• East Asian mathematical journal
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• v.36 no.5
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• pp.593-604
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• 2020

Let the circle act on a compact oriented manifold with a discrete fixed point set. At each fixed point, there are positive integers called weights, which describe the local action of S¹ near the fixed point. In this paper, we provide the author's original proof that only uses the Atiyah-Singer index formula for the classification of the weights at the fixed points if the dimension of the manifold is 4 and there are at most 4 fixed points, which made the author possible to give a classification for any finite number of fixed points.

• East Asian mathematical journal
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• v.35 no.3
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• pp.357-363
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• 2019

Let the circle act on a compact almost complex manifold M with a non-empty discrete fixed point set. To each fixed point, there are associated non-zero integers called weights. A positive weight w is called primitive if it cannot be written as the sum of positive weights, other than w itself. In this paper, we show that if every weight is primitive, then the Todd genus Todd(M) of M is positive and there are $Todd(M){\cdot}2^n$ fixed points, where dim M = 2n. This generalizes the result for symplectic semi-free actions by Tolman and Weitsman [8], the result for semi-free actions on almost complex manifolds by the author [6], and the result for certain symplectic actions by Godinho [1].

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.943-960
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• 2018

Our aim is to introduce the notion of a parametric $N_b-metric$ and study some basic properties of parametric $N_b-metric$ spaces. We give some fixed-point results on a complete parametric $N_b-metric$ space. Some illustrative examples are given to show that our results are valid as the generalizations of some known fixed-point results. As an application of this new theory, we prove a fixed-circle theorem on a parametric $N_b-metric$ space.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1295-1298
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• 2023

It is known that the complex projective space ℂℙⁿ admits a spin structure if and only if n is odd. In this paper, we provide another proof that ℂℙ^2m does not admit a spin structure, by using a circle action.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.35 no.3
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• pp.209-214
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• 1999

The turning circle of a ship is the path followed by her center of gravity in making a turn of 360$^{\circ}$degrees or more with helm at constant angle. But generally it means her path traced at full angle of the rudder. For the ordinary ship the bow will be inside and the stern outside this circle.It has been usually understood that the turning circle is not essentinally affected by ship's speed at Froude numbers less than about 0.30. However, it is recently reported that the speed provide considerable effects upon the turning circle in piloting many ships actually at sea. In this paper, the author analyzed what effects the speed could provide on the turning circle theoretically from the viewpoint of ship motions and examined how the alteration of the speed at Froude no. under 0.30 affect the turning circle actually, through experiments of actual ships of a small and large size.The main results were as follows.1. Even though ship's speed at Froude no. under 0.30, the alteration of the speed affects the turning circle considerably.2. When the full ahead speeds at Froude no. under 0.30 of small and large ships were increased about 3 times slow ahead speeds, the mean rates of increase of the advances, tactical diameters and final diameters of thease ships were about 16%, 21% and 19% respectively.3. When the full ahead speeds at Froued no. under 0.30 of small and large ships were increased about 3 times slow ahead speed, the mean rate of increase of the turning circle elements of large ships was greater 10% than that of small ships. 4. When the full ahead speeds at Froued no. under 0.30 of small and large ships were increased about 3times slow ahead speeds, the mean rates of increase of the tactical diameter and final diameter of thease ships were greater than that of the advances of thease ships. 5. When only alteration of speed or sip's head turning is the effective action to avoid navigational fixed hagards, reducing the speed is always more advantageous than increasing the speed in order to shorten fore or transverse distance.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.35 no.3
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• pp.210-210
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• 1999

The turning circle of a ship is the path followed by her center of gravity in making a turn of 360$^{\circ}$degrees or more with helm at constant angle. But generally it means her path traced at full angle of the rudder. For the ordinary ship the bow will be inside and the stern outside this circle.It has been usually understood that the turning circle is not essentinally affected by ship's speed at Froude numbers less than about 0.30. However, it is recently reported that the speed provide considerable effects upon the turning circle in piloting many ships actually at sea. In this paper, the author analyzed what effects the speed could provide on the turning circle theoretically from the viewpoint of ship motions and examined how the alteration of the speed at Froude no. under 0.30 affect the turning circle actually, through experiments of actual ships of a small and large size.The main results were as follows.1. Even though ship's speed at Froude no. under 0.30, the alteration of the speed affects the turning circle considerably.2. When the full ahead speeds at Froude no. under 0.30 of small and large ships were increased about 3 times slow ahead speeds, the mean rates of increase of the advances, tactical diameters and final diameters of thease ships were about 16%, 21% and 19% respectively.3. When the full ahead speeds at Froued no. under 0.30 of small and large ships were increased about 3 times slow ahead speed, the mean rate of increase of the turning circle elements of large ships was greater 10% than that of small ships. 4. When the full ahead speeds at Froued no. under 0.30 of small and large ships were increased about 3times slow ahead speeds, the mean rates of increase of the tactical diameter and final diameter of thease ships were greater than that of the advances of thease ships. 5. When only alteration of speed or sip's head turning is the effective action to avoid navigational fixed hagards, reducing the speed is always more advantageous than increasing the speed in order to shorten fore or transverse distance.

