• Bulletin of the Korean Chemical Society
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• v.11 no.1
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• pp.15-19
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• 1990

The crystal structure of $(C_{12}H_{24}O_6{\cdot}K)_2K[Co(OH)_6Mo_6O_{18}]{\cdot}12H_2O$ has been determined by X-ray diffraction. Crystal data as follows ; monoclinic, space group $C_2/m,\;a\;=\;22.512(4)\;{\AA},\;b\;=\;18.304(4)\;{\AA},\;c\;=\;7.641(1)\;{\AA},\;{\beta}\;=\;90.52(2)\;{\AA}$, and Z = 2. A final conventional R value of 0.044 was obtained by least-squares refinement of 4173 independent observed $[{\mid}Fo{\mid}{\geq}3{\sigma}({\mid}Fo{\mid})]$ reflections. The $[Co(OH)_6Mo_6O_}{18}]^{-3}$ polyanion shows the well-known Anderson-structure and has approximate 3m symmetry. A $[Co(OH)_6Mo_6O_{18}]^{-3}$ polyanion is located between two crown ether complexed cations forming a sandwich structure. One potassium ion interacts with the crown ether via electrostatic interactions. The other potassium ion only interacts with the water molecules and terminal oxygen atoms of the polyanion.

• Geophysics and Geophysical Exploration
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• v.25 no.1
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• pp.44-49
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• 2022

Closed-form expressions of vector gravity and gravity gradient tensor based on a line segment are derived. If a cylindrical object with axial symmetry is observed from a distance, it is possible to approximate it as a line segment; therefore, it is necessary to compute the gravity and the gravity gradient tensor due to a line source by using closed-form expressions. The gravitational potential for a line segment is defined as a one-dimensional integral, and this integral is differentiated with respect to the Cartesian coordinate system to derive the vector gravity. The expressions of the gravity gradient tensor are derived by differentiating the vector gravity once more in the same coordinate system.

• Journal of The Korean Astronomical Society
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• v.56 no.2
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• pp.287-292
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• 2023

This paper investigates the number of scatterings a photon undergoes in random walks before escaping from a medium. The number of scatterings in random walk processes is commonly approximated as τ + τ² in the literature, where τ is the optical thickness measured from the center of the medium. However, it is found that this formula is not accurate. In this study, analytical solutions in sphere and slab geometries are derived for both optically thin and optically thick limits, assuming isotropic scattering. These solutions are verified using Monte Carlo simulations. In the optically thick limit, the number of scatterings is found to be 0.5 τ² and 1.5 τ² in a sphere and slab, respectively. In the optically thin limit, the number of scatterings is ≈ τ in a sphere and ≈ τ (1 - γ - ln τ + τ) in a slab, where γ ≃ 0.57722 is the Euler-Mascheroni constant. Additionally, we present approximate formulas that reasonably reproduce the simulation results well in intermediate optical depths. These results are applicable to scattering processes that exhibit forward and backward symmetry, including both isotropic and Thomson scattering.

• Communications for Statistical Applications and Methods
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• v.31 no.4
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• pp.409-425
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• 2024

Logistic regression models are commonly used to explain binary health outcome variable using independent variables such as patient characteristics in medical science and public health research. Although there is no distributional assumption required for independent variables in logistic regression, variables with severely right-skewed distribution such as lab values are often log-transformed to achieve symmetry or approximate normality. However, lab values often have zeros due to limit of detection which makes it impossible to apply log-transformation. Therefore, preprocessing to handle zeros in the observation before log-transformation is necessary. In this study, five methods that remove zeros (shift by 1, shift by half of the smallest nonzero, shift by square root of the smallest nonzero, replace zeros with half of the smallest nonzero, replace zeros with the square root of the smallest nonzero) are investigated in logistic regression setting. To evaluate performances of these methods, we performed a simulation study based on randomly generated data from log-normal distribution and logistic regression model. Shift by 1 method has the worst performance, and overall shift by half of the smallest nonzero method, replace zeros with half of the smallest nonzero method, and replace zeros with the square root of the smallest nonzero method showed comparable and stable performances.

