• Publications of The Korean Astronomical Society
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• v.15 no.1
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• pp.15-19
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• 2000

The lens mass determined from the photometrically obtained Einstein time scale suffers from large uncertainty due to the lens parameter degeneracy. The uncertainty can be substantially reduced if the mass is determined from the lens proper motion obtained from astrometric measurements of the source image centroid shifts, ${\delta}{\theta}_c$, by using high precision interferometers from space-based platform such as the Space Interferometry Mission (SIM), and ground-based interferometers soon available on several 8-10m class telescopes. However, for the complete resolution of the lens parameter degeneracy it is required to determine the lens parallax by measuring the parallax-induced deviations in the centroid shifts trajectory, ${\Delta}{\delta}{\theta}_c$ aloe. In this paper, we investigate the detectabilities of ${\delta}{\theta}_c$ and ${\Delta}{\delta}{\theta}_c$ by determining the distributions of the maximum centroid shifts, $f({\delta}{\theta}_{c,max})$, and the average maximum deviations, $(<{\Delta}{\delta}_{c,max}>)$, for different types of Galactic microlensing events caused by various masses. From this investigation, we find that as long as source stars are bright enough for astrometric observations it is expected that $f({\delta}{\theta}_c)$ for most events caused by lenses with masses greater than 0.1 $M_\bigodot$ regardless of the event types can be easily detected from observations by using not only the SIM (with a detection threshold but also the ${\delta}{\theta}_{th}\;\~3{\mu}as)$ but also the ground-based interferometers $(with\;{\delta}{\theta}_{th}\;\~3{\mu}as)$. However, from ground-based observations, it will be difficult to detect ${\Delta}{\delta}{\theta}_c$ for most Galactic bulge self-lensing events, and the detection will be restricted only for small fractions of disk-bulge and halo-LMC events for which the deviations are relatively large. From observations by using the SIM, on the other hand, detecting ${\Delta}{\delta}{\theta}_c$ will be possible for majority of disk and halo events and for a substantial fraction of bulge self-lensing events. For the complete resolution of the lens parameter degeneracy, therefore, SIM observations will be essential.

• Journal of the Korean Chemical Society
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• v.43 no.6
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• pp.614-620
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• 1999

The critical micelle concentration (CMC) and the counterion binding constant (${\beta}$) at the CMC of the mixtures of Dodecylpyridinium chloride (DPC) and Tetradecyltrimethylammonium bromide (TTAB) have been determined from the concentration dependence of electrical conductance at various temperatures from $4^{\circ}C$ to $36^{\circ}C$. Thermodynamic parameters (${\Delta}C_p$, ${\Delta}G^o_m$, ${\Delta}H^o_m$ and ${\Delta}S^o_m$), associated with the micelle formation of DPC/TTAB mixtures, have been estimated from the temperature dependence of CMC and ${\beta}$values. The measured values of ${\Delta}C_p$ and ${\Delta}G^o_m$ are negative but the values of ${\Delta}S^o_m$ are positive in the whole measured temperature region. The values of ${\Delta}H^o_m$ are positive at low temperature region and negative at high temperature region. The results show that all of the thermodynamic parameters are dependent on temperature and mole fraction of DPC(${\alpha}_DPC$).

• Journal of the Korean Mathematical Society
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• v.15 no.1
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• pp.39-57
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• 1978

