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    <title>耳朵同的博客</title>
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    <pubDate>Sat, 18 Apr 2026 01:24:09 GMT</pubDate>
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      <title>耳朵同的博客</title>
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    <category>blog</category>
    <category>卡片/moc</category>
    <category>卡片/普通</category>
    <item>
      <title>站点地图</title>
      <link>https://blog.erduotong.com/catalog.html</link>
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      <source url="https://blog.erduotong.com/rss.xml">站点地图</source>
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      <pubDate>Tue, 01 Oct 2024 00:00:00 GMT</pubDate>
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<h1>站点地图</h1>
<h2>本站全部文章的索引</h2>
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    <item>
      <title>项目</title>
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      <source url="https://blog.erduotong.com/rss.xml">项目</source>
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    <item>
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      <pubDate>Wed, 30 Jul 2025 00:00:00 GMT</pubDate>
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      <title>卡片笔记</title>
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      <title>关于</title>
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      <link>https://blog.erduotong.com/about_site/friend.html</link>
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      <source url="https://blog.erduotong.com/rss.xml">友情链接</source>
      <pubDate>Sun, 20 Oct 2024 00:00:00 GMT</pubDate>
    </item>
    <item>
      <title>个人介绍</title>
      <link>https://blog.erduotong.com/about_site/intro.html</link>
      <guid>https://blog.erduotong.com/about_site/intro.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">个人介绍</source>
      <description>似乎这里还什么都没有？</description>
      <pubDate>Mon, 23 Sep 2024 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<p>似乎这里还什么都没有？</p>
]]></content:encoded>
    </item>
    <item>
      <title>关于本站</title>
      <link>https://blog.erduotong.com/about_site/%E5%85%B3%E4%BA%8E%E6%9C%AC%E7%AB%99.html</link>
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      <description>这里是关于本站</description>
      <pubDate>Tue, 01 Oct 2024 00:00:00 GMT</pubDate>
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    <item>
      <title>博客</title>
      <link>https://blog.erduotong.com/40%20Archive/%E5%8D%9A%E5%AE%A2/</link>
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      <pubDate>Wed, 30 Jul 2025 00:00:00 GMT</pubDate>
    </item>
    <item>
      <title>just tauri todo</title>
      <link>https://blog.erduotong.com/20%20Area/%E5%85%B3%E4%BA%8E%E6%88%91/%E4%B8%AA%E4%BA%BA%E9%A1%B9%E7%9B%AE%E5%88%97%E8%A1%A8/just%20tauri%20todo.html</link>
      <guid>https://blog.erduotong.com/20%20Area/%E5%85%B3%E4%BA%8E%E6%88%91/%E4%B8%AA%E4%BA%BA%E9%A1%B9%E7%9B%AE%E5%88%97%E8%A1%A8/just%20tauri%20todo.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">just tauri todo</source>
      <description>基本信息 链接: https://github.com/erduotong/just-tauri-todo Release: https://github.com/erduotong/just-tauri-todo/releases/latest 简介 这是一个基于Tauri的练手项目，旨在帮助了解Tauri的前后端通信/状态管理，采用了最经典的Tod...</description>
      <category>blog</category>
      <pubDate>Fri, 15 Nov 2024 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>基本信息</h2>
<ul>
<li>链接: <a href="https://github.com/erduotong/just-tauri-todo" target="_blank" rel="noopener noreferrer">https://github.com/erduotong/just-tauri-todo</a></li>
<li>Release: <a href="https://github.com/erduotong/just-tauri-todo/releases/latest" target="_blank" rel="noopener noreferrer">https://github.com/erduotong/just-tauri-todo/releases/latest</a></li>
</ul>
<h2>简介</h2>
<p>这是一个基于Tauri的练手项目，旨在帮助了解Tauri的前后端通信/状态管理，采用了最经典的Todo。<br>
经过测试，可以正常构建+运行<br>
应用截图:</p>
<figure><img src="/image/IMG-20251018 220106568-just tauri todo.png" alt="IMG-20251018 220106568-just tauri todo.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 220106568-just tauri todo.png</figcaption></figure>
<h2>技术栈</h2>
<h3>前端</h3>
<ul>
<li>Vue</li>
<li>Typescript</li>
<li>tailwind css</li>
</ul>
<h3>框架</h3>
<ul>
<li>Tauri</li>
</ul>
<h3>IDE</h3>
<ul>
<li>前端开发: Webstorm</li>
<li>后端(Rust端): Vscode + RustRover(不得不说RR真难用)</li>
</ul>
<h2>项目亮点</h2>
<ul>
<li>使用Tauri开发</li>
<li>极小的打包体积</li>
<li>Rust后端</li>
</ul>
]]></content:encoded>
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    </item>
    <item>
      <title>README</title>
      <link>https://blog.erduotong.com/20%20Area/%E5%85%B3%E4%BA%8E%E6%88%91/%E4%B8%AA%E4%BA%BA%E9%A1%B9%E7%9B%AE%E5%88%97%E8%A1%A8/project-%E4%B8%AA%E4%BA%BA%E9%A1%B9%E7%9B%AE%E5%88%97%E8%A1%A8.html</link>
      <guid>https://blog.erduotong.com/20%20Area/%E5%85%B3%E4%BA%8E%E6%88%91/%E4%B8%AA%E4%BA%BA%E9%A1%B9%E7%9B%AE%E5%88%97%E8%A1%A8/project-%E4%B8%AA%E4%BA%BA%E9%A1%B9%E7%9B%AE%E5%88%97%E8%A1%A8.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">README</source>
      <description>前端 应用 just tauri todo 一个简单的，基于Tauri的Todo应用</description>
      <pubDate>Fri, 09 May 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<hr>
<h1>前端</h1>
<ul>
<li></li>
</ul>
<h1>应用</h1>
<div class="ab-note drop-shadow"><div class="ab-items ab-card ab-lay-vfall ab-col3"><div class="ab-items-item"><div class="ab-items-title markdown-rendered"><div><p><a class="route-link" href="/20 Area/关于我/个人项目列表/just%20tauri%20todo.html">just tauri todo</a></p>
</div></div><div class="ab-items-content markdown-rendered"><div><p>一个简单的，基于Tauri的Todo应用</p>
</div></div></div></div></div>]]></content:encoded>
    </item>
    <item>
      <title>10.1 MOC-物理题目分析（初中）</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1%20MOC-%E7%89%A9%E7%90%86%E9%A2%98%E7%9B%AE%E5%88%86%E6%9E%90%EF%BC%88%E5%88%9D%E4%B8%AD%EF%BC%89.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1%20MOC-%E7%89%A9%E7%90%86%E9%A2%98%E7%9B%AE%E5%88%86%E6%9E%90%EF%BC%88%E5%88%9D%E4%B8%AD%EF%BC%89.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">10.1 MOC-物理题目分析（初中）</source>
      <description>专题分析 注意事项 作图 方法 做题思路/思想</description>
      <category>卡片/moc</category>
      <pubDate>Tue, 13 May 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>专题分析</h2>
<ul>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1a%20%E6%9D%A0%E6%9D%86%E8%BD%AC%E5%8A%A8%E6%97%B6%E5%8A%A8%E5%8A%9B%E4%B8%8D%E5%8F%98%E5%88%86%E6%9E%90.html" target="_blank">10.1a 杠杆转动时动力不变分析</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1b%20%E6%B5%AE%E5%8A%9B%E4%B8%8E%E7%94%B5%E5%AD%90%E7%A7%A4%E9%87%8D%E9%87%8F%E7%9A%84%E5%88%86%E6%9E%90.html" target="_blank">10.1b 浮力与电子秤重量的分析</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1j%20%E6%B3%A8%E5%B0%84%E5%99%A8%E6%B5%8B%E5%A4%A7%E6%B0%94%E5%8E%8B%E5%BC%BA.html" target="_blank">10.1j 注射器测大气压强</a></li>
</ul>
<h2>注意事项</h2>
<ul>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1d%20%E7%94%B5%E8%B7%AF%E8%B0%83%E6%95%B4%E6%B3%A8%E6%84%8F%E4%BA%8B%E9%A1%B9.html" target="_blank">10.1d 电路调整注意事项</a></li>
</ul>
<h3>作图</h3>
<ul>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1e%20%E6%9D%A0%E6%9D%86%E4%BD%9C%E5%9B%BE%E6%B3%A8%E6%84%8F%E4%BA%8B%E9%A1%B9.html" target="_blank">10.1e 杠杆作图注意事项</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1f%20%E5%9B%BE%E8%A1%A8%E9%A2%98%E6%B3%A8%E6%84%8F%E4%BA%8B%E9%A1%B9.html" target="_blank">10.1f 图表题注意事项</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1e1%20%E5%85%89%E5%AD%A6%E4%BD%9C%E5%9B%BE%E6%B3%A8%E6%84%8F%E4%BA%8B%E9%A1%B9.html" target="_blank">10.1e1 光学作图注意事项</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1g%20%E5%8A%9B%E7%9A%84%E6%96%B9%E5%90%91%E7%9A%84%E5%88%86%E6%9E%90.html" target="_blank">10.1g 力的方向的分析</a></li>
</ul>
<h2>方法</h2>
<ul>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1c%20%E6%B5%8B%E9%87%8F%E6%B3%A8%E5%B0%84%E5%99%A8%E6%A8%AA%E6%88%AA%E9%9D%A2%E7%A7%AF.html" target="_blank">10.1c 测量注射器横截面积</a></li>
</ul>
<h2>做题思路/思想</h2>
<ul>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/5.1a%20%E7%89%A9%E7%90%86%E7%94%B5%E8%B7%AF%E5%88%86%E6%9E%90%E4%B8%AD%E7%9A%84%E7%BF%BB%E8%BD%AC%E6%80%9D%E6%83%B3.html" target="_blank">5.1a 物理电路分析中的翻转思想</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/5.1b%20%E9%80%8F%E9%95%9C%E4%B8%AD%E7%9A%84%E7%BF%BB%E8%BD%AC%E6%80%9D%E7%BB%B4.html" target="_blank">5.1b 透镜中的翻转思维</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/5.1c%20%E7%89%A9%E4%BD%93%E7%9B%B8%E5%AF%B9%E8%BF%90%E5%8A%A8%E6%91%A9%E6%93%A6%E5%8A%9B%E4%B8%AD%E7%9A%84%E6%96%B9%E5%90%91.html" target="_blank">5.1c 物体相对运动摩擦力中的方向</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/5.1a1%20%E7%89%A9%E7%90%86%E5%9B%BE%E8%A1%A8%E4%B8%AD%E7%9A%84%E7%BF%BB%E8%BD%AC%E6%80%9D%E7%BB%B4.html" target="_blank">5.1a1 物理图表中的翻转思维</a></li>
</ul>
]]></content:encoded>
    </item>
    <item>
      <title>10.1a 杠杆转动时动力不变分析</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1a%20%E6%9D%A0%E6%9D%86%E8%BD%AC%E5%8A%A8%E6%97%B6%E5%8A%A8%E5%8A%9B%E4%B8%8D%E5%8F%98%E5%88%86%E6%9E%90.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1a%20%E6%9D%A0%E6%9D%86%E8%BD%AC%E5%8A%A8%E6%97%B6%E5%8A%A8%E5%8A%9B%E4%B8%8D%E5%8F%98%E5%88%86%E6%9E%90.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">10.1a 杠杆转动时动力不变分析</source>
      <description>题目描述 用竖直向上的力拉动一个质量分布均匀的杠杆 有一个阻力，物体的G，始终保持垂直 问拉力F的大小变化情况？ 解答 不变 Drawing 2025-04-15 22.19.07.excalidraw 可以看到，因为这两个力始终竖直向下，所以我们可以构造出两个相似三角形 因为两个作用点的位置是一致的，所以相似比一定就是一致的 那么我们就可以知道，两条...</description>
      <category>卡片/普通</category>
      <pubDate>Tue, 15 Apr 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>题目描述</h2>
<ul>
<li>用竖直向上的力拉动一个质量分布均匀的杠杆</li>
<li>有一个阻力，物体的G，始终保持垂直</li>
<li>问拉力F的大小变化情况？</li>
</ul>
<h2>解答</h2>
<ul>
<li>
<p><strong>不变</strong><br>
</p>
</li>
<li>
<p>可以看到，因为这两个力始终竖直向下，所以我们可以构造出两个相似三角形</p>
</li>
<li>
<p>因为两个作用点的位置是一致的，所以相似比一定就是一致的</p>
</li>
<li>
<p>那么我们就可以知道，两条力臂的长度比一定是一致的</p>
</li>
<li>
<p>根据 <span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>F</mi><mn>1</mn></msub><msub><mi>l</mi><mn>1</mn></msub><mo>=</mo><msub><mi>F</mi><mn>2</mn></msub><msub><mi>l</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">F_1l_1=F_2l_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0197em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0197em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> 可以知道，如果力臂长度比一定，那么另外两个力的比值一定是一样的</p>
</li>
<li>
<p>因为G固定，所以比值一定，F也固定</p>
</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
    </item>
    <item>
      <title>10.1b 浮力与电子秤重量的分析</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1b%20%E6%B5%AE%E5%8A%9B%E4%B8%8E%E7%94%B5%E5%AD%90%E7%A7%A4%E9%87%8D%E9%87%8F%E7%9A%84%E5%88%86%E6%9E%90.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1b%20%E6%B5%AE%E5%8A%9B%E4%B8%8E%E7%94%B5%E5%AD%90%E7%A7%A4%E9%87%8D%E9%87%8F%E7%9A%84%E5%88%86%E6%9E%90.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">10.1b 浮力与电子秤重量的分析</source>
      <description>题目描述 Drawing 2025-04-15 22.29.25.excalidrawDrawing 2025-04-15 22.29.25.excalidraw 有一个杯子，里面有一些水，测量电子秤示数为m1​ 放入一个物体，用绳子挂着，不沉底，测量电子秤示数为m2 让物体完全沉底，测量电子秤示数为m3​ 求浮力的表达式 解答 设水和杯子的质量 m水...</description>
      <category>卡片/普通</category>
      <pubDate>Tue, 15 Apr 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>题目描述</h2>
<figure><figcaption>Drawing 2025-04-15 22.29.25.excalidraw</figcaption></figure>
<ul>
<li>有一个杯子，里面有一些水，测量电子秤示数为<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">m_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></li>
<li>放入一个物体，用绳子挂着，不沉底，测量电子秤示数为<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi><mn>2</mn></mrow><annotation encoding="application/x-tex">m2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord mathnormal">m</span><span class="mord">2</span></span></span></span></li>
<li>让物体完全沉底，测量电子秤示数为<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mn>3</mn></msub></mrow><annotation encoding="application/x-tex">m_3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></li>
<li>求浮力的表达式</li>
</ul>
<h2>解答</h2>
<ul>
<li>设水和杯子的质量 <span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mtext>水</mtext></msub></mrow><annotation encoding="application/x-tex">m_水</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">水</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>，物体的质量<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mtext>物</mtext></msub></mrow><annotation encoding="application/x-tex">m_物</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">物</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>，拉力的量<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mtext>拉</mtext></msub></mrow><annotation encoding="application/x-tex">m_拉</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">拉</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> <code>因为转换成G也一样，就用m了，方便点</code></li>
<li>分析第三个杯子，使用整体法可以知道，现在质量就是二者相加，即 <span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mn>3</mn></msub><mo>=</mo><msub><mi>m</mi><mtext>水</mtext></msub><mo>+</mo><msub><mi>m</mi><mtext>物</mtext></msub></mrow><annotation encoding="application/x-tex">m_3 = m_水 + m_物</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">水</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">物</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></li>
<li>分析第二个杯子，可以知道对于物体来说，三力平衡 <span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mtext>物</mtext></msub><mo>=</mo><msub><mi>m</mi><mtext>浮</mtext></msub><mo>+</mo><msub><mi>m</mi><mtext>拉</mtext></msub></mrow><annotation encoding="application/x-tex">m_物 = m_浮 + m_拉</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">物</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">浮</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">拉</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></li>
<li>所以 <span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mtext>拉</mtext></msub><mo>=</mo><msub><mi>m</mi><mtext>物</mtext></msub><mo>−</mo><msub><mi>m</mi><mtext>浮</mtext></msub></mrow><annotation encoding="application/x-tex">m_拉 = m_物 - m_浮</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">拉</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">物</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">浮</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></li>
<li>分析一下，对于m2和m3中，m2引入了一个拉力，所以<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mn>2</mn></msub><mo>=</mo><msub><mi>m</mi><mn>3</mn></msub><mo>−</mo><msub><mi>m</mi><mtext>拉</mtext></msub><mo>=</mo><msub><mi>m</mi><mtext>水</mtext></msub><mo>+</mo><msub><mi>m</mi><mtext>物</mtext></msub><mo>−</mo><msub><mi>m</mi><mtext>拉</mtext></msub></mrow><annotation encoding="application/x-tex">m_2 = m_3 - m_拉 = m_水+m_物-m_拉</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">拉</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">水</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">物</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">拉</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></li>
<li>再带入刚刚的<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mtext>拉</mtext></msub><mo>=</mo><msub><mi>m</mi><mtext>物</mtext></msub><mo>−</mo><msub><mi>m</mi><mtext>浮</mtext></msub></mrow><annotation encoding="application/x-tex">m_拉 = m_物 - m_浮</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">拉</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">物</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">浮</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></li>
<li>那么我们就可以得到 <span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mn>2</mn></msub><mo>=</mo><msub><mi>m</mi><mtext>水</mtext></msub><mo>+</mo><msub><mi>m</mi><mtext>物</mtext></msub><mo>−</mo><mo stretchy="false">(</mo><msub><mi>m</mi><mtext>物</mtext></msub><mo>−</mo><msub><mi>m</mi><mtext>浮</mtext></msub><mo stretchy="false">)</mo><mo>=</mo><msub><mi>m</mi><mtext>水</mtext></msub><mo>+</mo><msub><mi>m</mi><mtext>浮</mtext></msub></mrow><annotation encoding="application/x-tex">m_2 = m_水 + m_物 - (m_物 - m_浮) = m_水 + m_浮</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">水</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">物</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">物</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">浮</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">水</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord cjk_fallback mtight">浮</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></li>
<li>这样，我们就知道 <span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">m_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> 是水和浮力的总和了，其他的也就可以推导出来了。</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
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    <item>
      <title>10.1d 电路调整注意事项</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1d%20%E7%94%B5%E8%B7%AF%E8%B0%83%E6%95%B4%E6%B3%A8%E6%84%8F%E4%BA%8B%E9%A1%B9.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1d%20%E7%94%B5%E8%B7%AF%E8%B0%83%E6%95%B4%E6%B3%A8%E6%84%8F%E4%BA%8B%E9%A1%B9.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">10.1d 电路调整注意事项</source>
      <description>常见设问 接下来，某个人的操作是... 断开开关 注意设问，不要硬套 滑动滑动变阻器的时候，要看着电表而不是灯泡/滑动变阻器 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Fri, 02 May 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">常见设问</div>
</div>
<div class="callout-content"><p>接下来，某个人的操作是...</p>
</div></div><ul>
<li><strong>断开开关</strong>
<ul>
<li>注意设问，不要硬套</li>
</ul>
</li>
<li>滑动滑动变阻器的时候，要看着电表而不是灯泡/滑动变阻器</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
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    <item>
      <title>10.1e 杠杆作图注意事项</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1e%20%E6%9D%A0%E6%9D%86%E4%BD%9C%E5%9B%BE%E6%B3%A8%E6%84%8F%E4%BA%8B%E9%A1%B9.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1e%20%E6%9D%A0%E6%9D%86%E4%BD%9C%E5%9B%BE%E6%B3%A8%E6%84%8F%E4%BA%8B%E9%A1%B9.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">10.1e 杠杆作图注意事项</source>
      <description>画最小作用力/阻力 找到离支点的最远点 注意最远点可能在杠杆两侧，而不是一定和阻力/作用力在相反的反向，也不一定是在同一方向 比如下图，画能最小动力，C点画的就是错误的，正确的在B点 Drawing 2025-05-13 23.28.28.excalidraw 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Tue, 13 May 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>画最小作用力/阻力</h2>
<ul>
<li>找到离支点的最远点<br>
注意<strong>最远点可能在杠杆两侧</strong>，而不是一定和阻力/作用力在相反的反向，也不一定是在同一方向</li>
<li>比如下图，画能最小动力，<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi></mrow><annotation encoding="application/x-tex">C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span></span></span></span>点画的就是错误的，正确的在<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>B</mi></mrow><annotation encoding="application/x-tex">B</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span></span>点<br>
</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
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    <item>
      <title>10.1e1 光学作图注意事项</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1e1%20%E5%85%89%E5%AD%A6%E4%BD%9C%E5%9B%BE%E6%B3%A8%E6%84%8F%E4%BA%8B%E9%A1%B9.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1e1%20%E5%85%89%E5%AD%A6%E4%BD%9C%E5%9B%BE%E6%B3%A8%E6%84%8F%E4%BA%8B%E9%A1%B9.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">10.1e1 光学作图注意事项</source>
      <description>垂直符号 虚线/实线 是否是真实光线 是不是反向延长线 注意描述 经过 --&amp;gt; 要出头 到达/发出 --&amp;gt; 不出头 具体题型</description>
      <category>卡片/普通</category>
      <pubDate>Tue, 20 May 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<ul>
<li><strong>垂直符号</strong></li>
<li>虚线/实线
<ul>
<li>是否是真实光线</li>
<li>是不是反向延长线</li>
</ul>
</li>
<li>注意描述
<ul>
