• 대한수학회논문집
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• 제32권4호
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• pp.875-883
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• 2017

In this work, we establish Heisenberg-type uncertainty principle for the Bessel-Struve Fock space ${\mathbb{F}}_{\nu}$ associated to the Airy operator $L_{\nu}$. Next, we give an application of the theory of extremal function and reproducing kernel of Hilbert space, to establish the extremal function associated to a bounded linear operator $T:{\mathbb{F}}_{\nu}{\rightarrow}H$, where H be a Hilbert space. Furthermore, we come up with some results regarding the extremal functions, when T are difference operators.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.461-468
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• 2004

Let W(z) be a power series with operator coefficients such that multiplication by W(z) is contractive in C(z). The overlapping space $L(\varphi)$ of H(W) in C(z) is a Herglotz space with Herglotz function $\varphi(z)$ which satisfies $\varphi(z)+\varphi^＊(z^{-1})=2[1-W^{*}(z^{-1})W(z)]$. The identity ${}_{L(\varphi)}={-}_{H(W)}$ holds for every f(z) in $L(\varphi)$ and for every vector c.

• 호남수학학술지
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• 제38권3호
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• pp.593-611
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• 2016

This paper is concerned with the classifications of quadric surfaces of first and second kinds in Euclidean 3-space satisfying the Jacobi condition with respect to their curvatures, the Gaussian curvature K, the mean curvature H, second mean curvature $H_{II}$ and second Gaussian curvature $K_{II}$. Also, we study the zero and non-zero constant curvatures of these surfaces. Furthermore, we investigated the (A, B)-Weingarten, (A, B)-linear Weingarten as well as some special ($C^2$, K) and $(C^2,\;K{\sqrt{K}})$-nonlinear Weingarten quadric surfaces in $E^3$, where $A{\neq}B$, A, $B{\in}{K,H,H_{II},K_{II}}$ and $C{\in}{H,H_{II},K_{II}}$. Finally, some important new lemmas are presented.

• Korean Journal of Mathematics
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• 제27권3호
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• pp.735-741
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• 2019

Let ${\mathcal{H}}$ be a complex Hilbert space and ${\mathcal{B}}({\mathcal{H}})$ the algebra of all bounded linear operators on ${\mathcal{H}}$. In this paper, we prove that if ${\varphi}:{\mathcal{B}}({\mathcal{H}}){\rightarrow}{\mathcal{B}}({\mathcal{H}})$ is a unital surjective bounded linear map, which preserves m- isometries m = 1, 2 in both directions, then there are unitary operators $U,V{\in}{\mathcal{B}}({\mathcal{H}})$ such that ${\varphi}(T)=UTV$ or ${\varphi}(T)=UT^{tr}V$ for all $T{\in}{\mathcal{B}}({\mathcal{H}})$, where $T^{tr}$ is the transpose of T with respect to an arbitrary but fixed orthonormal basis of ${\mathcal{H}}$.

• 천문학회지
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• 제50권5호
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• pp.139-149
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• 2017

The Korea Astronomy and Space Science Institute plans to develop a coronagraph in collaboration with National Aeronautics and Space Administration (NASA) and to install it on the International Space Station (ISS). The coronagraph is an externally occulted one-stage coronagraph with a field of view from 3 to 15 solar radii. The observation wavelength is approximately 400 nm, where strong Fraunhofer absorption lines from the photosphere experience thermal broadening and Doppler shift through scattering by coronal electrons. Photometric filter observations around this band enable the estimation of 2D electron temperature and electron velocity distribution in the corona. Together with a high time cadence (<12 min) of corona images used to determine the geometric and kinematic parameters of coronal mass ejections, the coronagraph will yield the spatial distribution of electron density by measuring the polarized brightness. For the purpose of technical demonstration, we intend to observe the total solar eclipse in August 2017 with the filter system and to perform a stratospheric balloon experiment in 2019 with the engineering model of the coronagraph. The coronagraph is planned to be installed on the ISS in 2021 for addressing a number of questions (e.g., coronal heating and solar wind acceleration) that are both fundamental and practically important in the physics of the solar corona and of the heliosphere.

