• 대한수학회보
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• 제54권1호
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• pp.85-97
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• 2017

We classify Kenmotsu 3-manifolds and cosymplectic 3-manifolds with ${\eta}-parallel$ Ricci operator.

• 대한수학회보
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• 제55권4호
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• pp.1013-1022
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• 2018

In this paper, we give a local and global classification of 3-dimensional H-contact manifolds whose Ricci tensor is ${\eta}$-parallel.

• 대한수학회지
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• 제60권6호
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• pp.1303-1336
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• 2023

In this paper, we study the 𝜂-parallelism of the Ricci operator of almost Kenmotsu 3-manifolds. First, we prove that an almost Kenmotsu 3-manifold M satisfying ∇_𝜉h = -2𝛼h𝜑 for some constant 𝛼 has dominantly 𝜂-parallel Ricci operator if and only if it is locally symmetric. Next, we show that if M is an H-almost Kenmotsu 3-manifold satisfying ∇_𝜉h = -2𝛼h𝜑 for a constant 𝛼, then M is a Kenmotsu 3-manifold or it is locally isomorphic to certain non-unimodular Lie group equipped with a left invariant almost Kenmotsu structure. The dominantly 𝜂-parallelism of the Ricci operator is equivalent to the local symmetry on homogeneous almost Kenmotsu 3-manifolds.

• 한국수소및신에너지학회논문집
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• 제2권1호
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• pp.47-56
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• 1990

Pure titanium rods were oxidized by anodic oxidation, furnace oxidation and flame oxidation and used as a electrode in the photodecomposition of water. The maximum photoelectrochemical conversion efficiency(${\eta}$) was found for flame oxidized electrode ($1200^{\circ}C$ for 2 min in air), 0.8 %. Anodically oxidized electrodes have minimum photoelectrochemical conversion efficiencies, 0.3 %. Furnace oxidized electrode ($800^{\circ}C$ for 10min in air) has 0.5% phtoelectrochemical efficiency and shows a band-gap energy of about 2.9eV. The efficiency shows a parallelism with the presence of the metallic interstitial compound $TiO_{O+X}$(X < 0.33) at the metal-semiconductor interface, the thickness of the sub oxide layer and that of the external rutile scale.