MEAN CURVATURE OF NON-DEGENERATE SECOND FUNDAMENTAL FORM OF RULED SURFACES

KIM, NAM GIL,YOON, DAE WON 호남수학회 2006 호남수학학술지 Vol.28 No.4

In this paper, we classify non-developable ruled surfaces in a Euclidean 3-spaces satisfying some algebraic equations in terms of the second mean curvature, the mean curvature and the Gaussian curvature.

Integral Absolute Mean Curvature를 이용한 다면체 간략화 기법에 관한 연구

김남우(Nam Woo Kim),임우종(Woo Jong Lim),안효민(Hyo Min Ahn),이병국(Byung Gook Lee) 한국컴퓨터게임학회 2004 한국컴퓨터게임학회논문지 Vol.5 No.-

According to Stan Melax's Edge cost formula which is fast and effective but don't fitted for characteric point. The short comings of Stan Melax approach is over come by curvature approach which is fitted for characteric point but it is not so effective. Our proposed formula having advantages of both formula that is simulated with Stan Melax approach and Integral approach. It is simple, effective and fitted for characteric points. 대용량의 데이터를 처리하기 위한 그래픽스 알고리즘을 Simplification이라 하며, Stan Melax의 Edge cost기법은 간결한 수식에 비해 빠르고, 효과적이어서 VRML이나 게임엔진 등에서 널리 응용되어지고 있는 좋은 예이다. 특히, 오늘날 Curvature를 이용한 Simplification방법들이 많이 제안되고 있는데, Edge cost 방법은Curvature를 이용한 Simplification 방법에 비해 각각의 연산수행이 느리고, 특징 점들을 잘 보존하지 못하는 단점이 있다. 본 논문에서는 Integral Absolute Mean Curvature에 Stan Melax의 Edge cost기법을 접목하여, 두 알고리즘의 장점들을 모두 보존할 수 있는 효과적인 Simplification 방법을 제안하고자 한다.

NON-ZERO CONSTANT CURVATURE FACTORABLE SURFACES IN PSEUDO-GALILEAN SPACE

Aydin, Muhittin Evren,Kulahci, Mihriban,Ogrenmis, Alper Osman Korean Mathematical Society 2018 대한수학회논문집 Vol.33 No.1

Factorable surfaces, i.e. graphs associated with the product of two functions of one variable, constitute a wide class of surfaces in differential geometry. Such surfaces in the pseudo-Galilean space with zero Gaussian and mean curvature were obtained in [2]. In this study, we provide new results relating to the factorable surfaces with non-zero constant Gaussian and mean curvature.

Deforming pinched hypersurfaces of the hyperbolic space by powers of the mean curvature into spheres

Shunzi Guo,Guanghan Li,Chuanxi Wu 대한수학회 2016 대한수학회지 Vol.53 No.4

This paper concerns closed hypersurfaces of dimension $n\geq 2$ in the hyperbolic space ${\mathbb{H}}_{\kappa}^{n+1}$ of constant sectional curvature $\kappa$ evolving in direction of its normal vector, where the speed equals a power $\beta \geq1$ of the mean curvature. The main result is that if the initial closed, weakly $h$-convex hypersurface satisfies that the ratio of the biggest and smallest principal curvature at everywhere is close enough to $1$, depending only on $n$ and $\beta$, then under the flow this is maintained, there exists a unique, smooth solution of the flow which converges to a single point in ${\mathbb{H}}_{\kappa}^{n+1}$ in a maximal finite time, and when rescaling appropriately, the evolving hypersurfaces exponential convergence to a unit geodesic sphere of ${\mathbb{H}}_{\kappa}^{n+1}$.

잠제 설치 연안역의 파동장에 미치는 해안곡률의 영향

허동수(Hur Dong-Soo),이우동(Lee Woo-Dong),염경선(Yeom Gyeong-Seon) 대한토목학회 2009 대한토목학회논문집 B Vol.29 No.5B

본 연구에서는 잠제가 설치된 연안역에서 해안의 곡률반경이 잠제 주변 파동장에 미치는 영향을 파악하기 위하여 파ㆍ구조물ㆍ해빈/해저지반의 상호작용을 해석할 수 있는 3차원 수치모델 LES-WASS-3D를 이용하여 시뮬레이션을 실시하였다. 먼저 기존의 수리모형실험결과와 비교ㆍ검토를 통하여 타당성과 유효성을 확인하였으며, 수치실험을 통해 얻어진 수치해석결과로부터 잠제 주변의 파고분포, 평균수위분포, 상층흐름분포, 평균류분포 그리고 연안에서의 처오름 높이분포를 비롯한 잠제주변의 3차원적 수리특성에 미치는 해안곡률의 영향에 관하여 고찰하였다. The aim of this study is to examine the effect of beach curvature on wave fields in coastal area with Submerged Breakwaters using the 3D numerical model that is able to simulate directly interaction of WAveㆍStructureㆍSandy beach (LES-WASS-3D). At first, the adopted model was validated through the comparison with an existing experimental data and showed fairly nice agreement. And then, the numerical simulations have been performed to investigate the effect of according to the variation of beach curvature. Based on the numerical results, the wave height, mean surface elevation, mean flow around submerged breakwaters and longshore distributions of run-up height have been discussed in relation to the variation of beach curvature.