<li>经过 --&gt; 要出头</li>
<li>到达/发出 --&gt; 不出头</li>
</ul>
</li>
</ul>
<h2>具体题型</h2>
<ul>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1e1a%20%E5%87%B8%E9%80%8F%E9%95%9C%E6%88%90%E5%83%8F%E7%9A%84%E7%BB%98%E5%88%B6.html" target="_blank">10.1e1a 凸透镜成像的绘制</a></li>
</ul>
]]></content:encoded>
    </item>
    <item>
      <title>10.1e1a 凸透镜成像的绘制</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1e1a%20%E5%87%B8%E9%80%8F%E9%95%9C%E6%88%90%E5%83%8F%E7%9A%84%E7%BB%98%E5%88%B6.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1e1a%20%E5%87%B8%E9%80%8F%E9%95%9C%E6%88%90%E5%83%8F%E7%9A%84%E7%BB%98%E5%88%B6.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">10.1e1a 凸透镜成像的绘制</source>
      <description>前言 已知一个物，求一个光屏上他的像？ 怎么做 将物进行旋转180° 将物进行左右对称 为什么 光沿直线传播，穿过透镜后会去到另一边 Drawing 2025-05-27 23.14.50.excalidraw 技巧 把物所在的试卷翻过来，在背面看 再转180°试卷，使其倒过来 观察背面看到的，记下来，再翻回去选 参见 参考文献</description>
      <category>卡片/普通</category>
      <pubDate>Tue, 27 May 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p>已知一个物，求一个光屏上他的像？</p>
</div></div><h2>怎么做</h2>
<ul>
<li>将物进行旋转<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>180</mn><mi mathvariant="normal">°</mi></mrow><annotation encoding="application/x-tex">180°</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">180°</span></span></span></span></li>
<li>将物进行左右对称</li>
</ul>
<h2>为什么</h2>
<ul>
<li>光沿直线传播，穿过透镜后会去到另一边<br>
</li>
</ul>
<h2>技巧</h2>
<ul>
<li>把物所在的试卷翻过来，在背面看</li>
<li>再转180°试卷，使其倒过来</li>
<li>观察背面看到的，记下来，再翻回去选</li>
</ul>
<h2>参见</h2>
<ul>
<li><a href="/40%20Archive/2022-2025%20%E5%88%9D%E4%B8%AD/%E5%AD%A6%E7%A7%91%E7%AC%94%E8%AE%B0/%E7%89%A9%E7%90%86%E9%94%99%E9%A2%98/%E5%91%A8%E6%B5%8B/week21/%E9%80%8F%E9%95%9C%E4%BD%9C%E5%9B%BE.html" target="_blank">透镜作图</a></li>
</ul>
<h2>参考文献</h2>
]]></content:encoded>
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      <title>10.1f 图表题注意事项</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1f%20%E5%9B%BE%E8%A1%A8%E9%A2%98%E6%B3%A8%E6%84%8F%E4%BA%8B%E9%A1%B9.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1f%20%E5%9B%BE%E8%A1%A8%E9%A2%98%E6%B3%A8%E6%84%8F%E4%BA%8B%E9%A1%B9.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">10.1f 图表题注意事项</source>
      <description>前言 沟槽的图表题 注意表述 绘制出表格中的数据(不能多画) 画出关系图象 （画完整） 能否经过原点 反比例函数不能画到0上 如果电学有R1​的图的话，也注意不能到0点(但是可以用虚线) 注意取值范围 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Tue, 13 May 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p>沟槽的图表题</p>
</div></div><ul>
<li>注意表述
<ul>
<li>绘制出表格中的数据(不能多画)</li>
<li>画出关系图象 （画完整）</li>
</ul>
</li>
<li>能否经过原点
<ul>
<li>反比例函数不能画到0上</li>
<li>如果电学有<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>1</mn><mi>R</mi></mfrac></mrow><annotation encoding="application/x-tex">\frac{1}{R}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.1901em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.00773em;">R</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>的图的话，也注意<strong>不能到0点</strong>(但是可以用虚线)</li>
</ul>
</li>
<li>注意取值范围</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
    </item>
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      <title>10.1j 注射器测大气压强</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1j%20%E6%B3%A8%E5%B0%84%E5%99%A8%E6%B5%8B%E5%A4%A7%E6%B0%94%E5%8E%8B%E5%BC%BA.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1j%20%E6%B3%A8%E5%B0%84%E5%99%A8%E6%B5%8B%E5%A4%A7%E6%B0%94%E5%8E%8B%E5%BC%BA.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">10.1j 注射器测大气压强</source>
      <description>题目参考 小明利用的轻质注射器等器材测量大气压。 为得到活塞横截面积，需要量取的长度为 ___ cm。当注射器中活塞刚开始滑动时弹簧测力计的示数如图所示，记下弹簧测力计稳定时的示数为 ___ 考虑到摩擦因素，小明取下橡皮帽，再次拉动注射器筒，记下弹簧测力计稳定时的示数为 0.7N。此过程中活塞受到的摩擦力方向___ 利用以上数据可估算大气压强是 ___...</description>
      <category>卡片/普通</category>
      <pubDate>Tue, 29 Apr 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>题目参考</h2>
<p>小明利用的轻质注射器等器材测量大气压。</p>
<ol>
<li>为得到活塞横截面积，需要量取的长度为 ___ cm。当注射器中活塞刚开始滑动时弹簧测力计的示数如图所示，记下弹簧测力计稳定时的示数为 ___</li>
<li>考虑到摩擦因素，小明取下橡皮帽，再次拉动注射器筒，记下弹簧测力计稳定时的示数为 0.7N。此过程中活塞受到的摩擦力方向___</li>
<li>利用以上数据可估算大气压强是 ___Pa。已知实验时外界大气压为 <span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1.0</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup></mrow><annotation encoding="application/x-tex">1.0 \times 10^5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1.0</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">5</span></span></span></span></span></span></span></span></span></span></span> Pa，则造成该偏差的最有可能原因是：___</li>
</ol>
<figure><img src="/image/IMG-20251018 215536007-10.1j 注射器测大气压强.png" alt="IMG-20251018 215536007-10.1j 注射器测大气压强.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536007-10.1j 注射器测大气压强.png</figcaption></figure>
<h2>解答</h2>
<h3>第一问</h3>
<p>参见 <a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/10.1c%20%E6%B5%8B%E9%87%8F%E6%B3%A8%E5%B0%84%E5%99%A8%E6%A8%AA%E6%88%AA%E9%9D%A2%E7%A7%AF.html" target="_blank">10.1c 测量注射器横截面积</a>，其他的就是基本读数</p>
<h3>第二问</h3>
<ul>
<li>第一小空 测力
<ul>
<li><strong>橡皮帽</strong>指的是注射器针头上的东西</li>
<li>所以取下橡皮帽，内外压强一致，所以测得就是纯摩擦</li>
<li>没取下测的就是最终结果+摩擦，就是大气压强造成的压力（注意要<strong>刚好拉动</strong>）</li>
</ul>
</li>
<li>第二空 问摩擦力方向
<ul>
<li>注射器壁向右运动</li>
<li>相对来说，活塞向左运动</li>
<li>那么摩擦力就是向右</li>
<li>可以参考<a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/5.1c%20%E7%89%A9%E4%BD%93%E7%9B%B8%E5%AF%B9%E8%BF%90%E5%8A%A8%E6%91%A9%E6%93%A6%E5%8A%9B%E4%B8%AD%E7%9A%84%E6%96%B9%E5%90%91.html" target="_blank">5.1c 物体相对运动摩擦力中的方向</a></li>
</ul>
</li>
</ul>
<h3>第三问</h3>
<ul>
<li>测不准的原因：<strong>空气未排尽</strong></li>
<li>大气压强用 <span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo>=</mo><mfrac><mi>F</mi><mi>S</mi></mfrac></mrow><annotation encoding="application/x-tex">p = \frac{F}{S}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">p</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2173em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8723em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.05764em;">S</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">F</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span> ，把刚刚测得的压力和横截面积送进去就行</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
      <enclosure url="https://blog.erduotong.com/image/IMG-20251018 215536007-10.1j 注射器测大气压强.png" type="image/png"/>
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    <item>
      <title>11.2a 正切-和差角公式</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/11.2a%20%E6%AD%A3%E5%88%87-%E5%92%8C%E5%B7%AE%E8%A7%92%E5%85%AC%E5%BC%8F.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/11.2a%20%E6%AD%A3%E5%88%87-%E5%92%8C%E5%B7%AE%E8%A7%92%E5%85%AC%E5%BC%8F.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">11.2a 正切-和差角公式</source>
      <description>表示两个tan的值相加/相减 主体 tan(α±β)=1∓tanαtanβtanα±tanβ​ TIP 其中的±是和∓相反的 也就是如果使用的是tan(α+β) 那么右侧的分母就应该用1−tanαtanβ 参考文献 三角函数差角公式_百度百科</description>
      <category>卡片/普通</category>
      <pubDate>Sat, 17 May 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<ul>
<li>表示两个tan的值相加/相减</li>
</ul>
<h2>主体</h2>
<p v-pre="" class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>tan</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>α</mi><mo>±</mo><mi>β</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mi>tan</mi><mo>⁡</mo><mi>α</mi><mo>±</mo><mi>tan</mi><mo>⁡</mo><mi>β</mi></mrow><mrow><mn>1</mn><mo>∓</mo><mi>tan</mi><mo>⁡</mo><mi>α</mi><mi>tan</mi><mo>⁡</mo><mi>β</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\tan(\alpha \pm \beta) = \frac{\tan\alpha \pm \tan\beta}{1 \mp \tan\alpha \tan\beta}
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">tan</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.0037em;">α</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05278em;">β</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.2519em;vertical-align:-0.8804em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∓</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mop">tan</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.0037em;">α</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">tan</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.05278em;">β</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mop">tan</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.0037em;">α</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mop">tan</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.05278em;">β</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.8804em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>

<div class="callout" data-callout="note">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-pencil"><path d="M17 3a2.85 2.83 0 1 1 4 4L7.5 20.5 2 22l1.5-5.5Z"></path><path d="m15 5 4 4"></path></svg>
</div>
<div class="callout-title-inner">TIP</div>
</div>
<div class="callout-content"><p>其中的<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>±</mo></mrow><annotation encoding="application/x-tex">\pm</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">±</span></span></span></span>是和<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>∓</mo></mrow><annotation encoding="application/x-tex">\mp</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em;"></span><span class="mord">∓</span></span></span></span>相反的<br>
也就是如果使用的是<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>tan</mi><mo>⁡</mo><mo stretchy="false">(</mo><mi>α</mi><mo>+</mo><mi>β</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\tan(\alpha + \beta)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">tan</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.0037em;">α</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05278em;">β</span><span class="mclose">)</span></span></span></span><br>
那么右侧的分母就应该用<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo>−</mo><mi>tan</mi><mo>⁡</mo><mi>α</mi><mi>tan</mi><mo>⁡</mo><mi>β</mi></mrow><annotation encoding="application/x-tex">1 - \tan\alpha \tan\beta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mop">tan</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.0037em;">α</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">tan</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.05278em;">β</span></span></span></span></p>
</div></div><h2>参考文献</h2>
<ul>
<li><a href="https://baike.baidu.com/item/%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0%E5%B7%AE%E8%A7%92%E5%85%AC%E5%BC%8F/1687728" target="_blank" rel="noopener noreferrer">三角函数差角公式_百度百科</a></li>
</ul>
]]></content:encoded>
    </item>
    <item>
      <title>2.1 Proxifier</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.1%20Proxifier.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.1%20Proxifier.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.1 Proxifier</source>
      <description>简介 Proxifier是一款socket5代理工具，它可以让精确的指定应用获得代理 下载 前往Proxifier官网下载 (支持Windows、MacOS、Android)，随后正常安装 激活 见</description>
      <category>卡片/普通</category>
      <pubDate>Sat, 07 Dec 2024 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>简介</h2>
<p><a href="https://www.proxifier.com/" target="_blank" rel="noopener noreferrer">Proxifier</a>是一款socket5代理工具，它可以让精确的指定应用获得代理</p>
<h2>下载</h2>
<p>前往<a href="https://www.proxifier.com/" target="_blank" rel="noopener noreferrer">Proxifier官网下载</a> (支持Windows、MacOS、Android)，随后正常安装</p>
<h2>激活</h2>
<p>见<a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.1a%20Proxifier%E6%BF%80%E6%B4%BB.html" target="_blank">2.1a Proxifier激活</a></p>
]]></content:encoded>
    </item>
    <item>
      <title>2.10 浏览器资源提示符</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10%20%E6%B5%8F%E8%A7%88%E5%99%A8%E8%B5%84%E6%BA%90%E6%8F%90%E7%A4%BA%E7%AC%A6.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10%20%E6%B5%8F%E8%A7%88%E5%99%A8%E8%B5%84%E6%BA%90%E6%8F%90%E7%A4%BA%E7%AC%A6.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.10 浏览器资源提示符</source>
      <description>前言 随着前端的发展，出现了不同资源的加载需求 所以出现了资源提示符来改善加载速度，让开发者更完全的控制 为什么？ 控制不同资源的加载时机 加快页面访问 参见 用于&amp;lt;script&amp;gt;标签 用于&amp;lt;link&amp;gt;标签 参考文献 资源提示符【渡一教育】_哔哩哔哩_bilibili 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Wed, 26 Mar 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p>随着前端的发展，出现了不同资源的加载需求<br>
所以出现了资源提示符来改善加载速度，让开发者更完全的控制</p>
</div></div><h2>为什么？</h2>
<ul>
<li>控制不同资源的加载时机</li>
<li>加快页面访问</li>
</ul>
<h2>参见</h2>
<h3>用于&lt;script&gt;标签</h3>
<ul>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10a%20async%E6%8F%90%E7%A4%BA%E7%AC%A6.html" target="_blank">2.10a async提示符</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10b%20defer%E6%8F%90%E7%A4%BA%E7%AC%A6.html" target="_blank">2.10b defer提示符</a></li>
</ul>
<h3>用于&lt;link&gt;标签</h3>
<ul>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10c%20preload%E6%8F%90%E7%A4%BA%E7%AC%A6.html" target="_blank">2.10c preload提示符</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10d%20prefetch%E6%8F%90%E7%A4%BA%E7%AC%A6.html" target="_blank">2.10d prefetch提示符</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10e%20dns-prefetch%E6%8F%90%E7%A4%BA%E7%AC%A6.html" target="_blank">2.10e dns-prefetch提示符</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10f%20prerender%E6%8F%90%E7%A4%BA%E7%AC%A6.html" target="_blank">2.10f prerender提示符</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10g%20preconnect%E6%8F%90%E7%A4%BA%E7%AC%A6.html" target="_blank">2.10g preconnect提示符</a></li>
</ul>
<h2>参考文献</h2>
<p><a href="https://www.bilibili.com/video/BV1M5XVYxENz/?vd_source=55526ae438eb9f21ccd7738267eaf0e8" target="_blank" rel="noopener noreferrer">资源提示符【渡一教育】_哔哩哔哩_bilibili</a></p>
<h2>脚注</h2>
]]></content:encoded>
    </item>
    <item>
      <title>2.10a async提示符</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10a%20async%E6%8F%90%E7%A4%BA%E7%AC%A6.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10a%20async%E6%8F%90%E7%A4%BA%E7%AC%A6.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.10a async提示符</source>
      <description>用法 用于 &amp;lt;script&amp;gt;标签 作用 资源提示符 async&amp;defer.excalidraw资源提示符 async&amp;defer.excalidraw 在加载脚本的同时，继续执行DOM (异步执行) 但是脚本加载完毕后，就会阻塞DOM，开始执行 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Wed, 26 Mar 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>用法</h2>
<ul>
<li>用于 <code>&lt;script&gt;</code>标签</li>
</ul>
<div class="language-html line-numbers-mode" data-highlighter="shiki" data-ext="html" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-html"><span class="line"><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">&lt;</span><span style="--shiki-light:#E45649;--shiki-dark:#E06C75">script</span><span style="--shiki-light:#986801;--shiki-dark:#D19A66"> async</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">&gt;&lt;/</span><span style="--shiki-light:#E45649;--shiki-dark:#E06C75">script</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">&gt;</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div><h2>作用</h2>
<figure><figcaption>资源提示符 async&amp;defer.excalidraw</figcaption></figure>
<ul>
<li>在加载脚本的同时，继续执行DOM (异步执行)</li>
<li>但是脚本加载完毕后，就会阻塞DOM，开始执行</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
    </item>
    <item>
      <title>2.10b defer提示符</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10b%20defer%E6%8F%90%E7%A4%BA%E7%AC%A6.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10b%20defer%E6%8F%90%E7%A4%BA%E7%AC%A6.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.10b defer提示符</source>
      <description>用法 用于 &amp;lt;script&amp;gt;标签 作用 资源提示符 async&amp;defer.excalidraw资源提示符 async&amp;defer.excalidraw 加载的script的同时，继续解析DOM 在DOM解析完成后，再运行 使用的时候，就可以保证能访问完整的DOM了 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Wed, 26 Mar 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>用法</h2>
<ul>
<li>用于 <code>&lt;script&gt;</code>标签</li>
</ul>
<div class="language-html line-numbers-mode" data-highlighter="shiki" data-ext="html" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-html"><span class="line"><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">&lt;</span><span style="--shiki-light:#E45649;--shiki-dark:#E06C75">script</span><span style="--shiki-light:#986801;--shiki-dark:#D19A66"> defer</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">&gt;&lt;/</span><span style="--shiki-light:#E45649;--shiki-dark:#E06C75">script</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">&gt;</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div><h2>作用</h2>
<figure><figcaption>资源提示符 async&amp;defer.excalidraw</figcaption></figure>
<ul>
<li>加载的script的同时，继续解析DOM</li>
<li>在DOM解析完成后，再运行</li>
<li>使用的时候，就可以保证能访问完整的DOM了</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
    </item>
    <item>
      <title>2.10c preload提示符</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10c%20preload%E6%8F%90%E7%A4%BA%E7%AC%A6.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10c%20preload%E6%8F%90%E7%A4%BA%E7%AC%A6.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.10c preload提示符</source>
      <description>用法 用于 &amp;lt;link&amp;gt;标签 用完之后，还需要再正常引入一次资源 作用 预先下载一些资源，到时候要用的时候，随时可以用 拥有较高的优先级 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Wed, 26 Mar 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>用法</h2>
<ul>
<li>用于 <code>&lt;link&gt;</code>标签</li>
</ul>
<div class="language-html line-numbers-mode" data-highlighter="shiki" data-ext="html" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-html"><span class="line"><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">&lt;</span><span style="--shiki-light:#E45649;--shiki-dark:#E06C75">link</span><span style="--shiki-light:#986801;--shiki-dark:#D19A66"> rel</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">=</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379">"preload"</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">&gt;</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div><ul>
<li>用完之后，还需要再正常引入一次资源</li>
</ul>
<h2>作用</h2>
<ul>
<li>预先下载一些资源，到时候要用的时候，随时可以用</li>
<li>拥有较高的优先级</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
    </item>
    <item>
      <title>2.10d prefetch提示符</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10d%20prefetch%E6%8F%90%E7%A4%BA%E7%AC%A6.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10d%20prefetch%E6%8F%90%E7%A4%BA%E7%AC%A6.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.10d prefetch提示符</source>
      <description>用法 用于 &amp;lt;link&amp;gt;标签 用完之后，还需要再正常引入一次资源 作用 在空闲事件加载可能要用的资源（以后要用的），比如其他页面 优先级比低 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Wed, 26 Mar 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>用法</h2>
<ul>
<li>用于 <code>&lt;link&gt;</code>标签</li>
</ul>
<div class="language-html line-numbers-mode" data-highlighter="shiki" data-ext="html" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-html"><span class="line"><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">&lt;</span><span style="--shiki-light:#E45649;--shiki-dark:#E06C75">link</span><span style="--shiki-light:#986801;--shiki-dark:#D19A66"> rel</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">=</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379">"prefetch"</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">&gt;</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div><ul>
<li>用完之后，还需要再正常引入一次资源</li>
</ul>
<h2>作用</h2>
<ul>
<li>在空闲事件加载可能要用的资源（以后要用的），比如其他页面</li>
<li>优先级比<a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10c%20preload%E6%8F%90%E7%A4%BA%E7%AC%A6.html" target="_blank">2.10c preload提示符</a>低</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
    </item>
    <item>
      <title>2.10e dns-prefetch提示符</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10e%20dns-prefetch%E6%8F%90%E7%A4%BA%E7%AC%A6.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10e%20dns-prefetch%E6%8F%90%E7%A4%BA%E7%AC%A6.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.10e dns-prefetch提示符</source>
