• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.609-618
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• 1994

F. Rhodes [2] introduced the fundamental group $\sigma(X, x_0, G)$ of a transformation group (X,G) as a generalization of the fundamental group $\pi_1(X, x_0)$ of a topological space X and showed a sufficient condition for $\sigma(X, x_0, G)$ to be isomorphic to $\pi_1(X, x_0) \times G$, that is, if (G,G) admits a family of preferred paths at e, $\sigma(X, x_0, G)$ is isomorphic to $\pi_1(X, x_0) \times G$. B.J.Jiang [1] introduced the Jiang subgroup $J(f, x_0)$ of the fundamental group of X which depends on f and showed a condition to be $J(f, x_0)$ = Z(f_\pi(\pi_1(X, x_0)), \pi_1(X, f(x_0)))$.

• Proceedings of the Korea Institute of Convergence Signal Processing
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• 2001.06a
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• pp.105-108
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• 2001

In this paper, we proposed a variable structure controller with fuzzy PI-쇼pe reaching law. we fuzzified as inputs to fuzzy system Rf(representative point's orthogonal distance(rd) to switching surface and RP's distance(r) to the origin of the 2-dimensional space whose coordinates are the error and the error rate. The increments of the coefficients $k_{p}$ and $k_{i}$, of the reaching law are calculated appropriate by the simplified Mamdanl inference. The proposed fuzzy PI-type reaching law makes it reduce the chattering and has no need to tune the PI parameters of reaching law. The effectiveness of the proposed fuzzy PI-type reaching law is shown by the simulation results of the control of a Ball-balance System.

• Journal of Navigation and Port Research
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• v.38 no.4
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• pp.349-356
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• 2014

In the underwater communication, the performance of system is reduced because of the inter-symbol interference occur by the multi-path. In the recent years, to deal with poor channel environment and improve the throughput, the efficient concatenated structure of equalization, channel codes and Space Time Codes has been studied as MIMO system in the underwater communication. Space Time Codes include Space Time Block Codes and Space Time Trellis Codes in underwater communication. Space Time Trellis Codes are optimum for equalization and channel codes among the Space Time Codes to apply in the MIMO environment. Therefore, in this paper, turbo pi codes are used for the outer code to efficiently transmit in the multi-path channel environment. The inner codes consist of Space Time Trellis Codes with transmission diversity and coding gain in the MIMO system. And Zero Forcing method is used to remove inter-symbol interference. Finally, the performance of this model is simulated in the underwater channel.

• Proceedings of the KIEE Conference
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• 1998.07f
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• pp.1944-1946
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• 1998

This paper presents a novel current control system to eliminate the steady state control error for PWM AC-DC converter. A general mathematical model of the converter which is represented as a state-space model is established. The state-space model is used for the simulation of converter with the proposed tracking control system of sinusoidal current. In this system, a novel current control which do not require coordinate transformations using internal principle of PI controller is described. It is proved that the steady state deviation reduce to zero through a transfer function of source current control system. Finally, simulations show good source current control characteristics by means of a simplified control system which do not require coordinate transformations.

• Journal of The Korean Astronomical Society
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• v.52 no.4
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• pp.121-131
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• 2019

I investigate the origin of arc degeneracies in satellite microlens parallax ${\pi}_E$ measurements with only late time data, e.g., t > $t_0+t_E$ as seen from the satellite. I show that these are due to partial overlap of a series of osculating, exactly circular, degeneracies in the ${\pi}_E$ plane, each from a single measurement. In events with somewhat earlier data, these long arcs break up into two arclets, or (with even earlier data) two points, because these earlier measurements give rise to intersecting rather than osculating circles. The two arclets (or points) then constitute one pair of degeneracies in the well-known four-fold degeneracy of space-based microlens parallax. Using this framework of intersecting circles, I show that next-generation microlens satellite experiments could yield good ${\pi}_E$ determinations with only about five measurements per event, i.e., about 30 observations per day to monitor 1500 events per year. This could plausibly be done with a small (hence cheap, in the spirit of Gould & Yee 2012) satellite telescope, e.g., 20 cm.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.653-655
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• 2006

