• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.169-179
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• 2021

In this paper, we extend the definition of p-harmonic maps between two Riemannian manifolds. We prove a Liouville type theorem for generalized p-harmonic maps. We present some new properties for the generalized stress p-energy tensor. We also prove that every generalized p-harmonic map from a complete Riemannian manifold into a Riemannian manifold admitting a homothetic vector field satisfying some condition is constant.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.15 no.2
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• pp.23-29
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• 2015

The baby-step giant-step algorithm seeks b in a discrete logarithm problem when a,c,p of $a^b{\equiv}c$(mod p) are already given. It does so by dividing p by m block of $m={\lceil}{\sqrt{p}}{\rceil}$ length and letting one giant walk straight toward $a^0$ with constant m strides in search for b. In this paper, I basically reduce $m={\lceil}{\sqrt{p}}{\rceil}$ to p/l, $a^l$ > p and replace a giant with an adult who is designed to walk straight with constant l strides. I also extend the algorithm to allow $2^k$ adults to walk simultaneously. As a consequence, the proposed algorithm quarters the execution time of the basic adult-walk method when applied to $2^k$, (k=2) in the range of $1{\leq}b{\leq}p-1$. In conclusion, the proposed algorithm greatly shorten the step number of baby-step giant-step.

• Journal of Soil and Groundwater Environment
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• v.21 no.6
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• pp.46-55
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• 2016

This experimental study was aimed to estimate interfacial tension of brine-$CO_2$ by using a pendant bubble method and image analysis. Measurements were performed for wide ranges of temperatures, pressures, and salinities covering reservoir conditions in Pohang basin, a possible candidate for $CO_2$ storage operation in Korea. The profiles of $CO_2$ bubbles in brine obtained from image analysis with the densities of brine and $CO_2$ from previous studies were applied to Laplace-Young equation for calculating interfacial twnsion in brine-$CO_2$ system. The experimental results reveals that the interfacial tension is significantly affected by reservoir conditions such as pressure, temperature and water salinity. For conditions of constant temperature and water salinity, the interfacial tension decreases as pressure increases for low pressures (P < $P_c$), and approaches to a constant value for high pressures. For conditions of constant pressure and water salinity, the interfacial tension increases as temperature increases for T < $T_c$, with an asymptotic trend towards a constant value for high temperatures. For conditions of constant pressure and temperature, the interfacial tension increases with increasing water salinity. The trends in changes of interfacial tension can be explained by the effects of the reservoir conditions on the density difference of brine and $CO_2$, and the solubility of $CO_2$ in brine. The information on interfacial tensions obtained from this research can be applied in predicting the migration and distribution of injecting and residual fluids in brine-$CO_2$-rock systems in deep geological environments during geological $CO_2$ sequestrations.

• Bulletin of the Korean Chemical Society
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• v.29 no.4
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• pp.785-789
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• 2008

The present study is the first report of utilizing $TiO_2$ photocatalyst to analytically calibrate the hydroperoxyl radical ($HO_2\;^{\cdot}$). An in-situ calibration method of $HO_2\;^{\cdot}$ is proposed for air monitoring by using an 2-methyl-6-(pmethoxyphenyl)- 3,7-dihydroimidazo-[1,2-a]pyrazin-3-one (MCLA)-chemiluminescence (CL) technique. In this method, $HO_2\;^{\cdot}$($pK_a$ = 4.80) is produced by the ultraviolet (UV) photolysis of immobilized $TiO_2$ using a constant flow rate of air equilibrated water, in which $HO_2\;^{\cdot}$ is controlled by using various lengths of knotted tubing reactor (KTR). The principle of the proposed calibration is based on the experimentally determined halflife ($t_{1/2}$) of $HO_2\;^{\cdot}$ and its empirically observed pH-dependent rate constant, $k_{obs}$, at a given pH. The concentration of $HO_2\;^{\cdot}$/$O_2\;^{\cdot}$− is increased as pH increases. This pH dependence is due to the different disproportionative reactivities between $HO_2\;^{\cdot}$/$O_2\;^{\cdot}$− and $HO_2\;^{\cdot}$/$O_2\;^{\cdot}$−. Experimental results indicate the practical feasibility of the approach, producing very promising method.

