• Communications for Statistical Applications and Methods
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• v.21 no.4
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• pp.317-325
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• 2014

Consider a nonlinear transform ${\Phi}(x)$ of x in $\mathbb{R}^p$ to Hilbert space H and assume that the dot product between ${\Phi}(x)$ and ${\Phi}(x^{\prime})$ in H is given by < ${\Phi}(x)$, ${\Phi}(x^{\prime})$ >= K(x, x'). The aim of this paper is to propose a mathematical technique to take screen shots of the multivariate dataset mapped to Hilbert space H, particularly suited to Gaussian kernel $K({\cdot},{\cdot})$, which is defined by $K(x,x^{\prime})={\exp}(-{\sigma}{\parallel}x-x^{\prime}{\parallel}^2)$, ${\sigma}$ > 0. Several numerical examples are given.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.131-140
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• 2014

In this paper we investigate (n+1)($n{\geq}3$)-dimensional contact CR-submanifolds M of (n-1) contact CR-dimension in a complete simply connected Sasakian space form of constant ${\phi}$-holomorphic sectional curvature $c{\neq}-3$ which satisfy the condition h(FX, Y)+h(X, FY) = 0 for any vector fields X, Y tangent to M, where h and F denote the second fundamental form and a skew-symmetric endomorphism (defined by (2.3)) acting on tangent space of M, respectively.

• The Bulletin of The Korean Astronomical Society
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• v.42 no.2
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• pp.89.1-89.1
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• 2017

In this poster, we present standard calibration processes and results for photometry of $H-{\alpha}$ filter using broadband filters. We took data from a night in stable weather condition. And we derived parameters for band pass calibration including color terms. The corrected photometry results from broadband filters like V and R filters showed high correlation enough to replace instrumental $H-{\alpha}$ magnitude. We plan to extend these standardizing processes to another narrowband filters and flux calibration of narrowband filters from photometry of PNe.

• Bulletin of the Korean Mathematical Society
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• v.34 no.4
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• pp.549-560
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• 1997

For positive integers $n_i \geq 2, i = 1, 2, 3, 4$, such that $\Sigma \frac{n_i}{1} < 2$, there exists a quadrilateral $P = P_1 P_2 P_3 P_4$ in the hyperbolic plane $H^2$ with the interior angle $\frac{n_i}{\pi}$ at $P_i$. Let $\Gamma \subset Isom(H^2)$ be the (discrete) group generated by reflections in each side of $P$. Then the quotient space $H^2/\gamma$ is a differentiable orbifold of type $(^* n_1 n_2 n_3 n_4)$. It will be shown that the deformation space of $Rp^2$-structures on this orbifold can be mapped continuously and bijectively onto the cell of dimension 4 - \left$\mid$ {i$\mid$n_i = 2} \right$\mid$$.

• Bulletin of the Korean Space Science Society
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• 2004.10b
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• pp.321-324
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• 2004

We used BV CCD images to study the dynamical substructures of three globular clusters - M5, NGC6934, NGC7006 - analyzing the radial variations of ellipticity and position angle from the point spread function stellar photometry and the ellipse surface photometry. Several populations were classified by the brightness on color-magnitude diagrams of each globular cluster. Ellipse analyses to the images, removed stars of each population from the original images of the clusters, show radial variations in ellipticity and position angle, with the amount of $0.01\~0.25$ in ellipticity and $+90\~-90$ degrees in position angle up to roughly three times of half light radius $(r_h)$. It is also apparent that there are no significant discrepancies in the dynamical substructures beyond $r_h$ among the different populations. However, dynamical substructures on the central region (i.e., inner than $\~r_h$) reflect the contributions of populations of bright red giant stars and horizontal branch stars.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.1131-1158
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• 2019

An ideal right-angled pentagon in hyperbolic 4-space ${\mathbb{H}}^4$ is a sequence of oriented geodesics ($L_1,{\ldots},L_5$) such that $L_i$ intersects $L_{i+1},i=1,{\ldots},4$, perpendicularly in ${\mathbb{H}}^4$ and the initial point of $L_1$ coincides with the endpoint of $L_5$ in the boundary at infinity ${\partial}{\mathbb{H}}^4$. We study the geometry of such pentagons and the various possible augmentations and prove identities for the associated quaternion half side lengths as well as other geometrically defined invariants of the configurations. As applications we look at two-generator groups ${\langle}A,B{\rangle}$ of isometries acting on hyperbolic 4-space such that A is parabolic, while B and AB are loxodromic.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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• pp.595-622
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• 2019

An ideal right-angled pentagon in hyperbolic 4-space ${\mathbb{H}}^4$ is a sequence of oriented geodesics ($L_1,{\ldots},L_5$) such that Li intersects $L_{i+1},\;i=1,\;{\ldots},\;4$, perpendicularly in ${\mathbb{H}}^4$ and the initial point of $L_1$ coincides with the endpoint of $L_5$ in the boundary at infinity ${\partial}{\mathbb{H}}^4$. We study the geometry of such pentagons and the various possible augmentations and prove identities for the associated quaternion half side lengths as well as other geometrically defined invariants of the configurations. As applications we look at two-generator groups ${\langle}A,B{\rangle}$ of isometries acting on hyperbolic 4-space such that A is parabolic, while B and AB are loxodromic.

• Bulletin of the Korean Space Science Society
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• 2000.04a
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• pp.50-50
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• 2000

No Abstract, See Full Text

• The Bulletin of The Korean Astronomical Society
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• v.42 no.1
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• pp.39.3-39.3
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• 2017

To see scientific potential of MIRIS Paschen-${\alpha}$ ($Pa{\alpha}$) Galactic Plane Survey (MIPAPS), we have selected a portion, Galactic longitude from $+96^{\circ}$ to $116^{\circ}$, and inspected $Pa{\alpha}$ detections for 212 sources in WISE H II region catalog. We also list up $35Pa{\alpha}$ large features and $32Pa{\alpha}$ point-like blobs, which have not been cataloged in WISE catalog. For all the sources, we have performed the photometry of $Pa{\alpha}$ emission line, and obtained their $Pa{\alpha}$ intensities and $Pa{\alpha}$ fluxes. For the quantitative comparison, we also make the $H{\alpha}$ mosaic image of the same region by using IPHAS data which have been globally calibrated and released recently. Comparing MIPAPS $Pa{\alpha}$ fluxes with the IPHAS $H{\alpha}$ fluxes enables us to estimate dust extinction and spectral types of ionizing sources. We present the results for some sources.

• Bulletin of the Korean Space Science Society
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• 2008.10a
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• pp.33.2-33.2
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• 2008

Korea Astronomy and Space Science Institute (KASI) is developing an empirical model for Korean Space Weather Prediction Center (KSWPC). This model predicts the geomagnetic storm strength (Dst minimum) by using only CME parameters, such as the source location (L), speed (V), earthward direction (D), and magnetic field orientation of an overlaying potential field at CME source region. To derive an empirical formula, we considered that (1) the direction parameter has best correlation with the storm strength (2) west $15^{\circ}$ offset from the central meridian gives best correlation between the source location and the storm strength (3) consideration of two groups of CMEs according to their magnetic field orientation (southward or northward) provide better forecast. In this talk, we introduce current status of the empirical storm prediction model development.