• Journal of the Optical Society of Korea
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• 제15권1호
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• pp.68-73
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• 2011

This study investigated, using the Orbscan II topography system, the influence of age and sex related changes on the corneal thickness and anterior corneal curvature, more specifically the fine structure of the cornea, in a Korean young population. The Orbscan II topography system is a computer-assisted slit-beam scanning technology that can map the anterior section of the cornea. The mean central corneal thickness of all subjects was $547.532{\pm}44.529\;{\mu}m$. There was no statistical difference (p>0.5) in the mean central corneal thickness between males and females. Sex and age related changes in the mean central corneal thickness had no specific statistical difference (P>0.5). There was a negative correlation between the anterior corneal curvature and the central corneal thickness in all subjects, except for the twenty year olds. However, the thickness relationship between the mean central corneal and the eight paracentral corneal thicknesses had strong statistical differences in all subjects. Also age and sex related changes in the central corneal thickness and the anterior corneal curvature in all subjects had no statistically significant difference, except from 20-26 years old (p>0.05). This information could be a suitable reference basis for future studies in the young population of Asia and for the development of examination tools for corneal refractive surgery.

• 대한수학회논문집
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• 제10권4호
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• pp.931-941
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• 1995

The definitions and techniques, which deals with homotopic harmonic maps from a compact Riemannian manifold into a compact metric space, developed by N. J. Korevaar and R. M. Schoen [7] can be applied to more general situations. In this paper, we prove that for a complicated domain, possibly noncompact Riemannian manifold with infinitely generated fundamental group, the existence of homotopic harmonic maps can be proved if the initial map is simple in some sense.

• 대한수학회논문집
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• 제29권1호
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• pp.155-161
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• 2014

Let M be a complete Riemannian manifold and let N be a Riemannian manifold of non-positive sectional curvature. Assume that $Ric^M{\geq}-\frac{4(p-1)}{p^2}{\mu}_0$ at all $x{\in}M$ and Vol(M) is infinite, where ${\mu}_0$ > 0 is the infimum of the spectrum of the Laplacian acting on $L^2$-functions on M. Then any p-harmonic map ${\phi}:M{\rightarrow}N$ of finite p-energy is constant Also, we study Liouville type theorem for p-harmonic morphism.

• 대한수학회지
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• 제53권5호
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• pp.1077-1100
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• 2016

We develop an invariant local theory of Lorentz surfaces in pseudo-Euclidean 4-space by use of a linear map of Weingarten type. We find a geometrically determined moving frame field at each point of the surface and obtain a system of geometric functions. We prove a fundamental existence and uniqueness theorem in terms of these functions. On any Lorentz surface with parallel normalized mean curvature vector field we introduce special geometric (canonical) parameters and prove that any such surface is determined up to a rigid motion by three invariant functions satisfying three natural partial differential equations. In this way we minimize the number of functions and the number of partial differential equations determining the surface, which solves the Lund-Regge problem for this class of surfaces.

• 대한수학회보
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• 제29권2호
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• pp.233-236
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• 1992

Let f:M.rarw.N be a smooth map between Rioemannian manifolds M and N. If f maps geodesics of M to geodesics of N, f is called totally geodesic. As is well known, totally geodesic maps are harmonic and the image f(M) of a totally geodesic map f:M.rarw. N is an immersed totally geodesic submanifold of N (cf. .cint. 6.3 of [W]). We are interested in the following question: When is a harmonic map f:M .rarw. N with rank .leq. 1 everywhere on M totally geodesic\ulcorner In other words, when is the image of a harmonic map f:M .rarw. N with rank .leq. 1 everywhere on M geodesics of N\ulcorner In this note, we give some sufficient conditions on curvatures of M. It is interesting that no curvature assumptions on target manifolds are necessary in Theorems 1 and 2. Some properties of totally geodesic maps are also given in Theorem 3. We think our Theorem 3 is somewhat unusual in view of the following classical theorem of Eells and Sampson (see pp.124 of [ES]).

• 정보처리학회논문지B
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• 제15B권6호
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• pp.501-506
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• 2008

기존 스네이크 알고리즘은 에너지 함수의 정의에 의해 복잡한 객체의 윤곽을 추출하는데 어려움이 있고, GVF 방법은 에너지 맵 계산 시간이 많이 소요되는 문제점이 있다. 본 논문에서는 빠르고, 복잡한 객체의 윤곽을 잘 추출하는 방법을 제안한다. 객체 윤곽의 복잡도는 곡률로 정의하여 곡률 값이 임계치 이상이면 스네이크 포인트를 추가하여 객체의 윤곽을 추출하였다. 다수의 복잡한 영상에 실험을 통해 계산속도 및 윤곽 추출 성능을 개선하는 결과를 보여준다.

• 한국지반공학회논문집
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• 제30권12호
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• pp.15-25
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• 2014

본 연구에서는 지리산 북쪽의 과거 산사태 발생영역에서 조사된 절리특성과 GIS를 이용하여 추출한 지형특성을 근거하여 연구지역에서 예상되는 암반사면 파괴유형을 분석하였다. 또 해발고도, 사면방향, 사면경사, 음영도, 곡률, 하천 이격거리 등 6개의 지형특성 인자의 빈도비를 중첩하여 산사태 예측도를 작성하였으며, 산사태 예측도와 도로 및 주거지와 같은 지역의 인문적인 인자를 고려한 산사태 피해도를 조합하여 최종적으로 연구지역의 산사태 위험도를 작성하였다. 연구지역에서 발생한 산사태의 지형적 특성을 분석한 결과, 해발고도 330~710m에서 88%, 사면방향 동남-남-남서 방향($90{\sim}270^{\circ}$)에서 77.7%, 사면경사 $10{\sim}40^{\circ}$에서 93.39%, 음영도 등급3~7에서 82.78%, 곡률특성 -5~+5에서 86.28%, 하천 이격거리 400m 이내에서 82.92%가 발생하였다. 산사태가 발생한 영역의 75%는 산사태 위험도에서 위험 등급이 '높음' 이상인 지역이어서 위험 예측에 대한 신뢰성이 확인되었으며, 연구지역의 13.27%는 산사태 위험에 노출된 것으로 분석되었다.

• 호남수학학술지
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• 제38권2호
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• pp.385-391
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• 2016

We consider Jacobi filds as the first derivatives for ${\varepsilon}$, the energy of harmonic extensions, in a given manifold. In this paper we see that the Jacobi fild is bounded by the given boundary map. Here we give no restriction concerned with the curvature for the given manifold.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2010년도 추계학술대회 논문집
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• pp.141-142
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• 2010

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.299-306
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• 2010

In this article we consider axes of a complete embedded minimal surface in $R^3$ of finite total curvature, and then prove that there is no planar ends at which the Gauss map have the minimum branching order if the minimal surface has a single axis.