      <description>用法 用于 &amp;lt;link&amp;gt;标签 用完之后，还需要再正常引入一次资源 作用 预先进行DNS解析 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Wed, 26 Mar 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>用法</h2>
<ul>
<li>用于 <code>&lt;link&gt;</code>标签</li>
</ul>
<div class="language-html line-numbers-mode" data-highlighter="shiki" data-ext="html" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-html"><span class="line"><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">&lt;</span><span style="--shiki-light:#E45649;--shiki-dark:#E06C75">link</span><span style="--shiki-light:#986801;--shiki-dark:#D19A66"> rel</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">=</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379">"dns-prefetch"</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">&gt;</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div><ul>
<li>用完之后，还需要再正常引入一次资源</li>
</ul>
<h2>作用</h2>
<ul>
<li>预先进行DNS解析</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
    </item>
    <item>
      <title>2.10f prerender提示符</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10f%20prerender%E6%8F%90%E7%A4%BA%E7%AC%A6.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10f%20prerender%E6%8F%90%E7%A4%BA%E7%AC%A6.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.10f prerender提示符</source>
      <description>用法 用于 &amp;lt;link&amp;gt;标签 作用 在后台预渲染某个页面 让用户点过去的时候可以立刻访问 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Wed, 26 Mar 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>用法</h2>
<ul>
<li>用于 <code>&lt;link&gt;</code>标签</li>
</ul>
<div class="language-html line-numbers-mode" data-highlighter="shiki" data-ext="html" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-html"><span class="line"><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">&lt;</span><span style="--shiki-light:#E45649;--shiki-dark:#E06C75">link</span><span style="--shiki-light:#986801;--shiki-dark:#D19A66"> rel</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">=</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379">"prerender"</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">&gt;</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div><h2>作用</h2>
<ul>
<li>在后台预渲染某个页面</li>
<li>让用户点过去的时候可以立刻访问</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
    </item>
    <item>
      <title>2.10g preconnect提示符</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10g%20preconnect%E6%8F%90%E7%A4%BA%E7%AC%A6.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.10g%20preconnect%E6%8F%90%E7%A4%BA%E7%AC%A6.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.10g preconnect提示符</source>
      <description>用法 用于 &amp;lt;link&amp;gt;标签 作用 预先进行连接 减少DNS查找、TCP握手等时间 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Wed, 26 Mar 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>用法</h2>
<ul>
<li>用于 <code>&lt;link&gt;</code>标签</li>
</ul>
<div class="language-html line-numbers-mode" data-highlighter="shiki" data-ext="html" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-html"><span class="line"><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">&lt;</span><span style="--shiki-light:#E45649;--shiki-dark:#E06C75">link</span><span style="--shiki-light:#986801;--shiki-dark:#D19A66"> rel</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">=</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379">"preconnect"</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">&gt;</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div><h2>作用</h2>
<ul>
<li>预先进行连接</li>
<li>减少DNS查找、TCP握手等时间</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
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    <item>
      <title>2.11 用国内手机号注册谷歌账号</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.11%20%E7%94%A8%E5%9B%BD%E5%86%85%E6%89%8B%E6%9C%BA%E5%8F%B7%E6%B3%A8%E5%86%8C%E8%B0%B7%E6%AD%8C%E8%B4%A6%E5%8F%B7.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.11%20%E7%94%A8%E5%9B%BD%E5%86%85%E6%89%8B%E6%9C%BA%E5%8F%B7%E6%B3%A8%E5%86%8C%E8%B0%B7%E6%AD%8C%E8%B4%A6%E5%8F%B7.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.11 用国内手机号注册谷歌账号</source>
      <description>前言 一般来说国内手机号+86是很难注册谷歌账号的，按网上的攻略也很难。截止到本卡片创建的时间，其他方法基本不可行 不过这个方法可行 操作 推荐使用Chrome浏览器 (下载) 打开设置，语言切到中文繁体 IMG-20251018 215536008-2.11 用国内手机号注册谷歌账号.pngIMG-20251018 215536008-2.11 用国...</description>
      <category>卡片/普通</category>
      <pubDate>Thu, 29 May 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p>一般来说国内手机号<code>+86</code>是很难注册谷歌账号的，按网上的攻略也很难。截止到本卡片创建的时间，其他方法基本不可行<br>
不过这个方法可行</p>
</div></div><h2>操作</h2>
<ul>
<li>推荐使用<strong>Chrome</strong>浏览器 (下载)</li>
<li>打开设置，语言切到<code>中文繁体</code></li>
</ul>
<figure><img src="/image/IMG-20251018 215536008-2.11 用国内手机号注册谷歌账号.png" alt="IMG-20251018 215536008-2.11 用国内手机号注册谷歌账号.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536008-2.11 用国内手机号注册谷歌账号.png</figcaption></figure>
<ul>
<li>点右上角，打开一个无痕窗口</li>
</ul>
<figure><img src="/image/IMG-20251018 215536632-2.11 用国内手机号注册谷歌账号.png" alt="IMG-20251018 215536632-2.11 用国内手机号注册谷歌账号.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536632-2.11 用国内手机号注册谷歌账号.png</figcaption></figure>
<ul>
<li>打开clash，打开<code>系统代理</code>，代理模式选择<code>全局</code></li>
<li>节点选择<strong>香港</strong>的</li>
<li>访问 <a href="https://gmail.com" target="_blank" rel="noopener noreferrer">gmail</a></li>
<li>按照正常流程注册</li>
<li>一路正常填信息就可以，等到填手机号的时候换成大陆的<code>+86</code>，手机也可以正常收到验证码</li>
<li>注册成功</li>
</ul>
<h2>一些可能的原理</h2>
<ul>
<li>香港离我国大陆很近</li>
<li>香港人有一个大陆手机号很合理</li>
<li>从某种程度上来看，谷歌也是挺合理的</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<ul>
<li><a href="https://bbs.scumaker.org/t/topic/558" target="_blank" rel="noopener noreferrer">https://bbs.scumaker.org/t/topic/558</a></li>
</ul>
]]></content:encoded>
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      <title>2.11a Google ai studio 无法保存的急救方法</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.11a%20Google%20ai%20studio%20%E6%97%A0%E6%B3%95%E4%BF%9D%E5%AD%98%E7%9A%84%E6%80%A5%E6%95%91%E6%96%B9%E6%B3%95.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.11a%20Google%20ai%20studio%20%E6%97%A0%E6%B3%95%E4%BF%9D%E5%AD%98%E7%9A%84%E6%80%A5%E6%95%91%E6%96%B9%E6%B3%95.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.11a Google ai studio 无法保存的急救方法</source>
      <description>前言 google的ai studio的自动保存真的是有时好有时坏的 经常就是没发现，继续对话后突然发现一直保存不上 这个卡片就是抢救数据的方法 打开Get SDK Code的页面 &amp;lt; &amp;gt; IMG-20251018 215536009-2.11a Google ai studio 无法保存的急救方法.pngIMG-20251018 215536009-...</description>
      <category>卡片/普通</category>
      <pubDate>Sat, 07 Jun 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p>google的ai studio的自动保存真的是有时好有时坏的<br>
经常就是没发现，继续对话后突然发现一直保存不上<br>
这个卡片就是抢救数据的方法</p>
</div></div><ul>
<li>打开Get SDK Code的页面 <code>&lt; &gt;</code></li>
</ul>
<figure><img src="/image/IMG-20251018 215536009-2.11a Google ai studio 无法保存的急救方法.png" alt="IMG-20251018 215536009-2.11a Google ai studio 无法保存的急救方法.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536009-2.11a Google ai studio 无法保存的急救方法.png</figcaption></figure>
<ul>
<li>打开 <code>Prompt history</code></li>
</ul>
<figure><img src="/image/IMG-20251018 215536633-2.11a Google ai studio 无法保存的急救方法.png" alt="IMG-20251018 215536633-2.11a Google ai studio 无法保存的急救方法.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536633-2.11a Google ai studio 无法保存的急救方法.png</figcaption></figure>
<ul>
<li></li>
</ul>
<figure><img src="/image/IMG-20251018 215548580-2.11a Google ai studio 无法保存的急救方法.png" alt="IMG-20251018 215548580-2.11a Google ai studio 无法保存的急救方法.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215548580-2.11a Google ai studio 无法保存的急救方法.png</figcaption></figure>
<p>可以看到，数据都还在</p>
<ul>
<li>到时候本地Python再做转换即可</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
]]></content:encoded>
      <enclosure url="https://blog.erduotong.com/image/IMG-20251018 215536009-2.11a Google ai studio 无法保存的急救方法.png" type="image/png"/>
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      <title>2.14 破解Davinci Resolve Studio</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.14%20%E7%A0%B4%E8%A7%A3Davinci%20Resolve%20Studio.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.14%20%E7%A0%B4%E8%A7%A3Davinci%20Resolve%20Studio.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.14 破解Davinci Resolve Studio</source>
      <description>破解方法 使用项目:resolve patch 从release里面下载exe，然后运行 一段时间后，应该可以自己完成破解 这样，达芬奇Studio就完成破解了 已知问题 在18.6.2版本以上时，破解后的达芬奇导出时顶部会出现闪烁的白边 正版则没这个问题</description>
      <category>卡片/普通</category>
      <pubDate>Tue, 12 Aug 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>破解方法</h2>
<ul>
<li>使用项目:<a href="https://github.com/unknowntrojan/resolvepatch" target="_blank" rel="noopener noreferrer">resolve patch</a></li>
<li>从release里面下载exe，然后运行</li>
<li>一段时间后，应该可以自己完成破解</li>
<li>这样，达芬奇Studio就完成破解了</li>
</ul>
<h2>已知问题</h2>
<p>在18.6.2版本以上时，破解后的达芬奇导出时顶部会出现闪烁的白边<br>
正版则没这个问题</p>
]]></content:encoded>
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    <item>
      <title>2.14a  解决达芬奇破解的渲染问题</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.14a%20%20%E8%A7%A3%E5%86%B3%E8%BE%BE%E8%8A%AC%E5%A5%87%E7%A0%B4%E8%A7%A3%E7%9A%84%E6%B8%B2%E6%9F%93%E9%97%AE%E9%A2%98.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.14a%20%20%E8%A7%A3%E5%86%B3%E8%BE%BE%E8%8A%AC%E5%A5%87%E7%A0%B4%E8%A7%A3%E7%9A%84%E6%B8%B2%E6%9F%93%E9%97%AE%E9%A2%98.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.14a  解决达芬奇破解的渲染问题</source>
      <description>前言 通过 里面的方法对达芬奇进行破解后，会出现渲染问题 下列方法任选一个就行 降级达芬奇到18.6.2 购买正版达芬奇 使用ffmpeg处理 修改导出页面的时间线大小（比如时间线是1920×1080，那么我们就选择1920×1400） 导出 此时可以发现渲染出问题的地方只影响到我们刚刚增加的，没有内容的区域了 使用其他软件将这些没内容的区域裁切掉（可...</description>
      <category>卡片/普通</category>
      <pubDate>Tue, 12 Aug 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p>通过<a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.14%20%E7%A0%B4%E8%A7%A3Davinci%20Resolve%20Studio.html" target="_blank">2.14 破解Davinci Resolve Studio</a> 里面的方法对达芬奇进行破解后，会出现渲染问题</p>
</div></div><p>下列方法任选一个就行</p>
<ol>
<li>降级达芬奇到18.6.2</li>
<li>购买正版达芬奇</li>
<li>使用ffmpeg处理
<ol>
<li>修改导出页面的时间线大小（比如时间线是<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1920</mn><mo>×</mo><mn>1080</mn></mrow><annotation encoding="application/x-tex">1920\times 1080</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1920</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1080</span></span></span></span>，那么我们就选择<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1920</mn><mo>×</mo><mn>1400</mn></mrow><annotation encoding="application/x-tex">1920\times 1400</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">1920</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1400</span></span></span></span>）</li>
<li>导出 此时可以发现渲染出问题的地方只影响到我们刚刚增加的，没有内容的区域了</li>
<li>使用其他软件将这些没内容的区域裁切掉（可以使用ffmpeg、剪映等）</li>
<li>完成，视频就像预想的一样完美</li>
</ol>
</li>
</ol>
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    </item>
    <item>
      <title>2.16d 主定理</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.16d%20%E4%B8%BB%E5%AE%9A%E7%90%86.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.16d%20%E4%B8%BB%E5%AE%9A%E7%90%86.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.16d 主定理</source>
      <description>Tip 本主定理为简化版 形式 如果已知: T(n)=aT(⌈bn​⌉)+O(nd)(a&amp;gt;0,b&amp;gt;1,d≥0) 那么我们就可以将其转换为大O表示法: T(n)=⎩⎨⎧​O(nd)O(ndlogn)O(nlogb​a)​if d&amp;gt;logb​aif d=logb​aif d&amp;lt;logb​a​ 简单的解释 我们可以对 a、b、d进行如下解释: a: 每个问题会...</description>
      <category>卡片/普通</category>
      <pubDate>Tue, 16 Sep 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="tip">
<div class="callout-title">
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<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-flame"><path d="M8.5 14.5A2.5 2.5 0 0 0 11 12c0-1.38-.5-2-1-3-1.072-2.143-.224-4.054 2-6 .5 2.5 2 4.9 4 6.5 2 1.6 3 3.5 3 5.5a7 7 0 1 1-14 0c0-1.153.433-2.294 1-3a2.5 2.5 0 0 0 2.5 2.5z"></path></svg>
</div>
<div class="callout-title-inner">Tip</div>
</div>
<div class="callout-content"><p>本主定理为简化版</p>
</div></div><h2>形式</h2>
<p>如果已知:</p>
<p v-pre="" class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>T</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mi>a</mi><mi>T</mi><mrow><mo fence="true">(</mo><mrow><mo fence="true">⌈</mo><mfrac><mi>n</mi><mi>b</mi></mfrac><mo fence="true">⌉</mo></mrow><mo fence="true">)</mo></mrow><mo>+</mo><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mi>d</mi></msup><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mi>a</mi><mo>&gt;</mo><mn>0</mn><mo separator="true">,</mo><mi>b</mi><mo>&gt;</mo><mn>1</mn><mo separator="true">,</mo><mi>d</mi><mo>≥</mo><mn>0</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">T(n) = aT\left( \left\lceil \frac{n}{b} \right\rceil \right) + O(n^d) 
 ( a &gt; 0, b &gt; 1, d \geq 0 )
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.836em;vertical-align:-0.686em;"></span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size2">(</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size2">⌈</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.1076em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">b</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size2">⌉</span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size2">)</span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.1491em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8991em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">d</span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mopen">(</span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">0</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0</span><span class="mclose">)</span></span></span></span></span></p>
<p>那么我们就可以将其转换为大O表示法:</p>
<p v-pre="" class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>T</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mrow><mo fence="true">{</mo><mtable rowspacing="0.36em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mi>d</mi></msup><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>if&nbsp;</mtext><mi>d</mi><mo>&gt;</mo><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mi>b</mi></msub><mi>a</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mi>d</mi></msup><mi>log</mi><mo>⁡</mo><mi>n</mi><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>if&nbsp;</mtext><mi>d</mi><mo>=</mo><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mi>b</mi></msub><mi>a</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mrow><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mi>b</mi></msub><mi>a</mi></mrow></msup><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>if&nbsp;</mtext><mi>d</mi><mo>&lt;</mo><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mi>b</mi></msub><mi>a</mi></mrow></mstyle></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">T(n) = 
\begin{cases} 
O(n^d) &amp; \text{if } d &gt; \log_b a \\
O(n^d \log n) &amp; \text{if } d = \log_b a \\
O(n^{\log_b a}) &amp; \text{if } d &lt; \log_b a 
\end{cases}

</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:4.32em;vertical-align:-1.91em;"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35em;"><span style="top:-2.2em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-2.192em;"><span class="pstrut" style="height:3.15em;"></span><span style="height:0.316em;width:0.8889em;"><svg xmlns="http://www.w3.org/2000/svg" width="0.8889em" height="0.316em" style="width:0.8889em" viewBox="0 0 888.89 316" preserveAspectRatio="xMinYMin"><path d="M384 0 H504 V316 H384z M384 0 H504 V316 H384z"></path></svg></span></span><span style="top:-3.15em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.292em;"><span class="pstrut" style="height:3.15em;"></span><span style="height:0.316em;width:0.8889em;"><svg xmlns="http://www.w3.org/2000/svg" width="0.8889em" height="0.316em" style="width:0.8889em" viewBox="0 0 888.89 316" preserveAspectRatio="xMinYMin"><path d="M384 0 H504 V316 H384z M384 0 H504 V316 H384z"></path></svg></span></span><span style="top:-4.6em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.85em;"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.41em;"><span style="top:-4.41em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">d</span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span><span style="top:-2.97em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">d</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span><span style="top:-1.53em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mop mtight"><span class="mop mtight"><span class="mtight">l</span><span class="mtight">o</span><span class="mtight" style="margin-right:0.01389em;">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2302em;"><span style="top:-2.2341em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2659em;"><span></span></span></span></span></span></span><span class="mspace mtight" style="margin-right:0.1952em;"></span><span class="mord mathnormal mtight">a</span></span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.91em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:1em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.41em;"><span style="top:-4.41em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord text"><span class="mord">if&nbsp;</span></span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.242em;"><span style="top:-2.4559em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">a</span></span></span><span style="top:-2.97em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord text"><span class="mord">if&nbsp;</span></span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.242em;"><span style="top:-2.4559em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">a</span></span></span><span style="top:-1.53em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord text"><span class="mord">if&nbsp;</span></span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.242em;"><span style="top:-2.4559em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.91em;"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<h2>简单的解释</h2>
<p>我们可以对 a、b、d进行如下解释:</p>
<ul>
<li>a: 每个问题会分裂的子问题个数</li>
<li>b: 问题规模缩小的因子</li>
<li><span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>n</mi><mi>d</mi></msup></mrow><annotation encoding="application/x-tex">n^d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8491em;"></span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">d</span></span></span></span></span></span></span></span></span></span></span>: 每个子问题处理的代价<br>
所以，对于原式中的两个式:</li>
<li><span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><mi>T</mi><mrow><mo fence="true">(</mo><mrow><mo fence="true">⌈</mo><mfrac><mi>n</mi><mi>b</mi></mfrac><mo fence="true">⌉</mo></mrow><mo fence="true">)</mo></mrow></mrow><annotation encoding="application/x-tex">aT\left( \left\lceil \frac{n}{b} \right\rceil \right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2em;vertical-align:-0.35em;"></span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size1">(</span></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size1">⌈</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6954em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">b</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size1">⌉</span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size1">)</span></span></span></span></span></span>: 当前的分裂子问题所消耗的成本</li>
