• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.397-410
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• 2002

In this paper, some inequalities for vector-valued maximal functions over locally compact Vienkin groups are obtained.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.677-690
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• 2006

We show that a group of three closure properties including the selectively Pytkeev property coincide on $C_k$(X) for a locally compact X. We also introduce a new game characterization of these properties for such spaces.

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.899-912
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• 2011

We introduce ${\varphi}$-frames in $L^2$(G), as a generalization of a-frames defined in [8], where G is a locally compact Abelian group and ${\varphi}$ is a topological automorphism on G. We give a characterization of ${\varphi}$-frames with regard to usual frames in $L^2$(G) and show that ${\varphi}$-frames share several useful properties with frames. We define the associated ${\varphi}$-analysis and ${\varphi}$-preframe operators, with which we obtain criteria for a sequence to be a ${\varphi}$-frame or a ${\varphi}$-Bessel sequence. We also define ${\varphi}$-Riesz bases in $L^2$(G) and establish equivalent conditions for a sequence in $L^2$(G) to be a ${\varphi}$-Riesz basis.

• Journal of the Optical Society of Korea
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• v.13 no.2
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• pp.206-212
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• 2009

This study presents the compact zoom lens with a zoom ratio of 5x for a mobile camera by using a prism. The lens modules and aberrations are applied to the initial design for a four-group inner-focus zoom system. An initial design with a focal length range of 4.4 to 22.0 mm is derived by assigning the first-order quantities and third-order aberrations to each module along with the constraints required for optimum solutions. We separately designed a real lens for each group and then combined them to establish an actual zoom system. The combination of the separately designed groups results in a system that satisfies the basic properties of the zoom system consisting of the original lens modules. In order to have a slim system, we directly inserted the right-angle prism in front of the first group. This configuration resulted in a more compact zoom system with a depth of 8 mm. The finally designed zoom lens has an f-number of 3.5 to 4.5 and is expected to fulfill the requirements for a slim mobile zoom camera having high zoom ratio of 5x.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.813-821
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• 2010

Let G and H be compact connected Lie groups with biinvariant Riemannian metrics g and h respectively, ${\phi}$ a group isomorphism of G onto H, and $E:={\phi}^{-1}TH$ the induced bundle by $\phi$ over the base manifold G of the tangent bundle TH of H. Let ${\nabla}$ and $^H{\nabla}$ be the Levi-Civita connections for the metrics g and h respectively, $\tilde{\nabla}$ the induced connection by the map ${\phi}$ and $^H{\nabla}$. Then, a necessary and sufficient condition for $\tilde{\nabla}$ in the bundle (${\phi}^{-1}TH$, G, ${\pi}$) to be a Yang- Mills connection is the fact that the Levi-Civita connection ${\nabla}$ in the tangent bundle over (G, g) is a Yang- Mills connection. As an application, we get the following: Let ${\psi}$ be an automorphism of a compact connected semisimple Lie group G with the canonical metric g (the metric which is induced by the Killing form of the Lie algebra of G), ${\nabla}$ the Levi-Civita connection for g. Then, the induced connection $\tilde{\nabla}$, by ${\psi}$ and ${\nabla}$, is a Yang-Mills connection in the bundle (${\phi}^{-1}TH$, G, ${\pi}$) over the base manifold (G, g).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.1
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• pp.25-33
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• 2001

Let G be a finite group with a probability measure. We investigate the random walks on G in terms of ergodicity of the associated skew product transformation.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.27 no.5
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• pp.471-481
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• 2016

We introduce the design technique and test results of a millimeter-wave compact antenna test range. Physical optics is employed for the analysis of the plane wave collimated by an electrical large parabolic reflector of the compact range in the test zone. The performance of the manufactured compact range is verified with the field probing test on the quiet zone and the measurement of high gain antenna. A millimeter-wave compact range designed in the frequency range of 75~110 GHz with a diameter of the test zone of 50 cm shows the magnitude variation of less than 0.75 dB.

• Bulletin of the Korean Mathematical Society
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• v.33 no.2
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• pp.303-310
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• 1996

The Gottlieb group of a compact connected ANR X, G(X), consists of all $\alpha \in \prod_{1}(X)$ such that there is an associated map $A : S^1 \times X \to X$ and a homotopy commutative diagram $$ S^1 \times X \longrightarrow^A X $$ $$incl \uparrow \nearrow \alpha \vee id $$ $$ S^1 \vee X $$.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.557-570
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• 2015

Let $\mathbb{G}$ be a von Neumann algebraic locally compact quantum group, in the sense of Kustermans and Vaes. In this paper, as a consequence of a notion of amenability for actions of Lau algebras, we show that $\hat{\mathbb{G}}$, the dual of $\mathbb{G}$, is co-amenable if and only if there is a state $m{\in}L^{\infty}(\hat{\mathbb{G}})^*$ which is invariant under a left module action of $L^1(\mathbb{G})$ on $L^{\infty}(\hat{\mathbb{G}})^*$. This is the quantum group version of a result by Stokke [17]. We also characterize amenable action of Lau algebras by several properties such as fixed point property. This yields in particular, a fixed point characterization of amenable groups and H-amenable representation of groups.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.117-139
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• 2017

This paper presents a systematic study for theoretical aspects of a unified approach to the abstract relative Fourier transforms over canonical homogeneous spaces of semi-direct product groups with Abelian normal factor. Let H be a locally compact group, K be a locally compact Abelian (LCA) group, and ${\theta}:H{\rightarrow}Aut(K)$ be a continuous homomorphism. Let $G_{\theta}=H{\ltimes}_{\theta}K$ be the semi-direct product of H and K with respect to ${\theta}$ and $G_{\theta}/H$ be the canonical homogeneous space (left coset space) of $G_{\theta}$. We introduce the notions of relative dual homogeneous space and also abstract relative Fourier transform over $G_{\theta}/H$. Then we study theoretical properties of this approach.