• 충청수학회지
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• 제15권1호
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• pp.61-73
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• 2002

We consider the inverse shadowing property of a dynamical system which is an "inverse" form of the shadowing property of the system. In particular, we show that every Morse-Smale system f on a compact smooth manifold has the inverse shadowing property with respect to the class $\mathcal{T}_h(f)$ of continuous methods generated by homeomorphisms, but the system f does not have the inverse\mathrm{T} shadowing property with respect to the class $\mathcal{T}_c(f)$ of continuous methods.

• 대한수학회지
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• 제33권1호
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• pp.101-119
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• 1996

A complex $n(\geq 2)$-dimensional Kaehlerian manifold of constant holomorphic sectional curvature c is called a complex space form, which is denoted by $M_n(c)$.

• 대한수학회논문집
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• 제36권1호
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• pp.135-147
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• 2021

In this paper, we introduce the harmonicity of a covector field on a Riemannian manifold (M, g) to its cotangent bundle T∗ M equipped with g-natural metric. Afterward we also construct some examples of harmonic covector fields.

• Journal of Photoscience
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• 제6권2호
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• pp.61-65
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• 1999

The fluorescence properties and photoisomerization behavior of 1-(9-anthryl)-2-(n-quinolinyl)ethene (n-AQE, n=2-4) have been investigated in various solvents. t-3-AQE is strongly fluorescent, but does not accomplish photoisomerization, similar to parent hydrocarbon compound, t-1-(9-anthryl)-2-phenylethene (t-9-APE) or t-1-(9-anthryl)-2-(1-naphthyl)ethene (t-1-ANE). Fluorescence and photoisomerization oft-2-AQE and t-4-AQE are strongly affected by solvent polarity. Dependence of fluorescence quantum yield on the solvent polarity is moderate for t-2-AQE and large for t-4-AQE. In nonpolar solvent (in n-hexane), they exhibit relatively strong fluorescence, but do not isomerize to cis isomer on irradiation, even if inefficient isomerization is observed for t-4-AQE. However, as solvent polarity increases, their fluorescences become weak with efficient photoisomerization to corresponding cis isomer. Intramolecular charge-transfer excited state is presumed to contribute to photoisomerization. The S$_1$ decay parameters were found to be solvent-dependent due to the charge-transfer character of lowest S$_1$ state. In polar solvents, the activation barrier to twisting is reduced enhancing the isomerization of r-2-AQE and t-4-AQE in the singlet manifold.

• Elastomers and Composites
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• 제49권4호
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• pp.275-283
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• 2014

건축용 접착제로 활용되고 있는 부틸고무는 주로 시트의 형태로 사용된다. 본 연구에서는 컴퓨터 해석을 통해 부틸고무 시트 압출용 다이를 설계하였다. 압출용 다이의 내부는 크게 매니폴드와 랜드로 나뉜다. 매니폴드는 다이중앙에서 유입되는 재료가 폭 방향으로 흐름이 이루어 지도록 하는 역할을 한다. 랜드는 재료가 흐름 방향으로 균일하게 흐르게 하여 균일한 두께의 시트가 성형되도록 한다. 다이는 매니폴드와 랜드 외에도 아일랜드를 설치하여 흐름의 안정을 주도록 하는 경우가 많다. 본 연구에서는 컴퓨터 해석을 통하여 다이에서 매니폴드의 각도와 길이, 랜드 길이 그리고 아일랜드를 설계 변수로 하여 다이 출구에서 다이 폭 방향으로 균일한 흐름이 형성되도록 하는 최적의 다이형상을 연구하였다.

• 충청수학회지
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• 제28권1호
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• pp.65-72
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• 2015

The (affine) development of a smooth curve in a smooth manifold M with respect to an arbitrarily given affine connection in the bundle of affine frames over M is well known (cf. S.Kobayashi and K.Nomizu, Foundations of Differential Geometry, Vol.1). In this paper, we get the generalized affine development of a smooth curve $x_t$ ($t{\in}[0,1]$) in M into the affine tangent space at $x_0$ (${\in}M$) with respect to a given generalized affine connection in the bundle of affine frames over M.

• 대한수학회보
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• 제48권3호
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• pp.469-474
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• 2011

The Kauffman bracket skein module $K_t$(M) of a 3-manifold M becomes an algebra for t = -1. We prove that this algebra has no non-trivial nilpotent elements for M being the exterior of the twist knot in 3-sphere and, therefore, it is isomorphic to the $SL_2(\mathbb{C})$-character ring of the fundamental group of M. Our proof is based on some properties of Chebyshev polynomials.

• 대한수학회보
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• 제37권3호
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• pp.587-599
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• 2000

In this paper we study some nonpositively curved Riemannian manifolds acted on by a Lie group of isometries with principal orbits of codimension one. Among other results it is proved that if the universal covering manifold satisfies some conditions then every nonexceptional singular orbit is a totally geodesic submanifold. When M is flat and is not toruslike, it is proved that either each orbit is isometric to $R^k\timesT^m$or there is a singular orbit. If the singular orbit is unique and nonexceptional, then it is isometric to $R^k\timesT^m$.

• 충청수학회지
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• 제28권2호
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• pp.229-241
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• 2015

In this paper, we decompose the curvature tensor (field) on the homogeneous Riemannian manifold SU(3)=T (k, l) with an arbitrarily given SU(3)-invariant Riemannian metric into three curvature-like tensor fields, and investigate geometric properties.

• 대한수학회논문집
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• 제16권2호
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• pp.243-252
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• 2001

The purpose of this paper is to study some properties of n-dimensional recurrent space-like complex hypersurfaces in an (n+1)-dimensional semi-definite complex space form M(sub)0+t(sup)n+1 (c), t = 0 or 1, c$\neq$0.