Green's function of a given IVP. Implementation of the proposed algorithm in Maple is also presented with sample computations.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국제학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.562-565
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• 1993

It is well known that H$_{\infty}$ control problem involves solving an algebraic Riccati equation which includes a pair of parameters (.gamma., .epsilon.). Focusing on .epsilon. the maximum of .epsilon.. We discuss in this paper about the properties between the H$_{\infty}$ norm of a trnsfer function matrix and the parameters(.gamma., .epsilon.). We can change the algebraic relattion between .gamma. and .epsilon. by the similarity transformation of a considered system and we can find a proper transformation to get a simple quadratic algebraic equation between .gamma. and .epsilon.. This relation provide the H$_{\infty}$ norm of a transfer function.on.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1995년도 Proceedings of the Korea Automation Control Conference, 10th (KACC); Seoul, Korea; 23-25 Oct. 1995
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• pp.10-13
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• 1995

This paper considers the linear-quadratic optimal regulator problem for nonstandard singularly perturbed systems making use of the recursive technique. We first derive a generalized Riccati differential equation by the Hamilton-Jacobi equation. In order to obtain the feedback gain, we must solve the generalized algebraic Riccati equation. Using the recursive technique, we show that the solution of the generalized algebraic Riccati equation converges with the rate of convergence of O(.epsilon.). The existence of a bounded solution of error term can be proved by the implicit function theorem. It is enough to show that the corresponding Jacobian matrix is nonsingular at .epsilon. = 0. As a result, the solution of optimal regulator problem for nonstandard singularly perturbed systems can be obtained with an accuracy of O(.epsilon.$^{k}$ ). The proposed technique represents a significant improvement since the existing method for the standard singularly perturbed systems can not be applied to the nonstandard singularly perturbed systems.

• 정보보호학회논문지
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• 제14권4호
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• pp.49-59
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• 2004

공개되지 않은 함수에 대한 입력과 그에 따른 출력을 이용하여 그 함수와 같은 입출력을 가지는 부울함수표현을 찾아내는 것이 부울함수 합성문제이다. 전자공학 및 암호학 분야에서는 이 문제가 수리계획법의 한 부류인 0-1 integer programming 문제로 귀결되며, 본 논문에서는 부울함수 합성문제를 해결하는 하나의 예로 DES 의 비공개 논리인 입력 6비트, 출력 4비트의 S-box에 대한 부울함수표현을 찾는다. 이러한 결과는 임의의 함수에 대한 효율적인 하드웨어 구현과 블록암호 알고리즘의 대수적 구조를 이용한 암호분석기법에 이용될 수 있다.

• 대한수학교육학회지:수학교육학연구
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• 제23권2호
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• pp.213-235
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• 2013

본 연구는 수학과목 학습이 부진하고, 특히 함수식과 그래프의 관계에 대한 이해가 부족한 특성화 고등학생들을 대상으로 학생들에게 친숙한 엑셀 프로그램을 사용하여 지도한 효과를 살펴보았다. 엑셀의 식, 표, 그래프를 한 화면에 담을 수 있는 기능과 스크롤바를 이용하여 그래프를 움직이는 기능이 주로 사용되었다. 함수개념을 과정관점과 대상관점으로 나누고, 함수 표상을 표, 식, 그래프로 나누었을 때 학생들이 지도를 통하여 표상 내에서 또는 관점 간 유연한 전환이 일어나는 것을 목표로 지도하였고 긍정적인 효과가 나타났다. 실험은 특성화 고등학교 2학년 학생 5명을 대상으로 5일간 컴퓨터실에서 실시되었다. 학생들에 대한 진단평가를 토대로 중학교 수준의 함수와 그래프를 엑셀을 이용해서 지도하였다. 학생들에게는 엑셀파일이 제공되었고, 학생들은 수업 중에 실제 조작해보고 조작결과를 배포된 활동지에 적고 함께 토론하는 방식으로 수업을 진행하였다.