• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.649-668
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• 2000

In this paper we prove the following : Let M be a real (2n-1)-dimensional compact minimal semi-invariant submanifold in a complex projective space P(sub)n+1C. If the scalar curvature $\geq$2(n-1)(2n+1), then m is a homogeneous type $A_1$ or $A_2$. Next suppose that the third fundamental form n satisfies dn = 2$\theta\omega$ for a certain scalar $\theta$$\neq$c/2 and $\theta$$\neq$c/4 (4n-1)/(2n-1), where $\omega$(X,Y) = g(X,øY) for any vectors X and Y on a semi-invariant submanifold of codimension 3 in a complex space form M(sub)n+1 (c). Then we prove that M has constant principal curvatures corresponding the shape operator in the direction of the distingusihed normal and the structure vector ξ is an eigenvector of A if and only if M is locally congruent to a homogeneous minimal real hypersurface of M(sub)n (c).

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.159-166
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• 1999

For classical elliptic pseudodifferential operators $A({\lambda})$ of order $m$ > 0 with parameter ${\lambda}$ of weight ${\chi}$ > 0, it is known that $logDet_{\theta}A({\lambda})$ admits an asymptotic expansion as ${\theta}{\rightarrow}+{\infty}$. In this paper we show, with some assumptions, that the coefficients of ${\lambda}^-{\frac{n}{\chi}}$ can be expressed by the values of zeta functions at 0 for some elliptic ${\psi}$DO's on $M{\times}S^1{\times}{\cdots}{\times}S^1$ multiplied by $\frac{m}{c_{n-1}}$.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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• pp.271-285
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• 2020

In this paper, we have introduced a new type of covering property ${\beta}^t_{({\omega}_r,s)}$-closedness, stronger than $P^t_{({\omega}_r,s)}$-closedness [3] in terms of (r, s)-β-open sets [9] and β-ω_t-closures in bitopological spaces along with its several characterizations via filter bases and grills [15] and various properties. Further grill generalizations of ${\beta}^t_{({\omega}_r,s)}$-closedness (namely, ${\beta}^t_{({\omega}_r,s)}$-closedness modulo grill) and associated concepts have also been investigated.

• Journal of the Korean Mathematical Society
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• v.43 no.5
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• pp.991-1018
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• 2006

Hypermaps are cellular embeddings of hypergraphs in compact and connected surfaces, and are a generalisation of maps, that is, 2-cellular decompositions of closed surfaces. There is a well known correspondence between hypermaps and co-compact subgroups of the free product $\Delta=C_2*C_2*C_2$. In this correspondence, hypermaps correspond to conjugacy classes of subgroups of $\Delta$, and hypermap coverings to subgroup inclusions. Towards the end of [9] the authors studied regular hypermaps with extra symmetries, namely, G-symmetric regular hypermaps for any subgroup G of the outer automorphism Out$(\Delta)$ of the triangle group $\Delta$. This can be viewed as an extension of the theory of regularity. In this paper we move in the opposite direction and restrict regularity to normal subgroups $\Theta$ of $\Delta$ of finite index. This generalises the notion of regularity to some non-regular objects.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2003.10a
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• pp.938-940
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• 2003

고출력 반도체 레이저(500mW)의 출력광 파장 809nm과 반도체 레이저로 여기되는 Nd:YVO4레이저의 출력광 파장 1064nm를 공진기 내부에서 비선형 광학 소자인 KTP(Potassium titanyl posphate : KTPiOPO$_4$)를 사용하여 합주파 발생 실험을 행하여 459nm의 청색레이저를 얻었다. 제2의 위상 정합 정합조건($\psi$=90$^{\circ}$, $\theta$=90$^{\circ}$)에서 반도체 레이저의 입력광 세기가 400mW일 때 청색레이저의 최대 출력 0.95mW를 얻었으며, 청색레이저의 발진문턱입력 세기는 120mW이었다.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.41 no.3
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• pp.213-218
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• 2017

In this study, a reverse design of the F-theta lens was proposed for a 2D scanner in remote welding applications. The curvature and distance of the lens were set as variables, and the focal length of the lens was set as the marginal ray height. The ZEMAX commercial software was used to perform a simulation with unlimited iterations for the optimization process. The target value was optimized using the internal Merit function with the weight factors of focal length and spot diameter. The number of lenses was four, and the focal length obtained from the results was 135mm that is slightly less than that of the commercial lens, which is set with a focal length of 185 mm. The calculated spot diameters are $1.3{\mu}m$, $6.2{\mu}m$, and $16.1{\mu}m$ for $0^{\circ}$, $12.5^{\circ}$ and $23^{\circ}$ of incident laser beam, respectively. It is expected that an optimized lens design is possible by performing the reverse design of a lens by the ray tracing method.

