• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.157-164
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• 2018

A $C_0$-semigroup ${\tau}=(T_t)_{t{\geq}0}$ on a Banach space X is called subspace-supercyclic for a subspace M, if $\mathbb{C}Orb({\tau},x){\bigcap}M=\{{\lambda}T_tx\;:\;{\lambda}{\in}\mathbb{C},\;t{\geq}0\}{\bigcap}M$ is dense in M for a vector $x{\in}M$. In this paper we characterize the notion of subspace-supercyclic $C_0$-semigroup. At the same time, we also provide a subspace-supercyclicity criterion $C_0$-semigroup and offer two equivalent conditions of this criterion.

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.323-329
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• 1998

In this paper, we introduce a new class of sets, called $m$-sets, and the notion of $m$-continuity. In particular, $m$-sets and $m$-continuity are used to extend known results for ${\alpha}$-continuity and semi-continuity and precontinuity.

• Proceedings of the Korea Water Resources Association Conference
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• 2006.05a
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• pp.583-587
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• 2006

국부세굴의 발생은 일반적으로 흐름조건, 구조물 조건과 하상재료 세 가지의 주 원인으로 구분할 수 있다. 흐름조건의 경우 구조물 영향으로 발생되는 3차원적인 와류가 주요원인이며 하상재료의 경우 여러 요인이 있겠지만 비중이 같은 입자라 가정할 경우 입자의 크기를 주요 변수로 정할 수 있다. 교각 국부세굴에 관한 연구는 1960년대 이후 연구자들에 의해 매우 다양하게 수행되어 졌으며 많은 산정공식도 제시되었다. 하지만 기존 연구는 최대세굴심 조건으로 다양한 하상재료와 시간에 대한 세굴변동(홍수사상 등)에 대한 영향을 고려하는데 어려움이 있다. 특히 국내의 경우 다양한 하상재료와 홍수빈도를 고려할 때 이에 대한 세굴적용은 매우 중요한 인자라 할 수 있다. 따라서 교각세굴에 대한 궁극적인 목적은 다양한 하상재료와 홍수빈도를 고려할 수 있는 세굴평가를 제안하는데 있다. 이를 위해 본 연구에서는 우선적인 연구로 입자의 다양성과 이미지 기법을 이용한 실시간 측정을 통해 보완하여 입자에 따른 시간적 변화를 분석하였다. 현재 4가지의 하상재료의 입경차이에 따른 국부세굴의 시간적 변화와 초기세굴 발생의 수리적 조건을 파악하고 기존연구와 비교분석하였으며, 이를 기초자료로 세굴심$(S,\;S_{max})$, 교량주변 전단력$({\tau}_p,\;{\tau}_{pc})$, 접근수로부 전단력$({\tau}_a)$와 입자한계전단력$({\tau}_c)$에 대한 시간분석 (time effect)을 통해 다양한 하상재료와 홍수빈도를 해석을 위한 초기분석을 수행하는데 목적이 있다. 수리모형실험에 사용된 가변경사수로의 제원은 $0.6m(W){\times}20m(L){\times}2m(H)$이며 모형구조물은 투명한 아크릴로 제작하였다. 실험방법은 교각 내부에 CC카메라를 전 후면 및 상측면에 설치하여 세굴 발생을 실시간으로 촬영한 후 이미지 분석을 통해 분석하였다.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.17 no.8
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• pp.823-829
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• 2004

In this paper, non-self-aligned SiGe HBTs with ${f}_\tau$ and${f}_max $above 50 GHz have been fabricated using an RPCVD(Reduced Pressure Chemical Vapor Deposition) system for wireless applications. In the proposed structure, in-situ boron doped selective epitaxial growth(BDSEG) and TiSi$_2$ were used for the base electrode to reduce base resistance and in-situ phosphorus doped polysilicon was used for the emitter electrode to reduce emitter resistance. SiGe base profiles and collector design methodology to increase ${f}_\tau$ and${f}_max $ are discussed in detail. Two SiGe HBTs with the collector-emitter breakdown voltages ${BV}_CEO$ of 3 V and 6 V were fabricated using SIC(selective ion-implanted collector) implantation. Fabricated SiGe HBTs have a current gain of 265 ∼ 285 and Early voltage of 102 ∼ 120 V, respectively. For the $1\times{8}_\mu{m}^2$ emitter, a SiGe HBT with ${BV}_CEO$= 6 V shows a cut-off frequency, ${f}_\tau$of 24.3 GHz and a maximum oscillation frequency, ${f}_max $of 47.6 GHz at $I_c$of 3.7 mA and$V_CE$ of 4 V. A SiGe HBT with ${BV}_CEO$ = 3 V shows ${f}_\tau$of 50.8 GHz and ${f}_max $ of 52.2 GHz at $I_c$ of 14.7 mA and $V_CE$ of 2 V.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2091-2106
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• 2017

The authors investigate f-biharmonic maps u : (M, g) ${\rightarrow}$ (N, h) from a Riemannian manifold into a Riemannian manifold with non-positive sectional curvature, and derive that if $\int_{M}f^p{\mid}{\tau}(u){\mid}^pdv_g$ < ${\infty}$, $\int_{M}{\mid}{\tau}(u){\mid}^2dv_g$ < ${\infty}$ and $\int_{M}{\mid}du{\mid}^2dv_g$ < ${\infty}$, then u is harmonic. When u is an isometric immersion, the authors also get that if u satisfies some integral conditions, then it is minimal. These results give an affirmative partial answer to conjecture 4 (generalized Chen's conjecture for f-biharmonic submanifolds).

