• 통합자연과학논문집
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• 제9권2호
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• pp.152-154
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• 2016

Arbitrary polynomial of degree n can be written in Chebyshev form. In this paper, we generalize this Chebyshev form and study its root distributions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권4호
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• pp.307-314
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• 2009

In this work, we introduce a new quatnary approximating subdivision scheme for curve and deal with its analysis (convergence and regularity) using Laurent polynomials method. We also discuss various properties, such as approximation order and support of basic limit function.

• 한국정보처리학회논문지
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• 제6권9호
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• pp.2431-2441
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• 1999

우리는 등식으로 표현된 많은 정보들을 다룬다. 이러한 정보에 관한 가장 근본적인 문제중의 하나는 '어떤 주어진 등식이 한 가지 방법이다. Rewrite system은 주어진 항(term)에 rewrite 규칙(rule)들을 적용하여 단순화한다. 따라서 어떤 항이라도 단순화 과정이 무한히 계속되지 않아야 함은 rewrite system의 중요한 성질이다. Rewrite system의 이러한 종료(termination) 여부를 결정하는 방법들 중 하나가 다항식 순서(polynomial ordering)이다. 이 방법은 rewrite system의 함수기호에 적절한 다항식을 대응시켜주는 방법이다. 그러나, 주어진 rewrite system이 종료함을 보이는 다항식 순서를 자동적으로 생성하는 방법은 알려져 있지 않다. 본 논문에서는 유전자 알고리즘을 사용하여, 다항식을 자동으로 생성하는 방법을 제시한다.

• Journal of applied mathematics & informatics
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• 제37권1_2호
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• pp.23-35
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• 2019

Self-reciprocal polynomials are important because it is possible to specify only half of the coefficients. The special case of the self-reciprocal polynomial, the maximum weight polynomial, is particularly important. In this paper, we analyze even cell 90/150 cellular automata with linear rule blocks of the form < $a_1,{\cdots},a_n,d_1,d_2,b_n,{\cdots},b_1$ >. Also we show that there is no 90/150 CA of the form < $U_n{\mid}R_2{\mid}U^*_n$ > or < $\bar{U_n}{\mid}R_2{\mid}\bar{U^*_n}$ > whose characteristic polynomial is $f_{2n+2}(x)=x^{2n+2}+{\cdots}+x+1$ where $R_2$ =< $d_1,d_2$ > and $U_n$ =< $0,{\cdots},0$ >, and $\bar{U_n}$ =< $1,{\cdots},1$ >.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 1998년도 추계종합학술대회 논문집
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• pp.679-682
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• 1998

This paper presents the VLSI implementation of RS(reed-solomon) decoder using the Modified Euclidean Algorithm(hereafter MEA) for DVD(Digital Versatile Disc) and CD(Compact Disc). The decoder has a capability of correcting 8-error or 16-erasure for DVD and 2-error or 4-erasure for CD. The technique of polynomial evaluation is introduced to realize syndrome calculation and a polynomial expansion circuit is developed to calculate the Forney syndrome polynomial and the erasure locator polynomial. Due to the property of our system with buffer memory, the MEA architecture can have a recursive structure which the number of basic operating cells can be reduced to one. We also proposed five criteria to determine an uncorrectable codeword in using the MEA. The overall architecture is a simple and regular and has a 4-stage pipelined structure.

• 환경영향평가
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• 제16권5호
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• pp.341-350
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• 2007

Lake Youngrang is a lagoon whose effluent flows into the East Sea. Because two resort towns and two golf courses are situated at the lake basin, many tourists visit this area. Stormwater runoff surveys were carried out for the eight storm events from 2004 to 2005 in the eutrophic lake watershed to give a basic data for the diffuse pollution control of the lake. Dimensionless mass-volume curves indicating the distribution of pollutant mass vs. volume were used to analyze the first flush phenomenon. The mass-volume curves were fitted with a power function and polynomial equation curves. The regression analysis showed that the polynomial equation curves were better than the power function in representing the tendency of the first flush, and second degree polynomial equation curves indicated the strength of the first flush effectively.

