• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.901-910
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• 2008

For some generalized N-function ${\Phi}$, some Holder type inequalities and bounded operators on spaces of type $W_M^{\Omega,\Phi}$ generalizing the $W^p$-spaces due to Pathak and Upadhyay are obtained.

• 한국신재생에너지학회:학술대회논문집
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• 2010.11a
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• pp.50.2-50.2
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• 2010

Indium Tin Oxide (ITO)는 투과도가 높고, 전기 전도도가 뛰어나 TFT, 태양전지 등 여러 가지 산업에서 전극의 재료로 널리 사용되고 있다. 전극의 재료로써 가장 중요하게 고려되어야 할 사항 중의 하나는 전극과 접촉하는 물질과의 접촉 저항이다. 특히, 태양전지에서 높은 접촉 저항은 셀을 직렬저항 요소를 증가시켜 태양전지의 효율 저하를 가져 온다. 본 연구에서는 ITO를 실리콘 태양전지에 적용하기 위하여, ITO - n-type emitter간, ITO - Ag 간의 접촉 특성을 Transfer Length Method(TLM)을 통하여 분석하였다. p-type 실리콘의 전면을 도핑하여 pn접합을 형성한 후, 그 위에 ITO 패턴을 형성하여 ITO-emitter 간의 접촉 특성을 측정하였고, 두껍게 증착한 SiNx 박막 전면에 ITO를 증착한 후, Ag 패턴을 형성하여 ITO-Ag간의 접촉 특성을 측정 하였다. 측정 결과, ITO와 emitter 간의 접촉 비저항은 $0.9{\Omega}-cm^2 $을 나타내었고, ITO와 Ag와의 접촉 비저항은 $0.096{\Omega}-cm^2 $을 나타내었다.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2000.11a
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• pp.13-16
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• 2000

(PbS)$_{1-x}$ -(CuS)$_{x}$ thin films(x=0, 0.5, 1) were grown on glass substrates by using a chemical bath deposition method. The molecular ratio of Pb to Cu for the PbS-CuS thin films(x=0.5) was measured about 7:3 by using EDX and XRF. The resistivity of non-annealed (PbS)$_{1-x}$ -(CuS)$_{x}$ thin films was about 10 $\Omega$ . cm. However, after annealing, the resistivity of PbS showed a little change, while PbS-CuS and CuS significantly decreased in the range of 0.002 to 0.005$\Omega$.cm. PbS was p-type and CuS was n-type.-type.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.757-780
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• 2022

In this article, we study the weak and extra-weak type integral inequalities for the modified integral Hardy operators. We provide suitable conditions on the weights ω, ρ, φ and ψ to hold the following weak type modular inequality $${\mathcal{U}}^{-1}\({\int_{{\mid}{\mathcal{I}}f{\mid}>{\gamma}}}\;{\mathcal{U}}({\gamma}{\omega}){\rho}\){\leq}{\mathcal{V}}^{-1}\({\int}_{0}^{\infty}{\mathcal{V}}(C{\mid}f{\mid}{\phi}){\psi}\),$$ where ${\mathcal{I}}$ is the modified integral Hardy operators. We also obtain a necesary and sufficient condition for the following extra-weak type integral inequality $${\omega}\(\{{\left|{\mathcal{I}}f\right|}>{\gamma}\}\){\leq}{\mathcal{U}}{\circ}{\mathcal{V}}^{-1}\({\int}_{0}^{\infty}{\mathcal{V}}\(\frac{C{\mid}f{\mid}{\phi}}{{\gamma}}\){\psi}\).$$ Further, we discuss the above two inequalities for the conjugate of the modified integral Hardy operators. It will extend the existing results for the Hardy operator and its integral version.

• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.167-193
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• 2023

Let f be a self-dual primitive Maass or modular forms for level 4. For such a form f, we define N^s_f(T):=|{ρ ∈ ℂ : |𝕵(ρ)| ≤ T, ρ is a non-trivial simple zero of L_f(s)}|.. We establish an omega result for N^s_f(T), which is $N^s_f(T) = \Omega(T^{\frac{1}{6}-{\epsilon}})$ for any ∊ > 0. For this purpose, we need to establish the Weyl-type subconvexity for L-functions attached to primitive Maass forms by following a recent work of Aggarwal, Holowinsky, Lin, and Qi.

• East Asian mathematical journal
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• v.39 no.3
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• pp.355-367
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• 2023

Extending [14], we establish the existence of multiple positive solutions for a Schrödinger-type singular elliptic equation: $$\{{-{\Delta}u+V(x)u={\lambda}{\frac{f(u)}{u^{\beta}}},\;x{\in}{\Omega}, \atop u=0,\;x{\in}{\partial}{\Omega},$$ where 0 ∈ Ω is a bounded domain in ℝ^N, N ≥ 1, with a smooth boundary ∂Ω, β ∈ [0, 1), f ∈ C[0, ∞), V : Ω → ℝ is a bounded function and λ is a positive parameter. In particular, when f(s) > 0 on [0, σ) and f(s) < 0 for s > σ, we establish the existence of at least three positive solutions for a certain range of λ by using the method of sub and supersolutions.