<li><span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mi>d</mi></msup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(n^d)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0991em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">d</span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span>: 每个子问题所消耗的成本</li>
</ul>
<p>考虑一颗递归树，这就是两股势力的竞争，哪股势力增长越快，谁就能主导大O表示法<br>
因此，我们将<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi></mrow><annotation encoding="application/x-tex">d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">d</span></span></span></span>和<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mi>b</mi></msub><mi>a</mi></mrow><annotation encoding="application/x-tex">\log_b a</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9386em;vertical-align:-0.2441em;"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.242em;"><span style="top:-2.4559em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">a</span></span></span></span>进行比较即可，哪个大选哪个</p>
<p v-pre="" class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>T</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mrow><mo fence="true">{</mo><mtable rowspacing="0.36em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mi>d</mi></msup><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>if&nbsp;</mtext><mi>d</mi><mo>&gt;</mo><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mi>b</mi></msub><mi>a</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mrow><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mi>b</mi></msub><mi>a</mi></mrow></msup><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>if&nbsp;</mtext><mi>d</mi><mo>&lt;</mo><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mi>b</mi></msub><mi>a</mi></mrow></mstyle></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">T(n) = 
\begin{cases} 
O(n^d) &amp; \text{if } d &gt; \log_b a \\
O(n^{\log_b a}) &amp; \text{if } d &lt; \log_b a 
\end{cases}

</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:3em;vertical-align:-1.25em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em;"><span style="top:-3.69em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">d</span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span><span style="top:-2.25em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mop mtight"><span class="mop mtight"><span class="mtight">l</span><span class="mtight">o</span><span class="mtight" style="margin-right:0.01389em;">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2302em;"><span style="top:-2.2341em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2659em;"><span></span></span></span></span></span></span><span class="mspace mtight" style="margin-right:0.1952em;"></span><span class="mord mathnormal mtight">a</span></span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:1em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em;"><span style="top:-3.69em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord text"><span class="mord">if&nbsp;</span></span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.242em;"><span style="top:-2.4559em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">a</span></span></span><span style="top:-2.25em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord text"><span class="mord">if&nbsp;</span></span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.242em;"><span style="top:-2.4559em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em;"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<p>如果他们相等的话，任何一边的影响就都无法忽略不计了，因为一共有<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>o</mi><mi>g</mi><mi>n</mi></mrow><annotation encoding="application/x-tex">log n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">n</span></span></span></span>层，所以我们再乘上<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mi>o</mi><mi>g</mi><mi>n</mi></mrow><annotation encoding="application/x-tex">log n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal">n</span></span></span></span><br>
最终合并起来:</p>
<p v-pre="" class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>T</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mrow><mo fence="true">{</mo><mtable rowspacing="0.36em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mi>d</mi></msup><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>if&nbsp;</mtext><mi>d</mi><mo>&gt;</mo><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mi>b</mi></msub><mi>a</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mi>d</mi></msup><mi>log</mi><mo>⁡</mo><mi>n</mi><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>if&nbsp;</mtext><mi>d</mi><mo>=</mo><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mi>b</mi></msub><mi>a</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mrow><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mi>b</mi></msub><mi>a</mi></mrow></msup><mo stretchy="false">)</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mtext>if&nbsp;</mtext><mi>d</mi><mo>&lt;</mo><msub><mrow><mi>log</mi><mo>⁡</mo></mrow><mi>b</mi></msub><mi>a</mi></mrow></mstyle></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">T(n) = 
\begin{cases} 
O(n^d) &amp; \text{if } d &gt; \log_b a \\
O(n^d \log n) &amp; \text{if } d = \log_b a \\
O(n^{\log_b a}) &amp; \text{if } d &lt; \log_b a 
\end{cases}

</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:4.32em;vertical-align:-1.91em;"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.35em;"><span style="top:-2.2em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-2.192em;"><span class="pstrut" style="height:3.15em;"></span><span style="height:0.316em;width:0.8889em;"><svg xmlns="http://www.w3.org/2000/svg" width="0.8889em" height="0.316em" style="width:0.8889em" viewBox="0 0 888.89 316" preserveAspectRatio="xMinYMin"><path d="M384 0 H504 V316 H384z M384 0 H504 V316 H384z"></path></svg></span></span><span style="top:-3.15em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.292em;"><span class="pstrut" style="height:3.15em;"></span><span style="height:0.316em;width:0.8889em;"><svg xmlns="http://www.w3.org/2000/svg" width="0.8889em" height="0.316em" style="width:0.8889em" viewBox="0 0 888.89 316" preserveAspectRatio="xMinYMin"><path d="M384 0 H504 V316 H384z M384 0 H504 V316 H384z"></path></svg></span></span><span style="top:-4.6em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.85em;"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.41em;"><span style="top:-4.41em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">d</span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span><span style="top:-2.97em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">d</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span><span style="top:-1.53em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8491em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mop mtight"><span class="mop mtight"><span class="mtight">l</span><span class="mtight">o</span><span class="mtight" style="margin-right:0.01389em;">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2302em;"><span style="top:-2.2341em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2659em;"><span></span></span></span></span></span></span><span class="mspace mtight" style="margin-right:0.1952em;"></span><span class="mord mathnormal mtight">a</span></span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.91em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:1em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.41em;"><span style="top:-4.41em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord text"><span class="mord">if&nbsp;</span></span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.242em;"><span style="top:-2.4559em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">a</span></span></span><span style="top:-2.97em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord text"><span class="mord">if&nbsp;</span></span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.242em;"><span style="top:-2.4559em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">a</span></span></span><span style="top:-1.53em;"><span class="pstrut" style="height:3.008em;"></span><span class="mord"><span class="mord text"><span class="mord">if&nbsp;</span></span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mop"><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.242em;"><span style="top:-2.4559em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">b</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">a</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.91em;"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<h2>没有这种形式怎么办</h2>
<p>尝试变形成这种形式</p>
<ul>
<li>换元法</li>
<li>使用更通用的主定理</li>
</ul>
<h2>不能用主定理的情况</h2>
<ul>
<li>非分治递归 （如<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mi>T</mi><mo stretchy="false">(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mo>+</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">T(n)=T(n-1)+...</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.1056em;"></span><span class="mord">...</span></span></span></span>)</li>
<li><span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi></mrow><annotation encoding="application/x-tex">a</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">a</span></span></span></span>或<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>b</mi></mrow><annotation encoding="application/x-tex">b</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">b</span></span></span></span>并非常数</li>
</ul>
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      <title>2.1a Proxifier激活</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.1a%20Proxifier%E6%BF%80%E6%B4%BB.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.1a%20Proxifier%E6%BF%80%E6%B4%BB.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.1a Proxifier激活</source>
      <description>背景 的功能很强大，但是这是付费软件，需要购买激活码。 生成激活码 首先，前往Proxifier-Keygen，下载项目中的Proxifier_Keygen.py 文件 运行下列命令，生成一个激活码 激活 把刚刚获得的激活码再Proxifier中的注册框输入 IMG-20251018 215536018-2.1a Proxifier激活.pngIMG-...</description>
      <category>卡片/普通</category>
      <pubDate>Sat, 07 Dec 2024 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>背景</h2>
<p><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.1%20Proxifier.html" target="_blank">2.1 Proxifier</a>的功能很强大，但是这是付费软件，需要购买激活码。</p>
<h2>生成激活码</h2>
<ol>
<li>首先，前往<a href="https://github.com/y9nhjy/Proxifier-Keygen" target="_blank" rel="noopener noreferrer">Proxifier-Keygen</a>，下载项目中的<code>Proxifier_Keygen.py</code> 文件</li>
<li>运行下列命令，生成一个激活码</li>
</ol>
<div class="language-bash line-numbers-mode" data-highlighter="shiki" data-ext="bash" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-bash"><span class="line"><span style="--shiki-light:#4078F2;--shiki-dark:#61AFEF">python</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> Proxifier_Keygen.py</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div><h2>激活</h2>
<p>把刚刚获得的激活码再Proxifier中的注册框输入</p>
<figure><img src="/image/IMG-20251018 215536018-2.1a Proxifier激活.png" alt="IMG-20251018 215536018-2.1a Proxifier激活.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536018-2.1a Proxifier激活.png</figcaption></figure>
<p>随便写一个名字，下面填入激活码</p>
<figure><img src="/image/IMG-20251018 215536639-2.1a Proxifier激活.png" alt="IMG-20251018 215536639-2.1a Proxifier激活.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536639-2.1a Proxifier激活.png</figcaption></figure>
<p>点击 <code>OK</code> ，然后就大功告成！</p>
<h2>一些生成过的激活码</h2>
<div class="language-setup line-numbers-mode" data-highlighter="shiki" data-ext="setup" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-setup"><span class="line"><span>CLOT5-J3GYK-VGPYE-BDPMN-WKWMU</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div><div class="language-portable line-numbers-mode" data-highlighter="shiki" data-ext="portable" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-portable"><span class="line"><span>NY8VX-Z2NH2-TFXWY-IL5YC-GARRM</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div><div class="language-mac line-numbers-mode" data-highlighter="shiki" data-ext="mac" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-mac"><span class="line"><span>57J8Z-D2QD5-A37WU-LEG4E-43WYH</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div>]]></content:encoded>
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      <title>2.1b Proxifier转发到Fiddler</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.1b%20Proxifier%E8%BD%AC%E5%8F%91%E5%88%B0Fiddler.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.1b%20Proxifier%E8%BD%AC%E5%8F%91%E5%88%B0Fiddler.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.1b Proxifier转发到Fiddler</source>
      <description>前言 Fiddler可以对网络进行抓包，但是一些程序没办法被Fiddler直接抓到。为此，我们就需要来代理，将所有都转发给Fiddler 操作流程 打开软件，选择配置文件 --&amp;gt; 高级 --&amp;gt; HTTP代理服务器 --&amp;gt; 启用HTTP代理服务器支持 IMG-20251018 215536021-2.1b Proxifier转发到Fiddler.pngI...</description>
      <category>卡片/普通</category>
      <pubDate>Sun, 08 Dec 2024 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>前言</h2>
<p>Fiddler可以对网络进行抓包，但是一些程序没办法被Fiddler直接抓到。为此，我们就需要<a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.1%20Proxifier.html" target="_blank">2.1 Proxifier</a>来代理，将所有都转发给Fiddler</p>
<h2>操作流程</h2>
<ol>
<li>打开软件，选择配置文件 --&gt; 高级 --&gt; HTTP代理服务器 --&gt; 启用HTTP代理服务器支持</li>
</ol>
<figure><img src="/image/IMG-20251018 215536021-2.1b Proxifier转发到Fiddler.png" alt="IMG-20251018 215536021-2.1b Proxifier转发到Fiddler.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536021-2.1b Proxifier转发到Fiddler.png</figcaption></figure>
<figure><img src="/image/IMG-20251018 215536640-2.1b Proxifier转发到Fiddler.png" alt="IMG-20251018 215536640-2.1b Proxifier转发到Fiddler.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536640-2.1b Proxifier转发到Fiddler.png</figcaption></figure>
<ol start="2">
<li>设置代理服务器和Fiddler的代理设置相匹配(这里只考虑默认情况)
<ol>
<li>首先，打开配置文件--&gt;代理服务器--&gt;添加，设置为<code>127.0.0.1:8888</code>，协议选择<code>Https</code>，然后点击确定</li>
</ol>
</li>
</ol>
<figure><img src="/image/IMG-20251018 215548583-2.1b Proxifier转发到Fiddler.png" alt="IMG-20251018 215548583-2.1b Proxifier转发到Fiddler.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215548583-2.1b Proxifier转发到Fiddler.png</figcaption></figure>
<figure><img src="/image/IMG-20251018 215548800-2.1b Proxifier转发到Fiddler.png" alt="IMG-20251018 215548800-2.1b Proxifier转发到Fiddler.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215548800-2.1b Proxifier转发到Fiddler.png</figcaption></figure>
<pre><code>2. 设置代理规则，一般来说会自动创建 `Fiddler.exe [auto-created`，如果没有就稍作等待
</code></pre>
<figure><img src="/image/IMG-20251018 215550618-2.1b Proxifier转发到Fiddler.png" alt="IMG-20251018 215550618-2.1b Proxifier转发到Fiddler.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215550618-2.1b Proxifier转发到Fiddler.png</figcaption></figure>
<figure><img src="/image/IMG-20251018 215551507-2.1b Proxifier转发到Fiddler.png" alt="IMG-20251018 215551507-2.1b Proxifier转发到Fiddler.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215551507-2.1b Proxifier转发到Fiddler.png</figcaption></figure>
<ol start="3">
<li>打开Fiddler-&gt;Tools-&gt;Options-&gt;HTTPS，然后全勾选即可</li>
</ol>
<figure><img src="/image/IMG-20251018 215551697-2.1b Proxifier转发到Fiddler.png" alt="IMG-20251018 215551697-2.1b Proxifier转发到Fiddler.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215551697-2.1b Proxifier转发到Fiddler.png</figcaption></figure>
<ol start="5">
<li>选择Options-&gt;Connections，配置Fiddler的port，要和上方保持一致(例如8888)</li>
</ol>
<figure><img src="/image/IMG-20251018 215551841-2.1b Proxifier转发到Fiddler.png" alt="IMG-20251018 215551841-2.1b Proxifier转发到Fiddler.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215551841-2.1b Proxifier转发到Fiddler.png</figcaption></figure>
<ol start="6">
<li>设置完成，接下来就可以在Fiddler愉快的抓包了</li>
</ol>
<h2>参考链接</h2>
<p><a href="https://www.cnblogs.com/xiaozi/p/11684221.html" target="_blank" rel="noopener noreferrer">FIddler+Proxifer 实现PC客户端抓包 - Bypass - 博客园</a></p>
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      <title>2.2 Tauri和Tracing一起使用时无法写入到文件</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.2%20Tauri%E5%92%8CTracing%E4%B8%80%E8%B5%B7%E4%BD%BF%E7%94%A8%E6%97%B6%E6%97%A0%E6%B3%95%E5%86%99%E5%85%A5%E5%88%B0%E6%96%87%E4%BB%B6.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.2%20Tauri%E5%92%8CTracing%E4%B8%80%E8%B5%B7%E4%BD%BF%E7%94%A8%E6%97%B6%E6%97%A0%E6%B3%95%E5%86%99%E5%85%A5%E5%88%B0%E6%96%87%E4%BB%B6.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.2 Tauri和Tracing一起使用时无法写入到文件</source>
      <description>描述 在Tauri和tracing一起使用的时候，如果在Tauri中使用命令，从前端调用后端记录日志，控制台有输出，但是无法写入到文件中，文件中只有在其他地方调用的日志 解决办法 换用其他的日志库 flexi_logger是可用的，一切正常 猜想 Tracing的实现逻辑和其他日志库不一样，导致Tauri的异步调用无法记录进去。</description>
      <category>卡片/普通</category>
      <pubDate>Sun, 01 Dec 2024 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>描述</h2>
<p>在Tauri和<a href="https://docs.rs/tracing/latest/tracing/" target="_blank" rel="noopener noreferrer">tracing</a>一起使用的时候，如果在Tauri中使用命令，从前端调用后端记录日志，控制台有输出，但是无法写入到文件中，文件中只有在其他地方调用的日志</p>
<h2>解决办法</h2>
<p>换用其他的日志库 <code>flexi_logger是可用的，一切正常</code></p>
<h2>猜想</h2>
<p>Tracing的实现逻辑和其他日志库不一样，导致Tauri的异步调用无法记录进去。</p>
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      <title>2.22 koishi遇到this.getIndexes is not a function解决方案</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.22%20koishi%E9%81%87%E5%88%B0this.getIndexes%20is%20not%20a%20function%E8%A7%A3%E5%86%B3%E6%96%B9%E6%A1%88.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.22%20koishi%E9%81%87%E5%88%B0this.getIndexes%20is%20not%20a%20function%E8%A7%A3%E5%86%B3%E6%96%B9%E6%A1%88.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.22 koishi遇到this.getIndexes is not a function解决方案</source>
      <description>背景 刚刚通过docker完成koishi的安装后，一接受消息就会报错 而且，在沙盒里面还会有无法调整用户权限等级的问题 IMG-2.22 koishi遇到this.getIndexes is not a function解决方案-5B5199214C0EA61BF9287034967C4ECE.pngIMG-2.22 koishi遇到this.get...</description>
      <category>卡片/普通</category>
      <pubDate>Mon, 27 Oct 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>背景</h2>
<p>刚刚通过docker完成koishi的安装后，一接受消息就会报错<br>
而且，在沙盒里面还会有无法调整用户权限等级的问题</p>
<div class="language- line-numbers-mode" data-highlighter="shiki" data-ext="" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-"><span class="line"><span>TypeError: this.getIndexes is not a function  </span></span>
<span class="line"><span>at SQLiteDriver.prepareIndexes (/koishi/node_modules/minato/lib/index.cjs:1928:35)  </span></span>
<span class="line"><span>at Proxy.prepare (/koishi/node_modules/minato/lib/index.cjs:973:18)  </span></span>
<span class="line"><span>at async Proxy.prepare (/koishi/node_modules/minato/lib/index.cjs:965:5)</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><figure><img src="/image/IMG-2.22 koishi遇到this.getIndexes is not a function解决方案-5B5199214C0EA61BF9287034967C4ECE.png" alt="IMG-2.22 koishi遇到this.getIndexes is not a function解决方案-5B5199214C0EA61BF9287034967C4ECE.png" tabindex="0" loading="lazy"><figcaption>IMG-2.22 koishi遇到this.getIndexes is not a function解决方案-5B5199214C0EA61BF9287034967C4ECE.png</figcaption></figure>
<h2>问题分析</h2>
<p>SQLiteDriver过期，<code>database-sqlite</code>版本过老了</p>
<h2>解决方案</h2>
<p>更新 <code>database-sqlite</code> 插件</p>

<div class="callout" data-callout="note">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-pencil"><path d="M17 3a2.85 2.83 0 1 1 4 4L7.5 20.5 2 22l1.5-5.5Z"></path><path d="m15 5 4 4"></path></svg>
</div>
<div class="callout-title-inner">建议</div>
</div>
<div class="callout-content"><p>在安装完成koishi后就<a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.22a%20%E6%9B%B4%E6%96%B0koishi%E6%89%80%E6%9C%89%E4%BE%9D%E8%B5%96.html" target="_blank">更新koishi所有依赖</a></p>
