• 천문학논총
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• 제15권1호
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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.

• 대한화학회지
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• 제43권6호
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• pp.614-620
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• 1999

양이온 계면활성제인 Dodecylpyridinium chloride(DPC)와 Tetradecyltrimethylammonium bromide(TTAB)로 구성된 혼합계면활성제의 임계마이셀농도(CMC)와 반대이온의 결합상수(${\beta}$)를 $4^{\circ}C$에서 $36^{\circ}C$까지 전도도법으로 측정하였다. CMC와 ${\beta}$값의 온도에 따른 변화로부터 DPC/TTAB 혼합계면활성제의 마이셀화에 대한 여러 가지 열역학 함수값(${\Delta}C_p$, ${\Delta}G^o_m$, ${\Delta}H^o_m$ 및 ${\Delta}S^o_m$)을 계산하였다. ${\Delta}C_p$와 ${\Delta}G^o_m$은 측정한 온도범위 내에서 모두 음의 값을 나타내었으며, ${\Delta}S^o_m$은 모두 양의 값을 나타내었다. 한편 ${\Delta}H^o_m$은 낮은 온도에서는 양의 값을 그리고 높은 온도에서는 음의 값을 띠었다. 또한 이러한 열역학 함수값은 온도와 몰분율 조성 (${\alpha}_DPC$)에 따라 큰 변화를 보였다.

• 대한수학회지
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• 제15권1호
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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.

• 대한화학회지
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• 제37권1호
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• pp.3-9
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• 1993

메탄올 및 에탄올 수용액내에서 1-adamantyl fluoroformate의 가용매분해반응속도를 여러 압력하에서 전도도방법을 이용하여 측정하였다. 이들 속도상수로부터 활성화부피(${\Delta}V^{\neq}{_o}$), 활성화압축율계수(${\Delta}{\beta}^{\neq}$), 활성화엔탈피(${Delta}H^{\neq}$), 활성화엔트로피(${Delta}S^{\neq}$), 그리고 활성화 착물에서의 charge development(△P)를 구하였다. 또한 에탄올 수용액내에서 가용매분해반응으로 인한 생성물에 대한 selectivity를 GC를 이용하여 측정하였다. 그 결과 ${\Delta}V^{\neq}{_o}$와 ${\Delta}{\beta}^{\neq}$의 값은 모두 음의 값을 ${Delta}H^{\neq}$는 양의 값을 ${Delta}S^{\neq}$은 큰 음의 값을 얻었다. 이 현상을 용매구조변화에 대하여 논의하였다. 이들 결과로부터 본 반응은 acyl carbon을 공격하는 이분자성반응과 가용매분해과정(S-D)인 용매-분리이온쌍반응으로 추정할 수가 있었다.

• 대한화학회지
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• 제48권3호
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• pp.254-260
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• 2004

아세토니트릴 용매내에서 파라치환 염화벤조일류($p-CH_3$, p-H, $p-NO_2$)와 피리딘의 반응속도를 온도와 압력변화에 따라 전기전도도법으로 측정하여 유사 1차반응속도상수와 2차반응속도상수를 구하였다. 이들 반응속도상수로부터 활성화파라미터들(${\Delta}V{\ddagger},\;{\Delta}{\beta}{\ddagger},\;{\Delta}H{\ddagger},\;{\Delta}S{\ddagger},\;{\Delta}G{\ddagger}$ 과 Hammett ${\rho}$를 구하였다. 이때 ${\Delta}V{\ddagger},\;{\Delta}{\beta}{\ddagger}$ 및 ${\Delta}S{\ddagger}$는 모두 음의 값을 나타내었으며, 모든 압력 조건에서 기질의 치환기효과 ${\rho}_Y$는 양의 값을 나타내었다. 압력과 치환기 변화에 따른 속도론적 연구를 종합하면, 전체적인 반응은 전형적인 $SN_2$ 반응메카니즘을 따르며, 압력 증가에 따라 결합 형성이 더욱 촉진된 반응메카니즘으로 진행됨을 알 수 있다.

• 대한화학회지
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• 제37권6호
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• pp.577-584
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• 1993

아세토니트릴 용매내에서 파라치환 염화벤조일류와 피리딘류의 반응속도를 온도와 압력변화에 따라 전기전도도법으로 측정하여 유사1차반응속도상수와 2차반응속도상수를 구하였다. 이들 반응속도상수로부터 활성화파라미터들(${\Delta}V^\neq, {\Delta}{\beta}^{\neq}, {\Delta}H^{\neq}, {\Delta}S^{\neq} {\Delta}G^{\neq}$)과 Hammett ρ를 구하였다. 이때 ${\Delta}V^\neq, {\Delta}{\beta}^{\neq}및 {\Delta}S^{\neq}$는 모두 음의 값을 나타내었으며, 모든 압력 조건에서 친핵체의 치환기 효과 ρ$_X$는 음의 값을 기질의 치환기효과 ρ$_Y$는 양의 값을 나타내었다. 압력과 치환기 변화에 따른 속도론적 연구를 종합하면, 전체적인 반응은 전형적인 S$_N$2 반응메카니즘을 따르며, 압력 증가에 따라 결합형성이 더욱 촉진된 반응메카니즘으로 진행됨을 알 수 있다.

• 충청수학회지
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• 제10권1호
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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.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집E
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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.

• 한국세라믹학회지
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• 제35권9호
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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.

• 대한수학회지
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• 제15권1호
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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 ${\delta}$.