• ETRI Journal
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• v.29 no.6
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• pp.817-819
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• 2007

A low-stress organic polymer membrane is proposed as a deformable mirror that can be incorporated into a cellular phone camera to achieve auto focusing without motor-type moving parts. It is demonstrated that our fabricated device has an optical power of 20 diopters and can switch focus in 14 ms. The surface roughness of the organic membrane is measured around 15 nm, less than ${\lambda}$/20 of the visible light. With curve fitting, we found that the actuated membrane is almost parabolic in shape, which leads to less aberration than spherical surfaces. It is suitable for reflective-optics systems.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.10 no.2
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• pp.95-102
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• 2001

In general there are many degrees of freedom(DOFs) in industrial robots. So they have many poses of several special end-effectors positions and orientations. For that reason, industrial robots are used in a wide scope of industrial applica-tions such as welding, spray painting, deburring, and so on. In this research, an off-line continuous path planning method based on linear interpolation with parabolic blend is developed. The method safely maintains the constant orientation for base frame and end-effectors path within allowable error and minimizes the number of segments in path. This algorithm may apply to welding and painting in which the orientation is particularly significant. The simulation study of cartesian curve is carried out to show the performance of this algorithm.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.25 no.10
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• pp.1077-1086
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• 2014

We propose a design method of a Rotman lens for curved array antenna applicable to conformal array. In this paper, design equations are derived to obtain an array curve, transmission line lengths of a Rotman lens in conjunction with a curved array antenna, and the phase error of a Rotman lens based on these design equations is minimized through the beam curve optimization procedure and the refocusing procedure. Rotman lenses designed by the proposed design equations and design procedures still maintain 3 focal points, can feed a convex or concave array antenna with circular curve, parabolic curve, V-shaped curve, etc as well as a straight line array antenna, and have minimal phase error.

• Structural Engineering and Mechanics
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• v.39 no.5
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• pp.661-667
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• 2011

In the famous equivalent elasticity modulus method proposed by Ernst for the geometrical nonlinear analysis of stay cables, the cable shape was assumed as a parabolic curve, and only a part of the gravity load normal to the chord was taken into account with the other part of gravity load parallel to the chord being ignored. Using the actual catenary curve and considering the entire gravity load of stay cables, the present study has derived the equivalent stiffness method to analyze the sag effect of stay cables in cable-stayed bridges. The derived equivalent stiffness can be degenerated into Ernst's equivalent elasticity modulus method with some approximations. Therefore, the Ernst's method is a special and approximate formulation of the present method. The derived equivalent stiffness provides a theoretical explanation for the famous Ernst's formula.

• Tunnel and Underground Space
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• v.6 no.3
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• pp.234-238
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• 1996

Three empirical criteria of rock failure are analyzed in order to understand the meaning of coefficients. Transformation of equations is discussed to apply in the numerical analysis. New failure criterion for intact rocks is proposed in this study, which can be used directly in programming. New equation has the form of parabolic curve($\alpha$=0.5~1.0), and is based on Mohr's shear failure using data from triaxial tests. Its validity will be discussed in the next report.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.925-933
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• 2015

It is well-known that the area of parabolic region between a parabola and any chord $P_1P_2$ on the parabola is four thirds of the area of triangle ${\Delta}P_1P_2P$. Here we denote by P the point on the parabola where the tangent is parallel to the chord $P_1P_2$. In the previous works, the first and third authors of the present paper proved that this property is a characteristic one of parabolas. In this paper, with respect to triangles ${\Delta}P_1P_2PQ$ where Q is the intersection point of two tangents to X at $P_1$ and $P_2$ we establish some characterization theorems for parabolas.

• Structural Engineering and Mechanics
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• v.3 no.6
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• pp.541-553
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• 1995

The determination of the stress intensity factors is investigated by using the surface integral defined around the crack tip of the structure. In this work, the integral method is derived naturally from the standard path integral J. But the use of the surface integral is also extended to the case where body forces act. Computer program for obtaining the stress intensity factors $K_I$ and $K_{II}$ is developed, which prepares input variables from the result of the conventional finite element analysis. This paper provides a parabolic smooth curve function. By the use of the function and conventional element meshes in which the aspect ratio (element length at the crack tip/crack length) is about 25 percent, relatively accurate $K_I$ and K_{II}$ values can be obtained for the outer integral radius ranging from 1/3 to 1 of the crack length and for inner one zero.

• The Bulletin of The Korean Astronomical Society
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• v.43 no.1
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• pp.56.1-56.1
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• 2018

Tidal disruption events (TDEs) provide evidence for quiescent supermassive black holes (SMBHs) in the centers of inactive galaxies. TDEs occur when a star on a parabolic orbit approaches close enough to a SMBH to be disrupted by the tidal force of the SMBH. The subsequent super-Eddington accretion of stellar debris falling back to the SMBH produces a characteristic flare lasting several months. The theoretically expected bolometric light curve decays with time as proportional to $t^{-5/3}$. However, the light curves observed in most of the optical-UV TDEs deviate from the $t^{-5/3}$ decay rate especially at early time, while the light curves of some soft-X-ray TDEs are overall in good agreement with the $t^{-5/3}$ law. Therefore, it is required to construct the theoretical model for explaining these light curve variations consistently. In this paper, we revisit the mass fallback rates analytically and semi-analytically by taking account of the structure of the star, which is simply modeled by the polytrope. We find the relation between a polytropic index and the power law index of the mass fallback rate. We also discuss whether and how the decay curves, which we derived, fit the observed ones.

• Current Optics and Photonics
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• v.7 no.6
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• pp.701-707
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• 2023

In laser imaging, accurate extraction of the laser's center is essential. Several methods exist to extract the laser's center in an image, such as the geometric mean, the parabolic curve fitting, and the Gaussian curve fitting, etc. The Gaussian curve fitting is the most suitable because it is based on the physical properties of the laser. The width of the Gaussian laser beam depends on the distance from the laser source to the target object. It is assumed in general that the distance remains constant at a laser spot resulting in a symmetric Gaussian model for the laser image. However, on a curved surface of the object, the distance is not constant; The laser beam is narrower on the side closer to the focal point of the laser light and wider on the side closer to the laser source, which causes the distribution of the laser beam to skew. This study presents a modified Gaussian model in the laser imaging to incorporate the slant angle of a curved object. The proposed method is verified with simulation and experiments.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.48.2-48.2
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• 2019

Tidal disruption events (TDEs) provide evidence for quiescent supermassive black holes (SMBHs) in the centers of inactive galaxies. TDEs occur when a star on a parabolic orbit approaches close enough to a SMBH to be disrupted by the tidal force of the SMBH. The subsequent super-Eddington accretion of stellar debris falling back to the SMBH produces a characteristic flare lasting several months. It is theoretically expected that the bolometric light curve decays with time as proportional to $t^{-5/3}$. However, some of the observed X-ray light curves deviate from the $t^{-5/3}$ decay rate, while some of them are overall in good agreement with the $t^{-5/3}$ law. Therefore, it is required to construct the theoretical model for explaining these light curve variations consistently. In this paper, we revisit the mass fallback rates semi-analytically by taking account of the stellar internal structure, orbital eccentricity and penetration factor. We find that the mass fallback rate is shallower than the standard $t^{-5/3}$ decay rate independently of the polytropic index, and the orbital eccentricity only changes the magnitude of the mass fallback rate. Furthermore, the penetration factor significantly can modify the magnitude and variation of mass fallback rate. We confirm these results by performing the computational hydrodynamic simulations. We also discuss the relevance of our model by comparing these results with the observed light curves.