It is given in the Lecture Note [1] of Berger, Gauduchon and Mazet that, if ${\pi}$n: (${\tilde{M}}$, ${\tilde{g}}$)${\rightarrow}$(${\tilde{M}}$, ${\tilde{g}}$) is a Riemannian submersion with totally geodesic fibers, ${\Delta}$ and ${\tilde{\Delta}}$ are Laplace operators on (${\tilde{M}}$, ${\tilde{g}}$) and (M, g) respectively and f is an eigenfunction of ${\Delta}$, then its lift $f^L$ is also an eigenfunction of ${\tilde{\Delta}}$ with the common eigenvalue. But such a simple relation does not hold for an eigenform of the Laplace-Beltrami operator ${\Delta}=d{\delta}+{\delta}d$. If ${\omega}$ is an eigenform of ${\Delta}$ and ${\omega}^L$ is the horizontal lift of ${\omega}$, ${\omega}^L$ is not in genera an eigenform of the Laplace-Beltrami operator ${\tilde{\Delta}}$ of (${\tilde{M}}$, ${\tilde{g}}$). The present author has obtained a set of formulas which gives the relation between ${\tilde{\Delta}}{\omega}^L$ and ${\Delta}{\omega}$ in another paper [7]. In the present paper a Sasakian submersion is treated. A Sasakian manifold (${\tilde{M}}$, ${\tilde{g}}$, ${\tilde{\xi}}$) considered in this paper is such a one which admits a Riemannian submersion where the base manifold is a Kaehler manifold (M, g, J) and the fibers are geodesics generated by the unit Killing vector field ${\tilde{\xi}}$. Then the submersion is called a Sasakian submersion. If ${\omega}$ is a eigenform of ${\Delta}$ on (M, g, J) and its lift ${\omega}^L$ is an eigenform of ${\tilde{\Delta}}$ on (${\tilde{M}}$, ${\tilde{g}}$, ${\tilde{\xi}}$), then ${\omega}$ is called an eigenform of the first kind. We define a relative eigenform of ${\tilde{\Delta}}$. If the lift ${\omega}^L$ of an eigenform ${\omega}$ of ${\Delta}$ is a relative eigenform of ${\tilde{\Delta}}$ we call ${\omega}$ an eigenform of the second kind. Such objects are studied.

• Journal of the Korean Chemical Society
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• v.37 no.1
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• pp.3-9
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• 1993

Specific rates of solvolysis of 1-adamantyl fluoroformate in hydroxylic solvents have been measured by an electric conductivity method under various pressures. The activation parameters (${\Delta}V^{\neq}{_o},\;{\Delta}{\beta}^{\neq},\;{Delta}H^{\neq},\;{Delta}S^{\neq}$,/TEX>) and average pressure within the solvation-shell of activated complex (charge development) have been estimated from the rates. Also, the selectivities for the formation of solvolysis products in aqueous ethanol have been determined by response-calibrated GC. The values of ${\Delta}V^{\neq}{_o},\;and\;{\Delta}{\beta}^{\neq}$ are both negative, but ${Delta}H^{\neq}$ is positive and ${Delta}S^{\neq}$, is large negative. This behavior is discussed in terms of electrostriction of solvation. From these results, it could be postulated that the solvolysis of 1-adamantyl fluoroformate have two major reaction pathway.

• Journal of the Korean Chemical Society
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• v.48 no.3
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• pp.254-260
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• 2004

The reaction rates of para-substituted benzoyl chlorides ($p-CH_3$, p-H, $p-NO_2$) with pyridine have been measured employing the conductometry method in acetonitrile. The pseudo first-order and second-order rate constants were determined at various pressures and temperatures. The activation parameters (${\Delta}V{\ddagger},\;{\Delta}{\beta}{\ddagger},\;{\Delta}H{\ddagger},\;{\Delta}S{\ddagger},\;{\Delta}G{\ddagger}$) and the Hammett ${\rho}$-values are determined from the values of rate constant. The values of ${\Delta}V{\ddagger},\;{\Delta}{\beta}{\ddagger}\;and\;{\Delta}S{\ddagger}$ are all negative. The Hammett ${\rho}$-values are positive for the substrate (${\rho}_Y$) over the given pressure range. The results of kinetic studies, for the pressure and substituent changes, show that these reactions are proceeded by a typical $SN_2$reaction mechanism and its bond formation is favored with elevating pressure.

