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Curvature estimates for gradient expanding Ricci solitons
Liangdi Zhang 대한수학회 2021 대한수학회보 Vol.58 No.3
In this paper, we investigate the curvature behavior of complete noncompact gradient expanding Ricci solitons with nonnegative Ricci curvature. For such a soliton in dimension four, it is shown that the Riemann curvature tensor and its covariant derivatives are bounded. Moreover, the Ricci curvature is controlled by the scalar curvature. In higher dimensions, we prove that the Riemann curvature tensor grows at most polynomially in the distance function.
Curvature estimates for a class of fully nonlinear elliptic equations with general right hand sides
Jundong Zhou 대한수학회 2024 대한수학회보 Vol.61 No.2
In this paper, we establish the curvature estimates for a class of curvature equations with general right hand sides depending on the gradient. We show an existence result by using the continuity method based on a priori estimates. We also derive interior curvature bounds for solutions of a class of curvature equations subject to affine Dirichlet data.
박형근,옥종호 대한토목학회 2015 KSCE JOURNAL OF CIVIL ENGINEERING Vol.19 No.5
The exterior surfaces of the free form buildings contain the panels with very complex curvature. While the panels incarnate a symbolic and remarkable building facade in the urban environment, constructing the panels is extremely complex. Because the bigger the curvatures of the panels, the more expensive the construction cost, a free-form building designer needs to perform the process to mitigate the curvatures of the panels at the early design stage without damaging the features of the free-form façade in parallel with estimating the cost to construct the panels (i.e., panel optimization). However, at the upfront design phase, estimating cost of design alternatives and finding a good one that meets both design intention and budget limit is very difficult. Most designers lack understanding, technology, and data on panel optimization. This study suggests how to optimize the panels for free-form facade by using Grasshopper, a widely-used application that a building designer can easily approach as well as how to calculate the construction cost change in conjunction with the optimization process. The panel optimization is mainly carried out by connecting Grasshopper’s continuity analysis function with curvature analysis function. A case study is performed on a recently completed freeform building project in Korea to verify the applicability of the study result.
IDRS 시스템에서 Curve Fitting이 적용된 NLS 비용함수를 이용한 방위/거리 추정 기법
정태진,김대경,권범수,윤경식,이균경,Jung, Tae-Jin,Kim, Dae-Kyung,Kwon, Bum-Soo,Yoon, Kyung-Sik,Lee, Kyun-Kyung 한국군사과학기술학회 2011 한국군사과학기술학회지 Vol.14 No.4
The IDRS provides detection, classification and bearing/range estimation by performing wavefront curvature analysis on an intercepted active transmission from target. Especially, a estimate of the target bearing/range that significantly affects the optimal operation of own submarine is required. Target bearing/range can be estimated by wavefront curvature ranging which use the difference of time arrival at sensors. But estimation ambiguity occur in bearing/range estimation due to a number of peaks caused by high center frequency and limited bandwidth of the intercepted active transmission and distortion caused by noise. As a result the bearing/range estimation performance is degraded. To estimate target bearing/range correctly, bearing/range estimation method that eliminate estimation ambiguity is required. In this paper, therefore, for wavefront curvature ranging, NLS cost function with curve fitting method is proposed, which provide robust bearing/range estimation performance by eliminating estimation ambiguity. Through simulation the performance of the proposed bearing/range estimation methods are verified.
Harnack inequality and pinching estimates for anisotropic curvature flow of hypersurfaces
Kang, Hyunsuk,Lee, Ki-Ahm Elsevier 2018 Journal of mathematical analysis and applications Vol.464 No.1
<P><B>Abstract</B></P> <P>We obtain a differential Harnack inequality for anisotropic curvature flow of convex hypersurfaces in Euclidean space with its speed given by a curvature function of homogeneity degree one in a certain class, and restrictions depending only on the initial data and the anisotropic factor which reflects the influence of the ambient space. Moreover, the pinching estimate for such flows is derived from the maximum principle for tensors.</P>
Gradient estimates of a nonlinear elliptic equation for the $V$-Laplacian
Fanqi Zeng 대한수학회 2019 대한수학회보 Vol.56 No.4
In this paper, we consider gradient estimates for positive solutions to the following nonlinear elliptic equation on a complete Riemannian manifold: $$\Delta_{V}u+cu^{\alpha}=0,$$ where $c$, $\alpha$ are two real constants and $c\neq0$. By applying Bochner formula and the maximum principle, we obtain local gradient estimates for positive solutions of the above equation on complete Riemannian manifolds with Bakry-\'{E}mery Ricci curvature bounded from below, which generalize some results of \cite{MHL2017}.