• Journal of the Mineralogical Society of Korea
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• v.6 no.2
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• pp.116-121
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• 1993

A single crystla of zeolite $Na_{78}Rb_{28}-X$ (approximate composition) was prepared by exposing $Na_{92}-X$ at $350^{\circ}C$ to 0.1 Torr of rubidium vapor, and its structure was determined by single-crystal x-ray diffraction methods in the cubic space group, Fd3, ${\alpha}=25.045(4){\AA}$. The structure was refined to the final error indices $R_1=0.082$ and $R_2=0.084$ with 353 for which I>$3{\sigma}(I)$. Only about 28 of the 92 $Na^+$ ions per unit cell were reduced and only about 14 of the 28 $Na^0$ atoms produced were retained within the zeolite. A $Na_5{^{4+}}$ cluster is present within each sodalite cavity. It is a centered tetrahedron (like $CH_4$) with bond $length=2.80(2){\AA}$ and angle tetrahedral by symmetry, and shows the full symmetry of its site. $T_d$, at the center of the sodalite cavity. Each of the four terminal atoms of the $Na_5{^{4+}}$ cluster bond to three framework oxygens at $2.36(2){\AA}$. At the centers of some double 6-rings are sodium atoms which bridge linearly between $Na_5{^{4+}}$ clusters to form agglomerations such as short zig-zag chains $Na_5{^{4+}}$ clusters. Delocalized electrons, located primarily on the sodiums at centers of the sodalite and (likely) double-six-ring cavities, contribute to the stability of the clusters.

• Journal of the korean academy of Pediatric Dentistry
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• v.40 no.3
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• pp.209-215
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• 2013

Cleft lip and palate, the most common craniofacial anomalies, are severe congenital defects that have an incidence of 0.28 to 3.74 per 1000 live births. Although there has been great improvement in the field of cleft surgery, surgical approach cannot be the single solution to resolve the various problems encountered in patients with cleft lip and palate. The concept of presurgical infant orthopedics (PSIO) for gradual closure of the cleft gap and simplified surgical performance was first introduced by McNeil in 1950. Recently, there are many attempts not only to approximate the alveolar segments but also to reshape the nasal cartilage. Three infants with unilateral cleft lip and palate were referred from the department of Plastic Surgery for presurgical nasoalveolar molding (PNAM). Maxillary appliances using resin with orthodontic wire were fabricated. Then these appliance was applied until patients underwent lip surgery. In all cases, the patients could wear the appliance all day since they were able to eat even with the appliance on, This resulted in significant improvements in the nasal symmetry were found. Our appliance, namely K-NAM, extends the wearing time within the limited period and as a result it is expected to maximize the treatment effects. Used properly, this appliance would play a major role in enhancing nasal symmetry with satisfactory results.

• Bulletin of the Korean Chemical Society
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• v.15 no.1
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• pp.37-45
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• 1994

