• Journal of Institute of Control, Robotics and Systems
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• v.15 no.7
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• pp.671-674
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• 2009

Determining the Schur stability of a polynomial is one of fundamental steps in many engineering problems including digital control system design or digital filter design. Due to its importance a variety of techniques have been reported in the literature for checking the Schur stability of a given polynomial. However most of them focus on real polynomials, and few results are available for complex polynomials. This paper concerns the Schur stability of complex polynomials. A simplified Jury's table for real polynomials is extended to complex polynomials.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.231-236
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• 2018

A polynomial, $p(z)=a_0z^n+a_1z^{n-1}+{\cdots}+a_{n-1}z+a_n$, with real coefficients is called a stable or a Hurwitz polynomial if all its zeros have negative real parts. We show that if a polynomial is a Hurwitz polynomial then so is the polynomial $q(z)=a_nz^n+a_{n-1}z^{n-1}+{\cdots}+a_1z+a_0$ (with coefficients in reversed order). As consequences, we give simple ratio checking inequalities that would determine unstability of a polynomial of degree 5 or more and extend conditions to get some previously known results.

• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.767-779
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• 2020

This paper primarily discusses and proves the Hyers-Ulam stability of three types of polynomial equations: xn+a1x+a0 = 0, anxn+⋯+a1x+a0 = 0, and the infinite series equation: ${\sum\limits_{i=0}^{\infty}}\;a_ix^i=0$, in dislocated quasi-metric spaces under certain conditions by constructing contraction mappings and using fixed-point methods. We present an example to illustrate that the Hyers-Ulam stability of polynomial equations in dislocated quasi-metric spaces do not work when the constant term is not equal to zero.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.201-209
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• 2009

In this paper, we prove the stability of the functional equation $$\sum_{i=0}^3_3C_i(-1)^{3-i}f(ix+y)=0$$ in the sense of Th.M.Rassias on the punctured domain. Also, we investigate the superstability of the functional equation.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.887-900
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• 2013

In this paper, we investigate the stability for the functional equation f(3x+y)-3f(2x+y)+3f(x+y)-f(y)=0 in the sense of M. S. Moslehian and Th. M. Rassias.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.269-283
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• 2013

In this paper, we investigate a stability of the functional equation $$\sum^3_{i=0}_3C_i(-1)^{3-i}f(ix+y)=0$$ by using the fixed point theory in the sense of L. C$\breve{a}$dariu and V. Radu.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.8
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• pp.664-674
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• 2001

In this paper, as a new category of fuzzy-neural networks architecture, we propose Fuzzy Polynomial Neural Networks (FPNN) and discuss a comprehensive design methodology related to its architecture. FPNN dwells on the ideas of fuzzy rule-based computing and neural networks. The FPNN architecture consists of layers with activation nodes based on fuzzy inference rules. Here each activation node is presented as Fuzzy Polynomial Neuron(FPN). The conclusion part of the rules, especially the regression polynomial, uses several types of high-order polynomials such as linear, quadratic and modified quadratic. As the premise part of the rules, both triangular and Gaussian-like membership functions are studied. It is worth stressing that the number of the layers and the nods in each layer of the FPNN are not predetermined, unlike in the case of the popular multilayer perceptron structure, but these are generated in a dynamic manner. With the aid of two representative time series process data, a detailed design procedure is discussed, and the stability is introduced as a measure of stability of the model for the comparative analysis of various architectures.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.50 no.1
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• pp.1-7
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• 2001

For a parametric uncertain system, there are many results on stability analysis, but only a few synthesis methods. In this paper, we proposed a new target polynomial decision method for the parametric uncertain system to stabilize the closed loop system with maximal parametric $l_2$ stability margin. To this, we used both Lipatov Theorem and coefficient diagram method(CDM). To show the effectiveness of the proposed method, we designed a robust controller for the inverted pendulum system with parametric uncertainties using fixed order pole assignment(FOPA) method and its performance was compared with that of the ${\mu}$ synthesis methods.

• Proceedings of the Korean Society of Surveying, Geodesy, Photogrammetry, and Cartography Conference
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• 2004.04a
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• pp.279-284
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• 2004

This paper presents on adjustment methods of the vendor-provided RPC(Rational Polynomial Coefficient) of GEO-level stereo images for the IKONOS satellite. RPC are adjusted with control points by the first-order polynomial and the block adjustment method in this study. As results, the maximum error of 3D ground coordinates by the adjusted RPC model did not exceed 4m. The block adjustment method is more stability than the first-order polynomial method.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.937-956
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• 2018

This article gives the foundations of the colored Jones polynomial for singular knots. We extend Masbum and Vogel's algorithm [26] to compute the colored Jones polynomial for any singular knot. We also introduce the tail of the colored Jones polynomial of singular knots and use its stability properties to prove a false theta function identity that goes back to Ramanujan.