• 대한수학회보
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• 제41권1호
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• pp.117-123
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• 2004

It has been conjectured that, on a compact orient able manifold M, a critical point of the total scalar curvature functional restricted the space of unit volume metrics of constant scalar curvature is Einstein. In this paper we show that if a manifold is a 3-dimensional warped product, then (M, g) cannot be a critical point unless it is isometric to the standard sphere.

• 대한수학회보
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• 제35권2호
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• pp.195-201
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• 1998

We let (M,g) be a noncompact complete Riemannian manifold of dimension n $\geq$ 3 with scalar curvatue S, which is close to -1. We show the existence of a conformal metric $\bar{g}$, near to g, whose scalar curvature $\bar{S}$ = -1 by gluing solutions of the corresponding partial differential equation on each bounded subsets $K_i$ with ${\bigcup}K_i$ = M.

• 대한수학회보
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• 제58권6호
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• pp.1539-1561
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• 2021

We prove Perelman type 𝒲-entropy formulae and differential Harnack estimates for positive solutions to weighed doubly nonlinear diffusion equation on weighted Riemannian manifolds with CD(-K, m) condition for some K ≥ 0 and m ≥ n, which are also new for the non-weighted case. As applications, we derive some Harnack inequalities.

• 호남수학학술지
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• 제44권3호
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• pp.391-401
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• 2022

In this study, we investigate the explicit characterization of spherical curves using the Flc (Frenet like curve) frame in Euclidean 3-space. Firstly, the axis of curvature and the osculating sphere of a polynomial space curve are calculated using Flc frame invariants. It is then shown that the axis of curvature is on a straight line. The position vector of a spherical curve is expressed with curvatures connected to the Flc frame. Finally, a differential equation is obtained from the third order, which characterizes a spherical curve.

• 대한수학회지
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• 제60권5호
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• pp.1023-1041
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• 2023

In this paper, motivated by the work of Q. S. Zhang in [25], we derive optimal Li-Yau gradient bounds for positive solutions of the f-heat equation on closed manifolds with Bakry-Émery Ricci curvature bounded below.

• 대한수학회보
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• 제61권1호
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• pp.29-44
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• 2024

In this paper we consider the existence of rotationally symmetric entire solutions for the prescribed higher mean curvature spacelike equations in Minkowski spacetime. As a first step, we study the associated 0-Dirichlet problems on a ball, and then we prove that all possible solutions can be extended to + ∞. The proof of our main results are based upon the topological degree methods and the standard prolongability theorem of ordinary differential equations.

• 한국안광학회지
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• 제16권4호
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• pp.439-444
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• 2011

목적: 수평축과 수직축 비가 다른 토릭각막의 형상을 수학적인 함수로 표현하여 각막곡률 분포의 분석과 콘택트 렌즈 착용에 필요한 눈물두께 계산에 적용한다. 방법: 각막을 타원함수로 가정하고 함수로부터 유도된 곡률반경식과 각막 토포그라피 측정 곡률반경을 일치시켜 타원함수의 변수를 결정하였다. 계산은 작성한 엑셀프로그램을 사용하였다. 결과: 중심이 각막 정점에 위치하지 않는 리본(나비)형 토포그라피 이미지를 가지는 직난시 각막의 수평, 수직 각 축에 대해 각막의 형상을 수치적으로 알 수 있는 타원함수를 구하였다. 결론: 각막에 대해 고도의 수차 등이 요구되지 않는 응용, 예를 들면 콘택트렌즈 피팅, 난시교정 등에 각막 형상을 단순한 타원함수로 표현하는 것이 편리할 것으로 판단된다.

• 한국안광학회지
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• 제17권2호
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• pp.127-133
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• 2012

목적: 각막곡률계를 이용하여 비접촉식으로 안경렌즈의 곡률반경을 측정할 수 있는 방법에 관하여 조사하고자 한다. 방법: 각막곡률계의 전면부에 -9.50 D ~ -11.50 D의 시력검사용 시험렌즈를 부착한 후 안경렌즈를 각막곡률계의 전면부에서 약 25 cm 가량 떨어진 곳에 설치한다. 안경렌즈의 위치를 조금씩 변경시키며 선명한 마이어상을 관찰하여 곡률반경을 측정한 후, 구면계를 이용하여 곡률반경의 보정공식을 만든다. 결과: 전면부에 시험렌즈를 부착한 각막곡률계를 이용하여 곡률반경 측정이 성공적으로 수행되었다. 측정한 곡률반경은 구면계 데이터를 이용하여 보정값으로 변환 되었으며, 보정값을 만드는 직선의 방정식 5가지를 얻었다. 임의의 여러 가지 렌즈들을 전면부에 시험렌즈가 부착된 각막곡률계로 측정한 후 직선의 방정식을 이용하여 계산한 결과 3.5% 미만의 오차로 측정이 가능함을 알았다. 결론: 전면부에 시험렌즈를 부착한 각막곡률계를 이용하여 비접촉식으로 안경렌즈의 곡률반경을 측정하는 것이 가능하며, 그 정확도는 렌즈메져보다 오히려 높은 것으로 나타났다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2000년도 가을 학술발표회논문집
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• pp.190-197
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• 2000

A moment-curvature relationship to simulate the behavior of reinforced concrete beam under cyclic loading is introduced. Unlike previous moment-curvature models and the layered section approach, the proposed model takes into consideration the bond-slip effect by using monotonic moment-curvature relationship constructed on the basis of the bond-slip relation and corresponding equilibrium equation at each nodal point. In addition, the use of curved unloading and reloading branches inferred from the stress-strain relation of steel gives more exact numerical result. The advantages of the proposed model, comparing to layered section approach, may be on the reduction in calculation time and memory space in case of its application to large structures. The modification of the moment-curvature relation to reflect the fixed-end rotation and pinching effect is also introduced. Finally, correlation studies between analytical results and experimental studies are conducted to establish the validity of the proposed model.

• 로봇학회논문지
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• 제17권1호
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• pp.68-75
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• 2022

In this paper, we considered the deformation shape of the soft rotation actuator as a double curvature shell and proceeded with the analytical development. Since the response of the hyperelastic material has a large nonlinear deformation, the analytical approach is very complicated and the solution cannot be easily obtained. it is assumed that the behavior of the flexible body, which is a superelastic material, takes the form of a double curvature shell, and the formulas for calculating the deformation are simplified. In this process, equilibrium equations in the related coordinate system representing a double curvature shell were derived. In addition, assuming a thin shell, the stress component in the thickness direction was ignored, and the equation was developed by adding the assumption of free rotation without load. In order to verify the analytically calculated value in this way, an experiment was conducted and the results were compared.