• 충청수학회지
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• 제18권1호
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• pp.81-86
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• 2005

In this paper, we consider locally compact Hausdorff spaces having the closed unit interval of the real line as the remainder for an ESH-compactification and obtain that in the class of compact maps the extensions of homotopic maps on the respective ESH-compactifications remain homotopic under certain conditions.

• Korean Journal of Mathematics
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• 제29권3호
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• pp.493-499
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• 2021

Every closed subset of a compact topological space is compact. Also every compact subset of a Hausdorff topological space is closed. It follows that compact subsets are precisely the closed subsets in a compact Hausdorff space. It is also proved that a topological space is maximal compact if and only if its compact subsets are precisely the closed subsets. A locale is a categorical extension of topological spaces and a frame is an object in its opposite category. We investigate to find whether the closed sublocales are exactly the compact sublocales of a compact Hausdorff frame. We also try to investigate whether the closed sublocales are exactly the compact sublocales of a maximal compact frame.

• 대한수학회지
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• 제13권2호
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• pp.151-153
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• 1976

• 대한수학회논문집
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• 제10권2호
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• pp.357-363
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• 1995

We study non-existence of $L^2$-harmonic p-forms on a complete, non-compact Riemannian manifold without boundary as extension of results of K. Yano in the case of compact.

• 대한수학회지
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• 제41권6호
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• pp.1101-1114
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• 2004

We generalize a result of Dror Farjoun and Zabrodsky on the relationship between fixed point sets and homotopy fixed point sets, which is related to the generalized Sullivan Conjecture. As an application, we discuss extension problems considering actions on homogeneous spaces of p-compact groups.

• 대한수학회지
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• 제42권4호
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• pp.857-869
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• 2005

Let $(X,\;B,\;{\mu},\;T)$ be a dynamical system and (Y, A, v, S) be a factor. We investigate the relative sequence entropy of a partition of X via the maximal compact extension of (Y, A, v, S). We define relative sequence entropy pairs and using them, we find the relative topological ${\mu}-Kronecker$ factor over (Y, v) which is the maximal topological factor having relative discrete spectrum over (Y, v). We also describe the topological Kronecker factor which is the maximal factor having discrete spectrum for any invariant measure.

• 대한수학회보
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• 제41권3호
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• pp.457-464
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• 2004

Let X be a Banach space and Z a closed subspace of a Banach space Y. Denote by Ｌ(X, Y) the space of all bounded linear operators from X to Y and by Ｋ(X, Y) its subspace of compact linear operators. Using Hahn-Banach extension operators corresponding to ideal projections, we prove that if either $X^{**}$ or $Y^{*}$ has the Radon-Nikodym property and Ｋ(X, Y) is an M-ideal (resp. an HB-subspace) in Ｌ(X, Y), then Ｋ(X, Z) is also an M-ideal (resp. HB-subspace) in Ｌ(X, Z). If Ｌ(X, Y) has property SU instead of being an M-ideal in Ｌ(X, Y) in the above, then Ｋ(X, Z) also has property SU in Ｌ(X, Z). If X is a Banach space such that $X^{*}$ has the metric compact approximation property with adjoint operators, then M-ideal (resp. HB-subspace) property of Ｋ(X, Y) in Ｌ(X, Y) is inherited to Ｋ(X, Z) in Ｌ(X, Z).

• 대한수학회논문집
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• 제38권4호
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• pp.1127-1139
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• 2023

We investigate an extension of Schauder's theorem by studying the relationship between various s-numbers of an operator T and its adjoint T^*. We have three main results. First, we present a new proof that the approximation number of T and T^* are equal for compact operators. Second, for non-compact, bounded linear operators from X to Y, we obtain a relationship between certain s-numbers of T and T^* under natural conditions on X and Y . Lastly, for non-compact operators that are compact with respect to certain approximation schemes, we prove results for comparing the degree of compactness of T with that of its adjoint T^*.

• 대한수학회논문집
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• 제10권3호
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• pp.653-659
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• 1995

We prove that two essentially normal elements of a type $II_{\infty}$ factor von Neumann algebra are unitarily equivalent up to the compact ideal if and only if they have the identical essential spectrum and the same index data. Also we calculate the spectrum and essential spectrum of a non-unitary isometry of von Neumann algebra.

• Nuclear Engineering and Technology
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• 제19권3호
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• pp.169-179
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• 1987

소형시험편(1/2"T)을 이용, 균열진전량 및 J계산식에 따른 재료의 J-R (J-T) 곡선의 변화를 조사하여 신뢰성있는 J-R(J-T) 곡선을 구하기 위한 실험 및 해석방법을 고찰하였다. 시험은 국내 원자력발전소 압력용기감시 시험에 포함되어 있는 파괴인성시편과 꼭같이 SA 533 Grade 3, Class1 재료로 제작한 1/2"T, C-T 시편을 이용, Single Specimen Unloading Compliance Technique으로 수행하였다. 시험 및 해석결과 Ernst의 Deformation theory J (JD)식을 이용하여 초기 Uncracked ligament (be)의 25～30%까지 균열을 진전시켜 구한 J-R(J-T) 곡선이 대형시편의 결과와 가장 유사한 값을 나타내었다. 한편 Ernst의 Modified J (JM)식에 의한 J-R (J-T) 곡선은 Deformation theory J(JD)에 의한 J-R(J-T) 곡선보다 다소 높은 Instability 예측점을 얻을 수 있기 때문에 실제 압력용기 안전성 해석시에는 가동률향상 및 수명연장 측면에서 Modified J의 사용은 고려되어야 할 것이다.되어야 할 것이다.