• Honam Mathematical Journal
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• v.27 no.2
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• pp.195-203
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• 2005

We show that the exact Bergman kernel function associated to a $C^{\infty}$ bounded domain in the plane relates the derivatives of the Ahlfors map in an explicit way. And we find several formulas relating the exact Bergman kernel to classical kernel functions in potential theory.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1327-1340
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• 2019

We establish a monotonicity formula of V-harmonic maps by using the stress-energy tensor. Use the monotonicity formula, we can derive a Liouville type theorem for V-harmonic maps. As applications, we also obtain monotonicity and constancy of Weyl harmonic maps from conformal manifolds to Riemannian manifolds and ${\pm}holomorphic$ maps between almost Hermitian manifolds. Finally, a constant boundary-value problem of V-harmonic maps is considered.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1281-1298
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• 2023

Let (M^2m, 𝜑, g) be a B-manifold. In this paper, we introduce a new class of metric on (M^2m, 𝜑, g), obtained by a non-conformal deformation of the metric g, called a generalized Berger-type deformed metric. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. Finally, we study the proper biharmonicity of the identity map and of a curve on M with respect to a generalized Berger-type deformed metric.

• Korean Journal of Mathematics
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• v.24 no.1
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• pp.15-25
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• 2016

We obtain some estimations of the essential norm of a pull back operator induced by quasi-symmetric homeomorphisms. As a corollary, we deduce the compactness criterion of this operator.

• 한국전산유체공학회:학술대회논문집
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• 1995.10a
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• pp.82-89
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• 1995

In the present paper, a method of nearly orthogonal grid generation in an arbitrary simply-connected 3D domain will be presented. The method is a new direct and non-iterative scheme based on the concept of the decomposition of the global orthogonal transformation into consecutive mapping of a conformal mapping and an auxiliary orthogonal mapping, which was suggested by King and Leal [4]. In our numerical scheme. Kang and Leal's method is extended from 2D problems to 3D problems while the advantage of the non-iterative algorithm is maintained. The essence of the present mapping method is that an iterative scheme can be avoided by introducing a preliminary step. This preliminary step corresponds to a conformal map and is based on the boundary element method(BEM). This scheme is applied to generate several nearly-orthogonal grid systems which are orthogonal at boundaries.

• Journal of the Korean Geographical Society
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• v.49 no.3
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• pp.438-455
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• 2014

This study aims at providing a set of viable answers regarding the projection and cartographic scale of Daedongyeojido through a GIS-based planimetric accuracy analysis. Both global and local analyses were undertaken in the use of an analytical tool, MapAnalyst. The main results from the global analysis are threefold. First, the overall cartographic scale turned out to be between 1:158,000 and 1:162,000. Second, the rotation angles were between $2^{\circ}$ and $3^{\circ}$, and the equidistant cylindrical projection reported the smallest value. Third, in terms of position accuracy, the conformal cylindrical projection showed a best fit to the map. A local analysis was undertaken for the conformal cylindrical and equidistant azimuthal projections and its main results are threefold. First, the largest distortions in terms of the displacement vectors and distortion grid were found in the northern borderlands. Second, from the isoline maps of scales, it was acknowledged that local scales between 1:170,000 and 1:175,000 were found around the middle part of the Korean peninsula centered on Seoul. As away from the region to the north-south direction, increasingly larger scales were distributed, while the smallest ones were found in the western and eastern edges of the peninsula. Third, from the isoline maps of rotation, it was known that areas west of a northernmost city (Junggangjin) were substantially rotated to the west, while ones east of it to the east. For a more sophisticated analysis, some need to be done to have a larger set of control points, a better way of postulating the map projection, and a more advanced set of techniques for a local analysis.

• Journal of the Korean Mathematical Society
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• v.40 no.3
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• pp.447-460
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• 2003

In this paper we study the non-degenerate n-connected canonical domains with n>1 related to the conjecture of S. Bell in [4]. They are connected to the algebraic property of the Bergman kernel and the Szego kernel. We characterize the non-degenerate doubly connected canonical domains.

• Korean Journal of Remote Sensing
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• v.18 no.3
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• pp.171-179
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• 2002

Sampling rates become inconsistent when spatial data in the spherical coordinate are resampled with respect to latitudinal or longitudinal degree for mathematical processes such as Fourier Transform, and this results in distortions of the processed data in the wavenumber domain. These distortions are more evident in the polar regions. An example is presented to show such distortions during the recovery process of free-air gravity anomalies from ERS-1 satellite radar altimeter data from the Barents Sea in the Russian Arctic, and a method is presented to minimize the distortion using the Lambert Conformal Conic map projection. This approach was found to enhance the free-air gravity anomalies in both data and wavenumber domains.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.25 no.4
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• pp.309-317
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• 2007

Cadastral control points in Korea are refered to various origins, for example an early separated small triangulation, a separated small triangulation, a separated control surveying origin and an unified origin. Cadastral map with early separated small triangulation origin have difficulties to connect with national GIS data by refered an unified origin. We determined transformation parameters from old origin to unified origin using 2D conformal transformation method. To evaluate of transformation accuracy, we compared with GPS field surveying results. And we experiment on coordinate transformations with unified results between the local geodetic datum and the new Korea geodetic datum.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.17 no.3
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• pp.205-211
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• 1999

In this study, we utilized 2D conformal transformation method to give coordinatesbased on GPS surveying data to NAHMIS (National Highway Management Information System) drawings which are lack of coordinates. To determine the best method which is comparable with GPS digital map, we compared a transformation result obtained by unique parameters applied to the whole region of about 20 km of the NAHMIS drawings and the similar result of the tile based transformations. As the result of map joining, the error was within 2 m for both cases. In this way, NAHMIS can be used for a systematic management of construction drawings. Moreover, NAHMIS can contribute the management of highway and the data exchange between other systems by a unification of coordinate system.