• East Asian mathematical journal
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• v.40 no.3
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• pp.295-306
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• 2024

We investigate the existence of multiple positive solutions of the following elliptic equation with a Schrödinger-type term: $$\begin{cases}-{\Delta}u+V(x)u={\lambda}f(u){\quad} x{\in}{\Omega},\\{\qquad}{\qquad}{\quad}u=0, {\qquad}\;x{\in}\partial{\Omega},\end{cases}$$, where 0 ∈ Ω is a bounded domain in ℝ^N , N ≥ 1, with a smooth boundary ∂Ω, f ∈ C[0, ∞), V ∈ L^∞(Ω) and λ is a positive parameter. In particular, when f(s) > 0 for 0 ≤ s < σ and f(s) < 0 for s > σ, we establish the existence of at least three positive solutions for a certain range of λ by using the method of sub and supersolutions.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1441-1462
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• 2018

In this paper, we investigate the fractional p&q-Kirchhoff type system $$\{M_1([u]^p_{s,p})(-{\Delta})^s_pu+V_1(x){\mid}u{\mid}^{p-2}u\\{\hfill{10}}={\ell}k^{-1}F_u(x,\;u,\;v)+{\lambda}{\alpha}(x){\mid}u{\mid}^{m-2}u,\;x{\in}{\Omega}\\M_2([u]^q_{s,q})(-{\Delta})^s_qv+V_2(x){\mid}v{\mid}^{q-2}v\\{\hfill{10}}={\ell}k^{-1}F_v(x,u,v)+{\mu}{\alpha}(x){\mid}v{\mid}^{m-2}v,\;x{\in}{\Omega},\\u=v=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}{\subset}{\mathbb{R}}^N$ is an unbounded domain with smooth boundary ${\partial}{\Omega}$, and $0<s<1<p{\leq}q$ and sq < N, ${\lambda},{\mu}>0$, $1<m{\leq}k<p^*_s$, ${\ell}{\in}R$, while $[u]^t_{s,t}$ denotes the Gagliardo semi-norm given in (1.2) below. $V_1(x)$, $V_2(x)$, $a(x):{\mathbb{R}}^N{\rightarrow}(0,\;{\infty})$ are three positive weights, $M_1$, $M_2$ are continuous and positive functions in ${\mathbb{R}}^+$. Using variational methods, we prove existence of infinitely many high-energy solutions for the above system.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.634-639
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• 2003

It has been studied the flow near a rotating disk with surface topography. The system Ekman number is assumed very small, i.e., $E[{\equiv}\frac{\nu}{{\Omega}^{\ast}L^{\ast2}}]<<1$ in which $L^{\ast}$ denotes a disk radius, ${\nu}$ kinematic viscosity of the fluid and ${\Omega}^{\ast}$ angular velocity of the basic state. Disk surface has a sinusoidal topographic variation along radial coordinate, i.e., $z={\delta}cos(2{\pi}{\omega}r)$, where ${\delta}$ and ${\omega}$ are, respectively, nondimensional amplitude and wave number of the disk surface. Analytic solutions, being useful over the parametric ranges of ${\delta}{\sim}O$( $E^{1/2}$ ) and ${\omega}{\leq}O$ ( $E^{1/2}$ ), are secured in a series-function form of Fourier-Bessel type. An asymptotic behavior, when $E{\rightarrow}0$, is clarified as : for a disk with surface roughness, in contrast to the case of a flat disk, the azimuthal velocity increases in magnitude, together with the thickening boundary layer. The radial velocity, however, decreases in magnitude as the amplitude of surface waviness increases. Consequently, the overall Ekman pumping at the edge of the boundary layer remains unchanged, maintaining the constant value equal to that of the flat disk.

• Fire Science and Engineering
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• v.32 no.6
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• pp.1-6
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• 2018

This study is to analyze the characteristics of the yellow insulation ring type of the CSST used for tubing when it is artificially deteriorated and damaged by burning. The CSST for tubing consists of a tube, protective coating, nut, yellow insulation ring, packing, and socket. In addition, it is thought that a yellow insulation ring and rubber packing were used to connect the tube and socket in order to improve the airtightness and insulation performance. The result of the verification of the data acquired from the tests in the 95% confidence interval shows that the Anderson-Darling (AD) and P value were analyzed to be 0.945 and 0.015, respectively. This confirms that the test data of the CSST for tubing is reliable. The analysis of the arithmetic mean of the insulation resistance of a CSST showed that the CSST damaged by burning by a torch, and the one damaged by electrical burning, was $16.7k{\Omega}$ (the greatest relatively) and $208{\Omega}$ (the lowest), respectively, while it was $1.72k{\Omega}$ in the case of a normal product. Therefore, the analysis result of the insulation resistance of the CSST collected from the scene of a fire can be utilized to examine the cause of damage by burning. In addition, it was found that when the maximum current of 97 A was applied to the CSST for about 5 s using a Primary Current Injection Test System (PCITS) the protective film and insulation ring of the CSST has no difference from that of a normal product. However, a part of the metal tube was melted.