• Nonlinear Functional Analysis and Applications
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• 제27권1호
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• pp.141-148
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• 2022

Let p(z) be a polynomial of degree n having no zero in |z| < k, k ≤ 1, then Govil proved $$\max_{{\mid}z{\mid}=1}{\mid}p^{\prime}(z){\mid}{\leq}{\frac{n}{1+k^n}}\max_{{\mid}z{\mid}=1}{\mid}p(z){\mid}$$, provided |p'(z)| and |q'(z)| attain their maximal at the same point on the circle |z| = 1, where $$q(z)=z^n{\overline{p(\frac{1}{\overline{z}})}}$$. In this paper, we extend the above inequality to polar derivative of a polynomial. Further, we also prove an improved version of above inequality into polar derivative.

• 대한전기학회논문지:시스템및제어부문D
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• 제49권7호
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• pp.378-388
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• 2000

In this paper, we propose Fuzzy Polynomial Neural Networks(FPNN) based on Polynomial Neural Networks(PNN) and Fuzzy Neural Networks(FNN) for model identification of complex and nonlinear systems. The proposed FPNN is generated from the mutually combined structure of both FNN and PNN. The one and the other are considered as the premise part and consequence part of FPNN structure respectively. As the consequence part of FPNN, PNN is based on Group Method of Data Handling(GMDH) method and its structure is similar to Neural Networks. But the structure of PNN is not fixed like in conventional Neural Networks and self-organizing networks that can be generated. FPNN is available effectively for multi-input variables and high-order polynomial according to the combination of FNN with PNN. Accordingly it is possible to consider the nonlinearity characteristics of process and to get better output performance with superb predictive ability. As the premise part of FPNN, FNN uses both the simplified fuzzy inference as fuzzy inference method and error back-propagation algorithm as learning rule. The parameters such as parameters of membership functions, learning rates and momentum coefficients are adjusted using genetic algorithms. And we use two kinds of FNN structure according to the division method of fuzzy space of input variables. One is basic FNN structure and uses fuzzy input space divided by each separated input variable, the other is modified FNN structure and uses fuzzy input space divided by mutually combined input variables. In order to evaluate the performance of proposed models, we use the nonlinear function and traffic route choice process. The results show that the proposed FPNN can produce the model with higher accuracy and more robustness than any other method presented previously. And also performance index related to the approximation and prediction capabilities of model is evaluated and discussed.

• 제어로봇시스템학회논문지
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• 제8권2호
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• pp.126-135
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• 2002

The study is concerned with an approach to the design of new architectures of fuzzy neural networks and the discussion of comprehensive design methodology supporting their development. We propose an Adaptive Fuzzy Polynomial Neural Networks(APFNN) based on Fuzzy Neural Networks(FNN) and Self-organizing Networks(SON) for model identification of complex and nonlinear systems. The proposed AFPNN is generated from the mutually combined structure of both FNN and SON. The one and the other are considered as the premise and the consequence part of AFPNN, respectively. As the premise structure of AFPNN, FNN uses both the simplified fuzzy inference and error back-propagation teaming rule. The parameters of FNN are refined(optimized) using genetic algorithms(GAs). As the consequence structure of AFPNN, SON is realized by a polynomial type of mapping(linear, quadratic and modified quadratic) between input and output variables. In this study, we introduce two kinds of AFPNN architectures, namely the basic and the modified one. The basic and the modified architectures depend on the number of input variables and the order of polynomial in each layer of consequence structure. Owing to the specific features of two combined architectures, it is possible to consider the nonlinear characteristics of process system and to obtain the better output performance with superb predictive ability. The availability and feasibility of the AFPNN are discussed and illustrated with the aid of two representative numerical examples. The results show that the proposed AFPNN can produce the model with higher accuracy and predictive ability than any other method presented previously.

• 대한수학회논문집
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• 제12권4호
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• pp.855-864
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• 1997

Let K be a algebraically closed field of characteristic 0 and G a cyclic group of order n. We find the units and idempotent elements of the group ring KG by using the basic group table matrix of G.