• The Pure and Applied Mathematics
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• v.19 no.3
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• pp.229-237
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• 2012

In this article, we study generalized slant cylindrical surfaces (GSCS's) with pointwise 1-type Gauss map of the first and second kinds. Our main results state that the right circular cones are the only rational kind GSCS's with pointwise 1-type Gauss map of the second kind.

• The korean journal of orthodontics
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• v.18 no.1 s.25
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• pp.165-173
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• 1988

The purpose of this study was to investigate and evaluate what proportion is the characteristics in Korean dental arches with normal occlusion. Many others have already indicated Golden proportion in normal dental arches, but have not considered any racial and sociocultural differences. So the author postulated $(\sqrt{2})^n$ relations in Koreans. The materials were consisted of 134 dental casts with normal occlusion, which have never undergone orthodontic and prosthodontic procedures. Measurements were made on the arch dimensions using sliding caliper and data were computerized. The findings were as follows: 1. The width between the distal surfaces of the upper centrals, had $(\sqrt{2})^3$ relation with the width between the buccal surfaces of the upper 1 st premolars in Koreans. 2. The width between the distal surfaces of the lower laterals had $(\sqrt{2})$ relation with the width between the distal surfaces of the lower canines, and had $(\sqrt{2})^2$ relation with the distal surfaces of the upper centrals. 3. The width between the distal surfaces of the lower centrals had $(\sqrt{2})^2$ relation with the width between the distal surfaces of the lower laterals, and had $(\sqrt{2})^3$ relation with the width between the distal surfaces of the upper centrals.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.447-455
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• 2005

In this article, we introduce the notion of pointwise 1-type Gauss map of the first and second kinds and study surfaces of revolution with such Gauss map. Our main results state that surfaces of revolution with pointwise 1-type Gauss map of the first kind coincide with surfaces of revolution with constant mean curvature; and the right cones are the only rational surfaces of revolution with pointwise 1-type Gauss map of the second kind.

• Bulletin of the Korean Chemical Society
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• v.31 no.1
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• pp.104-111
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• 2010

The heterogeneous electron transfer at $SiMo_{12}O_{40}^{4-}$ monolayers on GC, HOPG, and Au electrode surfaces are investigated using cyclic voltammetric and electrochemical impedance spectroscopic (EIS) methods. The electron transfer of negatively charged $Fe(CN)_6^{3-}$ species is retarded at $SiMo_{12}O_{40}^{4-}$-modified electrode surfaces, while that of positively charged $Ru(NH_3)_6^{3+}$species is accelerated at the modified surfaces. This is due to the electrostatic interactions between $SiMo_{12}O_{40}^{4-}$ layers on surfaces and charged redox species. The electron transfer kinetics of a neutral redox species, 1,1‘-ferrocenedimethanol (FDM), is not affected by the modification of electrode surfaces with $SiMo_{12}O_{40}^{4-}$, indicating the $SiMo_{12}O_{40}^{4-}$ monolayers do not impart barriers to electron transfer of neutral redox species. This is different from the case of thiolate SAMs which always add barriers to electron transfer. The effect of $SiMo_{12}O_{40}^{4-}$ layers on the electron transfer of charged redox species is dependent on the kind of electrodes, where HOPG surfaces exhibit marked effects. Possible mechanisms responsible for different electron transfer behaviors at $SiMo_{12}O_{40}^{4-}$ layers are proposed.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.999-1013
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• 2017

In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized tractrices in Euclidean (n + 1)-space $\mathbb{E}^{n+1}$. Further, we introduce some kind of generalized rotational surfaces in Euclidean spaces $\mathbb{E}^3$ and $\mathbb{E}^4$, respectively. We have also obtained some basic properties of generalized rotational surfaces in $\mathbb{E}^4$ and some results of their curvatures. Finally, we give some examples of generalized Beltrami surfaces in $\mathbb{E}^3$ and $\mathbb{E}^4$, respectively.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1329-1343
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• 2013

In this paper, we define translation surfaces in the 3-dimensional Heisenberg group $\mathcal{H}_3$ obtained as a product of two planar curves lying in planes, which are not orthogonal, and study minimal translation surfaces in $\mathcal{H}_3$.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.377-394
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• 2015

In this paper, we generalize some results about Bertrand curves and Razzaboni surfaces in Euclidean 3-space to the case that the ambient space is Minkowski 3-space. Our discussion is divided into three different cases, i.e., the parent Bertrand curve being timelike, spacelike with timelike principal normal, and spacelike with spacelike principal normal. For each case, first we show that Razzaboni surfaces and their mates are related by a reciprocal transformation; then we give B$\ddot{a}$cklund transformations for Bertrand curves and for Razzaboni surfaces; finally we prove that the reciprocal and B$\ddot{a}$cklund transformations on Razzaboni surfaces commute.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.935-949
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• 2013

In this paper, we study surfaces in $\mathb{E}^3$ whose Gauss map G satisfies the equation ${\Box}G=f(G+C)$ for a smooth function $f$ and a constant vector C, where ${\Box}$ stands for the Cheng-Yau operator. We focus on surfaces with constant Gaussian curvature, constant mean curvature and constant principal curvature with such a property. We obtain some classification and characterization theorems for these kinds of surfaces. Finally, we give a characterization of surfaces whose Gauss map G satisfies the equation ${\Box}G={\lambda}(G+C)$ for a constant ${\lambda}$ and a constant vector C.

• The Journal of Advanced Prosthodontics
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• v.8 no.3
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• pp.235-240
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• 2016

PURPOSE. In this study, the aim of this study was to evaluate the effect of implant surface treatment on cell differentiation of osteoblast cells. For this purpose, three surfaces were compared: (1) a modified SLA (MSLA: sand-blasted with large grit, acid-etched, and immersed in 0.9% NaCl), (2) a laser treatment (LT: laser treatment) titanium surface and (3) a laser and acid-treated (LAT: laser treatment, acid-etched) titanium surface. MATERIALS AND METHODS. The MSLA surfaces were considered as the control group, and LT and LAT surfaces as test groups. Alkaline phosphatase expression (ALP) was used to quantify osteoblastic differentiation of MC3T3-E1 cell. Surface roughness was evaluated by a contact profilometer (URFPAK-SV; Mitutoyo, Kawasaki, Japan) and characterized by two parameters: mean roughness (Ra) and maximum peak-to-valley height (Rt). RESULTS. Scanning electron microscope revealed that MSLA (control group) surface was not as rough as LT, LAT surface (test groups). Alkaline phosphatase expression, the measure of osteoblastic differentiation, and total ALP expression by surface-adherent cells were found to be highest at 21 days for all three surfaces tested (P<.05). Furthermore, ALP expression levels of MSLA and LAT surfaces were significantly higher than expression levels of LT surface-adherent cells at 7, 14, and 21 days, respectively (P<.05). However, ALP expression levels between MSLA and LAT surface were equal at 7, 14, and 21 days (P>.05). CONCLUSION. This study suggested that MSLA and LAT surfaces exhibited more favorable environment for osteoblast differentiation when compared with LT surface, the results that are important for implant surface modification studies.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1033-1050
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• 2013

We show the existence of smooth isolated curves of different degrees and genera in Calabi-Yau threefolds that are complete intersections in homogeneous spaces. Along the way, we classify all degrees and genera of smooth curves on BN general K3 surfaces of genus ${\mu}$, where $5{\leq}{\mu}{\leq}10$. By results of Mukai, these are the K3 surfaces that can be realised as complete intersections in certain homogeneous spaces.