• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.05a
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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.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.38-38
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• 2000

To fulfill recent requirements for high quality products in steel rolling process, fast responding and easily tunab control system is required and ILQ(Inverse Linear Quadratic) control system may be one of such alternatives. In this paper characteristics of ILQ control and its application to BUR(Back-Up-Roll) eccentricity in strip rolling mill is discussed and compared to polynomial control approaches. Also the rolling mill model and basic principle to control thickness of srip are introduced with control effect by polynomial methods.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.567-579
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• 2009

Recently, Peng et al. proposed a primal-dual interior-point method with new search direction and self-regular proximity for LP. This new large-update method has the currently best theoretical performance with polynomial complexity of O($n^{\frac{q+1}{2q}}\;{\log}\;{\frac{n}{\varepsilon}}$). In this paper we use this search direction to propose a primal-dual interior-point method for convex quadratic programming (QP). We overcome the difficulty in analyzing the complexity of the primal-dual interior-point methods for convex quadratic programming, and obtain the same polynomial complexity of O($n^{\frac{q+1}{2q}}\;{\log}\;{\frac{n}{\varepsilon}}$) for convex quadratic programming.

• Journal of the Korean School Mathematics Society
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• v.9 no.2
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• pp.121-139
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• 2006

This study identified the problems of teaching quadratic functions using a translation and a vertex form by completing squares of which method make teaching contents not to be interconnected and tend to interfere students' conceptual understanding. This seems to generated from which the current mathematics curriculum is not organized to deliver the related contents of quadratic functions from polynomial expressions students have already known. To resolve it this study investigates the properties of quadratic functions from a polynomial perspective and discusses classroom implications with a couple of concrete applications.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1311-1322
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• 2008

The Fifteen Theorem proved by Conway and Schneeberger is a criterion for positive definite quadratic forms over the rational integer ring to be universal. In this paper, we give a proof of an analogy of the Fifteen Theorem for definite quadratic forms over polynomial rings, which is known as the Four Conjecture proposed by Gerstein.

• Proceedings of the KIEE Conference
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• 1999.07g
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• pp.2856-2858
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• 1999

In this paper, the FPNN(Fuzzy Polynomial Neural Networks) algorithm with multi-layer fuzzy inference structure is proposed for the model identification of a complex nonlinear system. The FPNN structure is generated from the mutual combination of PNN (Polynomial Neural Network) structure and fuzzy inference method. The PNN extended from the GMDH(Group Method of Data Handling) uses several types of polynomials such as linear, quadratic and modifled quadratic besides the biquadratic polynomial used in the GMDH. In the fuzzy inference method, 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 a fuzzy rule and its structure is a kind of fuzzy-neural networks. Gas furnace data used to evaluate the performance of our proposed model.

• Journal of KIISE:Computer Systems and Theory
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• v.36 no.1
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• pp.21-25
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• 2009

In this paper, we study the problem to fit a piecewise-quadratic polynomial curve to points in the plane. The curve consists of quadratic polynomial segments and two points are connected by a segment. But it passes through a subset of points, and for the points not to be passed, the error between the curve and the points is estimated in $L^{\infty}$ metric. We consider two optimization problems for the above problem. One is to reduce the number of segments of the curve, given the allowed error, and the other is to reduce the error between the curve and the points, while the curve has the number of segments less than or equal to the given integer. For the number n of given points, we propose $O(n^2)$ algorithm for the former problem and $O(n^3)$ algorithm for the latter.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.659-675
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• 2023

Let K be an algebraically closed field of characteristic 0 and let f be a non-fibered planar quadratic polynomial map of topological degree 2 defined over K. We assume further that the meromorphic extension of f on the projective plane has the unique indeterminacy point. We define the critical pod of f where f sends a critical point to another critical point. By observing the behavior of f at the critical pod, we can determine a good conjugate of f which shows its statue in GIT sense.

• Proceedings of the KIEE Conference
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• 2004.11c
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• pp.337-339
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• 2004

In this paper, we discuss optimal design of Fuzzy Polynomial Neural Networks by means of Genetic Algorithms(GAs). Proceeding the layer, this model creates the optimal network architecture through the selection and the elimination of nodes by itself. So, there is characteristic of flexibility. We use a triangle and a Gaussian-like membership function in premise part of rules and design the consequent structure by constant and regression polynomial (linear, quadratic and modified quadratic) function between input and output variables. GAs is applied to improve the performance with optimal input variables and number of input variables and order. To evaluate the performance of the GAs-based FPNNs, the models are experimented with the use of Medical Imaging System(MIS) data.

• Proceedings of the KIEE Conference
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• 2000.11d
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• pp.800-802
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• 2000

In this paper, we propose the Self-Organizing Networks(SON) based on competitive Fuzzy Polynomial Neuron(FPN) for the optimal design of nonlinear process system. The SON architectures consist of layers with activation nodes based on fuzzy inference rules. Here each activation node is presented as FPN which includes either the simplified or regression Polynomial fuzzy inference rules. The proposed SON is a network resulting from the fusion of the Polynomial Neural Networks(PNN) and a fuzzy inference system. The conclusion part of the rules, especially the regression polynomial uses several types of high-order polynomials such as liner, quadratic and modified quadratic. As the premise part of the rules, both triangular and Gaussian-like membership functions are studied. Chaotic time series data used to evaluate the performance of our proposed model.