• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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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.

• Honam Mathematical Journal
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• v.29 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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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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• v.16 no.2
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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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• v.37 no.3
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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.

• Journal of the Korean Institute of Navigation
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• v.25 no.4
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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.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.12
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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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• v.17 no.2
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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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• v.39 no.1
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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.

• The Journal of the Acoustical Society of Korea
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• v.42 no.1
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• pp.25-31
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• 2023

In order to estimate the radial speed of an underwater object so-called target with active sonar, Continuous Wave (CW) pulse is generally used, but if a target is slow and at near distance, it is not easy to estimate the radial velocity of the target due to acoustic reverberation in the ocean. In 2017, Wang et al. utilized broadband signal of two Hyperbolic Frequency Modulation (HFM) pulses, which is known as a doppler-invariant pulse, with equal frequency band and in opposite sweep directions to overcome this problem and successfully estimate the radial speed of slow-moving nearby target. They demonstrated the estimation of the radial velocity with computer simulation using the parameters of two HFM starting time differences and receiving times. However, for it uses two HFM pulses with equal frequency, cross-correlation between the two pulses negatively affect the detection performance. To mitigate this cross-correlation effect, we suggest using two different band HFM with the opposite sweep directions. In this paper, a method of radial velocity estimation is derived and simulated using two HFM pulses with the pulse length of 1 second and bandwidth of 400 Hz. Applying the suggested method, the radial velocity was estimated with approximately 6 % of relative error in the simulation.