• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.1
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• pp.135-142
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• 2012

In this paper, we proposed a new architecture called radial basis function-based polynomial neural networks classifier that consists of heterogeneous neural networks such as radial basis function neural networks and polynomial neural networks. The underlying architecture of the proposed model equals to polynomial neural networks(PNNs) while polynomial neurons in PNNs are composed of Fuzzy-c means-based radial basis function neural networks(FCM-based RBFNNs) instead of the conventional polynomial function. We consider PNNs to find the optimal local models and use RBFNNs to cover the high dimensionality problems. Also, in the hidden layer of RBFNNs, FCM algorithm is used to produce some clusters based on the similarity of given dataset. The proposed model depends on some parameters such as the number of input variables in PNNs, the number of clusters and fuzzification coefficient in FCM and polynomial type in RBFNNs. A multiobjective particle swarm optimization using crowding distance (MoPSO-CD) is exploited in order to carry out both structural and parametric optimization of the proposed networks. MoPSO is introduced for not only the performance of model but also complexity and interpretability. The usefulness of the proposed model as a classifier is evaluated with the aid of some benchmark datasets such as iris and liver.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.4
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• pp.295-303
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• 2004

Previously it has been shown that the all pole systems resulting good time responses can be characterized by so called K-polynomial. The polynomial is defined in terms of the principal characteristic ratio $\alpha_1$ and the generalized time constant $\tau$ . In this paper, Part II presents several sensitivity analyses of such systems with respect to $\alpha_1$ and $\tau$ changes. We first deal with the root sensitivity to the perturbation of $\alpha_1$ . By way of determining the unnormalized function sensitivity, both time response sensitivity and frequency response sensitivity are derived. Finally, the root sensitivity relative to $\tau$ change is also analyzed. These results provide some useful insight and background theory when we select of and l to compose a reference model of which denominator is a K-polynomial, which is illustrated by examples.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.667-682
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• 2016

In this article we show a recursive method to compute the coefficients of the minimal polynomial of cos($2{\pi}/n$) explicitly for $n{\geq}3$. The recursion is not on n but on the coefficient index. Namely, for a given n, we show how to compute ei of the minimal polynomial ${\sum_{i=0}^{d}}(-1)^ie_ix^{d-i}$ for $i{\geq}2$ with initial data $e_0=1$, $e_1={\mu}(n)/2$, where ${\mu}(n)$ is the $M{\ddot{o}}bius$ function.

• The Korean Journal of Nuclear Medicine Technology
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• v.20 no.2
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• pp.69-74
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• 2016

Purpose Using a regression formula of the trendline near the coefficient of determination (R2) "1" by substituting the dependent variable of the standard curve to calculate the values of the independent variable. To determine the suitability of a regression equation by comparing the difference between the independent variables of the standard curve and the predicted independent variables. Materials and Methods Perkin Elmer Gamma-Counter machine was used for Standard curve of regression methods. TSH. TG-Ag (Thyroglobulin Antigen), Insulin that used materials and method test to compare the result from the Excel trendline of the regression formula. Results Each of the value of coefficient of determination ($R^2$) and Trendline $R^2=1$, Polynomial Trendline for TSH, $R^2=1$, Polynomial Trendline for TG-Ag, $R^2=0.9994$, Polynomial Trendline for Insulin. Conclusion We confirmed that IRMA immune method is found to the nearest trends elected a standard curve using polynomial trendline. The independent variables to predict the trend by using a polynomial trendline formula containing the error was a limitation.

• Communications of the Korean Mathematical Society
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• v.35 no.4
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• pp.1299-1307
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• 2020

We show that the Liechti-Strenner's example for the closed nonorientable surface in [13] minimizes the dilatation within the class of pseudo-Anosov homeomorphisms with an orientable invariant foliation and all but the first coefficient of the characteristic polynomial of the action induced on the first cohomology nonpositive. We also show that the Liechti-Strenner's example of orientation-reversing homeomorphism for the closed orientable surface in [13] minimizes the dilatation within the class of pseudo-Anosov homeomorphisms with an orientable invariant foliation and all but the first coefficient of the characteristic polynomial p(x) of the action induced on the first cohomology nonpositive or all but the first coefficient of p(x)(x ± 1)², p(x)(x² ± 1), or p(x)(x² ± x + 1) nonpositive.

