• 대한수학회지
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• 제38권1호
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• pp.135-146
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• 2001

Let M(sup)n be a space-ike submanifold in a de Sitter space M(sub)p(sup)n+p (c) with constant scalar curvature. We firstly extend Cheng-Yau's Technique to higher codimensional cases. Then we study the rigidity problem for M(sup)n with parallel normalized mean curvature vector field.

• 대한수학회지
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• 제31권3호
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• pp.393-400
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• 1994

Subminifolds of Euclidean spaces have been studied by examining geodesics of the submanifolds viewed as curves of the ambient Euclidean spaces ([3], [7], [8], [9]). K.Sakamoto ([7]) studied submanifolds of Euclidean space whose geodesics are plane curves, which were called submanifolds with planar geodesics. And he completely calssified such submanifolds as either Blaschke manifolds or totally geodesic submanifolds. We now ask the following: If there is a point p of the given submanifold in Euclidean space such that every geodesic of the submanifold passing through p is a plane curve, how much can we say about the submanifold\ulcorner In the present paper, we study submanifolds of euclicean space with such property.

• 대한수학회보
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• 제26권1호
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• pp.75-82
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• 1989

It is recently proved by Aiyama and the authors [2] that a complete space-like complex submanifold of a complex space form $M^{n+p}$$_{p}$ (c') (c'.geq.0) is to totally geodesic. This is a complex version of the Bernstein-type theorem in the Minkowski space due to Calabi [4] and Cheng and Yau [5], which is generalized by Nishikawa[7] in the Lorentz manifold satisfying the strong energy condition. The purpose of this paper is to consider his result in the complex Lorentz manifold and is to prove the following.e following.

• 충청수학회지
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• 제23권3호
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• pp.453-461
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• 2010

We first introduce a space of homogeneous type X, and develop the theory of the tent spaces on the generalized upper half-space $X{\times}(0,{\infty})$. The goal of this paper is to study that every element of the tent spaces $T_{\Omega}^{p}$($X{\times}(0,{\infty})$, $0, can be decomposed into elementary particles which are called "atoms."

• Journal of the Korean Statistical Society
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• 제10권
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• pp.83-90
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• 1981

Let (X, A) be a measurable space, i.e. X is a non-empty set and A is a $\sigma$-field of subsets of X. Let $\Omega$ be a parameter space and P be a family of probability measures $P_\theta, \theta \in \Omega$ defined on (X, A).

• Kyungpook Mathematical Journal
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• 제28권1호
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• pp.63-69
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• 1988

In this paper we define the athwart immersions with codimension p⩾2 into Euclidean space. Some results supported by geometric examples have been established. A comparison study has been carried out throughout the paper.

• Bulletin of the Korean Chemical Society
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• 제21권7호
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• pp.720-726
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• 2000

The analytic gradient method for the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) energy has been extended to employ a reduced molecular orbital (MO) space. Not only the innermost core MOs but also some of the outermost virtua l MOs can be dropped in the reduced MO space, and a substantial amount of computation time can be reduced without deteriorating the results. In order to study the magnitudes and trends of the effects of the dropped MOs, the geometries and vibrational properties of the ground and excited states of BF, CO, CN, N2, AlCl, SiS, P2, BCl, AIF, CS, SiO, PN and GeSe are calculated with different sizes of molecular orbital space. The 6-31 G* and the aug-cc-pVTZ basis sets are employed for all molecules except GeSc for which the 6-311 G* and the TZV+f basis sets are used. It is shown that the magnitudes of the drop-MO effects are about $0.005\AA$ in bond lengths and about 1% on harmonic frequencies and IR intensities provided that the dropped MOs correspond to (1s), (1s,2s,2p), an (1s,2s,2p,3s,3p) atomic orbitals of the first, the second, and the third row atoms, respectively. The geometries and vibrational properties of the first and the second excited states of HCN and HNC are calculated by using a drastically reduced virtual MO space as well as with the well defined frozen core MO space. The results suggest the possibility of using a very smalI MO space for qualitative study of valence excited states.

• Journal of Astronomy and Space Sciences
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• 제30권2호
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• pp.95-100
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• 2013

In this paper we examine a total of 16 dipolarization events that were observed by THEMIS spacecraft in space close to geosynchronous orbit, r < ${\sim}7\;R_E$. For the identified events, we examine the characteristics of the plasma flows and associated bubbles as defined based on $pV^{5/3}$, where p is the plasma pressure and V the volume of unit magnetic flux. First, we find that the flow speed in the near-geosynchronous region is very low, mostly within a few tens of km/s, except for a very few events for which the flow can rise up to ~200 km/s but only very near the dipolarization onset time. Second, the bubble parameter, $pV^{5/3}$, decreases by a much smaller factor after the dipolarization onset than for the events in the farther out tail region. We suggest that the magnetic dipolarization in the near-geosynchronous region generates or is associated with only very weak plasma bubbles. Such bubbles in the near-geosynchronous region would penetrate earthward only by a small distance before they stop at an equilibrium position or drift around the Earth.

• 천문학회보
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• 제35권2호
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• pp.27.2-27.2
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• 2010

We report the HST pixel analysis results of the interacting face-on spiral galaxy, NGC 5194 (M51), which is the first step of a new observational research project, PANCluG (Pixel Analysis of Nearby Cluster Galaxies). We derive several quantities describing the pixel color-magnitude diagram (pCMD) of NGC 5194, suitable for future comparisons with the pCMDs of other galaxies. We investigate the spatial distribution of pixel stellar populations, finding that the spiral arm pattern and the tidal interaction with NGC 5195 significantly affect the stellar populations in NGC 5194. We find that the pixels corresponding to the central active galactic nucleus (AGN) of NGC 5194 show a very tight sequence in the bright-end of the pCMD, of which spatial distribution seems to agree with the AGN torus region.

• 대한수학회보
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• 제59권6호
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• pp.1471-1493
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• 2022

The goal of this paper is to establish the boundedness of bilinear Calderón-Zygmund operator BT and its commutator [b₁, b₂, BT] which is generated by b₁, b₂ ∈ BMO(ℝⁿ) (or ${\dot{\Lambda}}_{\alpha}$(ℝⁿ)) and the BT on generalized variable exponent Morrey spaces 𝓛^p(·),𝜑(ℝⁿ). Under assumption that the functions 𝜑₁ and 𝜑₂ satisfy certain conditions, the authors proved that the BT is bounded from product of spaces 𝓛^{p₁(·),𝜑₁}(ℝⁿ)×𝓛^{p₂(·),𝜑₂}(ℝⁿ) into space 𝓛^p(·),𝜑(ℝⁿ). Furthermore, the boundedness of commutator [b₁, b₂, BT] on spaces L^p(·)(ℝⁿ) and on spaces 𝓛^p(·),𝜑(ℝⁿ) is also established.