• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.1 s.173
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• pp.225-231
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• 2000

Dimensional synthesis of planar and spatial mechanisms mostly requires solution-finding, procedure for a system of polynomial equations. In case the system is nonlinear, numerical techniques like Newton-Raphson are often used. But there are no logical ways for finding all possible solutions in such iterative methods. In this paper, algebraic elimination is used to get all solutions for the synthesis of 5-SS spatial mechanism with seven prescribed positions. The proposed algorithm is more suitable for computer implementation and takes less time than existing one. Two numerical examples are given to demonstrate the implemented algorithm.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.113-125
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• 2019

In this paper, we introduce the elimination ideal $I_D(G)$ associated to a simple finite graph G. We obtain the upper bound of Castelnuovo-Mumford regularity of elimination ideal for various classes of graphs.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.541-547
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• 2000

This paper presents the closed-form forward kinematics of the 6-6 Stewart platform of planar base and moving platform. Based on algebraic elimination method and with one extra linear sensor, it first derives an 8th-degree univariate equation and then finds tentative solution sets out of which the actual solution is to be selected. In order to provide more exact solution despite the error between measured sensor value and the theoretical one, a correction method is also used. The overall procedure requires so little computation time that it can be efficiently used for realtime applications. In addition, unlike the iterative schemes e.g. Newton-Raphson, the algorithm does not require initial estimates of solution and is free of the problems that it does not converge to actual solution within limited time. The presented method has been implemented in C language and a numerical example is given to confirm the effectiveness and accuracy of the developed algorithm.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.30B no.9
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• pp.18-26
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• 1993

This paper presents a multiplier free technique for the complex DFT by rotations and additions based on the complex approximation of the ring of algebraic integers. Speeding-up the computation time and reducing the dynamic range growth has been achieved by the elimination of multiplication. Moreover the DFT of no twiddle factor quantization errors is possible. Numerical examples are given to prove the algorithm and the applicable size of the DFT is 16 has been concluded.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.9
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• pp.1384-1390
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• 2001

This paper deals with the forward kinematics of the 6-6 Stewart platform of planar base and moving platform using one extra linear sensor. Based on algebraic elimination method, it first derives an 8th-degree univariate equation and then finds tentative solution sets out of which the actual solution is to be selected. In order to provide more exact solution despite the error between measured sensor value and the theoretic alone, a correction method is also used in this paper. The overall procedure requires so little computation time that it can be efficiently used for real-time applications. In addition, unlike the iterative scheme e.g. Newton-Raphson, the algorithm does not require initial estimates of solution and is free of the problems that it does not converge to actual solution within limited time. The presented method has been implemented in C language and a numerical example is given to confirm the effectiveness and accuracy of the developed algorithm.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.13 no.6
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• pp.529-534
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• 1988

This paper describes a new method to eliminate some selected harmonics in PWM waveforms using the Walsh series which substitute the linear algebraic equations for the nonlinear equations required in the Fourier series harmonic elimination. In addition, this method is simulated to synthesize periodic PWM waveforms and compare the Walsh analysis with the FOurier analysis, Experimental results are shown that a singel-phase PWM waveforms are identified with the proposed Walsh Series.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.1
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• pp.15-21
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• 2019

Let X be a reduced closed subscheme in ${\mathbb{P}}^n$ and $${\pi}_q:X{\rightarrow}Y={\pi}_q(X){\subset}{\mathbb{P}}^{n-1}$$ be an isomorphic projection from the center $q{\in}{\mathbb{P}}^n{\backslash}X$. Suppose that the minimal free presentation of $I_X$ is of the following form $$R(-3)^{{\beta}2,1}{\oplus}R(-4){\rightarrow}R(-2)^{{\beta}1,1}{\rightarrow}I_X{\rightarrow}0$$. In this paper, we prove that $H^1(I_X(k))=H^1(I_Y(k))$ for all $k{\geq}3$. This implies that Y is k-normal if and only if X is k-normal for $k{\geq}3$. Moreover, we also prove that reg(Y) ${\leq}$ max{reg(X), 4} and that $I_Y$ is generated by homogeneous polynomials of degree ${\leq}4$.

• School Mathematics
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• v.17 no.3
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• pp.407-421
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• 2015

Linear system is a basic subject matter of school mathematics courses. Even though elimination is a useful method to solve linear systems, its fundamental principles were not discussed pedagogically. The purpose of this study is to help the development of mathematical content knowledge on linear systems conceptions. To do this, various representations and translations among them were considered, and in particular, the basic principles for elimination method are analyzed geometrically. Rectangular representation is used to solve word problem treated in numbers of things in elementary mathematics and it is useful as a pre-stage to introduce elimination. Slopes and intercepts of lines associated linear equations are used to obtain the Cramer's formula and this solving method was showing the connection between algebraic and geometric procedures. Strategy deleting variables of linear systems by elementary operations is explored and associated with the movements of lines in the family of lines passing through a fixed point. The development of mathematical content knowledge is expected to enhance pedagogical content knowledges.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.53 no.7
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• pp.430-436
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• 2004

This paper presents an advanced control technique for power density maximization of the Brushless DC (BLDC) generator by using the linear tracking method. In a generator of given rating, the weight and size of the system affect the fuel consumption directly. Therefore, power density is one of the most important issues in a stand-alone generator. BLDC generator has high power density in the machine point of view and additional increases of power density by control means can be expected. Conventional rectification methods cannot achieve the maximum power possible because of hon-optimal current waveforms. The optimal current waveform to maximize power density and minimize machine size and weight in a nonsinusoidal power supply system has been derived, incorporated in a control system, and verified by simulation and experimental work. A new simple algebraic method has been proposed to accomplish the proposed control without an FFT which is time consuming and complicated.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.2
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• pp.181-188
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• 2021

Let X be a nondegenerate reduced closed subscheme in ℙⁿ. Assume that π_q : X → Y = π_q(X) ⊂ ℙ^n-1 is a generic projection from the center q ∈ Sec(X) \ X where Sec(X) = ℙⁿ. Let Z be the singular locus of the projection π_q(X) ⊂ ℙ^n-1. Suppose that I_X has the almost minimal presentation, which is of the form R(-3)^β_2,1 ⊕ R(-4) → R(-2)^β_1,1 → I_X → 0. In this paper, we prove the followings: (a) Z is either a linear space or a quadric hypersurface in a linear subspace; (b) $H^1({\mathcal{I}_X(k)})=H^1({\mathcal{I}_Y(k)})$ for all k ∈ ℤ; (c) reg(Y) ≤ max{reg(X), 4}; (d) Y is cut out by at most quartic hypersurfaces.