• Korean Journal of Mathematics
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• v.32 no.2
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• pp.285-295
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• 2024

In this work, we consider the function $${\Psi}(z)=\frac{z}{\ln(1+z)}=1+\sum\limits_{n=1}^{\infty}\,G_nz^n$$ whose coefficients G_n are the Gregory coefficients related to Stirling numbers of the first kind and introduce a new subclass ${\mathcal{G}}^{{\lambda},{\mu}}_{\Sigma}(\Psi)$ of analytic bi-univalent functions subordinate to the function Ψ. For functions belong to this class, we investigate the estimates for the general Taylor-Maclaurin coefficients by using the Faber polynomial expansions. In certain cases, our estimates improve some of those existing coefficient bounds.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.7
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• pp.970-976
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• 2007

In this study, Polynomial Network Pattern Classifier(PNC) based on Fuzzy Inference Mechanism is designed and its parameters such as learning rate, momentum coefficient and fuzzification coefficient are optimized by means of Particle Swarm Optimization. The proposed PNC employes a partition function created by Fuzzy C-means(FCM) clustering as an activation function in hidden layer and polynomials weights between hidden layer and output layer. Using polynomials weights can help to improve the characteristic of the linear classification of basic neural networks classifier. In the viewpoint of linguistic analysis, the proposed classifier is expressed as a collection of "If-then" fuzzy rules. Namely, architecture of networks is constructed by three functional modules that are condition part, conclusion part and inference part. The condition part relates to the partition function of input space using FCM clustering. In the conclusion part, a polynomial function caries out the presentation of a partitioned local space. Lastly, the output of networks is gotten by fuzzy inference in the inference part. The proposed PNC generates a nonlinear discernment function in the output space and has the better performance of pattern classification as a classifier, because of the characteristic of polynomial based fuzzy inference of PNC.

• Journal of Convergence for Information Technology
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• v.9 no.6
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• pp.1-6
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• 2019

In this study, the development of a weight estimation model of electronic scale with nonlinear characteristics is presented using polynomial regression analysis. The output voltage of the load cell was measured directly using the reference mass. And a polynomial regression model was obtained using the matrix and curve fitting function of MS Office Excel. The weight was measured in 100g units using a load cell electronic scale measuring up to 5kg and the polynomial regression model was obtained. The error was calculated for simple($1^{st}$), $2^{nd}$ and $3^{rd}$ order polynomial regression. To analyze the suitability of the regression function for each model, the coefficient of determination was presented to indicate the correlation between the estimated mass and the measured data. Using the third order polynomial model proposed here, a very accurate model was obtained with a standard deviation of 10g and the determinant coefficient of 1.0. Based on the theory of multi regression model presented here, it can be used in various statistical researches such as weather forecast, new drug development and economic indicators analysis using logistic regression analysis, which has been widely used in artificial intelligence fields.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1911-1924
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• 2015

A cyclotomic polynomial ${\Phi}_n(x)$ is said to be ternary if n = pqr for three distinct odd primes p < q < r. Let A(n) be the largest absolute value of the coefficients of ${\Phi}_n(x)$. If A(n) = 1 we say that ${\Phi}_n(x)$ is flat. In this paper, we classify all flat ternary cyclotomic polynomials ${\Phi}_{pqr}(x)$ in the case $q{\equiv}{\pm}1$ (mod p) and $4r{\equiv}{\pm}1$ (mod pq).

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.169-180
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• 2015

We study the braid indices of the Kanenobu knots. It is known that the Kanenobu knots have the same HOMFLYPT polynomial and the same Khovanov-Rozansky homology. The MFW inequality is known for giving a lower bound of the braid index of a link by applying the HOMFLYPT polynomial. Therefore, it is not easy to determine the braid indices of the Kanenobu knots. In our previous paper, we gave upper bounds and sharper lower bounds of the braid indices of the Kanenobu knots by applying the 2-cable version of the zeroth coefficient HOMFLYPT polynomial. In this paper, we give sharper upper bounds of the braid indices of the Kanenobu knots.