• 호남수학학술지
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• 제44권2호
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• pp.259-270
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• 2022

This paper is devoted to the geometry of vector fields and timelike flows in terms of anholonomic coordinates in three dimensional Lorentzian space. We discuss eight parameters which are related by three partial differential equations. Then, it is seen that the curl of tangent vector field does not include any component in the direction of principal normal vector field. This implies the existence of a surface which contains both s - lines and b - lines. Moreover, we examine a normal congruence of timelike surfaces containing the s - lines and b - lines. Considering the compatibility conditions, we obtain the Gauss-Mainardi-Codazzi equations for this normal congruence of timelike surfaces in the case of the abnormality of normal vector field is zero. Intrinsic geometric properties of these normal congruence of timelike surfaces are obtained. We have dealt with important results on these geometric properties.

• 대한수학회지
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• 제58권6호
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• pp.1485-1500
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• 2021

A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any space dimension: we prove that rectifying curves are geodesics on hypercones. We later use this association to characterize rectifying curves that are also slant helices in three-dimensional space as geodesics of circular cones. In addition, we consider curves that lie on a moving hyperplane normal to (i) one of the normal vector fields of the Frenet frame and to (ii) a rotation minimizing vector field along the curve. The former class is characterized in terms of the constancy of a certain vector field normal to the curve, while the latter contains spherical and plane curves. Finally, we establish a formal mapping between rectifying curves in an (m + 2)-dimensional space and spherical curves in an (m + 1)-dimensional space.

• 대한수학회지
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• 제55권6호
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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.

• 대한수학회지
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• 제32권3호
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• pp.509-518
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• 1995

Let $M^n$ be a hypersurface in the Euclidean space $R^{n+1}$ with position vector field x and unit normal vector field G.

• 천문학회보
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• 제44권2호
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• pp.71.3-71.3
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• 2019

Previously we developed a method of coronal force-free field construction using vector potentials. In this method, the boundary normal component of the vector potential should be adjusted at every iteration step to implement the boundary normal current density, which is provided by observations. The method was a variational method in the sense that the excessive kinetic energy is removed from the system at every iteration step. The boundary condition imposing the normal current density, however, is not compatible with the variational procedure seeking for the minimum energy state, which is employed by most force-free field solvers currently being used. To resolve this problem, we have developed a totally new method of force-free field construction. Our new method uses a unique magnetic field description using two scalar functions. Our procedure is non-variational and can impose the boundary normal current density exactly. We have tested the new force-free solver for standard Low & Lou fields and Titov-Demoulin flux ropes. Our code excels others in both examples, especially in Titov-Demoulin flux ropes, for which most codes available now yield poor results. Application to a real active region will also be presented.

• 대한수학회보
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• 제46권4호
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• pp.713-720
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• 2009

We find all left-invariant minimal unit vector fields and strongly normal unit vector fields on a Lie group which is isometric to the hyperbolic space.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제14권1호
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• pp.323-343
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• 2020

With the rapid development of computer and communication techniques, copyright protection of vector geographic data has attracted considerable research attention because of the high cost of such data. A novel adaptive watermark detection algorithm is proposed for vector geographic data that can be used to qualitatively analyze the robustness of watermarks against data addition attacks. First, a watermark was embedded into the vertex coordinates based on coordinate mapping and quantization. Second, the adaptive watermark detection model, which is capable of calculating the detection threshold, false positive error (FPE) and false negative error (FNE), was established, and the characteristics of the adaptive watermark detection algorithm were analyzed. Finally, experiments were conducted on several real-world vector maps to show the usability and robustness of the proposed algorithm.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.587-601
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• 2022

We find the characterizations of the curvatures of Legendre curves and magnetic curves in Kenmotsu manifolds with C-parallel and C-proper mean curvature vector fields in the tangent and normal bundles. Finally, an illustrative example is presented.

• 대한수학회보
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• 제39권4호
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• pp.671-680
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• 2002

In this article, we show that if a semi-Riemannian space form carries a conformal vector field V of which the tangential part $V^T$ on a connected hypersurface $M^N$ ecomes a conformal vector field and the normal part $V^N on $M^N$ does not vanish identically, then $M^N$ is totally umbilic. Furthermore, we give a complete description of conformal vector fields on semi-Riemannian space forms.

• Journal of Computational Design and Engineering
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• 제2권3호
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• pp.129-136
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• 2015

This paper proposes a novel method for shape design of a Bezier surface with given boundary curves. The surface is defined as the minimizer of an extended membrane functional or an extended thin plate functional under the guidance of a specified normal field together with an initial prescribed surface. For given boundary curves and the guiding normal field, the free coefficients of a Bezier surface are obtained by solving a linear system. Unlike previous PDE based surface modeling techniques which construct surfaces just from boundaries, our proposed method can be used to generate smooth and fair surfaces that even follow a specified normal field. Several interesting examples are given to demonstrate the applications of the proposed method in geometric modeling.