• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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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.

• Journal of the Korean Mathematical Society
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• v.60 no.6
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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.

• Transactions of the Korean hydrogen and new energy society
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• v.2 no.1
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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.