$(NH_4)_{4.5}[H_{3.5}{\alpha}-PtMo_6O_{24}]{\cdot}1.5\;H_2O(A),\;(NH_4)_4[H_4{\beta}-PtMo_6O_{24}]{\cdot}1.5\;H_2O(B),\;and\;K_{3.5}[H_{4.5}{\alpha}-PtMo_6O_{24}]{\cdot}3\;H_2O(C)$ have been synthesized and their molecular structures have been also determined by single-crystal X-ray diffraction technique. The space groups, unit cell parameters, and R factors are as follows: Compound A, monoclinic, $A_{2/a}$, a= 19.074 (3), b=21.490 (3), c=15.183 (2) ${\AA};\;{\beta}$=109.67 (1) ${\AA}$; z=8; R=0.075($IF_0I>4{\sigma}(IF_0I);$ Compound B, triclinic, P$bar{1}$, a=10.776 (2), b=15.174 (4), c=10.697 (3) ${\AA};\;{\alpha}$ =126.29 (2), ${\beta}$=111.55 (2), ${\gamma}$=93.18 (2) ${\AA}$; Z=2; R=0.046($IF_0I>3{\sigma}(IF_0I);$): Compound C, triclinic, Pl, a=12.426 (2), b=13.884 (2), c=10.089 (1) ${\AA}$; ${\alpha}$=102.59 (2), ${\beta}$=110.73 (1), ${\gamma}$=53.93 (1) ${\AA}$; Z=2; R=0.074 ($IF_0I>3{\sigma}(IF_0I)$. Compounds A and C contain the well-known Anderson structure (planar structure) heteropoly oxometalate having approximate $bar{3}_m(D_{3d})$ symmetry, while compound B contains the bent structure heteropoly oxometalate having appproximate $2_{mm}(C2_v)$ symmetry. The bent structure and the planar one are geometrical isomers. These compounds are rot only novel heteroply molybdates containing platinate(IV) but also the first example of geometrical isomerism in the hexamolybdoheteropoly oxometalates. That isomerization surprisingly occurred because of the change of only 0.5 non-acidic hydrogen atom attached to the polyanion such as $[H_{3.5}{\alpha} -PtMo_6O_{24}]^{4.5-}{\to}[H_4{\beta}-PtMo_6O_{24}]^{4-}{\to}[H_{4.5}{\alpha} -PtMo_6O_{24}]^{3.5-}$. It seems that the gradual protonation of the polyanion plays an important role in that isomerism. These heteropolyanions form dimers by strong hydrogen bonds between two heteropolyanions in the respective crystal system.

• Journal of Astronomy and Space Sciences
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• v.20 no.3
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• pp.205-216
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• 2003

The attitude motion of a spin-stabilized, upper-stage spacecraft is investigated based on a two-body model, consisting of a symmetric body, representing the spacecraft, and a spherical pendulum, representing the liquid slag pool entrapped in the aft section of the rocket motor. Exact time-varying nonlinear equations are derived and used to eliminate the drawbacks of conventional linear models. To study the stability of the spacecraft's attitude motion, both the spacecraft and pendulum are assumed to be in states of steady spin about the symmetry axis of the spacecraft and the coupled time-varying nonlinear equation of the pendulum is simplified. A quasi-stationary solution to that equation and approximate resonance conditions are determined in terms of the system parameters. The analysis shows that the pendulum is subject to a combination of parametric and external-type excitation by the main body and that energy from the excited pendulum is fed into the main body to develop the coning instability. In this paper, numerical examples are presented to explain the mechanism of the coning angle growth and how angular momenta and disturbance moments are generated.

• Geophysics and Geophysical Exploration
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• v.9 no.3
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• pp.241-249
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• 2006

Due to the long tectonic history and the very complex geologic formations in Korea, the anisotropic characteristics of subsurface material may often change very greatly and locally. The algorithms commonly used, however, may not give sufficiently precise computational results of traveltime data particularly for the complex and strong anisotropic model, since they are based on the two-dimensional (2D) earth and/or weak anisotropy assumptions. This study is intended to develope a three-dimensional (3D) modeling algorithm to precisely calculate the first arrival time in the complex anisotropic media. Considering the complex geology of Korea, we assume 3D TTI (tilted transversely isotropy) medium having the arbitrary symmetry axis. The algorithm includes the 2D non-linear interpolation scheme to calculate the traveltimes inside the grid and the 3D traveltime mapping to fill the 3D model with first arrival times. The weak anisotropy assumption, moreover, can be overcome through devising a numerical approach of the steepest descent method in the calculation of minimum traveltime, instead of using approximate solution. The performance of the algorithm developed in this study is demonstrated by the comparison of the analytic and numerical solutions for the homogeneous anisotropic earth as well as through the numerical experiment for the two layer model whose anisotropic properties are greatly different each other. We expect that the developed modeling algorithm can be used in the development of processing and inversion schemes of seismic data acquired in strongly anisotropic environment, such as migration, velocity analysis, cross-well tomography and so on.