BRANCHING AND BIFURCATION

PATRICK M. FITZPATRICK; JACOBO PEJSACHOWICZ

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BRANCHING AND BIFURCATION

机译：分支和分叉

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摘要

By relating the set of branch points B(f) of a Fredholm mapping f to linearized bifurcation, we show, among other things, that under mild local assumptions at a single point, the set B(f) is suciently large to separate the domain of the mapping. In the variational case, we will also provide estimates from below for the number of connected components of the complement of B(f).

机译：通过将Fredholm映射F的分支点B（f）与线性化分支的组分支点B（f）联系起来，除了在其他方面，我们展示了在单点的温和局部假设下，设置B（f）非常大，以分离域映射。在变分案例中，我们还将从下面提供估计，用于B（f）的补充的连接组件的数量。

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来源
《Discrete and continuous dynamical systems▼hSeries S》 |2019年第7期|1955-1975|共21页
作者
PATRICK M. FITZPATRICK; JACOBO PEJSACHOWICZ;
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作者单位

Department of Mathematics University of Maryland 4176 Campus Dr College Park MD 20742 USA;

INDAM Dipartimento di Scienze Matematiche Politecnico di Torino Duca degli Abruzzi 24 10129 Torino Italy;

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原文格式 PDF
正文语种 eng
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关键词
Branching; bifurcation; Fredholm mappings; parity; spectral flow;

机译：分枝;分叉;Fredholm映射;平价;光谱流量;

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1. Bifurcated abdominal aorta, with a coarctation over the right branch of the bifurcated abdominal aorta and aberrant renal arteries originating from the left branch of the bifurcated abdominal aorta. [J] . Yen TH, Chang CT, Huang CC, Renal failure. . 2004,第1期

机译：分叉的腹主动脉，在分叉的腹主动脉的右分支上缩窄，并且源自分叉的腹主动脉的左分支的异常肾动脉。
2. An Angiographic Tool for Risk Prediction of Side Branch Occlusion in Coronary Bifurcation Intervention The RESOLVE Score System (Risk prEdiction of Side branch OccLusion in coronary bifurcation interVEntion) [J] . Dou Kefei, Zhang Dong, Xu Bo, JACC. Cardiovascular interventions . 2015,第1期

机译：冠状动脉分叉术中支气管阻塞风险预测的血管造影工具RESOLVE评分系统（冠状动脉分叉术中支气管阻塞风险预测）
3. An Angiographic Tool for Risk Prediction of Side Branch Occlusion in Coronary Bifurcation Intervention The RESOLVE Score System (Risk prEdiction of Side branch OccLusion in coronary bifurcation interVEntion) [J] . Dou Kefei, Zhang Dong, Xu Bo, JACC. Cardiovascular interventions . 2015,第1aPta1期

机译：冠状动脉分支干预侧分支闭塞风险预测血管造影工具，解析得分系统（冠状动脉分岔干预侧分支闭塞风险预测）
4. Benchmark Models Representing Multiple Bifurcation, Hill-Top Branching and Degenerate Bifurcation [C] . Fumio Fujii, Makoto Ohsaki Computational Mechanics . 2004

机译：代表多分支，山顶分支和简并分支的基准模型
5. Bifurcation subsystem method and its application to diagnosis of power system bifurcations produced by discontinuities. [D] . Ben-Kilani, Khadija. 1997

机译：分叉子系统方法及其在不连续电力系统分叉诊断中的应用。
6. Original research: Randomised comparison of provisional side branch stenting versus a two-stent strategy for treatment of true coronary bifurcation lesions involving a large side branch: the Nordic-Baltic Bifurcation Study IV [O] . Indulis Kumsars, Niels Ramsing Holm, Matti Niemelä, 2020

机译：原始研究：临时侧支支架置入术与两支架策略治疗涉及大侧支的真正冠状动脉分叉病变的随机比较：北欧波罗的海分叉研究IV
7. The increased main branch to stent diameter ratio is associated with side branch decreased coronary flow in "true" coronary artery bifurcations treated by "provisional" stenting - a two-dimensional quantitative coronary angiography study [O] . Ivan Ilic, Radosav Vidakovic, Aleksandra Janicijevic, 2020

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8. Bifurcation Analysis Using Rigorous Branch and Bound Methods. [R] . Smith, A. P., Crespo, L. G., Munoz, C. A., 2014

机译：用严格分支定界法分岔分析。

BRANCHING AND BIFURCATION

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