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.787-805
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• 2023

Let (Ω, µ) be a measure space and {τ_α}_α∈Ω be a normalized continuous Bessel family for a finite dimensional Hilbert space 𝓗 of dimension d. If the diagonal ∆ := {(α, α) : α ∈ Ω} is measurable in the measure space Ω × Ω, then we show that $$\sup\limits_{{\alpha},{\beta}{\in}{\Omega},{\alpha}{\neq}{\beta}}\,{\mid}{\langle}{\tau}_{\alpha},\,{\tau}_{\beta}{\rangle}{\mid}^{2m}\,{\geq}\,{\frac{1}{({\mu}{\times}{\mu})(({\Omega}{\times}{\Omega}{\backslash}{\Delta})}\;\[\frac{{\mu}({\Omega})^2}{\({d+m-1 \atop m}\)}-({\mu}{\times}{\mu})({\Delta})\],\;{\forall}m{\in}{\mathbb{N}}.$$ This improves 48 years old celebrated result of Welch [41]. We introduce the notions of continuous cross correlation and frame potential of Bessel family and give applications of continuous Welch bounds to these concepts. We also introduce the notion of continuous Grassmannian frames.

• Journal of Korean Society for Atmospheric Environment
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• v.24 no.6
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• pp.629-640
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• 2008

This study investigates long-term trends and characteristics of aerosol optical depth ($\tau_a$) and Angstrom exponent (${\AA}$) around Korea in order to understand aerosol effects on the regional climate change. The analysis period is mainly from 1999 to 2006, and the analysis sites are Anmyun and Gosan, the background monitoring sites in Korea, and two other sites of Xianghe in China and Shirahama in Japan. The annual variations of $\tau_a$ at Anmyun and Gosan have slightly systematic increasing and decreasing trends, respectively. $\tau_a$ at Anmyun shows more substantial variation, probably because of it's being closer and vulnerable to anthropogenic influence from China and/or domestic sources than Gosan. Both values at Gosan and Anmyun are approximately 1.5 times greater than those at Shirahama. The monthly variation of $\tau_a$ exhibits the highest values at late Spring and the lowest at late-Summer, which are thought to be associated with the accumulation of fine aerosol formed through the photochemical reaction before the Jangma period and the scavenging effect after the Jangma period, respectively. Meanwhile, the episode-average $\tau_a$ for the Yellow dust period increases 2 times greater than that for the non-Yellow dust period. A significant decrease in ${\AA}$ for the Yellow dust period is attributable to an increase in the loading of especially the coarse particles. Also we found no weekly periodicity of $\tau_a$'s, but distinct weekly cycle of $PM_{10}$ concentrations, such as an increase on weekdays and a decrease on weekends at Anmyun and Gosan. We expect these findings would help to initiate a study on aerosol-cloud interactions through the combination of surface aerosol and satellite remote sensing (MODIS, Calipso and CloudSat) in East Asia.

• Journal of Korea Water Resources Association
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• v.32 no.6
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• pp.731-740
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• 1999

Autocorrelation function is widely used as a tool measuring linear dependence of hydrologic time series. However, it may not be appropriate for choosing decorrelation time or delay time ${\tau}_d$ which is essential in nonlinear dynamics domain and the mutual information have recommended for measuring nonlinear dependence of time series. Furthermore, some researchers have suggested that one should not choose a fixed delay time ${\tau}_d$ but, rather, one should choose an appropriate value for the delay time window ${\tau}_d={\tau}(m-1)$, which is the total time spanned by the components of each embedded point for the analysis of chaotic dynamics. Unfortunately, the delay time window cannot be estimated using the autocorrelation function or the mutual information. Basically, the delay time window is the optimal time for independence of time series and the delay time is the first locally optimal time. In this study, we estimate general dependence of hydrologic time series using the C-C method which can estimate both the delay time and the delay time window and the results may give us whether hydrologic time series depends on its linear or nonlinear characteristics which are very important for modeling and forecasting of underlying system.

• Honam Mathematical Journal
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• v.26 no.4
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• pp.455-462
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• 2004

We prove that if ${\mathbb{K}}^*$ is adjoint operator on $W_2{^2}({\Omega})$, then ${\mathbb{K}}^*v(t,\;{\tau})=,\;v(x,\;y){\in}W_2{^2}({\Omega})$ ; it is also related to the decomposition of solution of Fredholm equations.

• Kyungpook Mathematical Journal
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• v.48 no.4
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• pp.637-650
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• 2008

New sufficient conditions for the existence of at least one solution of Neumann type boundary value problems for second order nonlinear differential equations $$\array{\{{p(t)\phi(x'(t)))'=f(t,x(t),\;x(\tau_1(t)),\;{\cdots},\;x(\tau_m(t))),\;t\in[0,T],\\x'(0)=0,\;x'(T)=0,}\,}$$, are established.