• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.329-336
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• 2004

In this paper, we study relationships between zero characteristic properties and minimality of orbit closures or limit sets of points. Also, we characterize the set of points of zero characteristic properties. We show that the set of points of positive zero characteristic property in a compact spaces X is the intersection of negatively invariant open subsets of X.

• Korean Journal of Mathematics
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• v.16 no.1
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• pp.51-55
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• 2008

Let f be an analytic function with a simple zero in the reals or the complex numbers. An extraneous fixed-point of an iteration function is a fixed-point different from a zero of f. We prove that all extraneous fixed-points of Laguerre-like iteration functions and general Laguerre-like functions are repulsive.

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.127-134
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• 1998

It is proved [6] that there exists a basis of $L^\Gamma$ (the space of meromorphic vector fields on a Riemann surface, holomorphic away from two fixed points) represented by the vector fields which have the expected zero or pole order at the two points. In this paper, we carry out the same task for the quadratic differentials. More precisely, we compute a basis of $Q^\Gamma$ (the sapce of meromorphic quadratic differentials on a Riemann surface, holomorphic away from two fixed points). This basis consists of the quadratic differentials which have the expected zero or pole order at the two points. Furthermore, we show that $Q^\Gamma$ has a Lie algebra structure which is induced from the Krichever-Novikov algebra $L^\Gamma$.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.721-727
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• 2021

The convex hull of a generic triple of boundary points has non-zero finite volume in complex hyperbolic 2-space.

• Proceedings of the KOSOMBE Conference
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• v.1994 no.12
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• pp.39-42
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• 1994

An automatic multi-threshold algorithm for segmentation of 2D ultrasound images based on average filtering and the characteristics of speckle noise in 2D ultrasound image is proposed. To do this, we investigate the histogram of difference between $7{\times}7$ averaging histogram and $3{\times}3$ averaging histogram. And, we find zero crossing points in the positive portion of the differenced histogram and select middle points of the zero crossing points. We assign these selected points to characteristic points. The thresholds are the center of two characteristic points. Then we segment 2D ultrasound image by using these thresholds and extract edges from applying edge operator to optimal segmented image. Experimental results show that the segmented regions are devided accurately around the homogeneous region.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.36 no.5
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• pp.352-359
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• 1987

The cycloconverter operating on a circulating current-free mode has many zero crossing points. If an exact zero crossing points are not detected, the three phase-unbalanced currents will flow in a motor. In this paper, the current feedback using a current reference wave is proposed to improve the problems of zero crossing detection, three phase-unbalanced voltages, currents, and torgue ripples. To prevent the saturation of the air gap flux and keep the torque constant, the constant voltage / hertz control with IR compensation is adopted. The PI-controller is designed using the linearized model of the cycloconverterinduction motor system. Alsi, Z-80A single board computer has been used to implement the proposed scheme which results in the performance improvement of cycloconterter-fed induction motor speed control system.

• Structural Engineering and Mechanics
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• v.40 no.3
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• pp.335-346
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• 2011

This paper deals with the bifurcations of non-semi-simple eigenvalues at critical point of Hopf bifurcation to understand the dynamic behavior of the system. By using the Puiseux expansion, the expression of the bifurcation of non-semi-simple eigenvalues and the corresponding topological structure in the parameter space are obtained. The zero-order approximate solutions in the vicinity of the critical points at which the multiple Hopf bifurcation may occur are developed. A numerical example, the flutter problem of an airfoil in simplified model, is given to illustrate the application of the proposed method.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.825-831
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• 2021

The derivative of a polynomial p(z) of degree n, with respect to point α is defined by D_αp(z) = np(z) + (α - z)p'(z). Let p(z) be a polynomial having all its zeros in the unit disk |z| ≤ 1. The Sendov conjecture asserts that if all the zeros of a polynomial p(z) lie in the closed unit disk, then there must be a zero of p'(z) within unit distance of each zero. In this paper, we obtain certain results concerning the location of the zeros of D_αp(z) with respect to a specific zero of p(z) and a stronger result than Sendov conjecture is obtained. Further, a result is obtained for zeros of higher derivatives of polynomials having multiple roots.

• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.13-18
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• 1999

In this paper, we compute a basis of the space of meromorphic differentials on a Riemann surface, holomorphic away from two fixed points. This basis consists of the differentials which have the expected zero or pole order at the two fixed points.

• Journal of The Korean Astronomical Society
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• v.42 no.6
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• pp.161-174
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• 2009

Observation of standard stars is of crucial importance in stellar photometry. We have studied the standard transformation relations of the UBV RI CCD photometric system at the Maidanak Astronomical Observatory in Uzbekistan. All observations were made with the AZT-22 1.5m telescope, SITe 2k CCD or Fairchild 486 CCD, and standard Bessell UBV RI filters from 2003 August to 2007 September. We observed many standard stars around the celestial equator observed by SAAO astronomers. The atmospheric extinction coefficients, photometric zero points, and time variation of photometric zero points of each night were determined. Secondary extinction coefficients and photometric zero points were very stable, while primary extinction coefficients showed a distinct seasonal variation. We also determined the transformation coefficients for each filter. For B, V, R, and I filters, the transformation to the SAAO standard system could be achieved with a straight line or a combination of two straight lines. However, in the case of the U filter and Fairchild 486 CCD combination, a significant non-linear correction term - related to the size of Balmer jump or the strength of the Balmer lines - of up to 0:08 mags was required. We found that our data matched well the SAAO photometry in V, B - V, V - I, and R - I. But in U - B, the difference in zero point was about 3.6 mmag and the scatter was about 0.02 mag. We attribute the relatively large scatter in U -B to the larger error in U of the SAAO photometry. We confirm the mostly small differences between the SAAO standard UBV RI system and the Landolt standard system. We also attempted to interpret the seasonal variation of the atmospheric extinction coefficients in the context of scattering sources in the earth's atmosphere.