• 대한수학회지
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• 제59권1호
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• pp.53-69
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• 2022

In this paper, we are concerned with a class of mixed Hessian curvature equations with non-degeneration. By using the maximum principle and constructing an auxiliary function, we obtain the interior gradient estimate of (k - 1)-admissible solutions.

• 한국자동차공학회논문집
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• 제18권4호
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• pp.79-83
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• 2010

Recently, the flat wiper which is one piece wiper and subjected to a pressing force at a single center point is gaining wide applications on automotive windshields. However, nonuniform reactive pressure distributions takes place, so that wiping is not completed at such locations. The wiping performance of the flat wiper is best when a wiper and a curved windshield have perfect contact without gaps under the specified pressing force of 13 ~ 15 gf/cm. Therefore, it is necessary that the realistic curvature equation of a wiper spring-rail should be obtained. Finite element analysis, CATIA script-macro function, and the least square method were utilized to find out the curvature of a spring-rail for a perfect contact with a windshield under a specified concentrated load. The curvature equation became the third order polynomial.

• 대한수학회보
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• 제60권6호
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• pp.1673-1685
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• 2023

Inspired by Hongjie Dong and Qi S. Zhang's article [3], we find that the analyticity in time for a smooth solution of the heat equation with exponential quadratic growth in the space variable can be extended to any complete noncompact Riemannian manifolds with Bakry-Émery Ricci curvature bounded below and the potential function being of at most quadratic growth. Therefore, our result holds on all gradient Ricci solitons. As a corollary, we give a necessary and sufficient condition on the solvability of the backward heat equation in a class of functions with the similar growth condition. In addition, we also consider the solution in certain L^p spaces with p ∈ [2, +∞) and prove its analyticity with respect to time.

• 한국방재학회 논문집
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• 제9권2호
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• pp.11-15
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• 2009

본 논문에서는 균일 모멘트 하중을 받는 박판 아치의 탄성 좌굴에 관한 연구를 수행하였다. 초기 곡률을 고려한 비선형 변형률-변위 관계식을 전체 포텐셜 에너지 방정식의 이차 변분에 대입하여 초기 곡률 효과를 포함하는 에너지 방정식을 유도하였다. 휨 모멘트에 의한 단면 내 법선 변형률이 선형으로 분포한다는 초기 곡률 효과에 대한 가정사항을 유도과정에 일관되게 적용하였다. 균일 모멘트 하중을 받는 아치의 휨-비틀림 좌굴하중에 관한 제차해를 제시하고 타 연구자의 결과와 비교하였다.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2004년도 추계학술대회 논문집
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• pp.430-433
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• 2004

The ophthalmic lens manufacturing processes need to extract the aspherical surface equation from the unknown surface since its real profile can be adjusted by the process variables to make the ideal curve without the optical aberration. This paper presents a procedure to get the aspherical surface equation of an aspherical ophthalmic lens. Aspherical form generally consists of the Schulz formula to describe its profile. Therefore, the base curvature, conic constant, and high-order polynomial coefficient should be set to the original design equation. To find an estimated aspherical profile, firstly lens profile is measured by a contact profiler, which has a sub-micrometer measurement resolution. A mathematical tool is based on the minimization of the error function to get the estimated aspherical surface equation from the scanned aspherical profile. Error minimization step uses the Nelder-Mead simplex (direct search) method. The result of the refractive power measurement is compared with the curvature distribution on the estimated aspherical surface equation

• 대한수학회논문집
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• 제12권1호
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• pp.101-108
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• 1997

We let (M,g) be a noncompact complete Riemannina manifold of dimension $n \geq 3$ with finite volume and positive scalar curvature. We show the existence of a conformal metric with constant positive scalar curvature on (M,g) by gluing solutions of Yamabe equation on each compact subsets $K_i$ with $\cup K_i = M$ .

• 대한수학회논문집
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• 제16권4호
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• pp.637-648
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• 2001

An n-dimensional ME-manifold ME $X_{n}$ is a general-ized Riemannian manifold connected by the ME-connection which is both Einstein and of the form (2.13). The purpose of this paper is to study the properties of the ME-curvature tensors, the con-tracted ME-curvature tensors and the field equations in ME $X_{n}$)n)

• 천문학회보
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• 제44권2호
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• pp.58.4-58.4
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• 2019

In a homogeneous and isotropic universe, the solution to the Einstein Field equation is the Friedmann-Robertson-Lemaître-Walker metric, which describes an expanding Universe with spatial curvature. The curvature has profound implications, in particular regarding the early universe. In this talk, I will review the state-of-the-arts constraints on the spatial curvature of the Universe using different cosmological observations. In particular, I will focus on model-independent tests using baryon acoustic oscillations and supernovae.

• Kyungpook Mathematical Journal
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• 제60권1호
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• pp.185-195
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• 2020

This paper aims to study the 𝒲^⁎-curvature tensor on relativistic space-times. The energy-momentum tensor T of a space-time having a semi-symmetric 𝒲^⋆-curvature tensor is semi-symmetric, whereas the whereas the energy-momentum tensor T of a space-time having a divergence free 𝒲^⋆-curvature tensor is of Codazzi type. A space-time having a traceless 𝒲^⁎-curvature tensor is Einstein. A 𝒲^⁎-curvature flat space-time is Einstein. Perfect fluid space-times which admits 𝒲^⋆-curvature tensor are considered.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제4권1호
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• pp.27-33
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• 1997

Let (M = B$\times$f F, g) be an ($n \geq3$ )-dimensional differential manifold with Riemannian metric g. We solve the following elliptic nonlinear partial differential equation (equation omitted). where $\Delta_{g}$ is the Laplacian in the $\Delta$g-metric and ($h(\chi)$) is the scalar curvature of g and ($H(\chi)$) is a function on M.