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Optical Imaging‐Based 3D Reconstruction of Electrical Tree in Polypropylene Cable Insulation Under Mechanical Bending

High Voltage, EarlyView.
ABSTRACT This study proposes a nondestructive optical imaging‐based three‐dimensional (3D) reconstruction method to analyse electrical tree propagation in polypropylene (PP) cable insulation under mechanical bending. The technique combines focus‐stacked optical imaging with a feature fusion algorithm to segment in‐focus regions across depth layers ...
Heyu Wang, Zhonglei Li, Guoning Sun, Boxue Du   +3 more
wiley   +1 more source

On the existence of solutions of prescribing scalar curvature problem

On the existence of solutions of prescribing scalar curvature problem
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The prescribed scalar curvature problem for polyharmonic operator

Annali di Matematica Pura ed Applicata (1923 -), 2020
We consider the following prescribed curvature problem involving polyharmonic operator: $$\begin{aligned} D_mu=Q(|y'|,y'')u^{m^*-1}, \;u>0, \; u \in {\mathcal {H}}^{m}({\mathbb {S}}^{N}), \end{aligned}$$ where
Ting Liu, Yuxia Guo
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Symmetric solutions for the prescribed scalar curvature problem

Indiana University Mathematics Journal, 2000
The paper deals with the existence of symmetric solutions for the prescribed scalar curvature equation in \({\mathbb R}^N\) \[ -\Delta u=K(x) u^{(N+2)/(N-2)},\quad u>0\quad \text{in} {\mathbb R}^N,\;N\geq 3, \] \[ u(x)=O(|x|^{2-N})\quad \text{as} |x|\to\infty, \] and for the corresponding equation on the unit sphere \(S^N.\) Moreover, it is shown that,
Zhi-Qiang Wang, Florin Catrina
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Local uniqueness and periodicity for the prescribed scalar curvature problem of fractional operator in $${\mathbb {R}}^{N}$$ R N

Calculus of Variations and Partial Differential Equations, 2017
Consider the following prescribed scalar curvature problem involving the fractional Laplacian with critical exponent: 0.1 $$\begin{aligned} \left\{ \begin{array}{ll}(-\Delta )^{\sigma }u=K(y)u^{\frac{N+2\sigma }{N-2\sigma }} \text { in }~ {\mathbb {R}}^{N},\\ ~u>
Miaomiao Niu, Zhongwei Tang, Jianjun Nie, Yuxia Guo   +3 more
semanticscholar   +4 more sources

On the prescribed scalar curvature problem with very degenerate prescribed functions

Calculus of Variations and Partial Differential Equations, 2023
Peng Luo, Shuangjie Peng, Yang Zhou
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Dirichlet problem for space-like hypersurfaces with prescribed scalar curvature in $\mathbb R^{n,1}$

Calculus of Variations and Partial Differential Equations, 2003
In this paper under review, the author proves a Dirichlet problem for space-like hypersurfaces with prescribed scalar curvature in Minkowski space. Let \({\mathbb R}^{n,1}\) be the Minkowski space \(\displaystyle{{\mathbb R}^{n,1} = \bigl({\mathbb R}^{n+1}, \sum_{i=1}^n dx_i^2 - dx_{n+1}^2 \bigr)}\) with the canonical coordinates \((x_1, \dots, x_{n+1})
P. Bayard
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Prescribed scalar curvature plus mean curvature flows in compact manifolds with boundary of negative conformal invariant

Annals of Global Analysis and Geometry, 2016
Using a geometric flow, we study the following prescribed scalar curvature plus mean curvature problem: Let $$(M,g_0)$$(M,g0) be a smooth compact manifold of dimension $$n\ge 3$$n≥3 with boundary. Given any smooth functions f in M and h on $$\partial M$$∂
Xuezhang Chen, P. Ho, Liming Sun
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Prescribing scalar curvature on Sn and related problems, part II: Existence and compactness

Communications on Pure and Applied Mathematics, 1998
This is a sequel to Part I [J. Differ. Equations 120, No. 2, 319-410 (1995; Zbl 0827.53039)] which studies the prescribing scalar curvature problem on \(S^n\). First we present some existence and compactness results for \(n= 4\). The existence result extends those of \textit{A. Bahri} and \textit{J. M. Coron} [J. Funct. Anal. 95, No.
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Prescribed Chern scalar curvature flow on compact Hermitian manifolds with negative Gauduchon degree

Manuscripta mathematica
In this paper, we present a unified flow approach to prescribed Chern scalar curvature problem on compact Hermitian manifolds with negative Gauduchon degree.
Weike Yu
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