• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.869-877
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• 2022

In this paper, we consider the knot complement problem for not null-homologous knots in homology lens spaces. Let M be a homology lens space with H₁(M; ℤ) ≅ ℤ_p and K a not null-homologous knot in M. We show that, K is determined by its complement if M is non-hyperbolic, K is hyperbolic, and p is a prime greater than 7, or, if M is actually a lens space L(p, q) and K represents a generator of H₁(L(p, q)).

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.255-277
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• 2020

Divide knots and links, defined by A'Campo in the singularity theory of complex curves, is a method to present knots or links by real plane curves. The present paper is a sequel of the author's previous result that every knot in the major subfamilies of Berge's lens space surgery (i.e., knots yielding a lens space by Dehn surgery) is presented by an L-shaped curve as a divide knot. In the present paper, L-shaped curves are generalized and it is shown that every knot in the minor subfamilies, called sporadic examples of Berge's lens space surgery, is presented by a generalized L-shaped curve as a divide knot. A formula on the surgery coefficients and the presentation is also considered.

• Journal of the Optical Society of Korea
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• v.13 no.2
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• pp.201-205
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• 2009

We investigated the optimum adhesive thickness for athermalizing an elastomeric lens mount in our space optics application. Theoretical results were compared with finite element solutions using two different models; discrete circular pads and discrete circular pads with columns filling the insertion holes reflecting the reality. A noticeable difference between their optimal thicknesses was observed, and physical interpretation revealed the uncertainty of prevailing athermal equations. A pilot sample was made to check our results and thermo-optical stress was assessed using an interferometer after isothermal load. This study presented insight into preliminary design guidance in elastomeric lens mounting.

• Kyungpook Mathematical Journal
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• v.52 no.3
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• pp.245-264
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• 2012

We determine lens surgeries (i.e. Dehn surgery yielding a lens space) along the n-twisted Whitehead link. To do so, we first give necessary conditions to yield a lens space from the Alexander polynomial of the link as: (1) n = 1 (i.e. the Whitehead link), and (2) one of surgery coefficients is 1, 2 or 3. Our interests are not only lens surgery itself but also how to apply the Alexander polynomial for this kind of problems.

• Journal of Space Technology and Applications
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• v.1 no.1
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• pp.104-120
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• 2021

Some optical schemes of lenses for spacecraft developed by the author are considered. The main optical characteristics of telescope lenses of various architectures are compared. We propose compact solutions of mirror, lens-mirror, and lens systems with maximum available angular resolutions and other parameters. Examples of calculating the optical systems of lenses used for various tasks both in the field of astronomy and in the field of remote sensing of the Earth and other planets are given. The example of onboard computer system is discussed. Practical recommendations on the development and use of telescope lenses are given.

• The Bulletin of The Korean Astronomical Society
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• v.41 no.1
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• pp.57.3-58
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• 2016

We analyze an optical system of a telescope based on Fresnel type objective lens as suggested by Hyde (1999). The Fresnel objective lens can be thin, light-weight and foldable, and therefore it is possible to develop a space telescope with an aperture larger than that of traditional telescopes. Moreover a lens, whatever it is either Fresnel type or conventional, allows much larger fabrication tolerances. We design a medium-sized telescope adopting Fresnel lens as an objective lens for use in space and possibly on the ground. The well-known chromatic aberration of the Fresnel primary lens is corrected by a field lens and another Fresnel lens using Schupmann method. An additional lens is used for forming images. We analyze the chromatic and off-axis aberrations of the proposed system analytically and suggest methods for the minimization of off-axis aberrations and for the operation in wider spectral range. We also conduct ray tracing and optimize the whole optical system with commercial software. Finally we present the design parameters of a telescope with an aperture of 0.5 to 1 meters, enabling diffraction limited operation for a moderate field of view about 10 arc-minutes.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.1429-1434
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• 2003

A number of dust particles are intruded into ODD(Optical disk drive) due to the flow caused by disk rotation and are adhered to a lens or disk surface. The space between the disk and the lens is being reduced. Someone indicates the problems of this drive that are relatively small data storing capacity and slow access time. In recent, the problems of this optical disk drive mentioned above are being solved by adding the speed of the disk's revolution, making the actuator high-speed or light, and making the beam spot size smaller than making the space narrow between disk and lens. These particle contamination affects seriously RF Signal, readout signal in an ODD. Especially, the affected parts by a particle contamination in an ODD's readout signal are objective lens and media.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.29 no.8
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• pp.494-498
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• 2016

In this paper, we proposed the 3-dimenstional (3D) analysis for calculating the optical characteristics of an autostereoscopic display with electric field driven liquid crystal (ELC) lens. From 3D analysis considering the slanting of lens, we calculate the cross-talk of each images and the distortion of viewing zone. Using geometric opics and extended Jones matrix method (EJMM), phase retardation of ELC lens according to position is calcuated and then optical path difference in 3D space considering tilt and azimuth angle of incident light is gotten. Then, intensity distribution is presented in the space. Through camparing the intensity distribution using ideal lens with the ELC lens, we identify the noise and image distortion of ELC lens. As a result, this analysis is expected to provide optimum design conditions for realistic and rigorous 3D display with ELC lens.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.155-158
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• 2004

We give a certain uniqueness properties for the fiber of the Hopf fibration on lens spaces.

• Bulletin of the Korean Mathematical Society
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• v.36 no.3
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• pp.621-627
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• 1999

In this paper we compute Gottlieb groups for generalized lens spaces. Then we apply this result to compute Gottlieb groups for total spaces of a principal torus bundle over a lens space.