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.585-598
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• 2010

We deal with Matveev complexity of compact orientable 3-manifolds represented via Heegaard diagrams. This lead us to the definition of modified Heegaard complexity of Heegaard diagrams and of manifolds. We define a class of manifolds which are generalizations of Dunwoody manifolds, including cyclic branched coverings of two-bridge knots and links, torus knots, some pretzel knots, and some theta-graphs. Using modified Heegaard complexity, we obtain upper bounds for their Matveev complexity, which linearly depend on the order of the covering. Moreover, using homology arguments due to Matveev and Pervova we obtain lower bounds.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.7
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• pp.120-127
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• 2003

A novel three degrees of freedom sensing method utilizing binary grid pattern image and vision camera is presented. The binary grid pattern image is designed by Pseudo-Random Binary Arrays and referenced to encode in-plane position of a moving stage of the contact-free planar actuator. First, the yaw motion of the stage is detected using fast image processing and then the other planar positions, x and y, are decoded with a sequence of images. This method can be applied to the system that needs feedback of in-plane position, with advantages of a good accuracy and high resolution comparable with the encoder, a relatively compact structure, no friction, and a low cost. In this paper, all the procedures of the above sensing mechanism are described in detail, including simulation and experiment results.

• Journal of The Korean Astronomical Society
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• v.51 no.2
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• pp.27-36
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• 2018

In a solar coronagraph, the most important component is an occulter to block the direct light from the disk of the sun. Because the intensity of the solar outer corona is $10^{-6}$ to $10^{-10}$ times of that of the solar disk ($I_{\odot}$), it is necessary to minimize scattering at the optical elements and diffraction at the occulter. Using a Fourier optic simulation and a stray light test, we investigated the performance of a compact coronagraph that uses an external truncated-cone occulter without an internal occulter and Lyot stop. In the simulation, the diffracted light was minimized to the order of $7.6{\times}10^{-10}I_{\odot}$ when the cone angle ${\theta}_c$ was about $0.39^{\circ}$. The performance of the cone occulter was then tested by experiment. The level of the diffracted light reached the order of $6{\times}10^{-9}I_{\odot}$ at ${\theta}_c=0.40^{\circ}$. This is sufficient to observe the outer corona without additional optical elements such as a Lyot stop or inner occulter. We also found the manufacturing tolerance of the cone angle to be $0.05^{\circ}$, the lateral alignment tolerance was $45{\mu}m$, and the angular alignment tolerance was $0.043^{\circ}$. Our results suggest that the physical size of coronagraphs can be shortened significantly by using a cone occulter.

• East Asian mathematical journal
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• v.24 no.1
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• pp.35-43
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• 2008

Let E be a uniformly convex Banach space and K be a nonempty closed convex subset of E. Let ${\{T_i\}}^N_{i=1}$ be N nonexpansive self-mappings of K with $F\;=\;{\cap}^N_{i=1}F(T_i)\;{\neq}\;{\theta}$ (here $F(T_i)$ denotes the set of fixed points of $T_i$). Suppose that one of the mappings in ${\{T_i\}}^N_{i=1}$ is semi-compact. Let $\{{\alpha}_n\}\;{\subset}\;[{\delta},\;1-{\delta}]$ for some ${\delta}\;{\in}\;(0,\;1)$ and $\{{\beta}_n\}\;{\subset}\;[\tau,\;1]$ for some ${\tau}\;{\in}\;(0,\;1]$. For arbitrary $x_0\;{\in}\;K$, let the sequence {$x_n$} be defined iteratively by $\{{x_n\;=\;{\alpha}_nx_{n-1}\;+\;(1-{\alpha}_n)T_ny_n,\;\;\;\;\;\;\;\;\; \atop {y_n\;=\;{\beta}nx_{n-1}\;+\;(1-{\beta}_n)T_nx_n},\;{\forall}_n{\geq}1,}$, where $T_n\;=\;T_{n(modN)}$. Then {$x_n$} convergence strongly to a common fixed point of the mappings family ${\{T_i\}}^N_{i=1}$. The result presented in this paper generalized and improve the corresponding results of Chidume and Shahzad [C. E. Chidume, N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal. 62(2005), 1149-1156] even in the case of ${\beta}_n\;{\equiv}\;1$ or N=1 are also new.