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分析学Ⅰ复习
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分析学Ⅰ复习
Created
2025-09-04
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Updated
2026-05-15
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Naomiku
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https://naomikuuuu.github.io/2025/09/04/%E5%88%86%E6%9E%90%E5%AD%A6%E2%85%A0%E5%A4%8D%E4%B9%A0/
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分析学
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Basics of Morse Theory and the Poincaré-Hopf Theorem
Basics of Morse Theory and the Poincaré-Hopf Theorem We mainly focus on Morse Theory by J. Milnor. In Chapter 6, we will use Theorem 11.27 and Lemma 11.20 from From Calculus to Cohomology (by Madsen and Tornehave) to prove the Poincaré-Hopf theorem. 0. Preliminaries Definition 1 (Homotopy). Let \(f, g: X \to Y\) be continuous maps. We say \(f\) is homotopic to \(g\), denoted by \(f \simeq g\), if there exists a continuous map \(H : X \times I \to Y\) such that: \(\forall x \in X, \ H(x...
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HPCG实验操作流程实验环境配置基础实现配置 实验配置 参数版本 要求版本 平台 V100 - GPU数量 1或2 - HPCG 实现 nvidia-hpcg - Git 2.39.5 - OpenMPI 5.0.7 4.1 CUDA Toolkit 12.9.86 12.3 cuSPARSE 12.5.10.65 12.3 cuBLAS 12.9.1.4 12.2 gcc 13.4.0 13.0 nvpl 25.5 24.03 nccl 2.27.7 2.19 gfortran 13.4.0 - 编译与运行说明有两种方式获取并运行HPCG: 方式一：从源码获取下载nvidia提供的HPCG实现： 1git clone https://github.com/NVIDIA/nvidia-hpcg 随后将附在压缩包内的三个脚本放入到nvidia-hpcg/下： beforebuild.sh build_sample.sh run.sh 方式二：使用附件压缩包直接解压附在附件hpcg.zip，其中含有上述的三个脚本。 ...
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