</div></div><h2>参考</h2>
<ul>
<li><a href="https://github.com/koishijs/koishi/issues/1455" target="_blank" rel="noopener noreferrer">https://github.com/koishijs/koishi/issues/1455</a></li>
</ul>
]]></content:encoded>
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    <item>
      <title>2.22a 更新koishi所有依赖</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.22a%20%E6%9B%B4%E6%96%B0koishi%E6%89%80%E6%9C%89%E4%BE%9D%E8%B5%96.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.22a%20%E6%9B%B4%E6%96%B0koishi%E6%89%80%E6%9C%89%E4%BE%9D%E8%B5%96.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.22a 更新koishi所有依赖</source>
      <description>适用场景 更新koishi所有插件 更新koishi所有依赖 方法 打开koishi webui 在侧边栏找到依赖管理 350350 点击右上角的小火箭🚀 IMG-2.22a 更新koishi所有依赖-7787011250B7F003ADABEAB4179FAE4C.pngIMG-2.22a 更新koishi所有依赖-7787011250B7F003...</description>
      <category>卡片/普通</category>
      <pubDate>Mon, 27 Oct 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>适用场景</h2>
<ul>
<li>更新koishi所有插件</li>
<li>更新koishi所有依赖</li>
</ul>
<h2>方法</h2>
<ol>
<li>打开koishi webui</li>
<li>在侧边栏找到依赖管理</li>
</ol>
<figure><img src="/image/IMG-2.22a 更新koishi所有依赖-459BAAD53C105327EE9F5CD6599D5A97.png" alt="350" tabindex="0" loading="lazy"><figcaption>350</figcaption></figure>
<ol start="3">
<li>点击右上角的小火箭🚀</li>
</ol>
<figure><img src="/image/IMG-2.22a 更新koishi所有依赖-7787011250B7F003ADABEAB4179FAE4C.png" alt="IMG-2.22a 更新koishi所有依赖-7787011250B7F003ADABEAB4179FAE4C.png" tabindex="0" loading="lazy"><figcaption>IMG-2.22a 更新koishi所有依赖-7787011250B7F003ADABEAB4179FAE4C.png</figcaption></figure>
<ol start="4">
<li>按照提示更新即可</li>
</ol>
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      <title>2.3 Bandizip智能解压</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.3%20Bandizip%E6%99%BA%E8%83%BD%E8%A7%A3%E5%8E%8B.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.3%20Bandizip%E6%99%BA%E8%83%BD%E8%A7%A3%E5%8E%8B.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.3 Bandizip智能解压</source>
      <description>前言 解压的时候，如果压缩包的顶层有很多个文件，那么解压后就会得到一大堆文件，散落在文件夹中，很令人恼火。 所以，我们需要压缩软件来帮帮忙，正好bandizip能干这件事 功能 在压缩包顶端只有一个文件/文件夹的时候，直接解压到该文件夹里面 在压缩包里面有多个文件/文件夹/混合的时候，解压到 压缩包名\ 文件夹下，就和解压到....一样 如何使用 Ba...</description>
      <category>卡片/普通</category>
      <pubDate>Wed, 29 Jan 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p>解压的时候，如果压缩包的顶层有很多个文件，那么解压后就会得到一大堆文件，散落在文件夹中，很令人恼火。<br>
所以，我们需要压缩软件来帮帮忙，正好bandizip能干这件事</p>
</div></div><h2>功能</h2>
<ul>
<li>在压缩包顶端只有一个文件/文件夹的时候，直接解压到该文件夹里面</li>
<li>在压缩包里面有多个文件/文件夹/混合的时候，解压到 <code>压缩包名\</code> 文件夹下，就和解压到....一样</li>
</ul>
<h2>如何使用</h2>
<ul>
<li>Bandizip默认开启</li>
<li>点开压缩文件时，按<code>Z</code>，使用智能解压(自动解压)</li>
<li>如下图第五个 <code>自动解压(Z)</code></li>
</ul>
<figure><img src="/image/IMG-20251018 215536025-2.3 Bandizip智能解压.png" alt="IMG-20251018 215536025-2.3 Bandizip智能解压.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536025-2.3 Bandizip智能解压.png</figcaption></figure>
<h2>参见</h2>
<h2>脚注</h2>
<ul>
<li>参考: <a href="https://www.bandisoft.com/bandizip/help/auto_dest/" target="_blank" rel="noopener noreferrer">Bandizip - 如何使用智能解压至此</a></li>
</ul>
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      <title>2.4 Github Pages配置自定义域失效</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.4%20Github%20Pages%E9%85%8D%E7%BD%AE%E8%87%AA%E5%AE%9A%E4%B9%89%E5%9F%9F%E5%A4%B1%E6%95%88.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.4%20Github%20Pages%E9%85%8D%E7%BD%AE%E8%87%AA%E5%AE%9A%E4%B9%89%E5%9F%9F%E5%A4%B1%E6%95%88.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.4 Github Pages配置自定义域失效</source>
      <description>描述 众所周知，Github Page中可以自己绑定到自定义域上 IMG-20251018 215536026-2.4 Github Pages配置自定义域失效.pngIMG-20251018 215536026-2.4 Github Pages配置自定义域失效.png 但是有时候，每次重新构建，这个域名都会失效 解决 原因是 CNAME 文件被覆盖掉...</description>
      <category>卡片/普通</category>
      <pubDate>Sun, 22 Dec 2024 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>描述</h2>
<p>众所周知，Github Page中可以自己绑定到自定义域上</p>
<figure><img src="/image/IMG-20251018 215536026-2.4 Github Pages配置自定义域失效.png" alt="IMG-20251018 215536026-2.4 Github Pages配置自定义域失效.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536026-2.4 Github Pages配置自定义域失效.png</figcaption></figure>
<p>但是有时候，每次重新构建，这个域名都会失效</p>
<h2>解决</h2>
<p>原因是 <code>CNAME</code> 文件被覆盖掉导致的</p>
<p>设置完成后，我们可以看到，github自动帮我们把CNAME文件写了进去</p>
<figure><img src="/image/IMG-20251018 215536645-2.4 Github Pages配置自定义域失效.png" alt="IMG-20251018 215536645-2.4 Github Pages配置自定义域失效.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536645-2.4 Github Pages配置自定义域失效.png</figcaption></figure>
<p>CNAME文件里面写的就是我们刚刚的域</p>
<figure><img src="/image/IMG-20251018 215548583-2.4 Github Pages配置自定义域失效.png" alt="IMG-20251018 215548583-2.4 Github Pages配置自定义域失效.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215548583-2.4 Github Pages配置自定义域失效.png</figcaption></figure>
<p>因此，我们在部署的时候，直接把这个CNAME文件写进去就行了。<br>
比如Github Action，就可以这样写入</p>
<div class="language-yaml line-numbers-mode" data-highlighter="shiki" data-ext="yaml" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-yaml"><span class="line"><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF"> - </span><span style="--shiki-light:#E45649;--shiki-dark:#E06C75">name</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">: </span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379">Add CNAME</span></span>
<span class="line"><span style="--shiki-light:#E45649;--shiki-dark:#E06C75">   run</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">: </span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379">echo 'blog.erduotong.com' &gt; src/.vuepress/dist/CNAME</span></span></code></pre>
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      <title>2.4b Github 学生认证通过方法（2025）</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.4b%20Github%20%E5%AD%A6%E7%94%9F%E8%AE%A4%E8%AF%81%E9%80%9A%E8%BF%87%E6%96%B9%E6%B3%95%EF%BC%882025%EF%BC%89.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.4b%20Github%20%E5%AD%A6%E7%94%9F%E8%AE%A4%E8%AF%81%E9%80%9A%E8%BF%87%E6%96%B9%E6%B3%95%EF%BC%882025%EF%BC%89.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.4b Github 学生认证通过方法（2025）</source>
      <description>背景 Github的学生认证很有用，可以白嫖Github Copilot，但是申请比较困难，容易被拒 本卡片的手写信法在2025年实测可用，后面的时间未经过实践 实现步骤 假设你叫张三，目前在XX学校就读 填写信息 在个人的Public Profile中填写下列信息: Name: San Zhang [1] Company: XX School (填你...</description>
      <category>卡片/普通</category>
      <pubDate>Sat, 22 Nov 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>背景</h2>
<p>Github的学生认证很有用，可以白嫖Github Copilot，但是申请比较困难，容易被拒<br>
本卡片的手写信法在<em>2025年</em>实测可用，后面的时间未经过实践</p>
<h2>实现步骤</h2>
<blockquote>
<p>假设你叫<strong>张三</strong>，目前在XX学校就读</p>
</blockquote>
<h3>填写信息</h3>
<p>在个人的Public Profile中填写下列信息:</p>
<ul>
<li><code>Name</code>: San Zhang <sup class="footnote-ref"><a href="#footnote1">[1]</a><a class="footnote-anchor" id="footnote-ref1"></a></sup></li>
<li><code>Company</code>: XX School  (填你的学校英文名)</li>
<li><code>Location</code>: 学校的英文地址<br>
在<code>Billing and Licensing</code>中的<code>Payment Information</code> 填写如下信息</li>
<li><code>First name</code>: San</li>
<li><code>Last name</code>: Zhang <sup class="footnote-ref"><a href="#footnote1">[1:1]</a><a class="footnote-anchor" id="footnote-ref1:1"></a></sup></li>
<li><code>Address</code>: 学校的英文地址</li>
<li>剩下的地址按照实际情况填写即可</li>
</ul>
<h3>材料准备</h3>
<p>准备一张白纸，在上面写下如下内容（括号内不用写上去）:</p>
<div class="language- line-numbers-mode" data-highlighter="shiki" data-ext="" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-"><span class="line"><span>Student Verification Report for Github</span></span>
<span class="line"><span>Name: Zhang San</span></span>
<span class="line"><span>School: XX School (填你的学校英文名)</span></span>
<span class="line"><span>Student Number: 114514 (这里随便填都行)</span></span>
<span class="line"><span>Graduation Date: 2026.6 (大于目前的日期，最好多一年)</span></span>
<span class="line"><span>Status: Distance Learning</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><ul>
<li><strong>注意</strong>: 手写部分的<code>Name</code>要<strong>姓在前名在后</strong>的形式 <sup class="footnote-ref"><a href="#footnote2">[2]</a><a class="footnote-anchor" id="footnote-ref2"></a></sup></li>
</ul>
<h3>开始填写</h3>

<div class="callout" data-callout="note">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-pencil"><path d="M17 3a2.85 2.83 0 1 1 4 4L7.5 20.5 2 22l1.5-5.5Z"></path><path d="m15 5 4 4"></path></svg>
</div>
<div class="callout-title-inner">Note</div>
</div>
<div class="callout-content"><p>这里推荐使用手机，摄像头的画质较好，而且可以使用位置信息，可以获得相对精确的定位，可能能避免 <code>Why are you not on campus?</code>的问题<br>
如果遇到了，就选择<code>我在远程学习</code>这个选项，刚刚的<code>Status: Distance Learning</code>就是为了解决这个问题</p>
</div></div><ul>
<li>在<code>education benefits</code>里面开始认证</li>
<li>点击<code>student</code>，然后选择你的学校，并且点击<code>share location</code></li>
<li>点击下一步后，在弹出的证明页面选择<code>Dated School Id</code>，给你刚刚写好的纸拍一张照片 <sup class="footnote-ref"><a href="#footnote3">[3]</a><a class="footnote-anchor" id="footnote-ref3"></a></sup></li>
<li>提交</li>
</ul>
<h3>被拒的解决方法</h3>
<ul>
<li>换用手机，提供更精确的位置</li>
<li>提高照片拍摄的画质，不要用虚拟摄像头</li>
<li>观察被拒绝后给你发的邮件，根据其中的指引操作，其中列出的项目就是可能存在问题的地方<br>
如下图，这里<code>Profile</code>和<code>Billing Information</code>都有问题，可能就是两个都没填对/照片拍的有问题</li>
</ul>
<figure><img src="/image/IMG-2.4b Github 学生认证通过方法（2025）-DA5F00F433AA94B06448A907B3C06576.png" alt="IMG-2.4b Github 学生认证通过方法（2025）-DA5F00F433AA94B06448A907B3C06576.png" tabindex="0" loading="lazy"><figcaption>IMG-2.4b Github 学生认证通过方法（2025）-DA5F00F433AA94B06448A907B3C06576.png</figcaption></figure>
<h2>参考文献</h2>
<p><a href="https://zhuanlan.zhihu.com/p/1930927677419816873" target="_blank" rel="noopener noreferrer">Github学生认证一次过！（25.7.21） - 知乎</a></p>
<hr class="footnotes-sep">
<section class="footnotes">
<ol class="footnotes-list">
<li id="footnote1" class="footnote-item"><p>在<code>Profile</code>和<code>Payment Information</code>中，要写作姓在后名在前的形式。比如一个人叫张大伟，那么就应该填<code>DaWei Zhang</code> <a href="#footnote-ref1" class="footnote-backref">↩︎</a> <a href="#footnote-ref1:1" class="footnote-backref">↩︎</a></p>
</li>
<li id="footnote2" class="footnote-item"><p>在纸上写的时候，要写作姓在前名在后的形式。同样以张大伟为例，这里他就应该填<code>Zhang DaWei</code> <a href="#footnote-ref2" class="footnote-backref">↩︎</a></p>
</li>
<li id="footnote3" class="footnote-item"><p>这里需要清晰一点，似乎Github是用OCR/大模型来识别的，如果识别不清楚你的名字，和Profile / Payment Info里面对不上的话可能就会拒绝你 <a href="#footnote-ref3" class="footnote-backref">↩︎</a></p>
</li>
</ol>
</section>
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      <title>2.5 vuepress 打包后不自动退出</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.5%20vuepress%20%E6%89%93%E5%8C%85%E5%90%8E%E4%B8%8D%E8%87%AA%E5%8A%A8%E9%80%80%E5%87%BA.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.5%20vuepress%20%E6%89%93%E5%8C%85%E5%90%8E%E4%B8%8D%E8%87%AA%E5%8A%A8%E9%80%80%E5%87%BA.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.5 vuepress 打包后不自动退出</source>
      <description>描述 在用Vuepress构建的时候，部分情况会出现Build Successful后，不自动结束进程，导致一直卡住终端不进行下一步。 IMG-20251018 215536027-2.5 vuepress 打包后不自动退出.pngIMG-20251018 215536027-2.5 vuepress 打包后不自动退出.png 原因 在组件中，添加了S...</description>
      <category>卡片/普通</category>
      <pubDate>Wed, 02 Oct 2024 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<hr>
<h1>描述</h1>
<p>在用Vuepress构建的时候，部分情况会出现<code>Build Successful</code>后，不自动结束进程，导致一直卡住终端不进行下一步。</p>
<figure><img src="/image/IMG-20251018 215536027-2.5 vuepress 打包后不自动退出.png" alt="IMG-20251018 215536027-2.5 vuepress 打包后不自动退出.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536027-2.5 vuepress 打包后不自动退出.png</figcaption></figure>
<h1>原因</h1>
<p>在组件中，添加了SetInterval等组件，并且没有释放，如下图</p>
<div class="language-javascript line-numbers-mode" data-highlighter="shiki" data-ext="javascript" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-javascript"><span class="line"><span style="--shiki-light:#A626A4;--shiki-dark:#C678DD">const</span><span style="--shiki-light:#986801;--shiki-dark:#E5C07B"> interval</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2"> =</span><span style="--shiki-light:#4078F2;--shiki-dark:#61AFEF"> setInterval</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">(</span><span style="--shiki-light:#383A42;--shiki-dark:#E06C75">calculateTime</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">, </span><span style="--shiki-light:#986801;--shiki-dark:#D19A66">1000</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">);</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div><p>因为一直没有释放，所以导致<code>Node JS</code>一直无法结束事件循环，哪怕该组件不再使用</p>
<h1>解决办法</h1>
<p>在组件的生命周期中，挂载和卸载计时器</p>
<div class="language-javascript line-numbers-mode" data-highlighter="shiki" data-ext="javascript" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-javascript"><span class="line"><span style="--shiki-light:#4078F2;--shiki-dark:#61AFEF">onMounted</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">(() </span><span style="--shiki-light:#A626A4;--shiki-dark:#C678DD">=&gt;</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF"> {  </span></span>
<span class="line"><span style="--shiki-light:#A626A4;--shiki-dark:#C678DD">  const</span><span style="--shiki-light:#986801;--shiki-dark:#E5C07B"> interval</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2"> =</span><span style="--shiki-light:#4078F2;--shiki-dark:#61AFEF"> setInterval</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">(</span><span style="--shiki-light:#383A42;--shiki-dark:#E06C75">calculateTime</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">, </span><span style="--shiki-light:#986801;--shiki-dark:#D19A66">1000</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">); </span></span>
<span class="line"><span style="--shiki-light:#4078F2;--shiki-dark:#61AFEF">  onUnmounted</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">(() </span><span style="--shiki-light:#A626A4;--shiki-dark:#C678DD">=&gt;</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF"> {  </span></span>
<span class="line"><span style="--shiki-light:#4078F2;--shiki-dark:#61AFEF">    clearInterval</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">(</span><span style="--shiki-light:#383A42;--shiki-dark:#E06C75">interval</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">);  </span></span>
<span class="line"><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">  });  </span></span>
<span class="line"><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">});</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div>]]></content:encoded>
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      <title>2.5a Vuepress中插件添加客户端配置文件</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.5a%20Vuepress%E4%B8%AD%E6%8F%92%E4%BB%B6%E6%B7%BB%E5%8A%A0%E5%AE%A2%E6%88%B7%E7%AB%AF%E9%85%8D%E7%BD%AE%E6%96%87%E4%BB%B6.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.5a%20Vuepress%E4%B8%AD%E6%8F%92%E4%BB%B6%E6%B7%BB%E5%8A%A0%E5%AE%A2%E6%88%B7%E7%AB%AF%E9%85%8D%E7%BD%AE%E6%96%87%E4%BB%B6.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.5a Vuepress中插件添加客户端配置文件</source>
      <description>背景 在Vuepress中，插件可能需要修改一些客户端中的内容，因此需要提供客户端文件 实现方法 在插件的返回字段中，添加一个clientConfigFile字段 其中，clientConfigFile就是你的客户端配置文件。不过，需要指定一个路径。 在client.js中，就自由的填写配置文件吧 要点 path 和 getDirname 方法一定要从...</description>
      <category>卡片/普通</category>
      <pubDate>Sun, 08 Dec 2024 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>背景</h2>
<p>在Vuepress中，插件可能需要修改一些客户端中的内容，因此需要提供客户端文件</p>
<h2>实现方法</h2>
<p>在插件的返回字段中，添加一个<code>clientConfigFile</code>字段</p>
<div class="language-javascript line-numbers-mode" data-highlighter="shiki" data-ext="javascript" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-javascript"><span class="line"><span style="--shiki-light:#A626A4;--shiki-dark:#C678DD">const</span><span style="--shiki-light:#4078F2;--shiki-dark:#61AFEF"> plugin</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2"> =</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF"> () </span><span style="--shiki-light:#A626A4;--shiki-dark:#C678DD">=&gt;</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF"> {</span></span>
<span class="line"><span style="--shiki-light:#383A42;--shiki-dark:#E06C75">    clientConfigFile</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">: </span><span style="--shiki-light:#986801;--shiki-dark:#D19A66">null</span></span>
<span class="line"><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">}</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><p>其中，clientConfigFile就是你的客户端配置文件。不过，需要指定一个路径。</p>
<div class="language-javascript line-numbers-mode" data-highlighter="shiki" data-ext="javascript" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-javascript"><span class="line"><span style="--shiki-light:#A0A1A7;--shiki-light-font-style:italic;--shiki-dark:#7F848E;--shiki-dark-font-style:italic">// 假设你的客户端配置文件和插件文件在同一目录</span></span>
<span class="line"><span style="--shiki-light:#A0A1A7;--shiki-light-font-style:italic;--shiki-dark:#7F848E;--shiki-dark-font-style:italic">// plugin.js</span></span>
<span class="line"><span style="--shiki-light:#A0A1A7;--shiki-light-font-style:italic;--shiki-dark:#7F848E;--shiki-dark-font-style:italic">// client.js</span></span>
<span class="line"><span style="--shiki-light:#A626A4;--shiki-dark:#C678DD">import</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF"> {</span><span style="--shiki-light:#E45649;--shiki-dark:#E06C75">getDirname</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">,</span><span style="--shiki-light:#E45649;--shiki-dark:#E06C75">path</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">} </span><span style="--shiki-light:#A626A4;--shiki-dark:#C678DD">from</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> "vuepress/utils"</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">;</span></span>
<span class="line"></span>
<span class="line"><span style="--shiki-light:#A626A4;--shiki-dark:#C678DD">const</span><span style="--shiki-light:#986801;--shiki-dark:#E5C07B"> __dirname</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2"> =</span><span style="--shiki-light:#4078F2;--shiki-dark:#61AFEF">  getDirname</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">(</span><span style="--shiki-light:#A626A4;--shiki-dark:#C678DD">import</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">.</span><span style="--shiki-light:#E45649;--shiki-dark:#E06C75">meta</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">.</span><span style="--shiki-light:#E45649;--shiki-dark:#E06C75">url</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">)</span></span>
<span class="line"><span style="--shiki-light:#A626A4;--shiki-dark:#C678DD">const</span><span style="--shiki-light:#4078F2;--shiki-dark:#61AFEF"> plugin</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2"> =</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF"> () </span><span style="--shiki-light:#A626A4;--shiki-dark:#C678DD">=&gt;</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF"> {</span></span>
<span class="line"><span style="--shiki-light:#383A42;--shiki-dark:#E06C75">    clientConfigFile</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">: </span><span style="--shiki-light:#383A42;--shiki-dark:#E5C07B">path</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">.</span><span style="--shiki-light:#4078F2;--shiki-dark:#61AFEF">resolve</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">(</span><span style="--shiki-light:#383A42;--shiki-dark:#E06C75">__dirname</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">, </span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379">"client.js"</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">),</span></span>
