• School Mathematics
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• v.12 no.1
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• pp.27-43
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• 2010

In this article the conceptual meaning of expression, equation and identity used in Korean mathematics textbooks and American mathematics textbooks is compared and discussed. For this purpose definitions and examples in several mathematics textbooks which are used in Korean elementary school, the 1st grade of middle school and American middle school are investigated. It is founded out that at first there are some parts that give rise to misunderstanding and then there are differences between the Korean terminologies and their corresponding English counterparts. The definitions of expression, equation and identity are advised to examine in the view of middle mathematics curriculum.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 1997.11a
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• pp.183-188
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• 1997

유한체에서 정의된 선형부호의 경우 Newton 항등식을 이용한 복호방법이 알려져 있다. 본 논문에서는 유한체 뿐 만 아니라 Z$_4$위에서도 Newton 항등식이 존재함을 보이고, 이를 이용하여 Z$_4$위의 Calderbank-McGuire 부호의 복호방법을 제안하였다.

• Review of KIISC
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• v.2 no.4
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• pp.30-36
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• 1992

이 논문에서 우리는 여러 가지 분할 항등식을 유도했고 제한된 분할에 관한 새로운 항등식을 증명하고, 분할의 기본적인 이론과 분할함수(Partition Number Function)가 다항식 함수가 아니라는 것을 보이며, n 의 분할의 수 p(n)에 대한 하계(Lower Bound)를 얻기 위해 Stirling의 n ! 에 대한 근사값을 소개한다. 그리고 Hardy-Ramanujan 공식, Euler 항등식과 p(n) 의 순환식을 유도하며, 그리고 $d_m$(n)이n을m개의 부분으로 분할하는 분할의 수를 나타낼 때 우리는 $d_m$(n)에 관한 일반적인 공식을 p(n)과 함께 행렬식의 형태로 표현한다.

• Review of KIISC
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• v.2 no.4
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• pp.37-47
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• 1992

이 논문에서 우리는 여러 가지 분할 항등식을 유도했고 제한된 분할에 관한 새로운 항등식을 증명하고, 분할의 기본적인 이론과 분할함수(Partition Number Function)가 다항식 함수가 아니라는 것을 보이며, n의 분할의 수 p(n)에 대한 ㅎ계(Lower Bound)를 얻기 위해 Stirling의 n !에 대한 근사값을 소개한다. 그리고Hardy-Ramanujan 공식, Euler 항등식과 p(n)의 순환식을 유도하며, 그리고 d$_{m}$ (n)이 n을 m개의 부분으로 분할하는 분할의 수를 나타낼 때 우리는 d$_{m}$ (n) 에 관한 일반적인 공식을 p(n)과 함께 행렬식의 형태로 표현한다.

• Journal for History of Mathematics
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• v.21 no.4
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• pp.87-104
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• 2008

In this paper we investigate several properties and characteristics of the generalized Fibonacci sequence $\{g_n\}$={a, b, a+b, a+2b, 2a+3b, 3a+5b,...}. This concept is a generalization of the famous Fibonacci sequence. In particular we find the identities of sums and the nth term $g_n$ in detail. Also we find the generalizations of the Catalan's identity and A. Tagiuri's identity about the Fibonacci sequence, and investigate the relation between $g_n$ and Pascal's triangle, and how fast $g_n$ increases. Furthermore, we show that $g_n$ and $g_{n+1}$ are relatively prime if a b are relatively prime, and that the sequence $\{\frac{g_{n+1}}{g_n}\}$ of the ratios of consecutive terms converges to the golden ratio $\frac{1+\sqrt5}2$.

• Journal for History of Mathematics
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• v.25 no.2
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• pp.11-21
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• 2012

The interdisciplinary study explores the Euler's theology through his mathematical landmarks. From the mathematico-theological perspective, we first address Euler's theological backgrounds, and then show the implications of Euler's identity as his mathematical Christology.

• Journal of the Institute of Convergence Signal Processing
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• v.10 no.1
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• pp.60-65
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• 2009

In this paper, we propose a new exponential pulse shaping function based on Chebychev identity equation and Bessel coefficients. The proposed pulse shaping function can produce various pulses with the different characteristics in the time and frequency domain by changing its two parameters. By differentiating the exponential pulse shaping function, we obtain new different pulse functions, in which the even order derivatives of the exponential pulse shaping function are orthogonal to its odd order derivatives. To find the efficiency of the proposed exponential pulse shaping function we analyze its essential characteristics and compare them with those of the conventional Gaussian pulses. We can choose the most suitable exponential pulse waveform according to the design criteria of communication systems.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.41 no.3
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• pp.311-319
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• 1992

In this paper, a direct adaptive pole placement controller for an unknown linear time-invariant single-input single-output nonminimum phase plant is proposed. To design this direct adaptive pole placement controller, the auxiliary signals are introduced. Consequently, a linear equation error model is formulated for estimating both the controller parameters and the additional auxiliary parameters. To estimate the controller parameters and the additional auxiliary parameters, the exponentially weighted least-squares algorithm is implemented, and a method of selecting the characteristic polynomials of the sensitivity function filters is proposed. In this method, all the past measurement data are weighted exponentially. A series of simulations for a nonminimum phase plant is presented to illustrate some features of both the parameter estimation and the output response of this adaptive pole placement controller.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.8C
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• pp.765-770
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• 2003

In this paper, the complete weight enumerator of the Delsarte-Goethals code over Z$_4$ is obtained. This code is divided into 3 cases and the complete weight enumerator of each case is calculated. During this weight enumeration, the blown distribution of exponential sums and binary weight distribution of the sub-codes are used. By combining this result and MacWilliams identity, the complete weight enumerator of the Goethals code over Z$_4$can be easily obtained. This result is also used for finding 3-designs from the Goethals and Delsarte-Goethals codes over Z$_4$.

• Journal of the Korean Institute of Intelligent Systems
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• v.26 no.1
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• pp.50-55
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• 2016

This paper discusses a sampled-data controller design problem for nonlinear systems including singular perturbation. The concerned system is assumed to be modeled in Takagi--Sugeno (T--S) form. By introducing a novel Lyapunov function and an identity equation, the stability of the sampled-data closed-loop dynamics of the singularly perturbed T--S fuzzy system is analyzed. The design condition is represented in terms of linear matrix inequalities. A few discussions on the development are made that propose future research topics. Numerical simulation shows the effectiveness of the proposed method.