• Journal of the Korean Chemical Society
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• v.37 no.6
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• pp.577-584
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• 1993

The reaction rates of para-substituted benzoyl chlorides with substituted pyridines have been measured employing the conductometry method in acetonitrile, and pseudo-first order and second order rate constants are determined at various pressures and temperatures. The activation parameters (${\Delta}V^\neq, {\Delta}{\beta}^{\neq}, {\Delta}H^{\neq}, {\Delta}S^{\neq} {\Delta}G^{\neq}$) and the Hammett ρ-values are determined from the values of rate constants. The values of △${\Delta}V^\neq, {\Delta}{\beta}^{\neq}and {\Delta}S^{\neq}$ are all negative. The Hammett ρ-values are negative for the nucleophile (ρ$_X$), and positive for the substrate (ρ$_Y$) over the pressure range studied. The results of kinetic studies for pressure and substituent show that these reactions proceed in typical S$_N$2 reaction mechanism and in bond formation favored with elevating pressure.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.43-56
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• 1997

In this paper, we introduce a new class of ${\delta}$-frames and study its properties. To do so, we introduce ${\delta}$-filters, almost Lindel$\ddot{o}$f frames and Lindel$\ddot{o}$f frames. First, we show that a complete chain or a complete Boolean algebra is a ${\delta}$-frame. Next, we show that a ${\delta}$-frame L is almost Lindel$\ddot{o}$f iff for any ${\delta}$-filter F in L, ${\vee}\{x^*\;:\;x{\in}F\}{\neq}e$. Last, we show that every regular Lindelof ${\delta}$-frame is normal and a Lindel$\ddot{o}$f ${\delta}$-frame is preserved under a ${\delta}$-isomorphism which is dense and codense.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.450-455
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• 2001

An analytical study is made of transient adjustment process of an initially stationary, stably-stratified fluid in a square. The boundary walls are highly-conducting. The overall Rayleigh number $R_a$ is large. Considerations are given to both opposing (${\delta}w/{\delta}T>0$) and cooperating (${\delta}w/{\delta}T<0$) configurations. The flow character in opposing configuration can be classified into (a) a forced-convection dominaut mode (${\delta}w/{\delta}T>1/\sqrt{2}$), (b) a buoyancy-convection dominant mode ($0<{\delta}w/{\delta}T<1/\sqrt{2}$), and (c) a static mode (${\delta}w/{\delta}T{\cong}1/\sqrt{2}$). Global evolutionary processes are depicted. and physical rationalizations are provided.

• Journal of the Korean Ceramic Society
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• v.35 no.9
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• pp.995-1001
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• 1998

As a basic study for cathode materials of {{{{ { {LiMn }_{2 }O }_{4 } }}-based lithium-ion secondary batteries Li({{{{ { { { {Mn }_{1-$\delta$ }Nb }_{$\delta$} )}_{2 }O }_{4 } }} ($\delta$=0.05, 0.1, 0.2) materials which Nb is substituted for Mn were synthesized by the solid state reaction at 80$0^{\circ}C$ and 110$0^{\circ}C$ respectively. The second phase {{{{ { LiNbO}_{3 } }} appeared above $\delta$=0.1 As the result of im-pedance analysis as the amount of substituted Nb increased the resistivity of grain boundary increased greatly. Compared to undoped-{{{{ { {LiMn }_{2 }O }_{4 } }} the electrical conductivity of Li({{{{ { { { {Mn }_{1-$\delta$ }Nb }_{$\delta$} )}_{2 }O }_{4 } }} decreased slightly but is charging capacity and potential plateau increased.

• Journal of the Korean Mathematical Society
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• v.15 no.1
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• pp.59-61
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• 1978

Let $X_1$, $X_2$, ${\cdots}$, $X_n$ be i.i.d. uniform (0,1) random variables. Let $f_n(x)$ denote the probability density function (p.d.f.) of $T_n={\sum}^n_{i=1}X_i$. Consider a set S(x ; ${\delta}$) of lattice points defined by S(x ; ${\delta}$) = $x{\mid}x={\delta}+j$, j=0, 1, ${\cdots}$, n-1, $0{\leq}{\delta}{\leq}1$} The lattice distribution induced by the p.d.f. of $T_n$ is defined as follow: (1) $f_n^{(\delta)}(x)=\{f_n(x)\;if\;x{\in}S(x;{\delta})\\0\;otherwise.$. In this paper we show that $f_n{^{(\delta)}}(x)$ is a probability function thus we obtain a family of lattice distributions {$f_n{^{(\delta)}}(x)$ : $0{\leq}{\delta}{\leq}1$}, that the mean and variance of the lattice distributions are independent of ${\delta}$.