• 대한기계학회논문집
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• 제19권9호
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• pp.2223-2236
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• 1995

0The fields of turbomachinery and electrical generators provide many examples of flow through rotating internal passages. At the practicing Reynolds number, most of the flow motion is three dimensional and highly turbulent. The proper understanding for the characteristics of these turbulent flow is necessary for the design of thermo-fluid machinery of a good efficiency. The flow characteristics in the rotating duct with curvature are very complex in practice due to the curvature and rotational effect of the duct. The understanding of the effect of the curvature on the structure and rotational effect of the duct. The understanding of the effect of the curvature on the structure of turbulence in the curved passage and the characteristics of the flow in a rotating radial straight channel have been well studied separately by many workers. But the combined effects of curvature and rotation on the flow have not been well understood inspite of the importance of the phenomena in the practical design process. In this study, the characteristics of a developing turbulent flow in a square sectioned 90.deg. bend rotating at a constant angular velocity are measured by using hot-wire anemometer to seize the rotational effects on the flow characteristics. As the results of this study, centrifugal forces associated with the curvature of the bend and Coriolis forces and centripetal forces associated with the rotational affect directly both the mean motion and the turbulent fluctuations.

• 호남수학학술지
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• 제40권4호
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• pp.701-718
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• 2018

In this paper, we will study the constant mean curvature (CMC) surfaces foliated by ellipses in three dimensional Euclidean space $E^3$. We prove that: (1): Surfaces foliated by ellipses are CMC surfaces if and only if it is a part of generalized cylinder. (2): All surfaces foliated by ellipses are not minimal surfaces. (3): CMC surfaces foliated by ellipses are developable surfaces. (4): CMC surfaces foliated by ellipses are translation surfaces generated by a straight line and plane curve.

• Journal of Mechanical Science and Technology
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• 제16권4호
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• pp.564-571
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• 2002

Three-dimensional numerical analysis of the turbulent premixed flame propagation in a constant volume combustion chamber is performed using the KIVA-3V code (Amsden et. al. 1997) by the flame surface density (FSD) model. A simple near-wall boundary condition is eaployed to describe the interaction between turbulent premixed flame and the wall. A mean stretch factor is introduced to include the stretch and curvature effects of turbulence. The results from the FSD model are compared with the experimental results of schlieren photos and pressure measurements. It is found that the burned mass rate and flame propagation by the FSD model are in reasonable agreement with the experimental results. The FSD combustion model proved to be effective for description of turbulent premixed flames.

• 대한수학회지
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• 제52권6호
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• pp.1337-1346
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• 2015

We examine the relationship of the shape operator of a surface of Euclidean 3-space with its Gauss map of pointwise 1-type. Surfaces with constant mean curvature and right circular cones with respect to some properties of the shape operator are characterized when their Gauss map is of pointwise 1-type.

• 대한수학회보
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• 제47권4호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권4호
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• pp.369-377
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• 2011

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 GSCS's 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 polynomial kind GSCS's with pointwise 1-type Gauss map of the second kind.

• 한국정밀공학회지
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• 제22권5호
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• pp.55-62
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• 2005

This paper presents mainly a procedure to get the mathematical form of the manufactured aspherical lens. Generally Schulz formula describes the aspherical lens profile. Therefore, the base curvature, conic constant. and high-order polynomial coefficient should be set to get the approximated design equation. To find the best-approximated aspherical form, lens profile is measured by a commercial stylus profiler, which has a sub-micrometer measurement resolution. The optimization tool is based on the minimization of the root mean square of error sum to get the estimated aspherical surface equation from the scanned aspherical profile. Error minimization step uses the Nelder-Mead simplex (direct search) method. The result of the lens refractive power measurement shows the experimental consistency with the curvature distribution of the best-approximated aspherical surface equation

• 대한수학회논문집
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• 제35권4호
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• pp.1221-1244
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• 2020

In this paper we consider L_K-conjecture introduced in [5, 6] for hypersurface Mⁿ in space form Rⁿ⁺¹(c) with three principal curvatures. When c = 0, -1, we show that every L₁-biharmonic hypersurface with three principal curvatures and H₁ is constant, has H₂ = 0 and at least one of the multiplicities of principal curvatures is one, where H₁ and H₂ are first and second mean curvature of M and we show that there is not L₂-biharmonic hypersurface with three disjoint principal curvatures and, H₁ and H₂ is constant. For c = 1, by considering having three principal curvatures, we classify L₁-biharmonic hypersurfaces with multiplicities greater than one, H₁ is constant and H₂ = 0, proper L₁-biharmonic hypersurfaces which H₁ is constant, and L₂-biharmonic hypersurfaces which H₁ and H₂ is constant.

• 대한수학회보
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• 제34권2호
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• pp.155-171
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• 1997

Let $M^n$ be a connected subminifold of a Euclidean space $E^m$, equipped with the induced metric. Denoty by $\Delta$ the Laplacian operator of $M^n$ and by x the position vector. A well-known T. Takahashi's theorem [13] says that $\delta x = \lambda x$ for some constant $\lambda$ if and only if $M^n$ is either minimal subminifold of $E^m$ or minimal submanifold in a hypersphere of $E^m$. In [9], O. Garay studied the hypersurfaces $M^n$ in $E^{n+1}$ satisfying $\delta x = Dx$, where D is a diagonal matrix, and he classified such hypersurfaces. Garay's condition can be seen as a generalization of T.

• 대한수학회보
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• 제42권2호
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• pp.337-358
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• 2005

Let M be a real hypersurface with almost contact metric structure $(\phi,\;\xi,\;\eta,\;g)$ in a nonflat complex space form $M_n(c)$. In this paper, we prove that if the structure Jacobi operator $R_\xi$ commutes with both the structure tensor $\phi$ and the Ricc tensor S, then M is a Hopf hypersurface in $M_n(c)$ provided that the mean curvature of M is constant or $g(S\xi,\;\xi)$ is constant.