<span class="line"><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">}</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><p>在client.js中，就自由的填写配置文件吧</p>
<h2>要点</h2>
<ul>
<li><code>path</code> 和 <code>getDirname</code> 方法<strong>一定要从</strong> <code>vuepress/utils</code>中获得</li>
<li>如果从<code>fs</code>获得，就会导致路径解析出现问题</li>
</ul>
<h2>参考</h2>
<p><a href="https://vuepress.vuejs.org/zh/reference/plugin-api.html#clientconfigfile" target="_blank" rel="noopener noreferrer">插件 API | VuePress</a></p>
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      <title>2.5a1 添加Giscus评论</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.5a1%20%E6%B7%BB%E5%8A%A0Giscus%E8%AF%84%E8%AE%BA.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.5a1%20%E6%B7%BB%E5%8A%A0Giscus%E8%AF%84%E8%AE%BA.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.5a1 添加Giscus评论</source>
      <description>简介 Giscus是一个基于Github Discussions的评论系统，可以让用户登录github账号以评论。 在Vuepress Themehope主题中，已经提供了Giscus的支持，通过一些配置就可以方便的调用 配置 准备 首先，准备一个公有仓库，并且开启Dicussions功能，用于存放评论 安装Giscus的Github App，使Gis...</description>
      <category>卡片/普通</category>
      <pubDate>Fri, 18 Oct 2024 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>简介</h2>
<p><a href="https://giscus.app/zh-CN" target="_blank" rel="noopener noreferrer">Giscus</a>是一个基于Github Discussions的评论系统，可以让用户登录github账号以评论。<br>
在Vuepress Themehope主题中，已经提供了Giscus的支持，通过一些配置就可以方便的调用</p>
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      <title>2.5b 防止Vuepress标题被吞</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.5b%20%E9%98%B2%E6%AD%A2Vuepress%E6%A0%87%E9%A2%98%E8%A2%AB%E5%90%9E.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.5b%20%E9%98%B2%E6%AD%A2Vuepress%E6%A0%87%E9%A2%98%E8%A2%AB%E5%90%9E.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.5b 防止Vuepress标题被吞</source>
      <description>背景 在Vuepress中，若一篇Markdown文章中有多个 # h1 标题，则第一个标题会消失，即使已经指定了文章标题 解决办法 通过Markdown it插件解决，在文章开头加入分割线 但是因为存在frontmatter(yaml)这种东西，处理原始内容不太方便。 所以，反向思考，因为要处理的是 h1 的问题，所以在 h1 前面加入分割线就行。 ...</description>
      <category>卡片/普通</category>
      <pubDate>Sat, 19 Oct 2024 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<hr>
<h1>背景</h1>
<p>在Vuepress中，若一篇Markdown文章中有多个 <code># h1</code> 标题，则第一个标题会消失，即使已经指定了文章标题</p>
<h1>解决办法</h1>
<p>通过Markdown it插件解决，在文章开头加入分割线<br>
但是因为存在frontmatter(yaml)这种东西，处理原始内容不太方便。<br>
所以，反向思考，因为要处理的是 <code>h1</code> 的问题，所以在 <code>h1</code> 前面加入分割线就行。</p>
<blockquote>
<p>但是用`</p>
</blockquote>
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    <item>
      <title>2.5b1 jsdom导致无法使用localStorage</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.5b1%20jsdom%E5%AF%BC%E8%87%B4%E6%97%A0%E6%B3%95%E4%BD%BF%E7%94%A8localStorage.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.5b1%20jsdom%E5%AF%BC%E8%87%B4%E6%97%A0%E6%B3%95%E4%BD%BF%E7%94%A8localStorage.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.5b1 jsdom导致无法使用localStorage</source>
      <description>情况 在使用Anyblock插件的时候，通过源码安装时，出现Storage is not defined的报错 IMG-20251018 215536030-2.5b1 jsdom导致无法使用localStorage.pngIMG-20251018 215536030-2.5b1 jsdom导致无法使用localStorage.png 解决 首先，既然...</description>
      <category>卡片/普通</category>
      <pubDate>Sat, 26 Oct 2024 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>情况</h2>
<p>在使用<a href="Anyblock">Anyblock</a>插件的时候，通过源码安装时，出现<code>Storage is not defined</code>的报错</p>
<figure><img src="/image/IMG-20251018 215536030-2.5b1 jsdom导致无法使用localStorage.png" alt="IMG-20251018 215536030-2.5b1 jsdom导致无法使用localStorage.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536030-2.5b1 jsdom导致无法使用localStorage.png</figcaption></figure>
<h2>解决</h2>
<p>首先，既然你找不到Storage，那就写一个进去</p>
<div class="language-js line-numbers-mode" data-highlighter="shiki" data-ext="js" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-js"><span class="line"><span style="--shiki-light:#383A42;--shiki-dark:#E5C07B">global</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">.</span><span style="--shiki-light:#E45649;--shiki-dark:#E06C75">Storage</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2"> =</span><span style="--shiki-light:#986801;--shiki-dark:#D19A66"> null</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div><p>接下来，出现了新的报错<br>
<img src="/image/IMG-20251018 215536646-2.5b1 jsdom导致无法使用localStorage.png" alt="IMG-20251018 215536646-2.5b1 jsdom导致无法使用localStorage.png" loading="lazy"></p>
<p>然后，构造一个函数，既然需要<code>instanceof</code>，那么就给它</p>
<div class="language-js line-numbers-mode" data-highlighter="shiki" data-ext="js" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-js"><span class="line"><span style="--shiki-light:#383A42;--shiki-dark:#E5C07B">global</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">.</span><span style="--shiki-light:#4078F2;--shiki-dark:#61AFEF">Storage</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2"> =</span><span style="--shiki-light:#A626A4;--shiki-dark:#C678DD"> function</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">(){</span></span>
<span class="line"><span style="--shiki-light:#E45649;--shiki-dark:#E5C07B">    this</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">.</span><span style="--shiki-light:#4078F2;--shiki-dark:#61AFEF">temp_method</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2"> =</span><span style="--shiki-light:#A626A4;--shiki-dark:#C678DD"> function</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">() {}</span></span>
<span class="line"><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">}</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><p>这样，它就拥有了一个构造函数，里面也有方法可供访问。<br>
这样，就成功欺骗了想要 <code>Storage</code> 的某些函数，在nodejs环境下正常运行</p>
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    <item>
      <title>2.5b2 正则表达式无法匹配markdown链接</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.5b2%20%E6%AD%A3%E5%88%99%E8%A1%A8%E8%BE%BE%E5%BC%8F%E6%97%A0%E6%B3%95%E5%8C%B9%E9%85%8Dmarkdown%E9%93%BE%E6%8E%A5.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.5b2%20%E6%AD%A3%E5%88%99%E8%A1%A8%E8%BE%BE%E5%BC%8F%E6%97%A0%E6%B3%95%E5%8C%B9%E9%85%8Dmarkdown%E9%93%BE%E6%8E%A5.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.5b2 正则表达式无法匹配markdown链接</source>
      <description>背景 一般来说，正则表达式很强大，大部分的字符串基本都能处理。 但是，它对于处理markdown链接这一块具有较大的问题。 如下列表达式: 尝试匹配一个这样的字符串: 结果是: 原因 正则对这种不规则的嵌套很难处理，哪怕贪婪匹配也无法完成。 解决办法 不用正则表达式</description>
      <category>卡片/普通</category>
      <pubDate>Thu, 03 Oct 2024 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>背景</h2>
<p>一般来说，正则表达式很强大，大部分的字符串基本都能处理。<br>
但是，它对于处理markdown链接这一块具有较大的问题。<br>
如下列表达式:</p>
<div class="language-regex line-numbers-mode" data-highlighter="shiki" data-ext="regex" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-regex"><span class="line"><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2">\[</span><span style="--shiki-light:#383A42;--shiki-dark:#D19A66">(</span><span style="--shiki-light:#986801;--shiki-dark:#D19A66">[</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">^</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2">\]</span><span style="--shiki-light:#986801;--shiki-dark:#D19A66">]</span><span style="--shiki-light:#383A42;--shiki-dark:#D19A66">+)</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2">\]\(</span><span style="--shiki-light:#383A42;--shiki-dark:#D19A66">(</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">.</span><span style="--shiki-light:#383A42;--shiki-dark:#D19A66">+?)</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2">\)</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div><p>尝试匹配一个这样的字符串:</p>
<div class="language-markdown line-numbers-mode" data-highlighter="shiki" data-ext="markdown" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-markdown"><span class="line"><span style="--shiki-light:#986801;--shiki-dark:#ABB2BF">[</span><span style="--shiki-light:#4078F2;--shiki-dark:#61AFEF">IMG1</span><span style="--shiki-light:#986801;--shiki-dark:#ABB2BF">]</span><span style="--shiki-light:#A626A4;--shiki-dark:#E06C75">(</span><span style="--shiki-light:#A626A4;--shiki-light-text-decoration:inherit;--shiki-dark:#C678DD;--shiki-dark-text-decoration:underline">IMG1（1</span><span style="--shiki-light:#A626A4;--shiki-dark:#E06C75">)</span><span style="--shiki-light:#383A42;--shiki-dark:#ABB2BF">.png)</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div><p>结果是:</p>
<div class="language-markdown line-numbers-mode" data-highlighter="shiki" data-ext="markdown" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-markdown"><span class="line"><span style="--shiki-light:#986801;--shiki-dark:#ABB2BF">[</span><span style="--shiki-light:#4078F2;--shiki-dark:#61AFEF">IMG1</span><span style="--shiki-light:#986801;--shiki-dark:#ABB2BF">]</span><span style="--shiki-light:#A626A4;--shiki-dark:#E06C75">(</span><span style="--shiki-light:#A626A4;--shiki-light-text-decoration:inherit;--shiki-dark:#C678DD;--shiki-dark-text-decoration:underline">IMG1（1</span><span style="--shiki-light:#A626A4;--shiki-dark:#E06C75">)</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div><h2>原因</h2>
<p>正则对这种不规则的嵌套很难处理，哪怕贪婪匹配也无法完成。</p>
<h2>解决办法</h2>
<p>不用正则表达式</p>
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    <item>
      <title>2.5d permalink的使用</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.5d%20permalink%E7%9A%84%E4%BD%BF%E7%94%A8.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.5d%20permalink%E7%9A%84%E4%BD%BF%E7%94%A8.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.5d permalink的使用</source>
      <description>场景 你需要让一个文件不受文件夹约束，映射到一个URL 注意: 这也会影响面包屑、sidebar之类的生成，和直接文件夹移动是一样的，没办法做到路径别名 注意事项 前面要加 / 不加的话 =&amp;gt; 构建失败 结尾也要加 / 不加的话 =&amp;gt; 显示有毛病 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Fri, 02 May 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>场景</h2>
<ul>
<li>你需要让一个文件不受文件夹约束，映射到一个URL</li>
<li>注意: 这也会影响面包屑、sidebar之类的生成，和直接文件夹移动是一样的，没办法做到路径别名</li>
</ul>
<h2>注意事项</h2>
<ul>
<li>前面要加 <code>/</code> 不加的话 =&gt; 构建失败</li>
<li>结尾也要加 <code>/</code> 不加的话 =&gt; 显示有毛病</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
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    <item>
      <title>2.5e docsearch、cloudflare page与vuepress的兼容性问题</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.5e%20docsearch%E3%80%81cloudflare%20page%E4%B8%8Evuepress%E7%9A%84%E5%85%BC%E5%AE%B9%E6%80%A7%E9%97%AE%E9%A2%98.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.5e%20docsearch%E3%80%81cloudflare%20page%E4%B8%8Evuepress%E7%9A%84%E5%85%BC%E5%AE%B9%E6%80%A7%E9%97%AE%E9%A2%98.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.5e docsearch、cloudflare page与vuepress的兼容性问题</source>
      <description>前言 搞了我三个小时，然后弄不了... vuepress打包出来的产物，页面包括.html后缀 而cloudflare page会好心的帮你把带.html后缀的重定向到不带.html后缀的，并且给一个308重定向。 然后docsearch背后的algolia爬虫，遇到308就直接出错不爬内容了 IMG-20251018 215536031-2.5e d...</description>
      <category>卡片/普通</category>
      <pubDate>Fri, 13 Jun 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p>搞了我三个小时，然后弄不了...</p>
</div></div><ul>
<li>vuepress打包出来的产物，页面包括.html后缀</li>
<li>而cloudflare page会好心的帮你把带.html后缀的重定向到不带.html后缀的，并且给一个308重定向。</li>
<li>然后docsearch背后的algolia爬虫，遇到308就直接出错不爬内容了</li>
</ul>
<figure><img src="/image/IMG-20251018 215536031-2.5e docsearch、cloudflare page与vuepress的兼容性问题.png" alt="IMG-20251018 215536031-2.5e docsearch、cloudflare page与vuepress的兼容性问题.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536031-2.5e docsearch、cloudflare page与vuepress的兼容性问题.png</figcaption></figure>
<ul>
<li>所以慎用docsearch，要不就自己爬</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
]]></content:encoded>
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      <title>2.5e1 Vuepress配置algolia搜索</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.5e1%20Vuepress%E9%85%8D%E7%BD%AEalgolia%E6%90%9C%E7%B4%A2.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.5e1%20Vuepress%E9%85%8D%E7%BD%AEalgolia%E6%90%9C%E7%B4%A2.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.5e1 Vuepress配置algolia搜索</source>
      <description>前言 开源项目都可以用~ 申请 打开DocSearch申请网站，根据指导申请一下 等几个工作日（一般来说在三个以内），然后你会收到发过来的一个邮件: IMG-20251018 215536031-2.5e1 Vuepress配置algolia搜索.pngIMG-20251018 215536031-2.5e1 Vuepress配置algolia搜索.p...</description>
      <category>卡片/普通</category>
      <pubDate>Fri, 13 Jun 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p>开源项目都可以用~</p>
</div></div><h2>申请</h2>
<ul>
<li>打开<a href="https://docsearch.algolia.com/apply/" target="_blank" rel="noopener noreferrer">DocSearch申请</a>网站，根据指导申请一下</li>
<li>等几个工作日（一般来说在三个以内），然后你会收到发过来的一个邮件:</li>
</ul>
<figure><img src="/image/IMG-20251018 215536031-2.5e1 Vuepress配置algolia搜索.png" alt="IMG-20251018 215536031-2.5e1 Vuepress配置algolia搜索.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536031-2.5e1 Vuepress配置algolia搜索.png</figcaption></figure>
<h2>配置Vuepress</h2>
<ul>
<li>打开vuepress，安装<a href="https://ecosystem.vuejs.press/zh/plugins/search/docsearch.html" target="_blank" rel="noopener noreferrer">docsearch插件</a><div class="language-bash line-numbers-mode" data-highlighter="shiki" data-ext="bash" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-bash"><span class="line"><span style="--shiki-light:#4078F2;--shiki-dark:#61AFEF">pnpm</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> i</span><span style="--shiki-light:#986801;--shiki-dark:#D19A66"> -D</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> @vuepress/plugin-docsearch@next</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div></li>
</ul>
<div class="language- line-numbers-mode" data-highlighter="shiki" data-ext="" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-"><span class="line"><span>- 根据文档配置一下，填入邮件发过来的appid和apikey，比如这里我配置vuepress theme hope的:</span></span>
<span class="line"><span>  </span></span>
<span class="line"><span>![0f007d18292e594c1fd37001a6303d20.png](0f007d18292e594c1fd37001a6303d20.png)</span></span>
<span class="line"><span></span></span>
<span class="line"><span>## 配置爬虫</span></span>
<span class="line"><span>  - 点击刚刚邮件里面的邀请链接，按照提示注册账号</span></span>
<span class="line"><span>  - 打开dashboard，找到你刚刚的爬虫</span></span>
<span class="line"><span>    </span></span>
<span class="line"><span>![Pasted image 20250613225450.png](Pasted%20image%2020250613225450.png)</span></span>
<span class="line"><span></span></span>
<span class="line"><span>- 选择到editor</span></span>
<span class="line"><span>  </span></span>
<span class="line"><span>![Pasted image 20250613225529.png](Pasted%20image%2020250613225529.png)</span></span>
<span class="line"><span></span></span>
<span class="line"><span>- 根据官方文档配置一下 `注意不同的主题要用对应的配置`</span></span>
<span class="line"><span>    - [docsearch | VuePress 生态系统](https://ecosystem.vuejs.press/zh/plugins/search/docsearch.html)</span></span>
<span class="line"><span>      [搜索 | vuepress-theme-hope](https://theme-hope.vuejs.press/zh/guide/feature/search.html)</span></span>
<span class="line"><span>## 参见</span></span>
<span class="line"><span>## 参考文献</span></span></code></pre>
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    <item>
      <title>2.6a Windows Terminal代码片段</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.6a%20Windows%20Terminal%E4%BB%A3%E7%A0%81%E7%89%87%E6%AE%B5.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.6a%20Windows%20Terminal%E4%BB%A3%E7%A0%81%E7%89%87%E6%AE%B5.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.6a Windows Terminal代码片段</source>
      <description>前言 在编写脚本的时候，如果使用文件夹，一条条脚本分散开来，检索、使用都不是很方便。而代码片段，则解决了一部分这个问题 使用该功能，需要下载Windows Terminal 1.22[^1] 打开配置文件，并且找到 actions key IMG-20251018 215536033-2.6a Windows Terminal代码片段.pngIMG-2...</description>
      <category>卡片/普通</category>
      <pubDate>Wed, 08 Jan 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p>在编写脚本的时候，如果使用文件夹，一条条脚本分散开来，检索、使用都不是很方便。而代码片段，则解决了一部分这个问题</p>
</div></div><ul>
<li>使用该功能，需要下载<a href="Windows%20Terminal">Windows Terminal</a> 1.22[^1]</li>
<li>打开配置文件，并且找到 <code>actions</code> key</li>
</ul>
<figure><img src="/image/IMG-20251018 215536033-2.6a Windows Terminal代码片段.png" alt="IMG-20251018 215536033-2.6a Windows Terminal代码片段.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536033-2.6a Windows Terminal代码片段.png</figcaption></figure>
<figure><img src="/image/IMG-20251018 215536647-2.6a Windows Terminal代码片段.png" alt="IMG-20251018 215536647-2.6a Windows Terminal代码片段.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536647-2.6a Windows Terminal代码片段.png</figcaption></figure>
<ul>
<li>然后，在 <code>actions</code> 这个列表中，添加一个形如下面的对象<div class="language-json line-numbers-mode" data-highlighter="shiki" data-ext="json" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-json"><span class="line"></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div></li>
</ul>
<p>{<br>
"command":<br>
{<br>
"action": "sendInput",<br>
"input": "这里填你的命令"<br>
},<br>
"name": "这里填你的命令名称"<br>
}</p>
<div class="language- line-numbers-mode" data-highlighter="shiki" data-ext="" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-"><span class="line"><span> </span></span>
<span class="line"><span>&gt; [!tip] Tip</span></span>
<span class="line"><span>&gt; `action`这一栏只能填`sendInput`</span></span>
<span class="line"><span></span></span>
<span class="line"><span>- 然后按 `ctrl+shift+p` 打开命令面板，输入 `打开面板片段窗格` ，就可以看到刚刚添加的代码片段了</span></span>
<span class="line"><span></span></span>
<span class="line"><span>![IMG-20251018 215548590-2.6a Windows Terminal代码片段.png](/image/IMG-20251018%20215548590-2.6a%20Windows%20Terminal代码片段.png)</span></span>
<span class="line"><span></span></span>
<span class="line"><span>## 参见</span></span>
<span class="line"><span>[Windows 终端预览版 1.22 版 - Windows 命令行</span></span></code></pre>
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      <title>2.6d 关闭Windows11专注模式的自动免打扰</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.6d%20%E5%85%B3%E9%97%ADWindows11%E4%B8%93%E6%B3%A8%E6%A8%A1%E5%BC%8F%E7%9A%84%E8%87%AA%E5%8A%A8%E5%85%8D%E6%89%93%E6%89%B0.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.6d%20%E5%85%B3%E9%97%ADWindows11%E4%B8%93%E6%B3%A8%E6%A8%A1%E5%BC%8F%E7%9A%84%E8%87%AA%E5%8A%A8%E5%85%8D%E6%89%93%E6%89%B0.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.6d 关闭Windows11专注模式的自动免打扰</source>
      <description>背景 Windows11更新了专注模式功能，可以点击右下角的时间或者在&amp;quot;时钟&amp;quot;应用中启动 但是默认下，打开这个专注模式会启用请勿打扰，可能导致通知消息被错过 IMG-2.6d 关闭Windows11专注模式的自动免打扰-D7443FF90C4885E1E1CD3E13C6A7F075.pngIMG-2.6d 关闭Windows11专注模式的自动免打扰-...</description>
      <category>卡片/普通</category>
      <pubDate>Tue, 04 Nov 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>背景</h2>
<p>Windows11更新了专注模式功能，可以点击右下角的时间或者在"时钟"应用中启动<br>
但是默认下，打开这个专注模式会启用请勿打扰，可能导致通知消息被错过</p>
<figure><img src="/image/IMG-2.6d 关闭Windows11专注模式的自动免打扰-D7443FF90C4885E1E1CD3E13C6A7F075.png" alt="IMG-2.6d 关闭Windows11专注模式的自动免打扰-D7443FF90C4885E1E1CD3E13C6A7F075.png" tabindex="0" loading="lazy"><figcaption>IMG-2.6d 关闭Windows11专注模式的自动免打扰-D7443FF90C4885E1E1CD3E13C6A7F075.png</figcaption></figure>
<h2>关闭方法</h2>
<ul>
<li>打开设置 &gt; 系统 &gt; 专注</li>
<li>关闭 <code>启用"请勿打扰"</code></li>
</ul>
<figure><img src="/image/IMG-2.6d 关闭Windows11专注模式的自动免打扰-69710BE2DDEB1440EA43B02C1C296636.png" alt="IMG-2.6d 关闭Windows11专注模式的自动免打扰-69710BE2DDEB1440EA43B02C1C296636.png" tabindex="0" loading="lazy"><figcaption>IMG-2.6d 关闭Windows11专注模式的自动免打扰-69710BE2DDEB1440EA43B02C1C296636.png</figcaption></figure>
