• 충청수학회지
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• 제20권3호
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• pp.203-210
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• 2007

Let X be a hyperbolic region in the complex plane C such that the hyperbolic metrix ${\lambda}_X(w){\mid}dw{\mid}$ exists. Let $R(X)=sup\{{\delta}_X(w):w{\in}X\}$ where ${\delta}_X(w)$ is the euclidean distance from w to ${\partial}X$. Here ${\partial}X$ is the boundary of X. A hyperbolic region X is called a Bloch region if R(X) < ${\infty}$. In this paper, we obtain lower bounds for the hyperbolic metric on Bloch regions in terms of the distance to the boundary.

• 호남수학학술지
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• 제29권3호
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• pp.481-493
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• 2007

We will construct several types of semi-regular tilings of a hyperbolic unit disk model by defining geometric features of the definition of distance in a hyperbolic plane, area of triangle, and isometry of inversions. We researched the method of regular tilings and semi-regular tilings of hyperbolic unit disk model and wrote an semi-regular tiling construction algorithm using Cabri2 program and Cinderella program. Lastly, We want to make a product related to traditional heritage cultural patterns using Photoshop, so we'll model the advertising photos of cites; Seoul, Gwangju.

• 대한수학회보
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• 제53권2호
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• pp.399-410
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• 2016

In this paper, we study the relations between the Thurston metric and the hyperbolic metric on a closed surface of genus $g{\geq}2$. We show a rigidity result which says if there is an inequality between the marked length spectra of these two metrics, then they are isotopic. We obtain some inequalities on length comparisons between these metrics. Besides, we show certain distance distortions under conformal graftings, with respect to the $Teichm{\ddot{u}}ller$ metric, the length spectrum metric and Thurston's asymmetric metrics.

• East Asian mathematical journal
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• 제16권2호
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• pp.169-174
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• 2000

We give an easy proof that ${\phi}(z)=\frac{z^2_1}{1-z^2_2}$ induces the bounded composition operator $C_{\phi}:\mathcal{B}{\rightarrow}{\bigcap}H^p(B_2)$ defined by $C_{\phi}f=f\;o\;{\phi}$.

• East Asian mathematical journal
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• 제37권3호
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• pp.307-317
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• 2021

In this paper, we deal with a problem to determine the type of automorphisms of the unit disc in ℂ in terms of intrinsic geometry. We will characterize the hyperbolicity and parabolicity of automorphism by the distance function of the Poincaré metric.

• 한국항해학회지
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• 제25권4호
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• pp.371-379
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• 2001

We have reported the new measurement system which was substituted digital filter for the analog filter in order to develop the optimal system that could find the time delay between each sensors with high accuracy. And also we have confirmed through the experiments that the accuracy of measurements were differentiated by the methods what kind of digital filter had been adopted. This paper suggests two algorithms which approximate the sound source's bearing and distance. One is that sound source's relative bearing can be approximately regarded as the gradient of hyperbolic asymptote, the other is that the source's range can be approximated under the condition of a long range source relative to the sensor's interval. And a series of experiments were carried out with the source's distance 22.42meters and the random bearing interval within the limits of $-90^{\circ}$~$+90^{\circ}$. As a result, we have recognized that the approximation methods could measure the bearing and distance with higher accuracy than the method using trigonometric relation could do.

• 한국정밀공학회지
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• 제21권12호
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• pp.140-145
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• 2004

In this study, the design and analysis of a butterfly valve disk was performed to minimize the rubbing between the disk and the seat at opening and closing. The butterfly valve has double eccentric structure and the contact surface between the disk and the seat is a conical surface. At the instant of opening and closing the valve by the rotation of disk, the positions of zero contact point are changed. Also, if the cone surface is cut in the perpendicular direction to the rotation axis of the valve, the contour of cutting section is hyperbolic. Therefore minimum distance between the origin of the eccentric axis and the hyperbolic curve goes to the position of zero contact point. In order to consider the interferences between the disk and the seat, the thermal-structure coupled field analysis was performed by ANSYS.

• East Asian mathematical journal
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• 제17권2호
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• pp.303-308
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• 2001

Let K($z,\gamma$) denote the euclidean curvature of the curve $\gamma$ at the point z. Flinn and Osgood proved that if f is a univalent mapping of the open unit disk D={z:|z|<1} into itself with f(0)=0 and |f'(0)|<1, then $K(0,\gamma){\leq}K(0,f\;o\;\gamma)$ for any $C^2$ curve $\gamma$ on D through the origin with $K(0,\gamma){\geq}4$. In this paper we establish a generalization of the Flinn-Osgood Monotonicity Theorem.

• East Asian mathematical journal
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• 제39권1호
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• pp.11-21
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• 2023

Non-trivial automorphisms of the unit disc in the complex plane can be classified by three classes; elliptic, parabolic and hyperbolic automorphisms. This classification is due to a representation in the projective special linear group of the real field, or in terms of fixed points on the closure of the unit disc. In this paper, we will characterize this classification by the distance function of the Poincaré metric on the interior of the unit disc.

• 한국음향학회지
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• 제42권1호
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• pp.25-31
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• 2023

능동소나를 이용하여 수중물체의 속도를 추정하려면 Continuous Wave(CW) 펄스를 이용하는 것이 일반적이나, 수중물체의 속도가 느리고 근거리의 해양에서는 잔향음의 영향으로 수중물체의 속도 추정이 용이하지 않다. 2017년도에 Wang 연구진은 이를 극복하고자 수중물체의 속도에 의한 도플러 변이에 둔감한 광대역 신호인 Hyperbolic Frequency Modulation(HFM) 펄스 두 개를 상반된 스윕방향으로 이용하였다. 두 펄스 간 송신 시간간격과 탐지시간 차이의 변화를 통하여 수중물체 속도 추정이 가능하다는 것을 시뮬레이션으로 제시하였다. 하지만 동일한 대역을 이용하므로 상호상관성에 의해서 수중물체 탐지 성능이 영향을 받을 수 밖에 없다. 상호상관성에 의한 수중물체 탐지 성능저하를 방지하기 위하여 대역이 분리된 상반된 스윕방향의 두 HFM 펄스 이용을 제안한다. 본 논문에서는 상반된 스윕방향의 두 대역 HFM을 이용하여 수중물체의 시선속도 추정에 관한 이론을 도출하였고, 펄스길이와 대역폭이 1 s와 400 Hz인 HFM 펄스로 시뮬레이션을 수행하였다. 제안한 방법을 이용하여 수중물체의 시선속도를 추정하면 약 6 %의 오차로 표적 속도 추정이 가능하다는 것을 시뮬레이션을 통하여 확인하였다.