• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1177-1187
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• 2014

In the current paper we study absolutely pure representations of quivers. Then over some nice quivers including linear quivers some sufficient conditions guaranteeing a representation to be absolutely pure is characterized. Furthermore some relations between atness and absolute purity is investigated. Finally it is shown that the absolutely pure covering of representations of linear quivers (including $A^-_{\infty}$, $A^+_{\infty}$ and $A^{\infty}_{\infty}$) by R-modules whenever R is a coherent ring exists.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.389-398
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• 2013

Let R be a ring and $\mathcal{Q}$ be a quiver. In this paper we give another definition of purity in the category of quiver representations. Under such definition we prove that the class of all pure injective representations of $\mathcal{Q}$ by R-modules is preenveloping. In case $\mathcal{Q}$ is a left rooted semi-co-barren quiver and R is left Noetherian, we show that every cotorsion flat representation of $\mathcal{Q}$ is pure injective. If, furthermore, R is $n$-perfect and $\mathcal{F}$ is a flat representation $\mathcal{Q}$, then the pure injective dimension of $\mathcal{F}$ is at most $n$.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.1-13
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• 1999

Let G be the 3-dimensional Heisenberg group. A discrete subgroup of Isom(G), acting freely on G with non-compact quotient, must be isomorphic to either 1, Z, Z2 or the fundamental group of the Klein bottle. We classify all discrete representations of such groups into Isom(G) up to affine conjugacy. This yields an affine calssification of 3-dimensional non-compact infra-nilmanifolds.

• Journal of The Korean Astronomical Society
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• v.36 no.spc1
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• pp.117-124
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• 2003

Pre-launch calibration data have been analyzed for evaluating the point spread function (PSF) of Yohkoh Soft X-ray Telescope (SXT). Especially, it is found crucial that the effect of undersampling should be treated properly. The best fit solution of the SXT PSF, which is modeled by an elliptical Moffat function, has been derived by the comparison with the ground experiment data. In order to examine the off-axis variation of the SXT PSF, we need to define in advance the location of the optical axis on the CCD. According to the previous studies, the off-axis variation of effective area (the vignetting function) may be approximated either by two non-concentric cones or by a cone with some flat distortions. There have been, however, no fully approved representations for the SXT vignetting effect. The effect of the shift of the optical axis from the geometrical center of the telescope is investigated by numerical simulation. It is revealed from our study that the full width at half maximum (FWHM) of the SXT PSF stays nearly constant within an error bound over the central area of the CCD where the solar disk is located.

• Trans-
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• v.10
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• pp.1-13
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• 2021

If virtual reality is well known through the medias, it seems that a few visual concepts are clearly related to VR. We try to think about it and introduce to a philosophy of VR techniques. So, from techniques and media techno-powers promotional campaigns, we aim to areal technology, it means an objective reflection on the VR techniques. To do so, we study the representations of VR in films. And we conclude that a negative image is the most common representation, related, often, to an Orwellian vision of the future world. In the second part, we study some VR films, and especially some made by famous film directors (Iñárritu, Bigelow). 'Head-turn' and 'Walk-around' films are commented to check their limits. Finally, we consider that for the moment, VR remains only a new space to screen films (into VR platforms connected to the Internet).

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.13 no.7
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• pp.667-678
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• 2002

In this paper, a new radiating structure with a multi-layered two-dimensional metallic disk array was proposed for shaping the flat-topped element pattern. It is an infinite periodic planar array structure with metallic disks finitely stacked above the radiating circular waveguide apertures. The theoretical analysis was in detail performed using rigid full-wave analysis, and was based on modal representations for the fields in the partial regions of the array structure and for the currents on the metallic disks. The final system of linear algebraic equations was derived using the orthogonal property of vector wave functions, mode-matching method, boundary conditions and Galerkin's method, and also their unknown modal coefficients needed for calculation of the array characteristics were determined by Gauss elimination method. The application of the algorithm was demonstrated in an array design for shaping the flat-topped element patterns of $\pm$20$^{\circ}$ beam width in Ka-band. The optimal design parameters normalized by a wavelength for general applications are presented, which are obtained through optimization process on the basis of simulation and design experience. A Ka-band experimental breadboard with symmetric nineteen elements was fabricated to compare simulation results with experimental results. The metallic disks array structure stacked above the radiating circular waveguide apertures was realized using ion-beam deposition method on thin polymer films. It was shown that the calculated and measured element patterns of the breadboard were in very close agreement within the beam scanning range. The result analysis for side lobe and grating lobe was done, and also a blindness phenomenon was discussed, which may cause by multi-layered metallic disk structure at the broadside. Input VSWR of the breadboard was less than 1.14, and its gains measured at 29.0 GHz. 29.5 GHz and 30 GHz were 10.2 dB, 10.0 dB and 10.7 dB, respectively. The experimental and simulation results showed that the proposed multi-layered metallic disk array structure could shape the efficient flat-topped element pattern.