We give a simple proof of the statement that if T is a bounded linear operator on a complex HIlbert space then T is Fredholm if and only if ${\pi}(T)$ is not a TDZ, where ${\pi}(\cdot)$ is the Catkin homomorphism.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.393-402
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• 2013

For 0 < $p$ < ${\infty}$, ${\alpha}$ > -1 and 0 < $r$ < 1, we show that if $f$ is in the space of Dirichlet type $\mathfrak{D}^p_{p-1}$, then ${\int}_{1}^{0}M_{p}^{p}(r,f^{\prime})(1-r)^{p-1}rdr$ < ${\infty}$ and ${\int}_{1}^{0}M_{(2+{\alpha})p}^{(2+{\alpha})p}(r,f^{\prime})(1-r)^{(2+{\alpha})p+{\alpha}}rdr$ < ${\infty}$ where $M_p(r,f)=\[\frac{1}{2{\pi}}{\int}_{0}^{2{\pi}}{\mid}f(re^{it}){\mid}^pdt\]^{1/p}$. For 1 < $p$ < $q$ < ${\infty}$ and ${\alpha}+1$ < $p$, we show that if there exists some positive constant $c$ such that ${\parallel}f{\parallel}_{L^{q(d{\mu})}}{\leq}c{\parallel}f{\parallel}_{\mathfrak{D}^p_{\alpha}}$ for all $f{\in}\mathfrak{D}^p_{\alpha}$, then ${\parallel}f{\parallel}_{L^{q(d{\mu})}}{\leq}c{\parallel}f{\parallel}_{\mathcal{B}_p(q)}$ where $\mathcal{B}_p(q)$ is the weighted Besov space. We also find the condition of measure ${\mu}$ such that ${\sup}_{a{\in}D}{\int}_D(k_a(z)(1-{\mid}a{\mid}^2)^{(p-a-1)})^{q/p}d{\mu}(z)$ < ${\infty}$.

• Korean Journal of Mathematics
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• v.16 no.3
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• pp.355-362
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• 2008

We prove the existence of a unique positive solution for a class of systems of the following nonlinear suspension bridge equation with Dirichlet boundary conditions and periodic conditions $$\{{u_{tt}+u_{xxxx}+\frac{1}{4}u_{ttxx}+av^+={\phi}_{00}+{\epsilon}_1h_1(x,t)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,\\{v_{tt}+v_{xxxx}+\frac{1}{4}u_{ttxx}+bu^+={\phi}_{00}+{\epsilon}_2h_2(x,t)\;\;in\;(-\frac{\pi}{2},\frac{\pi}{2}){\times}R,$$ where $u^+={\max}\{u,0\},\;{\epsilon}_1,\;{\epsilon}_2$ are small number and $h_1(x,t)$, $h_2(x,t)$ are bounded, ${\pi}$-periodic in t and even in x and t and ${\parallel} h_1{\parallel}={\parallel} h_2{\parallel}=1$. We first show that the system has a positive solution, and then prove the uniqueness by the contraction mapping principle on a Banach space

• The Bulletin of The Korean Astronomical Society
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• v.30 no.2
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• pp.50.1-50.1
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• 2005

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.38 no.10
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• pp.992-997
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• 2010

The Propulsion Control Module(PCM) of Hall-thruster Propulsion System(HPS) for Science and Technology Satellite-3 (STSAT-3) has the flow control accuracy of less than ${\pm}$3% and the pressure control accuracy of less than ${\pm}$5%. The pressure controller adjusts pressure around the set point by using a Proportional Flow Control Valve (PFCV) and a high pressure transducer, while the flow controller regulates the flow rate using PFCV and the anode current telemetry of the Hall Thruster. The controllers are chosen as the Proportional and Integral(PI) type, and the PI gains are tuned based on the Matlab simulations. The result of the PCM test had the flow control accuracy of less than ${\pm}$1.87% and the pressure control accuracy of less than ${\pm}$5%. This paper describes the design, realization, and performance test results of the PCM.