• 충청수학회지
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• 제19권3호
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• pp.283-289
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• 2006

Roh[1] derived 2D g-Navier-Stokes equations from 3D Navier-Stokes equations. In this paper, we will see the space $L^2({\Omega},\;g)$, which is the weighted space of $L^2({\Omega})$, as natural generalized space of $L^2({\Omega})$ which is mathematical setting for Navier-Stokes equations. Our future purpose is to use the space $L^2({\Omega},\;g)$ as mathematical setting for the g-Navier-Stokes equations. In addition, we will see Helmoltz-Leray projection on $L^2_{per}({\Omega},\;g)$) and compare with the one on $L^2_{per}({\Omega})$.

• 대한수학회지
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• 제35권2호
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• pp.491-502
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• 1998

We obtain new fixed point theorems on maps defined on "locally G-convex" subsets of a generalized convex spaces. Our first theorem is a Schauder-Tychonoff type generalization of the Brouwer fixed point theorem for a G-convex space, and the second main result is a fixed point theorem for the Kakutani maps. Our results extend many known generalizations of the Brouwer theorem, and are based on the Knaster-Kuratowski-Mazurkiewicz theorem. From these results, we deduce new results on collectively fixed points, intersection theorems for sets with convex sections and quasi-equilibrium theorems.

• Journal of applied mathematics & informatics
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• 제7권3호
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• pp.1039-1044
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• 2000

We investigate the projectively flat warped product manifolds and study the geometric structure of the base space and its fibre. Specifically we find the conditions that the scalar curvature of the base space (B,g) vanishes if and only if f is harmonic on (B,g) and the fibre (F,$\bar{g}$) is a space of constant curvature.

• 천문학회보
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• 제31권1호
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• pp.23.2-23.2
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• 2006

• 천문학회보
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• 제42권2호
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• pp.56.4-57
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• 2017

The GMT-Consortium Large Earth Finder (G-CLEF) is the very first light instrument of the Giant Magellan Telescope (GMT) to be commissioned in 2022. The instrument is a fiber feed, optical band echelle spectrograph that is capable of extremely precise radial velocity measurement. Korea Astronomy and Space Science Institute (KASI) has been involved in the development of the G-CLEF as one member of the international consortium consisted of five astronomical institutes including Smithsonian Astrophysical Observatory (SAO), Observatories of the Carnegie Institution of Washington (OCIW). It is scheduled to have KASI side Critical Design Review in December 2017. In this presentation we will report the recent progress on the critical design activities for the G-CLEF Flexure Control Camera (FCC).

• 대한수학회지
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• 제45권3호
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• pp.781-794
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• 2008

Let $\mathbb{H}_g$ and $\mathbb{D}_g$ be the Siegel upper half plane and the generalized unit disk of degree g respectively. Let $\mathbb{C}^{(h,g)}$ be the Euclidean space of all $h{\times}g$ complex matrices. We present a partial Cayley transform of the Siegel-Jacobi disk $\mathbb{D}_g{\times}\mathbb{C}^{(h,g)}$ onto the Siegel-Jacobi space $\mathbb{H}_g{\times}\mathbb{C}^{(h,g)}$ which gives a partial bounded realization of $\mathbb{H}_g{\times}\mathbb{C}^{(h,g)}$ by $\mathbb{D}_g{\times}\mathbb{C}^{(h,g)}$. We prove that the natural actions of the Jacobi group on $\mathbb{D}_g{\times}\mathbb{C}^{(h,g)}$. and $\mathbb{H}_g{\times}\mathbb{C}^{(h,g)}$. are compatible via a partial Cayley transform. A partial Cayley transform plays an important role in computing differential operators on the Siegel Jacobi disk $\mathbb{D}_g{\times}\mathbb{C}^{(h,g)}$. invariant under the natural action of the Jacobi group $\mathbb{D}_g{\times}\mathbb{C}^{(h,g)}$ explicitly.

• 대한수학회지
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• 제57권6호
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• pp.1435-1449
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• 2020

In this article we make a local classification of n-dimensional Riemannian manifolds (M, g) with harmonic curvature and less than four Ricci eigenvalues which admit a smooth non constant solution f to the following equation $$(1)\hspace{20}{\nabla}df=f(r-{\frac{R}{n-1}}g)+x{\cdot} r+y(R)g,$$ where ∇ is the Levi-Civita connection of g, r is the Ricci tensor of g, x is a constant and y(R) a function of the scalar curvature R. Indeed, we showed that, in a neighborhood V of each point in some open dense subset of M, either (i) or (ii) below holds; (i) (V, g, f + x) is a static space and isometric to a domain in the Riemannian product of an Einstein manifold N and a static space (W, gW, f + x), where gW is a warped product metric of an interval and an Einstein manifold. (ii) (V, g) is isometric to a domain in the warped product of an interval and an Einstein manifold. For the proof we use eigenvalue analysis based on the Codazzi tensor properties of the Ricci tensor.

• 대한수학회지
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• 제54권1호
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• pp.117-139
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• 2017

This paper presents a systematic study for theoretical aspects of a unified approach to the abstract relative Fourier transforms over canonical homogeneous spaces of semi-direct product groups with Abelian normal factor. Let H be a locally compact group, K be a locally compact Abelian (LCA) group, and ${\theta}:H{\rightarrow}Aut(K)$ be a continuous homomorphism. Let $G_{\theta}=H{\ltimes}_{\theta}K$ be the semi-direct product of H and K with respect to ${\theta}$ and $G_{\theta}/H$ be the canonical homogeneous space (left coset space) of $G_{\theta}$. We introduce the notions of relative dual homogeneous space and also abstract relative Fourier transform over $G_{\theta}/H$. Then we study theoretical properties of this approach.

• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.569-585
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• 2022

A brief comparative survey of some generalizations of a metric space with three dimensional metric structures and different forms of the triangle inequality is done along with their topological properties. Then a common fixed point is obtained for reciprocally continuous and compatible self-maps in a G-metric space. Further, a common fixed point theorem is proved for a pair of weakly compatible self-maps on a G-metric space with the common limit range property.

• Journal of Astronomy and Space Sciences
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• 제37권1호
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• pp.43-50
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• 2020

We have developed an algorithm for tracking coronal mass ejection (CME) propagation that allows us to estimate CME speed and its arrival time at Earth. The algorithm may be used either to forecast the CME's arrival on the day of the forecast or to update the CME tracking information for the next day's forecast. In our case study, we successfully tracked CME propagation using the algorithm based on g-values of interplanetary scintillation (IPS) observation provided by the Institute for Space-Earth Environmental Research (ISEE). We were able to forecast the arrival time (Δt = 0.30 h) and speed (Δv = 20 km/s) of a CME event on October 2, 2000. From the CME-interplanetary CME (ICME) pairs provided by Cane & Richardson (2003), we selected 50 events to evaluate the algorithm's forecast capability. Average errors for arrival time and speed were 11.14 h and 310 km/s, respectively. Results demonstrated that g-values obtained continuously from any single station observation were able to be used as a proxy for CME speed. Therefore, our algorithm may give stable daily forecasts of CME position and speed during propagation in the region of 0.2-1 AU using the IPS g-values, even if IPS velocity observations are insufficient. We expect that this algorithm may be widely accepted for use in space weather forecasting in the near future.