• Journal of the Korean Mathematical Society
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• v.46 no.1
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• pp.151-170
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• 2009

Let m be a positive integer. We show that for any given real number ${\alpha}\;{\in}\;[0,\;1]$ and complex number $\mu$ with $|\mu|{\leq}1$ which satisfy $e^{2{\pi}i{\alpha}}{\mu}^m\;{\neq}\;1$, there exists a Blaschke product B of degree 2m + 1 which has a fixed point of multiplier ${\mu}^m$ at the point at infinity such that the restriction of the Blaschke product B on the unit circle is a critical circle map with rotation number $\alpha$. Moreover if the given real number $\alpha$ is irrational of bounded type, then a modified Blaschke product of B is quasiconformally conjugate to some rational function of degree m + 1 which has a fixed point of multiplier ${\mu}^m$ at the point at infinity and a Siegel disk whose boundary is a quasicircle containing its critical point.

• Journal of the Korean Institute of Landscape Architecture
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• v.28 no.3
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• pp.97-104
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• 2000

Studies on the principle of traditional moulding techniques of architecture or structure are very important in the point of the work could accomplish succession to modern design. As an attempt of these work, this study tried to examine traditional moulding techniques applied in planes of ancient architecture and structure closely. The major findings of this study are summarized as follows; It was verified that planes of ancient Korean architectures and structures analyzed in this study was moulded by its multiple partitions with the six or eight partitions of circumference as the fundamental form. The well unearthed in kyong-bok palace recently was moulded by a concentric circle assumed form of 4 circle which was extended with equal interval and divided into multiple of 8 partition of circumference. Chon-duk-jung in chang-duk palace also was moulded by a concentric circle assumed form of 3 circle extended with equal interval, but circle were divide by 6 partitions. It was also found that 6$^{\circ}$§8 partitions of circumference(or its multiple partition) was applied to not only above structures but also the moulding planes of ancient architecture, and as a results, figures revealed in architectures analyzed is classified into three classes. And, this study analyzed arrangements of two temples. As a results, it is discovered that the Grid used in moulding planes of each building fixed the arrangement of buildings. Therefore, moulding by equal partition of circumference decided the form of each building and the relation of element at the same time.

• The Journal of Information Technology
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• v.5 no.4
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• pp.165-171
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• 2002

We propose Dynamic Circle Location Register (DCLR) scheme where each visiting location register (VLR) has a given fixed circle registration area around itself and has IDs of other VLRs in this circle area. Whenever a terminal moves to another registration area (RA), system computes whether the terminal is located in the current DCLR area and sends the recent location information of terminal to the old or new DCLR according to computing results. Also, according to change DCLR circle dynamically, we can track terminal location by querying DCLR of the current terminal when a call originates. The our scheme solves the HLR bottleneck due to the terminals frequent RA crossings and distributes the registration traffic to each of the local signaling transfer point (LSTP) area in wireless communications (WC)

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.5
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• pp.525-529
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• 2009

Most of FLC received input data from error e and change-of-error e' with no relation with system complexity. Basic scheme follows typical PD and PI or PID Controller and that has been developed through fixed ME In this paper, We studied the relationship between MF and system response and system response through changing Fuzzy variable of consequence MF and propose the simple FLC using this relationship. The response of FLC is changed according to the width of Fuzzy variable of consequence MF. As changing the Fuzzy variable of consequence MF shows various nonlinear characteristic, we studied the relation between response and MF using analytical method. We designed the effective FLC using three-variable MF and nine rules and took simulation for verification. In this study, we propose the method to design system with FLC in stability point which is an impotent characteristic of designing system. The circle criterion which is adapted to analysis the nonlinear system is put to use for proposed method. Since SISO FLC has a time-invariant and odd characteristic we can use the critical point not disk which is generally used to determine the stability in the circle criterion, to determine the stability. Using this, we can get the maximum critical point plot of SISO FLC with changing the consequence fuzzy variables. The predetermined critical point plot of FLC can be used to decide the region of the system to be stable. This method is effectively used to design the SISO FLC.