• Journal of the Korean Society of Visualization
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• v.10 no.3
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• pp.42-47
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• 2012

Experimental data for the flows in a mixing tank with a bottom agitator are useful for the validation of CFD commercial code. A hybrid volume PIV measurement technique was constructed to measure the flows inside of the mixing tank. The measurement system consists of three cameras. An agitator was installed at the bottom of the tank and it rotates clockwise and counterclockwise. Using the constructed measurement system, instantaneous vector fields were obtained. A phase averaging technique was adopted for the measured instantaneous three-dimensional velocity vector fields. Turbulent properties were evaluated from the instantaneous vector fields.

• Bulletin of the Korean Mathematical Society
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• v.26 no.1
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• pp.43-46
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• 1989

In this paper, we are concerned with the pointwise-hypoellipticity (see Definition 2.1) of an m-dimensional Frobenious Lie algebra L of analytic complex vector fields in somel open subset .ohm. of $R^{m+1}$. That is, L is a set of complex vector fields in .ohm. with (real-) analytic coefficients satisfying: (A) each point of .ohm. has an open neighborhood in which L is generated by m linearly independent elements of L; (B) L is closed under the commutation bracket [A, B]. The pointwise-analytic hypoellipticity of L is completely characterized by M.S. Baouendi and F. Treves in [1]. Here, we shall prove that if L is hypoelliptic at a point then it must be analytic hypoelliptic in a full neighborhood of the same point. When the coefficients are $C^{\infty}$, hypoellipticity of L was discussed in [2].2].

• Journal of Korea Multimedia Society
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• v.12 no.11
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• pp.1623-1628
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• 2009

This paper presents the development of certain highly efficient and accurate method for computing tangent curves for two-dimensional vector fields. Unlike convention methods, such as Runge-Kutta, for computing tangent curves which produce only approximations, the method developed herein produces exact values on the tangent curves based on piecewise linear variation over a triangle in 2D. This new method assumes that the vector field is piecewise linearly defined over a triangle in 2D. It is also required to decompose the rectangular cell into two triangular cells. The critical points can be easily found by solving a simple linear system for each triangle. This method is to find exit points by producing a sequence of points on the curve with the computation of each subsequent point based on the previous. Because points on the tangent curves are calculated by the explicit solution for each triangle, this new method provides correct topologies in visualizing 2D vector fields.

• Journal of Computational Design and Engineering
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• v.2 no.2
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• pp.88-95
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• 2015

Recently, fiber composite materials have been attracting attention from industry because of their remarkable material characteristics, including light weight and high stiffness. However, the costs of products composed of fiber materials remain high because of the lack of effective manufacturing and designing technologies. To improve the relevant design technology, this paper proposes a novel simulation method for deforming fiber materials. Specifically, given a 3D model with constant thickness and known fiber orientation, the proposed method simulates the deformation of a model made of thick fiber-material. The method separates a 3D sheet model into two surfaces and then flattens these surfaces into two dimensional planes by a parameterization method with involves cross vector fields. The cross vector fields are generated by propagating the given fiber orientations specified at several important points on the 3D model. Integration of the cross vector fields gives parameterization with low-stretch and low-distortion.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.229-247
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• 2000

This paper is concerned with the impulsive Cauchy problem where the control function u is a possibly discontinuous vector-valued function with finite total variation. We assume that the vector fields f, $g_i$(i=1,…, m) are dependent on the time variable. The impulsive Cauchy problem is of the form x(t)=f(t,x) +$\SUMg_i(t,x)u_i(t)$, $t\in$[0,T], x(0)=$\in\; R^n$, where the vector fields f, $g_i$ : $\mathbb{R}\; \times\; \mathbb{R}\; \longrightarrow\; \mathbb(R)^n$ are measurable in t and Lipschitz continuous in x, If $g_i's$ satisfy a condition that $\SUM{\mid}g_i(t_2,x){\mid}{\leq}{\phi}$ $\forallt_1\; <\; t-2,x\; {\epsilon}\;\mathbb{R}^n$ for some increasing function $\phi$, then the imput-output function can be continuously extended to measurable functions of bounded variation.

• Kyungpook Mathematical Journal
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• v.52 no.1
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• pp.49-59
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• 2012

In this article, using the example of C. Camci([7]) we reconfirm necessary sufficient condition for a slant curve. Next, we find some necessary and sufficient conditions for a slant curve in a Sasakian 3-manifold to have: (i) a $C$-parallel mean curvature vector field; (ii) a $C$-proper mean curvature vector field (in the normal bundle).

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1163-1173
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• 2017

In this paper, we introduce the condition (I) (cf. Section 2) and prove that there is no nontrivial tangential holomorphic vector field of a certain hypersurface of infinite type in ${\mathbb{C}}^2$.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.393-400
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• 1994

Let M(f,η,ξ,g) be a (2m ＋ 1)-dimensional Sasakian manifold with soldering form dp ∈ ΓHom(Λ/sup q/TM, TM) (dp: canonical vector-valued 1-form) where f,η,ξ and g are the (1,1)-tensor field, the structure 1-form, the structure vector field and the metric tensor of M, respectively.(omitted)

• 한국초전도학회:학술대회논문집
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• v.11
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• pp.6-6
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• 2001

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1321-1336
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• 2018

In this paper, we obtain some necessary and sufficient conditions for the Reeb vector field of a trans-Sasakian 3-manifold to be minimal or harmonic. We construct some examples to illustrate main results. As applications of the above results, we obtain some new characteristic conditions under which a compact trans-Sasakian 3-manifold is homothetic to either a Sasakian or cosymplectic 3-manifold.