• Journal of the Korean Mathematical Society
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• v.41 no.6
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• pp.1007-1021
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• 2004

In this paper, we study rotation surfaces in the Minkowski 3-dimensional space with pointwise 1-type Gauss map and obtain by the use of the concept of pointwise finite type Gauss map, a characterization theorem concerning rotation surfaces and constancy of the mean curvature of certain open subsets on these surfaces.

• Journal of the Korean Mathematical Society
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• v.41 no.2
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• pp.379-396
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• 2004

In this article, we study rotation surfaces in the 4-dimensional pseudo-Euclidean space E$_2$$^4$. Also, we obtain the complete classification theorems for the flat rotation surfaces with finite type Gauss map, pointwise 1-type Gauss map and an equation in terms of the mean curvature vector. In fact, we characterize the flat rotation surfaces of finite type immersion with the Gauss map and the mean curvature vector field, namely the Gauss map of finite type, pointwise 1-type Gauss map and some algebraic equations in terms of the Gauss map and the mean curvature vector field related to the Laplacian of the surfaces with respect to the induced metric.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.23-27
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• 2005

In this paper, we study rotation surfaces in a Euclidean space with pointwise 1-type Gauss map and obtain by the use of the concept of pointwise finite type Gauss map, a characterization theorem for rotation surfaces of constant mean curvature.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.2
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• pp.63-70
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• 1997

This paper proposes a new algorithm for recognizing polyhedral objects using a single 2-D image. It is base don a new representation scheme having two level hierarchey. In the lower level, geometrical features of each primitive surface are represented using their signatures and the variation of signature due to rotation is represented suing the rotation map. In the higher level, topological features are represented in the inter-surface description table(SDT). Based on the proposed representaton scheme, loer level database searched to find a matching primitive surface. The srotation map determines the degree of rotation as well as the matchness. If all surfaces in a test object find their matching primitive surfaces, its structural information is compared with the SDTs of object models. If primitive surfaces of a test object equal to tha tof certain model and satisfy inter-surfaces relationship in SDT, a test object is recognized as the model.

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.667-676
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• 2017

We study the positive $C^1$ function z = f(x, y) defined on the plane ${\mathbb{R}}^2$. For a rectangular domain $[a,b]{\times}[c,d]{\subset}{\mathbb{R}}^2$, we consider the volume V and the surface area S of the graph of z = f(x, y) over the domain. We also denote by (${\bar{x}}_V,\;{\bar{y}}_V,\;{\bar{z}}_V$) and (${\bar{x}}_S,\;{\bar{y}}_S,\;{\bar{z}}_S$) the geometric centroid of the volume under the graph of z = f(x, y) and the centroid of the graph itself defined on the rectangular domain, respectively. In this paper, first we show that among nonconstant $C^2$ functions with isolated singularities, S = kV, $k{\in}{\mathbb{R}}$ characterizes the family of catenary rotation surfaces f(x, y) = k cosh(r/k), $r={\mid}(x,y){\mid}$. Next, we show that one of $({\bar{x}}_S,\;{\bar{y}}_S)=({\bar{x}}_V,\;{\bar{y}}_V)$, $({\bar{x}}_S,\;{\bar{z}}_S)=({\bar{x}}_V,\;2{\bar{z}}_V)$ and $({\bar{y}}_S,\;{\bar{z}}_S)=({\bar{y}}_V,\;2{\bar{z}}_V)$ characterizes the family of catenary rotation surfaces among nonconstant $C^2$ functions with isolated singularities.

• The KSFM Journal of Fluid Machinery
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• v.10 no.2 s.41
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• pp.32-40
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• 2007

The present study investigated local pressure drop in a rotating smooth square duct with turning region. The duct has a hydraulic diameter $(D_h)$ of 26.7mm and a divider wall of 6.0mm or $0.225D_h$. The distance between the tip of the divider and the outer wall of the duct is $1.0D_h$. The Reynolds number (Re) based on the hydraulic diameter is kept constant at 10,000, and the rotation number (Ro) is varied from 0.0 to 0.20. The pressure coefficient distribution $(C_p)$, the friction factor (f) and the thermal performance $({\eta})$ are presented on the leading, the trailing and the outer surfaces. It is found that the curvature of the $180^{\circ}-turn$ produces Dean vortices that cause the high pressure drop in the turning region. The duct rotation results in the pressure coefficient discrepancy between the leading and trailing surfaces. That is, the high pressure values appear on the trailing surface in the first-pass and on the leading and side surfaces in the second-pass. As the rotation number increases, the pressure discrepancy enlarges. In the fuming region, a pair of the Dean vortices in the stationary case transform into one large asymmetric vortex cell, and then the pressure drop characteristics also change.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.859-881
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• 2010

The helicoidal surface is a generalization of rotation surface in a Minkowski space. We study helicoidal surfaces in a Minkowski 3-space in terms of their Gauss map and provide some examples of new classes of helicoidal surfaces with constant mean curvature in a Minkowski 3-space.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.436-441
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• 2003

The present study investigates heat/mass transfer characteristics in rotating two-pass ducts of three different aspect ratios with 90-ribbed surfaces. The results show that the flows generated by the 180-turn, rib turbulators, and duct rotation. The curvature of the 180-turn produces Dean vortices causing high heat/mass transfer in the turning region and in the upstream region of the second-pass. The rib turbulators disturb the main flow by producing reattachment and separation near the ribbed surfaces, and increase heat/mass transfer in the region between the ribs. As the rotation number increases, the heat/mass transfer discrepancy between the leading and the trailing surfaces become larger.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.30 no.2 s.245
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• pp.126-135
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• 2006

The pressure drop characteristics in a rotating two-pass duct with rib turbulators are investigated in the present study. The square duct has a hydraulic diameter $(D_h)$ of 26.7 mm, and $1.5mm{\times}1.5mm$ square $90^{\circ}-rib$ turbulators are attached on the leading and trailing walls. The pitch-to-rib height ratio (p/e) is 10. The distance between the tip of the divider and the outer wall of the duct is $1.0D_h$ and the width of divider wall is 6.0mm or $0.225D_h$. The Reynolds number (Re) based on the hydraulic diameter is kept constant at 10,000 to exclude the Reynolds effect, and the rotation number (Ro) is varied from 0.0 to 0.20. The pressure drop distribution, the friction factor and thermal performance are presented for the leading, trailing and the outer surfaces. It is found that the curvature of the $180^{\circ}$-turn produces Dean vortices that cause high pressure drop in the turn. The channel rotation results in pressure drop discrepancy between leading and trailing surfaces so that non-dimensional pressure drops are higher on the trailing surface in the first-pass and on the leading and side surfaces in the second-pass. In the turning region, Dean vortices shown in the stationary case transform into one large asymmetric vortex cell, and subsequent pressure drop characteristics also change. As the rotation number increases, the pressure drop discrepancy enlarges.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1863-1874
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• 2014

In this paper, we study spacelike rotational surfaces which are called boost invariant surfaces in Minkowski 4-space $\mathbb{E}^4_1$. We give necessary and sufficient condition for flat spacelike rotational surface to have pointwise 1-type Gauss map. Also, we obtain a characterization for boost invariant marginally trapped surface with pointwise 1-type Gauss map.