• Journal of the Korean Electrochemical Society
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• v.7 no.4
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• pp.167-172
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• 2004

3,4-dihydroxybenzaldehyde(3,4-DHB) was oxidatively el electropolymerized on glassy carbon (GC) electrodes to prepare CC/p-3,4-DHB type electrodes, which were subsequently modified with 3,4-dihydroxybenzoic acid(3,4-DHBA) using 0.05M HCI as a catalyst. The esterification reactions were performed between -OH sites on the polymeric film surface of the p-3,4-DHB and the -COOH sites within the 3,4-DHBA molecules in solution. These reactions had a rate constant value of $1.1\times10^{-1}\;s^{-1}$ for the esterification step as obtained from the first-order rate constant in the solution. The electrochemical responses of the GC/p-3,4-DHB-3,4-DHBA electrodes exert an influence upon the buffer solution, its pH and applied potential ranges. The redox process of the electrode was more easily controlled by charge transfer kinetics than that of the CC/p-3,4-DHB. The modified electrodes had redox active sites that were 10 times more active than those present before modification. The electrical admittance of the modified electrodes was also three times higher than that of the unmodified electrodes. After being annealed in ethanol for 20 hrs the electrodes brought about a 3.3 times greater change of water molecules in the redox reaction. The modified electrodes are stable in the potential range of 0.4 to 0.55V.

• Journal of the Korean Society of Safety
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• v.20 no.4 s.72
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• pp.29-33
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• 2005

In this paper, reflectance and the dielectric characteristics for $P_2O_5-ZnO-BaO$ system and $SiO_2-ZnO-B_2O_3$ system have been investigated as a function of contents of $TiO_2$. The reflectance was decreased with increasing the contents of $TiO_2$ and the reflectance of $P_2O_5-ZnO-BaO$ system was lowered than that of $SiO_2-ZnO-B_2O_3$ system. The dielectric constant of $P_2O_5-ZnO-BaO$ system was higher than $SiO_2-ZnO-B_2O_3$ system, and the dielectric constant in the both system was increased with increasing of $TiO_2$ contents. This can be explained as the space charge effects. These results are could be applied to the under plate dielectrics of PDP required high reflective ratio and breakdown strength.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.417-426
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• 2011

Let ${\mu}$ be a finite positive Borel measure on the unit ball $B{\subset}{\mathbb{C}}^n$ and ${\nu}$ be the Euclidean volume measure such that ${\nu}(B)=1$. For the unit sphere $S=\{z:{\mid}z{\mid}=1\}$, ${\sigma}$ is the rotation-invariant measure on S such that ${\sigma}(S) =1$. Let ${\mathcal{P}}[f]$ be the Poisson-$Szeg{\ddot{o}}$ integral of f and $\tilde{\mu}$ be the Berezin transform of ${\mu}$. In this paper, we show that if there is a constant M > 0 such that ${\int_B}{\mid}{\mathcal{P}}[f](z){\mid}^pd{\mu}(z){\leq}M{\int_B}{\mid}{\mathcal{P}}[f](z){\mid}^pd{\nu}(z)$ for all $f{\in}L^p(\sigma)$, then ${\parallel}{\tilde{\mu}}{\parallel}_{\infty}{\equiv}{\sup}_{z{\in}B}{\mid}{\tilde{\mu}}(z){\mid}<{\infty}$, and we show that if ${\parallel}{\tilde{\mu}{\parallel}_{\infty}<{\infty}$, then ${\int_B}{\mid}{\mathcal{P}}[f](z){\mid}^pd{\mu}(z){\leq}C{\mid}{\mid}{\tilde{\mu}}{\mid}{\mid}_{\infty}{\int_S}{\mid}f(\zeta){\mid}^pd{\sigma}(\zeta)$ for some constant C.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.905-913
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• 2023

Suppose that M is a strictly convex hypersurface in the (n + 1)-dimensional Euclidean space 𝔼ⁿ⁺¹ with the origin o in its convex side and with the outward unit normal N. For a fixed point p ∈ M and a positive constant t, we put 𝚽_t the hyperplane parallel to the tangent hyperplane 𝚽 at p and passing through the point q = p - tN(p). We consider the region cut from M by the parallel hyperplane 𝚽_t, and denote by I_p(t) the (n + 1)-dimensional volume of the convex hull of the region and the origin o. Then Schneider's characterization theorem for ellipsoids states that among centrally symmetric, strictly convex and closed surfaces in the 3-dimensional Euclidean space 𝔼³, the ellipsoids are the only ones satisfying I_p(t) = 𝜙(p)t, where 𝜙 is a function defined on M. Recently, the characterization theorem was extended to centrally symmetric, strictly convex and closed hypersurfaces in 𝔼ⁿ⁺¹ satisfying for a constant 𝛽, I_p(t) = 𝜙(p)t^𝛽. In this paper, we study the volume I_p(t) of a strictly convex and complete hypersurface in 𝔼ⁿ⁺¹ with the origin o in its convex side. As a result, first of all we extend the characterization theorem to strictly convex and closed (not necessarily centrally symmetric) hypersurfaces in 𝔼ⁿ⁺¹ satisfying I_p(t) = 𝜙(p)t^𝛽. After that we generalize the characterization theorem to strictly convex and complete (not necessarily closed) hypersurfaces in 𝔼ⁿ⁺¹ satisfying I_p(t) = 𝜙(p)t^𝛽.

