• Journal of Integrative Natural Science
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• v.9 no.2
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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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• v.13 no.4
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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.

• The Transactions of the Korea Information Processing Society
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• v.6 no.9
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• pp.2431-2441
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• 1999

Equations are widely used in representing information. One of the basic questions about equations is to determine whether a given equation follows logically from the set of equations. Rewrite systems are one of the method to answer many instances of this problem. A rewrite system simplifies a given term by applying rewrite rules successively. Hence it is important that the process of simplification does not go on indefinitely. One of the methods to check whether a rewrite system terminates (that is, the rewrite system does not go on indefinitely) is polynomial orderings. A polynomial ordering assigns an appropriate polynomial to each function symbol. However, how to assign polynomials to function symbols is not known. We propose an automatic way of generating polynomial orderings using genetic algorithms.

• Journal of applied mathematics & informatics
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• v.37 no.1_2
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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 $\bar{U_n}$ =< $1,{\cdots},1$ >.

• Proceedings of the IEEK Conference
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• 1998.10a
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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.

• Journal of Environmental Impact Assessment
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• v.16 no.5
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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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• v.27 no.1
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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.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.7
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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.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.2
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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.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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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.