• 대한수학회보
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• 제44권4호
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• pp.795-806
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• 2007

We investigate F-traceless component of the conformal curvature tensor defined by (3.6) in $K\ddot{a}hler$ manifolds of dimension ${\geq}4$, and show that the F-traceless component is invariant under concircular change. In particular, we determine $K\ddot{a}hler$ manifolds with parallel F-traceless component and improve some theorems, provided in the previous paper([2]), which are concerned with the traceless component of the conformal curvature tensor and the spectrum of the Laplacian acting on $p(0{\leq}p{\leq}2)$-forms on the manifold by using the F-traceless component.

• 대한수학회지
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• 제61권2호
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• pp.255-277
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• 2024

In this paper, we introduce the notion of stress-energy tensor Q of the traceless Ricci tensor for Riemannian manifolds (Mⁿ, g), and investigate harmonicity of Riemannian curvature tensor and Weyl curvature tensor when (M, g) satisfies some geometric structure such as critical point equation or vacuum static equation for smooth functions.

• Bulletin of the Korean Chemical Society
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• 제32권10호
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• pp.3655-3659
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• 2011

The hydrogenolysis of polymer-bound arenesulfonates by 2-propylmagnesium chloride was performed through reductive cleavage of the C-S bond in the presence of a nickel catalyst. The reaction underwent in the highest efficiency by adding 15 equiv of the nucleophile in two additions with $dppfNiCl_2$ in THF. Various unfunctionalized naphthalene, biphenyl, and stilbene derivatives were produced in good yields by the traceless sulfonate linker system at room temperature.

• Archives of Pharmacal Research
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• 제27권4호
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• pp.371-375
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• 2004

The silicon linker is the foremost traceless linker used in solid-phase reactions. Hydrogen fluo-ride (HF) or trifluoroacetic aicd (TFA) can remove the silicon linker with the silicon atom being replaced by a hydrogen atom. In this experiment, the linkers 1c and 2d, which are the most useful in solid-phase reactions, were synthesized, Linker 1c is composed of seven linearly linked carbons and linker 2d includes an oxygen atom in the linear carbon chain to increase the solvation capacity. The carboxylic acid component of linker 1c and 2d forms an amide or ester bond with resin. The synthesized linkers 1c and 2d could be utilized in constructing a chemical compound library that includes indole, benzodiazepine and phenothiazine (aromatic ring compounds).

• Bulletin of the Korean Chemical Society
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• 제31권9호
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• pp.2459-2466
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• 2010

Unfunctionalized biaryl compounds were parallelly and combinatorially prepared by the traceless hydrogenolysis of biarylsulfonates supported on pentaerythritol. The hydrogenolysis using 2-propylmagnesium chloride in the presence of $dppfNiCl_2$ efficiently generated corresponding biaryl derivatives without any memory of the support. The strategy using pentaerythritol as a small soluble support was disclosed to have a potential to combine the benefits of both SPOS and solution-phase reaction with fast reaction rate, facile isolation of intermediates, easy analysis of intermediates and atom economical manner. The novel tetrapodal support is expected to be an efficient substitute for polymeric supports in many circumstances.

• 대한수학회보
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• 제56권5호
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• pp.1341-1353
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• 2019

For complete Riemannian manifolds with vanishing Bach tensor and positive constant scalar curvature, we provide a rigidity theorem characterized by some pointwise inequalities. Furthermore, we prove some rigidity results under an inequality involving $L^{\frac{n}{2}}$-norm of the Weyl curvature, the traceless Ricci curvature and the Sobolev constant.

• 대한수학회보
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• 제61권1호
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• pp.281-290
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• 2024

We consider the total scalar curvature functional, and show that if the second variation in the transverse traceless tensor direction is negative, then the metric is Einstein. We also find the relation between the second variation and the Lichnerowicz Laplacian.

• 대한수학회논문집
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• 제29권1호
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• pp.141-153
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• 2014

In this article, we apply the weak maximum principle in order to obtain a suitable characterization of the complete linearWeingarten hypersurfaces immersed in locally symmetric Riemannian manifold $N^{n+1}$. Under the assumption that the mean curvature attains its maximum and supposing an appropriated restriction on the norm of the traceless part of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or hypersurface is an isoparametric hypersurface with two distinct principal curvatures one of which is simple.

• 대한수학회보
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• 제57권6호
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• pp.1367-1382
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• 2020

We study rigidity results for the Einstein metrics as the critical points of a family of known quadratic curvature functionals involving the scalar curvature, the Ricci curvature and the Riemannian curvature tensor, characterized by some pointwise inequalities involving the Weyl curvature and the traceless Ricci curvature. Moreover, we also provide a few rigidity results for locally conformally flat critical metrics.

• 대한수학회지
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• 제58권2호
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• pp.401-418
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• 2021

For complete manifolds with α-Bach tensor (which is defined by (1.2)) flat, we provide some rigidity results characterized by some point-wise inequalities involving the Weyl curvature and the traceless Ricci curvature. Moveover, some Einstein metrics have also been characterized by some $L^{\frac{n}{2}}$-integral inequalities. Furthermore, we also give some rigidity characterizations for constant sectional curvature.