• Journal of Institute of Control, Robotics and Systems
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• v.10 no.9
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• pp.833-839
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• 2004

This paper proposes a method that minimizes the consumed energy by searching the optimal locations of the mass centers of links composing of a biped robot using Real-Coded Genetic Algorithm. Generally, in order to utilize optimization algorithms, the system model and design variables must be defined. Firstly, the proposed model is a 6-DOF biped robot composed of seven links, since many of the essential characteristics of the human walking motion can be captured with a seven-link planar biped walking in the saggital plane. Next, Fourth order polynomials are used for basis functions to approximate the walking gait. The coefficients of the fourth order polynomials are defined as design variables. In order to use the method generating the optimal gait trajectory by searching the locations of mass centers of links, three variables are added to the total number of design variables. Real-Coded GA is used for optimization algorithm by reason of many advantages. Simulations and the comparison of three methods to generate gait trajectories including the GCIPM were performed. They show that the proposed method can decrease the consumed energy remarkably and be applied during the design phase of a robot actually.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.417-445
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• 2020

The purpose of this article is to continue the study of q, 𝜔-special functions in the spirit of Wolfgang Hahn from the previous papers by Annaby et al. and Varma et al., with emphasis on q, 𝜔-Apostol Bernoulli and Euler polynomials, Ward-𝜔 numbers and multiple q, 𝜔power sums. Like before, the q, 𝜔-module for the alphabet of q, 𝜔-real numbers plays a crucial role, as well as the q, 𝜔-rational numbers and the Ward-𝜔 numbers. There are many more formulas of this type, and the deep symmetric structure of these formulas is described in detail.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.697-706
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• 2000

If an arithmetic progression F of length 2n and the number k with 2k$\leq$n are give, can we find two monic polynomials with the same degrees whose set of all zeros form F such that both the number of bad pairs and the number of nonreal zeros are 2k? We will consider the case that both the number of bad pairs and the number of nonreal zeros are two. Moreover, we will see the fundamental relation between the number of bad pairs and the number of nonreal zeros, and we will show that the polynomial in x where the coefficient of x(sup)k is the number of sequences having 2k bad pairs has all zeros real and negative.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.157-174
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• 2004

In this work we discuss "plank problems" for complex Banach spaces and in particular for the classical $L^{p}(\mu)$ spaces. In the case $1\;{\leq}\;p\;{\leq}\;2$ we obtain optimal results and for finite dimensional complex Banach spaces, in a special case, we have improved an early result by K. Ball [3]. By using these results, in some cases we are able to find best possible lower bounds for the norms of homogeneous polynomials which are products of linear forms. In particular, we give an estimate in the case of a real Hilbert space which seems to be a difficult problem. We have also obtained some results on the so-called n-th (linear) polarization constant of a Banach space which is an isometric property of the space. Finally, known polynomial inequalities have been derived as simple consequences of various results related to plank problems.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.919-928
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• 2023

Let P(z) be a polynomial of degree n and P(z) ≠ 0 in |z| < 1. Then for every real α and R > 1, Aziz [1] proved that $$\max\limits_{{\mid}z{\mid}=1}{\mid}P(Rz)-P(z){\mid}{\leq}{\frac{R^n-1}{2}}(M^2_{\alpha}+M^2_{{\alpha}+{\pi}})^{\frac{1}{2}}{\mid},$$ where $$M{\alpha}={\max\limits_{1{\leq}k{\leq}n}}{\mid}P(e^{i({\alpha}+2k{\pi})n}){\mid}.$$ In this paper, we establish some improvements and generalizations of the above inequality concerning the polynomials and their ordinary derivatives.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.67 no.2
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• pp.277-284
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• 2018

In this paper, a new numerical method of finding the roots of a nonlinear system is proposed, which extends the conventional fixed point iterative method by relaxing the constraints on it. The proposed method determines the real valued roots and expands the convergence region by relaxing the constraints on the conventional fixed point iterative method, which transforms the diverging root searching iterations into the converging iterations by employing the metric induced by the geometrical characteristics of a polynomial. A metric is set to measure the distance between a point of a real-valued function and its corresponding image point of its inverse function. The proposed scheme provides the convenience in finding not only the real roots of polynomials but also the roots of the nonlinear systems in the various application areas of science and engineering.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.1
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• pp.49-65
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• 2000

A method for inverting the Laplace transform is presented, using a finite series of the classical Legendre polynomials. The method recovers a real-valued function f(t) in a finite interval of the positive real axis when f(t) belongs to a certain class ${\mathcal{W}}_{\beta}$ and requires the knowledge of its Laplace transform F(s) only at a finite number of discrete points on the real axis s > 0. The choice of these points will be carefully considered so as to improve the approximation error as well as to minimize the number of steps needed in the evaluations. The method is tested on few examples, with particular emphasis on the estimation of the error bounds involved.

• Proceedings of the KIEE Conference
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• 1991.11a
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• pp.390-393
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• 1991

This paper describes nonlinear 4th order models for a natural circulation drum-boiler. The models lire derived from energy balance and mass balance principles. They can be characterized by a few physical parameters that are easily obtained from construction data. The models also require steam tables for a limited operating range, which can be approximated by polynomials. The models have been validated against real plant operating data.

• Journal of the Korean Data and Information Science Society
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• v.14 no.1
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• pp.131-141
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• 2003

In this paper, we prove that multi-variate fuzzy polynomials are universal approximators for multi-variate fuzzy functions which are the extension principle of continuous real-valued function under $T_W-based$ fuzzy arithmetic operations for a distance measure that Buckley et al.(1999) used. We also consider a class of fuzzy polynomial regression model. A mixed non-linear programming approach is used to derive the satisfying solution.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.3
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• pp.133-137
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• 2008

We prove an extended version of asymptotic behavior of the orthonormal cardinal refinable functions from Blaschke products introduced by Contronei et al [2]. In fact, we show the orthonormal cardinal refinable function ${\varphi}_{k,q}$ converges in $L^p(\mathbb{R})$ ($2{\leq}p{\leq}{\infty}$) to the Shannon refinable function as ${\kappa}{\rightarrow}{\infty}$ uniforml on a class $\mathcal{Q}_{A,B}$ of real symmetric polynomials determined by positive constants $A{\leq}B$.