• Journal of the Korean Ceramic Society
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• v.30 no.4
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• pp.289-298
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• 1993

Properties in terms of the variation of the glass compositions, which were density (p), molar volume(Vm), atom/ion packing density (Dp), refractive index (nD), transformation temperature (Tg), dilatometric softening point (Td), thermal expansion coefficient (α), Young's modulus (E), and knoop hardness (KHN) were investigated in CaO-SiO2 glasses and CaO-P2O5-SiO2 glasses containing less than 10mole% of P2O5. Those properties were measured by density measurement kit, Abbe refractometer, dilatometer, ultrasonic pulse echo equipment, and micro hardness tester. When CaO content was increased in CaO-SiO2 glasses, p, Dp, nD, Tg, Td, α, E and KHN were increased, while Vm was decreased. When P2O5 was added to the CaO-SiO2 glasses with constant CaO/SiO2 ratio as 1.07, p, Dp, nD, Tg, Td, α, E and KHN were decreased, while Vm was increased. When the amount of P2O5 in glasses was kept constant, the changes of the properties with variation of CaO content in the CaO-P2O5-SiO2 glasses were very similar to those of CaO-SiO2 glasses. These phenomena could be explained by the structural role of P2O5 in the CaO-P2O5-SiO2 glasses, which was polymerization of siicate structures and resulted in [PO4] monomer structure in glasses. Due to this structural characteristics, the bond strength and packing density were changed with compositions. Proportional relationships between 1) np and Dp, 2) Tg, Td, α and CaO content, 3) E and Vm-1, and 4) KHN and P2O5 content were evaluated in this investigation.

• Proceedings of the Korean Vacuum Society Conference
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• 1998.02a
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• pp.77-77
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• 1998

Present silicon dioxide (SiOz) 떠m as intennetal dielectridIMD) layers will result in high parasitic c capacitance and crosstalk interference in 비gh density devices. Low dielectric materials such as f f1uorina뼈 silicon oxide(SiOF) and f1uoropolymer IMD layers have been tried to s이ve this problem. I In the SiOF ftlm, as fluorine concentration increases the dielectric constant of t뼈 film decreases but i it becomes unstable and wa않r absorptivity increases. The dielectric constant above 3.0 is obtain어 i in these ftlms. Fluoropolymers such as polyte$\sigma$따luoroethylene(PTFE) are known as low dielectric c constant (>2.0) materials. However, their $\alpha$)Or thermal stability and low adhesive fa$\pi$e have h hindered 야1리ru뚱 as IMD ma따"ials. 1 The concept of a plasma processing a찌Jaratus with 비gh density plasma at low pressure has r received much attention for deposition because films made in these plasma reactors have many a advantages such as go여 film quality and gap filling profile. High ion flux with low ion energy in m the high density plasma make the low contamination and go어 $\sigma$'Oss피lked ftlm. Especially the h helicon plasma reactor have attractive features for ftlm deposition 야~au똥 of i앙 high density plasma p production compared with other conventional type plasma soun:es. I In this pa야Jr, we present the results on the low dielectric constant fluorocarbonated-SiOF film d밑JOsited on p-Si(loo) 5 inch silicon substrates with 00% of 0dFTES gas mixture and 20% of Ar g gas in a helicon plasma reactor. High density 띠asma is generated in the conventional helicon p plasma soun:e with Nagoya type ill antenna, 5-15 MHz and 1 kW RF power, 700 Gauss of m magnetic field, and 1.5 mTorr of pressure. The electron density and temperature of the 0dFTES d discharge are measUI벼 by Langmuir probe. The relative density of radicals are measured by optic허 e emission spe따'Oscopy(OES). Chemical bonding structure 3I피 atomic concentration 따'C characterized u using fourier transform infrared(FTIR) s야3띠"Oscopy and X -ray photonelectron spl:’따'Oscopy (XPS). D Dielectric constant is measured using a metal insulator semiconductor (MIS;AVO.4 $\mu$ m thick f fIlmlp-SD s$\sigma$ucture. A chemical stoichiome$\sigma$y of 야Ie fluorocarbina$textsc{k}$영-SiOF film 따~si야영 at room temperature, which t the flow rate of Oz and FTES gas is Isccm and 6sccm, res야~tvely, is form려 야Ie SiouFo.36Co.14. A d dielec$\sigma$ic constant of this fIlm is 2.8, but the s$\alpha$'!Cimen at annealed 5OOt: is obtain려 3.24, and the s stepcoverage in the 0.4 $\mu$ m and 0.5 $\mu$ m pattern 킹'C above 92% and 91% without void, res야~tively. res야~tively.