• 천문학회보
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• 제35권1호
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• pp.69.1-69.1
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• 2010

IC 443 is famous for its interaction with nearby molecular clouds and intense H2 emission lines in infrared. Therefore, it has been studied extensively for the understanding of molecular shocks. We observed H2 mission lines toward the shock-cloud interaction regions of IC 443, known as clumps B, C, and G. The observations were performed with the InfraRed Camera (IRC) onboard a satellite AKARI over 2.5-5.0 um, where previous space observations, e.g. Infrared Space Observatory (ISO) and Spitzer, do not cover. Our AKARI observations provide spectra of sequential pure-rotational and ro-vibrational H2 emission lines. For the clumps C and G, combining with previous mid-infrared observational results, we found that the H2 level populations show a significant separation between v=0 and v=1 levels; v=1 levels are under-populated than v=0 levels, therefore, the population cannot be described by two temperature LTE model, as many people have analyzed for the shocked H2 gas. We also applied the thermal admixture model, dN(H2; T)~T^(-b) dT, with varying ortho-to-para ratios according to the temperature, to describe the level population, and obtained plausible ranges of the H2 gas density and power-law index b.

• Journal of Astronomy and Space Sciences
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• 제29권4호
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• pp.329-336
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• 2012

Korea Astronomy and Space Science Institute researchers have installed and operated magnetometers at Bohyunsan Observatory to measure the Earth's magnetic field variations in South Korea. In 2007, we installed a fluxgate magnetometer (RFP-523C) to measure H, D, and Z components of the geomagnetic field. In addition, in 2009, we installed a Overhauser proton sensor to measure the absolute total magnetic field F and a three-axis magneto-impedance sensor for spectrum analysis. Currently three types of magnetometer data have been accumulated. In this paper, we use the H, D, Z components of fluxgate magnetometer data to investigate the characteristics of mid-latitude geomagnetic field variation. To remove the temporary changes in Earth's geomagnetic filed by space weather, we use the international quiet days' data only. In other words, we performed a superposed epoch analysis using five days per each month during 2008-2011. We find that daily variations of H, D, and Z shows similar tendency compared to previous results using all days. That is, H, D, Z all three components' quiet intervals terminate near the sunrise and shows maximum 2-3 hours after the culmination and the quiet interval start from near the sunset. Seasonal variations show similar dependences to the Sun. As it becomes hot season, the geomagnetic field variation's amplitude becomes large and the quiet interval becomes shortened. It is well-known that these variations are effects of Sq current system in the Earth's atmosphere. We confirm that the typical mid-latitude geomagnetic field variations due to the Sq current system by excluding all possible association with the space weather.

• 대한수학회보
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• 제61권2호
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• pp.401-419
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• 2024

Let K, H, K_II and H_II be the Gaussian curvature, the mean curvature, the second Gaussian curvature and the second mean curvature of a timelike tubular surface T_γ(α) with the radius γ along a timelike curve α(s) in Minkowski 3-space E³₁. We prove that T_γ(α) must be a (K, H)-Weingarten surface and a (K, H)-linear Weingarten surface. We also show that T_γ(α) is (X, Y)-Weingarten type if and only if its central curve is a circle or a helix, where (X, Y) ∈ {(K, K_II), (K, H_II), (H, K_II), (H, H_II), (K_II , H_II)}. Furthermore, we prove that there exist no timelike tubular surfaces of (X, Y)-linear Weingarten type, (X, Y, Z)-linear Weingarten type and (K, H, K_II, H_II)-linear Weingarten type along a timelike curve in E³₁, where (X, Y, Z) ∈ {(K, H, K_II), (K, H, H_II), (K, K_II, H_II), (H, K_II, H_II)}.

• 대한수학회보
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• 제38권4호
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• pp.719-725
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• 2001

For a p-compact group G, if G-space X is of finite S-type then we show that the localization $S^{-1}H^*(X_{hG})$is zero. By using this result, we prove the localization theorem for the pair G-space (X, A)

• 대한수학회지
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• 제55권1호
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• pp.59-71
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• 2018

In the present paper, we study and classify factorable surfaces in a 3-dimensional isotropic space with constant isotropic Gaussian (K) and mean curvature (H). We provide a non-existence result relating to such surfaces satisfying ${\frac{H}{K}}=const$. Several examples are also illustrated.