• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2000년도 춘계학술대회 학술발표 논문집
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• pp.130-133
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• 2000

In this paper, a new design methodology named FNNN(Fuzzy Polynomial Neural Network) algorithm is proposed to identify the structure and parameters of fuzzy model using PNN(Polynomial Neural Network) structure and a fuzzy inference method. The PNN is the extended structure of the GMDH(Group Method of Data Handling), and uses several types of polynomials such as linear, quadratic and modified quadratic besides the biquadratic polynomial used in the GMDH. The premise of fuzzy inference rules defines by triangular and gaussian type membership function. The fuzzy inference method uses simplified and regression polynomial inference method which is based on the consequence of fuzzy rule expressed with a polynomial such as linear, quadratic and modified quadratic equation are used. Each node of the FPNN is defined as fuzzy rules and its structure is a kind of neuro-fuzzy architecture Several numerical example are used to evaluate the performance of out proposed model. Also we used the training data and testing data set to obtain a balance between the approximation and generalization of proposed model.

• 한국전산구조공학회논문집
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• 제26권3호
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• pp.183-189
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• 2013

본 논문에서는 불확실성을 확률변수로 가정하고 구조물의 파손기준을 한계상태식(Limit State Equation)으로 정의하였다. 한계상태식을 Fleishman의 3차 다항식으로 근사하고 이론적인 확률 모멘트(Moments)를 계산하였다. Fleishman은 표준정규 분포 확률변수에 대해서만 3차 다항식을 제시하였으나, 본 논문에서는 이를 확장하여 베타, 감마, 균일 분포 등 다양한 확률 변수에 적용하였다. 확률 모멘트를 계산하기 위해서 누률(Cumulants)과 정규화된 한계상태식을 활용하였으며, 피어슨 시스템(Pearson System)을 통해 한계상태식의 확률분포를 근사하였다.

• 대한수학회보
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• 제51권1호
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• pp.77-82
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• 2014

We prove that if ${\mid}a_1{\mid}$ is large and ${\mid}a_0{\mid}$ is small enough, then every approximate zero of power series equation ${\sum}^{\infty}_{n=0}a_nx^n$=0 can be approximated by a true zero within a good error bound. Further, we obtain Hyers-Ulam stability of zeros of the polynomial equation of degree n, $a_nz^n$ + $a_{n-1}z^{n-1}$ + ${\cdots}$ + $a_1z$ + $a_0$ = 0 for a given integer n > 1.

• 대한수학회지
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• 제34권4호
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• pp.973-1008
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• 1997

We reconsider the problem of calssifying all classical orthogonal polynomial sequences which are solutions to a second-order differential equation of the form $$ \ell_2(x)y"(x) + \ell_1(x)y'(x) = \lambda_n y(x). $$ We first obtain new (algebraic) necessary and sufficient conditions on the coefficients $\ell_1(x)$ and $\ell_2(x)$ for the above differential equation to have orthogonal polynomial solutions. Using this result, we then obtain a complete classification of all classical orthogonal polynomials : up to a real linear change of variable, there are the six distinct orthogonal polynomial sets of Jacobi, Bessel, Laguerre, Hermite, twisted Hermite, and twisted Jacobi.cobi.

• 한국식품영양과학회지
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• 제30권3호
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• pp.466-470
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• 2001

Response surface methodology was used for monitoring extraction conditions, based on quality properties of old pumpkin extracts. Hunter's color L value of extracts was maximized at 101℃, 2.6 hr and decreased gradually after maximum point. The polynomial equation for Hunter's color L value showed 10% of significance level and 0.8799 of R². Hunter's color a value was minimized at 117℃, 3.9 hr and R² of polynomial equation was 0.9852 within 1% significance level. Hunter's color b value and ΔE value increased as the extracting temperature and time increased. Extraction yield of old pumpkin was maximized at 110℃, 4 hr and increased in proportional to the extracting temperature and time, but decreased after 113℃ and 2 hr. Viscosity of pumpkin extracts were maximized at 120℃, nearly 3 hr. R² of polynomial equations for yield, viscosity and sugar content were 0.9532, 0.9812 and 0.8869, respectively. Optimum ranges of extraction conditions for quality properties of old pumpkin were 102∼109℃, 2.5∼3.5 hr, respectively. Predicted values at the optimum extraction condition agreed with experimental values.

• 대한수학회지
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• 제40권6호
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• pp.1075-1083
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• 2003

The purpose of this paper is to investigate the piecewise wise polynomial approximation for the curved boundary. We analyze the error of an approximated solution due to this approximation and then compare the approximation errors for the cases of polygonal and piecewise polynomial approximations for the curved boundary. Based on the results of analysis, p-version numerical methods for solving Dirichlet's problems are applied to any smooth curved domain.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.41-60
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• 2000

In this paper we consider a series of algorithms for calculating radicals of matrix polynomial equations. A particular aspect of this problem arise in author's work. concerning parameter identification of linear dynamic stochastic system. Special attention is given of searching the solution of an equation in a neighbourhood of some initial approximation. The offered approaches and algorithms allow us to receive fast and quite exact solution. We give some recommendations for application of given algorithms.

• 대한수학회논문집
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• 제22권2호
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• pp.183-194
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• 2007

For an irreducible binomial polynomial $f(x)=x^n-b{\in}K[x]$ with a field K, we ask when does the mth iteration $f_m$ is irreducible but $m+1th\;f_{m+1}$ is reducible over K. Let S(n, m) be the set of b's such that $f_m$ is irreducible but $f_{m+1}$ is reducible over K. We investigate the set S(n, m) by taking K as the rational number field.

• 드라이브 ㆍ 컨트롤
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• 제12권4호
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• pp.8-14
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• 2015

A quick-acting hydraulic fuse, which is mainly composed of a poppet, a seat, and a spring, must be designed to minimize the leaked oil volume during fuse operation on a line rupture. The optimal design parameters of a quick-acting hydraulic fuse were searched using the design of experiments method and the complex method. First, the $L_{50}(5^4)$ orthogonal array is used to find the robust minimum point among the 625 points of design variables. The search range can then be narrowed around the robust minimum point. Second, the $L_{25}(5^4)$ orthogonal array is used to obtain the variations of the design variables in the narrowed search range. The variations of design variables are used to set the structure of a polynomial equation representing the leakage oil volume of the quick-acting hydraulic fuse. The least squares method is then applied to obtain the coefficients of polynomial equation. Finally, the complex method is used to find the optimal design parameters where the objective function is described by the polynomial equation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권1호
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• pp.1-15
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• 2016

The continuous analysis, such as smoothness and uniform convergence, for polynomials and polynomial-like functions using differential operators have been studied considerably, parallel to the study of discrete analysis for these functions, using difference operators. In this work, for the difference operator ${\nabla}_h$ with size h > 0, we verify that for an integer $m{\geq}0$ and a strictly decreasing sequence $h_n$ converging to zero, a continuous function f(x) satisfying $${\nabla}_{h_n}^{m+1}f(kh_n)=0,\text{ for every }n{\geq}1\text{ and }k{\in}{\mathbb{Z}}$$, turns to be a polynomial of degree ${\leq}m$. The proof used the polynomial convergence, and additionally, we investigated several conditions on convergence to polynomials.