GRADIENT ESTIMATES OF A NONLINEAR ELLIPTIC EQUATION FOR THE V -LAPLACIAN
Zeng, Fanqi Korean Mathematical Society 2019 대한수학회보 Vol.56 No.4
In this paper, we consider gradient estimates for positive solutions to the following nonlinear elliptic equation on a complete Riemannian manifold: $${\Delta}_Vu+cu^{\alpha}=0$$, where c, ${\alpha}$ are two real constants and $c{\neq}0$. By applying Bochner formula and the maximum principle, we obtain local gradient estimates for positive solutions of the above equation on complete Riemannian manifolds with Bakry-${\acute{E}}mery$ Ricci curvature bounded from below, which generalize some results of [8].
Fast Axis Estimation from 3D Axially-Symmetric Object's Fragment
리량(Liang Li),한동진(Dongjin Han),한헌수(Hernsoo Hahn) 한국지능시스템학회 2010 한국지능시스템학회논문지 Vol.20 No.6
깨어진 항아리 조각들을 가상 공간에서 조립하기 위하여 조각 표면을 이용한 빠른 3차원 회전축 추정 방법을 제안한다. 물체의 원형성과 표면의 국지적 평면성을 이용하여 대칭축을 찾는 방법을 사용한다. 항아리 조각 같은 회전축 대칭 물체는 반지름이 다른 여러 원통의 중첩으로 생각될 수 있다. 각 원통의 원형성을 회전축 계산에 이용한다. 먼저, 표면 위 임의의 한 점을 지정하고 그 점을 통과하는 여러 개의 원통상의 궤도를 각각의 곡률의 변화를 측정 검사하여 조사한다. 올바른 원의 궤도는 곡률의 변화가 없을 것이므로 가장 작은 곡률의 변화가 원의 궤도로 선택된다. 또한 원의 중심점으로 축이 통과하는 경로가 되므로 원의 중심점이 축의 위치가 된다. 표면의 국지적 평면성과 프로파일 곡선 근사를 통한 축 위치 추정 방법 또한 연구 되었다. 제안된 방법은 기존의 방법에 비해 계산 속도가 향상되었고 조각의 부위에 영향을 받지 않는 강건성을 가짐을 실험적으로 입증하였다. To reduce the computational cost required for assembling vessel fragments using surface geometry, this paper proposes a fast axis estimation method. Using circular constraint of pottery and local planar patch assumption, it finds the axis of the symmetry. First, the circular constraint on each cylinder is used. A circular symmetric pot can be thought of unions of many cylinders with different radii. It selects one arbitrary point on the pot fragment surface and searches a path where a circumference exists on that point. The variance of curvature will be calculated along the path and the path with the minimum variance will be selected. The symmetric axis will pass through the center of that circle. Second, the planar patch assumption and profile curve is used. The surface of fragment is divided into small patches and each patch is assumed as plane. The surface normal of each patch will intersects the axis in 3D space since each planar patch faces the center of the pot. A histogram method and minimization of the profile curve error are utilized to find the probability distribution of the axis location. Experimental results demonstrate the improvement in speed and robustness of the algorithms.
A LOWER ESTIMATE FOR THE FIRST DIRICHLET EIGENVALUE ON COMPACT MANIFOLDS
KIM, HYUN JUNG The Korean Society for Computational and Applied M 2021 Journal of applied mathematics & informatics Vol.39 No.1
We prove a lower estimate of Neumann eigenvalues on compact manifolds with the condition that the Ricci curvature is bounded below. We improved the earlier results.