• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.119-125
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• 2015

We find a necessary and sufficient condition for which a point star-configuration in $\mathbb{P}^n$ has generic Hilbert function. More precisely, a point star-configuration in $\mathbb{P}^n$ defined by general forms of degrees $d_1,{\ldots},d_s$ with $3{\leq}n{\leq}s$ has generic Hilbert function if and only if $d_1={\cdots}=d_{s-1}=1$ and $d_s=1,2$. Otherwise, the Hilbert function of a point star-configuration in $\mathbb{P}^n$ is NEVER generic.

• Journal of Advanced Navigation Technology
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• v.16 no.2
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• pp.240-246
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• 2012

The Hilbert transform, which has been hitherto discussed in coherent imaging, is for the first time investigated in the context of incoherent imaging. Because the Hilbert transform of the information is superposed coherently with the original light field. We present a two-pupil optical heterodyne scanning system and analyze mathematically the design of its two pupils such that the optical system can perform the Hilbert transform on incoherent objects. In this paper, we review and formulate the definition of an analytic signal of a function and from which we can obtain the Hilbert transform of the function. and we analyze the design of pupils so as to obtain the Hilbert transform and show some 2-D simulations. Computer simulation results of the idea clarify the theoretical results.

• Transactions on Electrical and Electronic Materials
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• v.17 no.5
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• pp.257-260
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• 2016

In this paper, two configurations (T-type and Y-type) of dual band Wilkinson Power Divider based upon Hilbert curves are presented. Formerly, the concept of Hilbert Curves was implemented in only designing microstrip antennas. In power dividers, this is the very first attempt of incorporating them for size reduction. In addition to this, an effect of inculcation of high-dielectric constant layer (Hafnium-oxide, HfO₂, ε_r= 25) between a substrate and top metallization in both configurations was investigated. The proposed configurations are designed on a high resistive silicon substrate (HRS) for L and S bands with resonating frequencies of 1.575 and 3.4 GHz. Both configurations have return loss that is better than 20 dB and an insertion loss of around 6 dB; isolation better than 30 dB was achieved for both models.

• Korean Journal of Mathematics
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• v.21 no.2
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• pp.197-201
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• 2013

Let D be an integral domain with quotient field K, * a star-operation on D, $GV^*(D)$ the set of nonzero finitely generated ideals J of D such that $J_*=D$, and $*_{\omega}$ a star-operation on D defined by $I_{*_{\omega}}=\{x{\in}K{\mid}Jx{\subseteq}I\;for\;some\;J{\in}GV^*(D)\}$ for all nonzero fractional ideals I of D. In this article, we give a simple proof of Hilbert basis theorem for $*_{\omega}$-Noetherian domains.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.699-704
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• 2010

In this paper, we prove that the Hilbert 2-class field tower of an imaginary quadratic function field $F=k({\sqrt{D})$ is infinite if $r_2({\mathcal{C}}(F))=4$ and exactly one monic irreducible divisor of D is of odd degree, except for one type of $R{\acute{e}}dei$ matrix of F. We also compute the density of such imaginary quadratic function fields F.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.14 no.1
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• pp.125-129
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• 2014

In this paper, design and fabrication of the GPS receiving antenna using Hilbert curve fractal structure was proposed. The size of the antenna was miniaturized by transforming dipole structure into monopole structure because its size increases if Hilbert curve fractal dipole structure is used. To use a Hilbert curve structure, the current directions of the radiator were made oppositely each other. The size of the antenna is $10{\times}10{\times}0.8[mm]$, the line width is 0.25[mm]. The resonant frequency is 1.58[GHz] and its range is 1.52[GHz] ~ 1.65[GHz]. Frequency bandwidth is 130[MHz]. Antenna maximum gain is 3.09[dBi].

• The Journal of the Korea Contents Association
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• v.7 no.4
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• pp.30-38
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• 2007

In this paper, UHF band RFID reader antenna using filbert curve fractal structure and adding the partially grounded plane at the bottom of antenna, which has a resonant frequency at 910MHz, is proposed. Input impedance of antenna is matched with the feed line of 50ohm by varying the length and width of line segment making up the antenna, and by moving the position of via hole. The gain and directivity of antenna is enhanced as varying the dimension of the partially grounded plane and adding the line segment. The size of fabricated antenna is $68mm\times68mm$. The impedance band width(VSWR<2) is $882\sim942MHz$. The return loss and the gain of fabricated antenna are -18.2dB, 5.3dBi at 910MHz.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.511-521
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• 2007

Let S($z_1$, $z_2$) be a power series with operator coefficients such that multiplication by 5($z_1$, $z_2$) is a contractive transformation in the Hilbert space $\mathbf{H}_2$($\mathbb{D}^2$, C). In this paper we show that there exists a Hilbert space D($\mathbb{D}$,$\bar{S}$) which is the state space of extended canonical linear system with a transfer fucntion $\bar{S}$(z).

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.91-95
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• 2012

In this paper, we show how to construct the first layer $k^{\alpha}_{1}$ of anti-cyclotomic ${\mathbb{{Z}}}_{3}$-extension of imaginary quadratic fields $k(=\;{\mathbb{{Q}}}(\sqrt{-d}))$ when the Sylow subgroup of class group of k is 3-elementary, and give an example. This example is different from the one we obtained before in the sense that when we write $k^{\alpha}_{1}\;=\;k({\eta}),{\eta}$ is obtained from non-units of ${\mathbb{{Q}}}({\sqrt{3d}})$.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.51 no.6
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• pp.272-277
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• 2002

This paper deals with the vibration deflection shape measurement technique for a sinusoidally excited structure using a continuously scanning laser Doppler vibrometer (CSLV). The CSLV output signal is an amplitude-modulated vibration in which the excitation signal is modulated by the deflection shapes, and thus the deflection shapes of vibration defined along a scan line can be derived by the envelop and the phase information of the CSLV output signal. In this work, a Hilbert transform based approach has been proposed for measurement of deflection shapes. This technique is as simple as the demodulation technique and allows more convenient experimental settings than the Fourier transform approach. The feasibility of the proposed technique is illustrated along with results of experiment.