DEFORMING PINCHED HYPERSURFACES OF THE HYPERBOLIC SPACE BY POWERS OF THE MEAN CURVATURE INTO SPHERES

Guo, Shunzi,Li, Guanghan,Wu, Chuanxi Korean Mathematical Society 2016 대한수학회지 Vol.53 No.4

This paper concerns closed hypersurfaces of dimension $n{\geq}2$ in the hyperbolic space ${\mathbb{H}}_{\kappa}^{n+1}$ of constant sectional curvature evolving in direction of its normal vector, where the speed equals a power ${\beta}{\geq}1$ of the mean curvature. The main result is that if the initial closed, weakly h-convex hypersurface satisfies that the ratio of the biggest and smallest principal curvature at everywhere is close enough to 1, depending only on n and ${\beta}$, then under the flow this is maintained, there exists a unique, smooth solution of the flow which converges to a single point in ${\mathbb{H}}_{\kappa}^{n+1}$ in a maximal finite time, and when rescaling appropriately, the evolving hypersurfaces exponential convergence to a unit geodesic sphere of ${\mathbb{H}}_{\kappa}^{n+1}$.

The least squares mean of positive Hilbert-Schmidt operators

Lawson, J.,Lim, Y. Academic Press 2013 Journal of mathematical analysis and applications Vol.403 No.2

We show that, the least squares mean on the Riemannian manifold Σ of positive operators in the extended Hilbert-Schmidt algebra of linear operators on a Hilbert space equipped with the canonical trace metric is the unique solution of the corresponding Karcher equation. This allows us to conclude that, the least squares mean is the restriction of the Karcher mean on the open cone of all bounded positive definite operators, and hence inherits the basic properties of that mean. Conversely, the Karcher mean on the positive definite operators is shown to be the unique monotonically strongly continuous extension of the least squares mean on Σ.

Classification of Ruled Surfaces with Non-degenerate Second Fundamental Forms in Lorentz-Minkowski 3-Spaces

Jung, Sunmi,Kim, Young Ho,Yoon, Dae Won Department of Mathematics 2007 Kyungpook mathematical journal Vol.47 No.4

In this paper, we study some properties of ruled surfaces in a three-dimensional Lorentz-Minkowski space related to their Gaussian curvature, the second Gaussian curvature and the mean curvature. Furthermore, we examine the ruled surfaces in a three-dimensional Lorentz-Minkowski space satisfying the Jacobi condition formed with those curvatures, which are called the II-W and the II-G ruled surfaces and give a classification of such ruled surfaces in a three-dimensional Lorentz-Minkowski space.

새로운 근사 평균 곡률을 이용한 메쉬 단순화

곽재희,이은정,유관희 한국게임학회 2002 한국게임학회 논문지 Vol.2 No.2

일반적으로 삼각형 메쉬는 가상 게임 캐릭터와 같은 기하학적 객체를 모델링하기 위해 사용되고 있다. 아주 조밀한 메쉬는 복잡한 객체를 세부적으로 표현하는 장점은 있지만 객체를 저장, 전송 및 렌더링하는데 많은 비용을 요구한다. 그러므로 세밀한 객체를 질 좋게 근사시킬 수 있는 기법, 즉 삼각형 메쉬의 단순화가 연구되어왔다. 본 논문에서는 주어진 메쉬를 단순화하기 위해 사용될 수 있는 정점과 에지에 관한 근사 평균 곡률이라는 새로운 측정치를 제시한다. 에지 평균 곡률은 이웃한 에지를 고려하게 계산되고 정점 평균 곡률은 부속된 에지의 평균 곡률의 평균으로 정의된다. 그리고 제안된 측정치를 토끼, 용 및 치아와 같은 모델에 적용한다. 결과로, 제안된 평균 곡률이 주어진 모델에 더 좋은 근사를 제공하기 위한 좋은 기준치로 사용될 수 있음을 알았다. In general, triangular meshes have been used for modeling geometric objects such as virtual game characters. The dense meshes give us considerable advantages in representing complex, highly detailed objects, while they are more expensive for storing, transmitting and rendering the objects. Therefore, several researches have been performed for producing a high quality approximation in place of detailed objects, that is, a simplification of triangular meshes. In this paper, we propose a new measure with respect to edges and vertices, which is called an approximate mean curvature and is used as criteria to simplify an original mesh. An edge mean curvature is computed by considering its neighboring edges, and a vertex mean curvature is defined as an average of its incident edges' mean curvatures. And we apply the proposed measure to simplify the models such as a bunny, dragon and teeth. As a result, we can see that the mean curvatures can be used as good criteria for providing much better approximation of models.

Assessing the Accuracy of Outlier Tests in Nonlinear Regression

Kahng, Myung-Wook,Kim, Bu-Yang The Korean Statistical Society 2009 Communications for statistical applications and me Vol.16 No.1

Given the specific mean shift outlier model, the standard approaches to obtaining test statistics for outliers are discussed. Accuracy of outlier tests is investigated using subset curvatures. These subset curvatures appear to be reliable indicators of the adequacy of the linearization based test. Also, we consider obtaining graphical summaries of uncertainty in estimating parameters through confidence curves. The results are applied to the problem of assessing the accuracy of outlier tests.