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      <title>2.7b1 Rslib打包Bundleless时的文件名问题</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.7b1%20Rslib%E6%89%93%E5%8C%85Bundleless%E6%97%B6%E7%9A%84%E6%96%87%E4%BB%B6%E5%90%8D%E9%97%AE%E9%A2%98.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.7b1%20Rslib%E6%89%93%E5%8C%85Bundleless%E6%97%B6%E7%9A%84%E6%96%87%E4%BB%B6%E5%90%8D%E9%97%AE%E9%A2%98.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.7b1 Rslib打包Bundleless时的文件名问题</source>
      <description>背景 在使用Rslib进行Bundleless打包的过程中，遇到了如下错误 发生了什么 rslib在处理components\VfToggleSwitch\src\这个目录时，发现了两个文件: ToggleSwitch.vue ToggleSwitch.ts 虽然这两个文件的拓展名不同，但是他们最终都会尝试生成一个js模块，二者的文件名就冲突了 解决办...</description>
      <category>卡片/普通</category>
      <pubDate>Sat, 18 Oct 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>背景</h2>
<p>在使用<a href="Rslib">Rslib</a>进行<a href="Bundleless">Bundleless</a>打包的过程中，遇到了如下错误</p>
<div class="language-bash line-numbers-mode" data-highlighter="shiki" data-ext="bash" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-bash"><span class="line"><span style="--shiki-light:#4078F2;--shiki-dark:#61AFEF">warn</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> Duplicate</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> entry</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> components</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2">\V</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379">fToggleSwitch</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2">\s</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379">rc</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2">\T</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379">oggleSwitch</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> from</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> src</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2">\c</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379">omponents</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2">\V</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379">fToggleSwitch</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2">\s</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379">rc</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2">\T</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379">oggleSwitch.vue</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> and</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> src</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2">\c</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379">omponents</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2">\V</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379">fToggleSwitch</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2">\s</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379">rc</span><span style="--shiki-light:#0184BC;--shiki-dark:#56B6C2">\T</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379">oggleSwitch.ts,</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> which</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> may</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> lead</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> to</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> the</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> incorrect</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> output,</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> please</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> rename</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> the</span><span style="--shiki-light:#50A14F;--shiki-dark:#98C379"> file.</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div><h2>发生了什么</h2>
<p>rslib在处理<code>components\VfToggleSwitch\src\</code>这个目录时，发现了两个文件:</p>
<ol>
<li><code>ToggleSwitch.vue</code></li>
<li><code>ToggleSwitch.ts</code><br>
虽然这两个文件的拓展名不同，但是他们最终都会尝试生成一个js模块，二者的文件名就冲突了</li>
</ol>
<h2>解决办法</h2>

<div class="callout" data-callout="note">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-pencil"><path d="M17 3a2.85 2.83 0 1 1 4 4L7.5 20.5 2 22l1.5-5.5Z"></path><path d="m15 5 4 4"></path></svg>
</div>
<div class="callout-title-inner">Note</div>
</div>
<div class="callout-content"><p>警告信息其实已经给出了方法 <code>please rename the file</code></p>
</div></div><p><strong>重命名文件</strong><br>
例如：</p>
<ul>
<li><code>ToggleSwitch.vue</code> 保留</li>
<li><code>ToggleSwitch.ts</code> --&gt; <code>ToggleSwitch.type.ts</code></li>
</ul>
]]></content:encoded>
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      <title>2.8 git使用ssh的同时使用watt toolkit加速github</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.8%20git%E4%BD%BF%E7%94%A8ssh%E7%9A%84%E5%90%8C%E6%97%B6%E4%BD%BF%E7%94%A8watt%20toolkit%E5%8A%A0%E9%80%9Fgithub.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.8%20git%E4%BD%BF%E7%94%A8ssh%E7%9A%84%E5%90%8C%E6%97%B6%E4%BD%BF%E7%94%A8watt%20toolkit%E5%8A%A0%E9%80%9Fgithub.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.8 git使用ssh的同时使用watt toolkit加速github</source>
      <description>问题由来 在使用ssh的方式拉取Git仓库的时候，如果使用watt tookit，通过host加速Github的链接的话，因为修改Host为如下这样: 所以会导致ssh推送失败，二者只能取其一。 分析 既然这两者冲突，那么我们需要解决其中的一个问题。 先考虑解决Github的加速问题，尝试过VPN，但是因为不稳定遂放弃。 因此，尝试使ssh能在开加速的...</description>
      <category>卡片/普通</category>
      <pubDate>Sat, 16 Nov 2024 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>问题由来</h2>
<p>在使用ssh的方式拉取Git仓库的时候，如果使用watt tookit，通过host加速Github的链接的话，因为修改Host为如下这样:</p>
<div class="language- line-numbers-mode" data-highlighter="shiki" data-ext="" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-"><span class="line"><span>127.0.0.1 github.com</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div><p>所以会导致ssh推送失败，二者只能取其一。</p>
<h2>分析</h2>
<p>既然这两者冲突，那么我们需要解决其中的一个问题。<br>
先考虑解决Github的加速问题，尝试过<a href="VPN">VPN</a>，但是因为不稳定遂放弃。<br>
因此，尝试使ssh能在开加速的情况下能推送到Github</p>
<h2>解决方案</h2>
<p>因为Github更新了 <code>RSA SSH Private Key</code></p>
<blockquote>
<p>Github自己把这个东西泄露出去了...，所以更新了<br>
见这边:<a href="https://github.blog/2023-03-23-we-updated-our-rsa-ssh-host-key/" target="_blank" rel="noopener noreferrer">Github Blog - We updated our RSA SSH host key</a></p>
</blockquote>
<p>所以，我们需要替换 <code>~/.ssh/known_hosts</code> 中老旧的信息。</p>
<ol>
<li>首先，让我们移除老旧的信息，让老旧的信息放到old文件里面去</li>
</ol>
<div class="language- line-numbers-mode" data-highlighter="shiki" data-ext="" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-"><span class="line"><span>ssh-keygen -R github.com</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div><ol start="2">
<li>接着，打开文件<code>~/.ssh/known_hosts</code>，把最新的key添加进去</li>
</ol>
<div class="language- line-numbers-mode" data-highlighter="shiki" data-ext="" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-"><span class="line"><span>github.com ssh-rsa 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</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div><p>大功告成，现在啥都正常啦！Push/Clone操作都很完美</p>
<blockquote>
<p>如果问题还没解决，记得把git push的加速关掉</p>
</blockquote>
<figure><img src="/image/IMG-20251018 215536043-2.8 git使用ssh的同时使用watt toolkit加速github.png" alt="IMG-20251018 215536043-2.8 git使用ssh的同时使用watt toolkit加速github.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536043-2.8 git使用ssh的同时使用watt toolkit加速github.png</figcaption></figure>
]]></content:encoded>
      <enclosure url="https://blog.erduotong.com/image/IMG-20251018 215536043-2.8 git使用ssh的同时使用watt toolkit加速github.png" type="image/png"/>
    </item>
    <item>
      <title>2.8a .gitignore书写</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.8a%20.gitignore%E4%B9%A6%E5%86%99.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.8a%20.gitignore%E4%B9%A6%E5%86%99.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.8a .gitignore书写</source>
      <description>前言 git仓库中总有一些不需要被上传的文件，这时候就需要.gitignore文件来排除了 .gitignore写法 总规则 一行一个规则 排除文件/文件夹 直接填入example就可以排除掉所有名字为example的目录/文件 无论嵌套深度 多深的嵌套 带/的情况 填入 / 则可以排除指定文件 *通配符的用法 *可以匹配任意个字符(不包括/) **可...</description>
      <category>卡片/普通</category>
      <pubDate>Mon, 27 Jan 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p>git仓库中总有一些不需要被上传的文件，这时候就需要.gitignore文件来排除了</p>
</div></div><h2>.gitignore写法</h2>
<h3>总规则</h3>
<p>一行一个规则</p>
<div class="language-gitignore line-numbers-mode" data-highlighter="shiki" data-ext="gitignore" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-gitignore"><span class="line"><span>node_modules //一行一个</span></span>
<span class="line"><span>.idea //这里是第二个</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div><div class="line-number"></div></div></div><h3>排除文件/文件夹</h3>
<ul>
<li>直接填入<code>example</code>就可以排除掉所有名字为<code>example</code>的目录/文件</li>
<li>无论嵌套深度 多深的嵌套</li>
</ul>
<div class="language-gitignore line-numbers-mode" data-highlighter="shiki" data-ext="gitignore" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-gitignore"><span class="line"><span>dist //排除所有名称为dist的文件夹/文件</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div></div></div><h3>带<code>/</code>的情况</h3>
<ul>
<li>填入 <code>/</code> 则可以排除指定文件</li>
</ul>
<div class="language-gitignore line-numbers-mode" data-highlighter="shiki" data-ext="gitignore" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-gitignore"><span class="line"><span>/a  //排除根目录下的a目录/文件</span></span>
<span class="line"><span>a/b //排除a目录下的b目录/文件</span></span>
<span class="line"><span>a/  //只排除名为a的目录</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h3><code>*</code>通配符的用法</h3>
<ul>
<li><code>*</code>可以匹配任意个字符(不包括<code>/</code>)</li>
<li><code>**</code>可以匹配任意个字符(包括<code>/</code>)</li>
</ul>
<div class="language-gitignore line-numbers-mode" data-highlighter="shiki" data-ext="gitignore" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-gitignore"><span class="line"><span>*.log #排除所有后缀为log的文件</span></span>
<span class="line"><span>a/**/*.log // 排除a目录下</span></span>
<span class="line"><span>           // 任意一个目录的后缀为</span></span>
<span class="line"><span>           // log的文件</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h3><code>?</code>的用法</h3>
<ul>
<li>只匹配一个字符</li>
</ul>
<div class="language-gitignore line-numbers-mode" data-highlighter="shiki" data-ext="gitignore" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-gitignore"><span class="line"><span>?.log //匹配所有log后缀的文件</span></span>
<span class="line"><span>      //但是只允许.log前面有一个字符</span></span>
<span class="line"><span>      //比如a.log可以匹配,b1.log不行</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h3><code>[]</code>的用法</h3>
<ul>
<li>带规则的匹配指定的一个字符</li>
</ul>
<div class="language-gitignore line-numbers-mode" data-highlighter="shiki" data-ext="gitignore" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-gitignore"><span class="line"><span>[0-9].log //匹配 [一个数字].log的文件</span></span>
<span class="line"><span>          //比如1.log 2.log...</span></span>
<span class="line"><span>          // a.log和12.log不会匹配</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h3><code>!</code>反选规则</h3>
<ul>
<li>以 <code>!</code> 开头的规则，表示将这一行规则相反匹配</li>
</ul>
<div class="language-gitignore line-numbers-mode" data-highlighter="shiki" data-ext="gitignore" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-gitignore"><span class="line"><span>*.log       //排除所有log文件</span></span>
<span class="line"><span>!upload.log //除了upload.log</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div><div class="line-number"></div></div></div><h3>注释</h3>
<ul>
<li>以 <code>#</code> 开头，单独占一行</li>
</ul>

<div class="callout" data-callout="tip">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-flame"><path d="M8.5 14.5A2.5 2.5 0 0 0 11 12c0-1.38-.5-2-1-3-1.072-2.143-.224-4.054 2-6 .5 2.5 2 4.9 4 6.5 2 1.6 3 3.5 3 5.5a7 7 0 1 1-14 0c0-1.153.433-2.294 1-3a2.5 2.5 0 0 0 2.5 2.5z"></path></svg>
</div>
<div class="callout-title-inner">注意</div>
</div>
<div class="callout-content"><p></p>
<ul>
<li>如果在规则行末尾添加，则会被视为规则的一部分，所以应该单独占一行</li>
</ul>
</div></div><div class="language-gitignore line-numbers-mode" data-highlighter="shiki" data-ext="gitignore" style="--shiki-light:#383A42;--shiki-dark:#abb2bf;--shiki-light-bg:#FAFAFA;--shiki-dark-bg:#282c34"><pre class="shiki shiki-themes one-light one-dark-pro vp-code"><code class="language-gitignore"><span class="line"><span></span></span>
<span class="line"><span>***</span></span>
<span class="line"><span># 这是一行注释</span></span>
<span class="line"><span>a.log</span></span></code></pre>
<div class="line-numbers" aria-hidden="true" style="counter-reset:line-number 0"><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div><div class="line-number"></div></div></div><h2>参见</h2>
<h2>脚注</h2>
<ul>
<li>参考资料：<a href="https://www.bilibili.com/video/BV1AvcqeBEnX/?vd_source=55526ae438eb9f21ccd7738267eaf0e8" target="_blank" rel="noopener noreferrer">【渡一教育】_哔哩哔哩_bilibili</a></li>
</ul>
]]></content:encoded>
    </item>
    <item>
      <title>2.8b watt toolkit与uv的下载问题</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.8b%20watt%20toolkit%E4%B8%8Euv%E7%9A%84%E4%B8%8B%E8%BD%BD%E9%97%AE%E9%A2%98.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/2.8b%20watt%20toolkit%E4%B8%8Euv%E7%9A%84%E4%B8%8B%E8%BD%BD%E9%97%AE%E9%A2%98.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">2.8b watt toolkit与uv的下载问题</source>
      <description>watt toolkit和uv不能一起开，不然可能下载不下来python 建议直接挂梯子+规则，流量不会很多的</description>
      <category>卡片/普通</category>
      <pubDate>Fri, 01 Aug 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<ul>
<li>watt toolkit和uv不能一起开，不然可能下载不下来python</li>
<li>建议直接挂梯子+规则，流量不会很多的</li>
</ul>
]]></content:encoded>
    </item>
    <item>
      <title>3.1 法西斯的三大特征</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.1%20%E6%B3%95%E8%A5%BF%E6%96%AF%E7%9A%84%E4%B8%89%E5%A4%A7%E7%89%B9%E5%BE%81.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.1%20%E6%B3%95%E8%A5%BF%E6%96%AF%E7%9A%84%E4%B8%89%E5%A4%A7%E7%89%B9%E5%BE%81.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.1 法西斯的三大特征</source>
      <description>独裁专政 摧毁资本主义民主制度，实行集权主义 极端民族主义 倡导种族优越论，为侵略制造理论依据 军国主义 崇拜战争，崇拜武力，认为战争能夺取一切</description>
      <category>卡片/普通</category>
      <pubDate>Tue, 26 Nov 2024 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<ul>
<li>独裁专政 <code>摧毁资本主义民主制度，实行集权主义</code></li>
<li>极端民族主义 <code>倡导种族优越论，为侵略制造理论依据</code></li>
<li>军国主义 <code>崇拜战争，崇拜武力，认为战争能夺取一切</code></li>
</ul>
]]></content:encoded>
    </item>
    <item>
      <title>3.10 领事裁判权</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.10%20%E9%A2%86%E4%BA%8B%E8%A3%81%E5%88%A4%E6%9D%83.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.10%20%E9%A2%86%E4%BA%8B%E8%A3%81%E5%88%A4%E6%9D%83.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.10 领事裁判权</source>
      <description>前言 一国公民在侨居国成为民事、刑事诉讼被告时，该国领事具有的按照本国法律，予以审判、定罪的权力。 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Sun, 30 Mar 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p></p>
</div></div><p>一国公民在侨居国成为民事、刑事诉讼被告时，该国领事具有的按照本国法律，予以审判、定罪的权力。</p>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
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    <item>
      <title>3.12 “左”倾</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.12%20%E2%80%9C%E5%B7%A6%E2%80%9D%E5%80%BE.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.12%20%E2%80%9C%E5%B7%A6%E2%80%9D%E5%80%BE.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.12 “左”倾</source>
      <description>前言 指激进派 在政治思想上超越客观，脱离社会现实条件 急于求成 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Fri, 04 Apr 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p></p>
</div></div><ul>
<li>指激进派</li>
<li>在政治思想上超越客观，脱离社会现实条件</li>
<li>急于求成</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
    </item>
    <item>
      <title>3.12a 右倾</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.12a%20%E5%8F%B3%E5%80%BE.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.12a%20%E5%8F%B3%E5%80%BE.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.12a 右倾</source>
      <description>前言 指保守派 认识落后于实际，不能随变化的客观情况改变 在政治斗争中往往放弃原则，牺牲无产阶级的根本利益而求得妥协 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Fri, 04 Apr 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
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<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p></p>
</div></div><ul>
<li>指保守派</li>
<li>认识落后于实际，不能随变化的客观情况改变</li>
<li>在政治斗争中往往放弃原则，牺牲无产阶级的根本利益而求得妥协</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
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      <title>3.13 正面战场</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.13%20%E6%AD%A3%E9%9D%A2%E6%88%98%E5%9C%BA.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.13%20%E6%AD%A3%E9%9D%A2%E6%88%98%E5%9C%BA.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.13 正面战场</source>
      <description>指日军入侵，我方与之正面交锋的战场 在这个战场上作战的中国军队主要是国民党军队 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Sat, 05 Apr 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<ul>
<li>指日军入侵，我方与之正面交锋的战场</li>
<li>在这个战场上作战的中国军队主要是国民党军队</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
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    <item>
      <title>3.13a 敌后战场</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.13a%20%E6%95%8C%E5%90%8E%E6%88%98%E5%9C%BA.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.13a%20%E6%95%8C%E5%90%8E%E6%88%98%E5%9C%BA.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.13a 敌后战场</source>
      <description>前言 指深入到日军占领区而开辟的战场。 中国共产党领导 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Sat, 05 Apr 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p></p>
</div></div><ul>
<li>指深入到日军占领区而开辟的战场。</li>
<li>中国共产党领导</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
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      <title>3.14 民族工业</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.14%20%E6%B0%91%E6%97%8F%E5%B7%A5%E4%B8%9A.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.14%20%E6%B0%91%E6%97%8F%E5%B7%A5%E4%B8%9A.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.14 民族工业</source>
      <description>前言 广义上的 中国人办的 包括国营、私营 狭义上的 只包括民营资本所办企业，不包含国营 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Sat, 05 Apr 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
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</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p></p>
</div></div><h2>广义上的</h2>
<ul>
<li>中国人办的</li>
<li>包括国营、私营</li>
</ul>
<h2>狭义上的</h2>
<ul>
<li>只包括民营资本所办企业，不包含国营</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
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      <title>3.14a 近代民族工业</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.14a%20%E8%BF%91%E4%BB%A3%E6%B0%91%E6%97%8F%E5%B7%A5%E4%B8%9A.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.14a%20%E8%BF%91%E4%BB%A3%E6%B0%91%E6%97%8F%E5%B7%A5%E4%B8%9A.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.14a 近代民族工业</source>
      <description>前言 指我国近代半殖民地半封建社会时期民族资本所办的企业 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Sat, 05 Apr 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
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<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p></p>
</div></div><ul>
<li>指我国近代半殖民地半封建社会时期民族资本所办的企业</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
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    <item>
      <title>3.14a1 民族资本主义</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.14a1%20%E6%B0%91%E6%97%8F%E8%B5%84%E6%9C%AC%E4%B8%BB%E4%B9%89.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.14a1%20%E6%B0%91%E6%97%8F%E8%B5%84%E6%9C%AC%E4%B8%BB%E4%B9%89.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.14a1 民族资本主义</source>
