• Bulletin of the Korean Mathematical Society
• /
• v.48 no.4
• /
• pp.847-851
• /
• 2011

In this paper we provide examples of pairs of conformally non-equivalent, but topologically equivalent, p-groups $H_1$, $H_2$ < Aut(S), where S is a closed Riemann surface of genus g ${\geq}$ 2, so that $S/H_j$ has genus zero and all its cone points are of order equal to p.

• International Journal of CAD/CAM
• /
• v.9 no.1
• /
• pp.103-109
• /
• 2010

Recently, various conformal geometric methods have been presented for non-rigid surface matching and registration. This work proposes to improve the robustness of conformal geometric methods to the boundaries by incorporating the symmetric information of the input surface. We presented two symmetric conformal mapping methods, which are based on solving Riemann-Cauchy equation and curvature flow respectively. Experimental results on geometric data acquired from real life demonstrate that the symmetric conformal mapping is insensitive to the boundary occlusions. The method outperforms all the others in terms of robustness. The method has the potential to be generalized to high genus surfaces using hyperbolic curvature flow.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.29 no.5B
• /
• pp.429-439
• /
• 2009

When Catastrophic extreme flood occurs due to dam break, the response time for flood warning is much shorter than for natural floods. Numerical models can be powerful tools to predict behaviors in flood wave propagation and to provide the information about the flooded area, wave front arrival time and water depth and so on. But flood wave propagation due to dam break can be a process of difficult mathematical characterization since the flood wave includes discontinuous flow and dry bed propagation. Nevertheless, a lot of numerical models using finite volume method have been recently developed to simulate flood inundation due to dam break. As Finite volume methods are based on the integral form of the conservation equations, finite volume model can easily capture discontinuous flows and shock wave. In this study the numerical model using Riemann approximate solvers and finite volume method applied to the conservative form for two-dimensional shallow water equation was developed. The MUSCL scheme with surface gradient method for reconstruction of conservation variables in continuity and momentum equations is used in the predictor-corrector procedure and the scheme is second order accurate both in space and time. The developed finite volume model is applied to 2D partial dam break flows and dam break flows with triangular bump and validated by comparing numerical solution with laboratory measurements data and other researcher's data.

• Journal of the Korean Mathematical Society
• /
• v.60 no.1
• /
• pp.71-90
• /
• 2023

We construct generalized Cauchy-Riemann equations of the first order for a pair of two ℝ-valued functions to deform a minimal graph in ℝ³ to the one parameter family of the two dimensional minimal graphs in ℝ⁴. We construct the two parameter family of minimal graphs in ℝ⁴, which include catenoids, helicoids, planes in ℝ³, and complex logarithmic graphs in ℂ². We present higher codimensional generalizations of Scherk's periodic minimal surfaces.

• Journal of Korea Water Resources Association
• /
• v.36 no.5
• /
• pp.777-785
• /
• 2003

A numerical model for the solution of two-dimensional free surface flow is developed on unstructured grid. By using fractional step method, the two-dimensional shallow water equations (SWE) are treated as two one-dimensional problems. Thus, it is possible to simulate computational hydraulic problems with higher computational efficiency. The one-dimensional problems are solved using upwind TVD version of second-order Weighted Averaged Flux (WAF) scheme with HLLC approximate Riemann solver. The numerical oscillations which are common with second-order numerical scheme are controlled by exploiting WAF flux limiter, Some idealized test problems are solved using this model and very accurate and stable solutions are obtained. It can be concluded as an efficient implement for the computation of SWE including dam break problems that concerning discontinuities, subcritical and supercritical flows and complex domain.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.29 no.2B
• /
• pp.121-129
• /
• 2009

In this study, dam-break flows are simulated numerically by using an efficient and accurate Cartesian cut-cell mesh system. In the system, most of the computational domain is discretized by the Cartesian mesh, while peculiar grids are done by a cutcell mesh system. The governing equations are then solved by the finite volume method. An HLLC approximate Riemann solver and TVD-WAF method are employed to calculation of advection flux of the shallow-water equations. To validate the numerical model, the model is applied to some problems such as a steady flow convergence on an ideal bed, a steady flow over an irregular bathymetry, and a rectangular tank problem. The present model is finally applied to a simulation of dam-break flow on an experimental channel. The predicted water surface elevations are compared with available laboratory measurements. A very reasonable agreement is observed.

• Bulletin of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.187-191
• /
• 1996

Let C be a nonsingular complex projective algebraic curve (or a compact Riemann surface) of genus g. Let $M(C)$ denote the field of meromorphic functions on C and N the set of all non-negative integers.

• Journal of the Korean Mathematical Society
• /
• v.45 no.3
• /
• pp.695-698
• /
• 2008

A simple proof of the fact that the j-invariants for Weierstrass equations are invariant under birational transformations which keep the forms of Weierstrass equations is given by finding a non-trivial explicit birational transformation which sends a normalized Weierstrass equation to the same equation.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2005.05b
• /
• pp.424-428
• /
• 2005

본 연구에서는 임의로 변화하는 지형상에 적용시에 보존 특성이 성립하는 쌍곡선형 천수방정식 해석 기법을 개발하였다. 일반적으로 쌍곡선형의 천수방정식은 상류와 사류를 쉽고 정확하게 해석할 수 있고, 또한 Euler 방정식 해석기법을 이용한 다양한 해석기법이 개발되어 있다는 장점을 지니고 있다. 그러나 바닥지형이 변화하는 경우, 생성항과 플럭스항 사이에 수치적 해석기법 차이에서 발생하는 수치적 불균형이 발생하여 수치모형의 적용성이 현저하게 저하된다. 따라서 본 연구에서는 이와 같은 현상을 개선하기 위하여, 기존의 표면경사법을 개선한 기법을 제시하였다. MUSCL-Hancock 기법과 HLLC 근사 Riemann 기법을 이용하였으며, 플럭스항과 수치적 균형을 이루기 위한 이산화기법을 제안하였다. 모형의 검증을 위하여 정상류 상태의 상류와 사류 해석을 수행하였고, 마른바닥에서의 댐붕괴파와 수직한 지형 변화를 갖는 수로상의 서지의 진행 등과 같은 부정류에 대하여 적용하였다. 적용결과, 매우 정확하고 수치적으로 안정된 계산결과를 얻었다.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.2
• /
• pp.411-415
• /
• 2012

In 1995 it was proved by Gonz$\acute{a}$lez-Diez that the cyclic group generated by a p-gonal automorphism of a closed Riemann surface of genus at least two is unique up to conjugation in the full group of conformal automorphisms. Later, in 2008, Gromadzki provided a different and shorter proof of the same fact using the Castelnuovo-Severi theorem. In this paper we provide another proof which is shorter and is just a simple use of Sylow's theorem together with the Castelnuovo-Severi theorem. This method permits to obtain that the cyclic group generated by a conformal automorphism of order p of a handlebody with a Kleinian structure and quotient the three-ball is unique up to conjugation in the full group of conformal automorphisms.