      <description>产生: 定义: 在半殖民地半封建社会背景下，中国本土发展起来的资本主义经济形态 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Sat, 05 Apr 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<ul>
<li>产生: <a href="/20%20Area/%E5%8E%86%E5%8F%B2/03%20%E5%85%AB%E4%B8%8A/%E5%8D%95%E8%AF%BE/4.%20%E6%B4%8B%E5%8A%A1%E8%BF%90%E5%8A%A8%E5%92%8C%E8%BE%B9%E7%96%86%E5%8D%B1%E6%9C%BA.html#%E6%B4%8B%E5%8A%A1%E8%BF%90%E5%8A%A8" target="_blank">4. 洋务运动和边疆危机#洋务运动</a></li>
<li>定义: 在半殖民地半封建社会背景下，中国<strong>本土</strong>发展起来的资本主义经济形态</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
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      <title>3.17 中国共产党领导的多党合作和政治协商制度</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.17%20%E4%B8%AD%E5%9B%BD%E5%85%B1%E4%BA%A7%E5%85%9A%E9%A2%86%E5%AF%BC%E7%9A%84%E5%A4%9A%E5%85%9A%E5%90%88%E4%BD%9C%E5%92%8C%E6%94%BF%E6%B2%BB%E5%8D%8F%E5%95%86%E5%88%B6%E5%BA%A6.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.17%20%E4%B8%AD%E5%9B%BD%E5%85%B1%E4%BA%A7%E5%85%9A%E9%A2%86%E5%AF%BC%E7%9A%84%E5%A4%9A%E5%85%9A%E5%90%88%E4%BD%9C%E5%92%8C%E6%94%BF%E6%B2%BB%E5%8D%8F%E5%95%86%E5%88%B6%E5%BA%A6.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.17 中国共产党领导的多党合作和政治协商制度</source>
      <description>地位: 是我国一项基本政治制度，是我国社会主义民主政治制度体系的重要组成部分 组织形式——中国人民政治协商会议: 是中国共产党领导的多党合作和政治协商的重要机构，是我国政治生活中发扬社会主义民主的重要形式 发展过程 建立: 中国人民政治协商会议 继续发挥作用: 1954年，后，政协作为统一战线组织继续存在，成为各民主党派和爱国人士参政议政的舞台 198...</description>
      <category>卡片/普通</category>
      <pubDate>Sat, 26 Apr 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<ul>
<li><code>地位</code>: 是我国一项基本政治制度，是我国社会主义民主政治制度体系的重要组成部分</li>
<li><code>组织形式——中国人民政治协商会议</code>: 是中国共产党领导的多党合作和政治协商的重要机构，是我国政治生活中发扬社会主义民主的重要形式</li>
</ul>
<h2>发展过程</h2>
<ul>
<li><code>建立</code>: <a href="#%E4%B8%AD%E5%9B%BD%E4%BA%BA%E6%B0%91%E6%94%BF%E6%B2%BB%E5%8D%8F%E5%95%86%E4%BC%9A%E8%AE%AE">中国人民政治协商会议</a></li>
<li><code>继续发挥作用</code>: 1954年，<a href="/20%20Area/%E5%8E%86%E5%8F%B2/04%20%E5%85%AB%E4%B8%8B/%E5%8D%95%E8%AF%BE/4.%20%E6%96%B0%E4%B8%AD%E5%9B%BD%E5%B7%A5%E4%B8%9A%E5%8C%96%E7%9A%84%E8%B5%B7%E6%AD%A5%E5%92%8C%E4%BA%BA%E6%B0%91%E4%BB%A3%E8%A1%A8%E5%A4%A7%E4%BC%9A%E5%88%B6%E5%BA%A6%E7%9A%84%E7%A1%AE%E7%AB%8B.html#%E4%BA%BA%E6%B0%91%E4%BB%A3%E8%A1%A8%E5%A4%A7%E4%BC%9A%E5%88%B6%E5%BA%A6%E7%9A%84%E7%A1%AE%E7%AB%8B" target="_blank">全国人大召开</a>后，政协作为统一战线组织继续存在，成为各民主党派和爱国人士参政议政的舞台</li>
<li>1982年，确立"长期共存、互相监督、肝胆相照、荣辱与共"的方针</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
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    <item>
      <title>3.18 MOC-历史概念</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.18%20MOC-%E5%8E%86%E5%8F%B2%E6%A6%82%E5%BF%B5.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.18%20MOC-%E5%8E%86%E5%8F%B2%E6%A6%82%E5%BF%B5.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.18 MOC-历史概念</source>
      <description>通用概念与方法 、 、 经济与外交概念 经济 外交 世界通史 史前时期 世界现代史 中国史 古代史 西域 近代史 (1840-1949) 现代史 (1949-今)</description>
      <category>卡片/moc</category>
      <pubDate>Tue, 29 Apr 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<hr>
<h1>通用概念与方法</h1>
<ul>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.7%20%E7%BA%AA%E4%BC%A0%E4%BD%93.html" target="_blank">3.7 纪传体</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.2%20%E6%B0%91%E4%B8%BB%E8%BF%90%E5%8A%A8.html" target="_blank">3.2 民主运动</a>、<a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.2a%20%E6%B0%91%E6%97%8F%E8%BF%90%E5%8A%A8.html" target="_blank">3.2a 民族运动</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.12%20%E2%80%9C%E5%B7%A6%E2%80%9D%E5%80%BE.html" target="_blank">3.12 “左”倾</a>、<a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.12a%20%E5%8F%B3%E5%80%BE.html" target="_blank">3.12a 右倾</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.5c%20%E5%A5%B4%E9%9A%B6%E5%88%B6%E7%A4%BE%E4%BC%9A%E7%9A%84%E7%89%B9%E7%82%B9.html" target="_blank">3.5c 奴隶制社会的特点</a></li>
</ul>
<h1>经济与外交概念</h1>
<h2>经济</h2>
<ul>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.9%20%E8%B4%B8%E6%98%93%E9%A1%BA%E5%B7%AE%EF%BC%88%E5%87%BA%E8%B6%85%EF%BC%89.html" target="_blank">3.9 贸易顺差（出超）</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.9a%20%E8%B4%B8%E6%98%93%E9%80%86%E5%B7%AE%EF%BC%88%E5%85%A5%E8%B6%85%EF%BC%89.html" target="_blank">3.9a 贸易逆差（入超）</a></li>
</ul>
<h2>外交</h2>
<ul>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.10a%20%E5%A4%96%E4%BA%A4.html" target="_blank">3.10a 外交</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.10%20%E9%A2%86%E4%BA%8B%E8%A3%81%E5%88%A4%E6%9D%83.html" target="_blank">3.10 领事裁判权</a></li>
</ul>
<h1>世界通史</h1>
<h2>史前时期</h2>
<ul>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.5%20%E6%97%A7%E7%9F%B3%E5%99%A8%E6%97%B6%E4%BB%A3.html" target="_blank">3.5 旧石器时代</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.5a%20%E6%96%B0%E7%9F%B3%E5%99%A8%E6%97%B6%E4%BB%A3.html" target="_blank">3.5a 新石器时代</a></li>
</ul>
<h2>世界现代史</h2>
<ul>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.1%20%E6%B3%95%E8%A5%BF%E6%96%AF%E7%9A%84%E4%B8%89%E5%A4%A7%E7%89%B9%E5%BE%81.html" target="_blank">3.1 法西斯的三大特征</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.3%20%E5%86%B7%E6%88%98%E7%9A%84%E5%90%AB%E4%B9%89.html" target="_blank">3.3 冷战的含义</a></li>
</ul>
<h1>中国史</h1>
<h2>古代史</h2>
<ul>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.5b%20%E4%B8%AD%E5%9B%BD%E7%9A%84%E4%BC%A0%E8%AF%B4%E6%97%B6%E6%9C%9F.html" target="_blank">3.5b 中国的传说时期</a></li>
<li>西域
<ul>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.6%20%E7%8B%AD%E4%B9%89%E4%B8%8A%E7%9A%84%E8%A5%BF%E5%9F%9F.html" target="_blank">3.6 狭义上的西域</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.6a%20%E5%B9%BF%E4%B9%89%E4%B8%8A%E7%9A%84%E8%A5%BF%E5%9F%9F%E5%9C%B0%E5%8C%BA.html" target="_blank">3.6a 广义上的西域地区</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.6a1%20%E6%B1%89%E4%BB%A3%E7%9A%84%E8%A5%BF%E5%9F%9F.html" target="_blank">3.6a1 汉代的西域</a></li>
</ul>
</li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.8%20%E7%BB%8F%E6%B5%8E%E4%B8%AD%E5%BF%83%E5%8D%97%E7%A7%BB%E7%9A%84%E5%90%AB%E4%B9%89.html" target="_blank">3.8 经济中心南移的含义</a></li>
</ul>
<h2>近代史 (1840-1949)</h2>
<ul>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.4%20%E5%8C%97%E6%B4%8B%E5%86%9B%E9%98%80.html" target="_blank">3.4 北洋军阀</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.4a%20%E5%8C%97%E6%B4%8B%E6%94%BF%E5%BA%9C.html" target="_blank">3.4a 北洋政府</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.13%20%E6%AD%A3%E9%9D%A2%E6%88%98%E5%9C%BA.html" target="_blank">3.13 正面战场</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.13a%20%E6%95%8C%E5%90%8E%E6%88%98%E5%9C%BA.html" target="_blank">3.13a 敌后战场</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.14%20%E6%B0%91%E6%97%8F%E5%B7%A5%E4%B8%9A.html" target="_blank">3.14 民族工业</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.14a%20%E8%BF%91%E4%BB%A3%E6%B0%91%E6%97%8F%E5%B7%A5%E4%B8%9A.html" target="_blank">3.14a 近代民族工业</a></li>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.14a1%20%E6%B0%91%E6%97%8F%E8%B5%84%E6%9C%AC%E4%B8%BB%E4%B9%89.html" target="_blank">3.14a1 民族资本主义</a></li>
</ul>
<h2>现代史 (1949-今)</h2>
<ul>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.17%20%E4%B8%AD%E5%9B%BD%E5%85%B1%E4%BA%A7%E5%85%9A%E9%A2%86%E5%AF%BC%E7%9A%84%E5%A4%9A%E5%85%9A%E5%90%88%E4%BD%9C%E5%92%8C%E6%94%BF%E6%B2%BB%E5%8D%8F%E5%95%86%E5%88%B6%E5%BA%A6.html" target="_blank">3.17 中国共产党领导的多党合作和政治协商制度</a></li>
</ul>
]]></content:encoded>
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      <title>3.2 民主运动</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.2%20%E6%B0%91%E4%B8%BB%E8%BF%90%E5%8A%A8.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.2%20%E6%B0%91%E4%B8%BB%E8%BF%90%E5%8A%A8.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.2 民主运动</source>
      <description>定义 国家对内反专制独裁统治，实现民主自由</description>
      <category>卡片/普通</category>
      <pubDate>Thu, 21 Nov 2024 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>定义</h2>
<p>国家对内反专制独裁统治，实现民主自由</p>
]]></content:encoded>
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    <item>
      <title>3.2a 民族运动</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.2a%20%E6%B0%91%E6%97%8F%E8%BF%90%E5%8A%A8.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.2a%20%E6%B0%91%E6%97%8F%E8%BF%90%E5%8A%A8.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.2a 民族运动</source>
      <description>定义 被压迫民族对外反帝国主义，实现民族解放 参考链接 民族运动_百度百科</description>
      <category>卡片/普通</category>
      <pubDate>Thu, 21 Nov 2024 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>定义</h2>
<p>被压迫民族对外反帝国主义，实现民族解放</p>
<h2>参考链接</h2>
<p><a href="https://baike.baidu.com/item/%E6%B0%91%E6%97%8F%E8%BF%90%E5%8A%A8/10843704" target="_blank" rel="noopener noreferrer">民族运动_百度百科</a></p>
]]></content:encoded>
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      <title>3.3 冷战的含义</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.3%20%E5%86%B7%E6%88%98%E7%9A%84%E5%90%AB%E4%B9%89.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.3%20%E5%86%B7%E6%88%98%E7%9A%84%E5%90%AB%E4%B9%89.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.3 冷战的含义</source>
      <description>后40多年间，以美国、苏联为首的两大集团之间，既非战争又非和平的对峙与竞争状态</description>
      <category>卡片/普通</category>
      <pubDate>Sun, 01 Dec 2024 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<p><a href="/20%20Area/%E5%8E%86%E5%8F%B2/06%20%E4%B9%9D%E4%B8%8B/%E5%8D%95%E8%AF%BE/15.%20%E7%AC%AC%E4%BA%8C%E6%AC%A1%E4%B8%96%E7%95%8C%E5%A4%A7%E6%88%98.html" target="_blank">第二次世界大战</a>后40多年间，以美国、苏联为首的两大集团之间，<strong>既非战争又非和平</strong>的对峙与竞争状态</p>
]]></content:encoded>
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      <title>3.4 北洋军阀</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.4%20%E5%8C%97%E6%B4%8B%E5%86%9B%E9%98%80.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.4%20%E5%8C%97%E6%B4%8B%E5%86%9B%E9%98%80.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.4 北洋军阀</source>
      <description>民国军阀势力之一 是以袁世凯为首的封建军事集团 参见 脚注 参考: 北洋军阀（民国军阀势力之一）_百度百科</description>
      <category>卡片/普通</category>
      <pubDate>Tue, 21 Jan 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<ul>
<li>民国军阀势力之一</li>
<li>是以袁世凯为首的<strong>封建军事集团</strong></li>
</ul>
<h2>参见</h2>
<h2>脚注</h2>
<ul>
<li>参考: <a href="https://baike.baidu.com/item/%E5%8C%97%E6%B4%8B%E5%86%9B%E9%98%80/366336" target="_blank" rel="noopener noreferrer">北洋军阀（民国军阀势力之一）_百度百科</a></li>
</ul>
]]></content:encoded>
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      <title>3.4a 北洋政府</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.4a%20%E5%8C%97%E6%B4%8B%E6%94%BF%E5%BA%9C.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.4a%20%E5%8C%97%E6%B4%8B%E6%94%BF%E5%BA%9C.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.4a 北洋政府</source>
      <description>又称&amp;quot;中华民国北京政府&amp;quot; 是中华民国期间，由袁世凯和其他将领控制的中华民国北京政府 参见 脚注 参考: 北洋政府_百度百科</description>
      <category>卡片/普通</category>
      <pubDate>Tue, 21 Jan 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<ul>
<li>又称"中华民国北京政府"</li>
<li>是中华民国期间，由袁世凯和其他<a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.4%20%E5%8C%97%E6%B4%8B%E5%86%9B%E9%98%80.html" target="_blank">北洋军阀</a>将领控制的中华民国北京政府</li>
</ul>
<h2>参见</h2>
<h2>脚注</h2>
<ul>
<li>参考: <a href="https://baike.baidu.com/item/%E5%8C%97%E6%B4%8B%E6%94%BF%E5%BA%9C/1311509" target="_blank" rel="noopener noreferrer">北洋政府_百度百科</a></li>
</ul>
]]></content:encoded>
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      <title>3.5 旧石器时代</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.5%20%E6%97%A7%E7%9F%B3%E5%99%A8%E6%97%B6%E4%BB%A3.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.5%20%E6%97%A7%E7%9F%B3%E5%99%A8%E6%97%B6%E4%BB%A3.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.5 旧石器时代</source>
      <description>前言 距今约300万年 --&amp;gt; 距今约一万年 标志: 使用磨制石器 参见 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Wed, 22 Jan 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p></p>
</div></div><ul>
<li>距今约300万年 --&gt; 距今约一万年</li>
<li>标志: 使用磨制石器</li>
</ul>
<h2>参见</h2>
<h2>脚注</h2>
]]></content:encoded>
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      <title>3.5a 新石器时代</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.5a%20%E6%96%B0%E7%9F%B3%E5%99%A8%E6%97%B6%E4%BB%A3.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.5a%20%E6%96%B0%E7%9F%B3%E5%99%A8%E6%97%B6%E4%BB%A3.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.5a 新石器时代</source>
      <description>前言 大约从一万多年前开始，结束时间从距今5000多年至4000多年。 以使用磨制石器为标志 参见 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Sun, 26 Jan 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p></p>
</div></div><ul>
<li>大约从一万多年前开始，结束时间从距今5000多年至4000多年。</li>
<li>以使用<strong>磨制石器</strong>为标志</li>
</ul>
<h2>参见</h2>
<h2>脚注</h2>
]]></content:encoded>
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    <item>
      <title>3.5b 中国的传说时期</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.5b%20%E4%B8%AD%E5%9B%BD%E7%9A%84%E4%BC%A0%E8%AF%B4%E6%97%B6%E6%9C%9F.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.5b%20%E4%B8%AD%E5%9B%BD%E7%9A%84%E4%BC%A0%E8%AF%B4%E6%97%B6%E6%9C%9F.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.5b 中国的传说时期</source>
      <description>前言 指夏朝以前的时期 参见 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Sun, 26 Jan 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p></p>
</div></div><ul>
<li>指夏朝以前的时期</li>
</ul>
<h2>参见</h2>
<h2>脚注</h2>
]]></content:encoded>
    </item>
    <item>
      <title>3.5c 奴隶制社会的特点</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.5c%20%E5%A5%B4%E9%9A%B6%E5%88%B6%E7%A4%BE%E4%BC%9A%E7%9A%84%E7%89%B9%E7%82%B9.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.5c%20%E5%A5%B4%E9%9A%B6%E5%88%B6%E7%A4%BE%E4%BC%9A%E7%9A%84%E7%89%B9%E7%82%B9.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.5c 奴隶制社会的特点</source>
      <description>生产领域大量使用奴隶 分为两大对立阶级: 奴隶主和奴隶 奴隶主通过军队、刑法、监狱等实现统治</description>
      <category>卡片/普通</category>
      <pubDate>Wed, 29 Jan 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<ul>
<li>生产领域大量使用奴隶</li>
<li>分为两大对立阶级: 奴隶主和奴隶</li>
<li>奴隶主通过军队、刑法、监狱等实现统治</li>
</ul>
]]></content:encoded>
    </item>
    <item>
      <title>3.6a 广义上的西域地区</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.6a%20%E5%B9%BF%E4%B9%89%E4%B8%8A%E7%9A%84%E8%A5%BF%E5%9F%9F%E5%9C%B0%E5%8C%BA.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.6a%20%E5%B9%BF%E4%B9%89%E4%B8%8A%E7%9A%84%E8%A5%BF%E5%9F%9F%E5%9C%B0%E5%8C%BA.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.6a 广义上的西域地区</source>
      <description>除外，还包括今中亚、西亚、印度半岛、欧洲东部等广大地区 参见 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Sun, 02 Feb 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<ul>
<li>除<a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.6%20%E7%8B%AD%E4%B9%89%E4%B8%8A%E7%9A%84%E8%A5%BF%E5%9F%9F.html" target="_blank">3.6 狭义上的西域</a>外，还包括今中亚、西亚、印度半岛、欧洲东部等广大地区</li>
</ul>
<h2>参见</h2>
<h2>脚注</h2>
]]></content:encoded>
    </item>
    <item>
      <title>3.6a1 汉代的西域</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.6a1%20%E6%B1%89%E4%BB%A3%E7%9A%84%E8%A5%BF%E5%9F%9F.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.6a1%20%E6%B1%89%E4%BB%A3%E7%9A%84%E8%A5%BF%E5%9F%9F.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.6a1 汉代的西域</source>
      <description>今甘肃阳关、玉门关以西 也就是新疆以及更远的广大地区 参见 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Sun, 02 Feb 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<ul>
<li>今甘肃阳关、玉门关以西</li>
<li>也就是新疆以及更远的广大地区</li>
</ul>
<h2>参见</h2>
<h2>脚注</h2>
]]></content:encoded>
    </item>
    <item>
      <title>3.7 纪传体</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.7%20%E7%BA%AA%E4%BC%A0%E4%BD%93.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.7%20%E7%BA%AA%E4%BC%A0%E4%BD%93.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.7 纪传体</source>
      <description>指通过记叙任务活动反应历史时间的体裁 纪 --&amp;gt; 指本纪，按年编写帝王的传记以及国家大事 传 --&amp;gt; 指列传，以传记的方式记录各类人物 参见 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Sun, 02 Feb 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<ul>
<li>指通过记叙任务活动反应历史时间的体裁</li>
<li>纪 --&gt; 指本纪，按年编写帝王的传记以及国家大事</li>
<li>传 --&gt; 指列传，以传记的方式记录各类人物</li>
</ul>
<h2>参见</h2>
<h2>脚注</h2>
]]></content:encoded>
    </item>
    <item>
      <title>3.8 经济中心南移的含义</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.8%20%E7%BB%8F%E6%B5%8E%E4%B8%AD%E5%BF%83%E5%8D%97%E7%A7%BB%E7%9A%84%E5%90%AB%E4%B9%89.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.8%20%E7%BB%8F%E6%B5%8E%E4%B8%AD%E5%BF%83%E5%8D%97%E7%A7%BB%E7%9A%84%E5%90%AB%E4%B9%89.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.8 经济中心南移的含义</source>
      <description>全国经济重心由黄河流域转移到长江流域 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Sat, 08 Mar 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<ul>
<li>全国经济重心由<strong>黄河流域</strong>转移到<strong>长江流域</strong></li>
</ul>
<h2>参见</h2>
<ul>
<li><a href="/20%20Area/%E5%8E%86%E5%8F%B2/%E4%B8%93%E9%A2%98/%E4%B8%AD%E5%9B%BD%E5%8F%A4%E4%BB%A3%E7%BB%8F%E6%B5%8E%E4%B8%AD%E5%BF%83%E5%8D%97%E7%A7%BB.html" target="_blank">中国古代经济中心南移</a></li>
</ul>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
    </item>
    <item>
      <title>3.9 贸易顺差（出超）</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.9%20%E8%B4%B8%E6%98%93%E9%A1%BA%E5%B7%AE%EF%BC%88%E5%87%BA%E8%B6%85%EF%BC%89.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.9%20%E8%B4%B8%E6%98%93%E9%A1%BA%E5%B7%AE%EF%BC%88%E5%87%BA%E8%B6%85%EF%BC%89.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.9 贸易顺差（出超）</source>
      <description>前言 一定时间内(一般为一年) 一国的商品出口额高于进口额 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Sun, 30 Mar 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p></p>
</div></div><ul>
<li>一定时间内(一般为一年)</li>
<li>一国的商品出口额高于进口额</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
    </item>
    <item>
      <title>3.9a 贸易逆差（入超）</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.9a%20%E8%B4%B8%E6%98%93%E9%80%86%E5%B7%AE%EF%BC%88%E5%85%A5%E8%B6%85%EF%BC%89.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/3.9a%20%E8%B4%B8%E6%98%93%E9%80%86%E5%B7%AE%EF%BC%88%E5%85%A5%E8%B6%85%EF%BC%89.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">3.9a 贸易逆差（入超）</source>
      <description>前言 一定时间内(一般为一年) 一国的商品进口额高于出口额 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Sun, 30 Mar 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p></p>
</div></div><ul>
<li>一定时间内(一般为一年)</li>
<li>一国的商品进口额高于出口额</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
    </item>
    <item>
      <title>4.1 医院看病流程</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/4.1%20%E5%8C%BB%E9%99%A2%E7%9C%8B%E7%97%85%E6%B5%81%E7%A8%8B.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/4.1%20%E5%8C%BB%E9%99%A2%E7%9C%8B%E7%97%85%E6%B5%81%E7%A8%8B.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">4.1 医院看病流程</source>
      <description>医院看病流程 梳理症状 带上你的/身份证 挂号 诊治 检查 开药 梳理症状 找出具体不适的部位和症状表现 梳理症状出现的时间 (可以日记记录) 症状具体的特点 难受的表现 刺痛 持续痛 加重/缓解的因素 昨天吃了西瓜后比今天更难受 整理既往病史 (不知道一定要和爸妈问) 挂号 分为线上挂号和线下挂号两种方式 线上挂号 绝大多数医院都可以直接通过微信搜索...</description>
      <category>卡片/普通</category>
      <pubDate>Sat, 16 Nov 2024 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<hr>
<h1>医院看病流程</h1>
<ul>
<li><a href="#%E6%A2%B3%E7%90%86%E7%97%87%E7%8A%B6">梳理症状</a></li>
<li>带上你的<a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/4.1a%20%E5%A6%82%E4%BD%95%E4%BD%BF%E7%94%A8%E5%8C%BB%E4%BF%9D.html" target="_blank">医保卡</a>/身份证</li>
<li><a href="#%E6%8C%82%E5%8F%B7">挂号</a></li>
<li><a href="#%E8%AF%8A%E6%B2%BB">诊治</a>
<ul>
<li><a href="#%E6%A3%80%E6%9F%A5">检查</a></li>
<li><a href="#%E5%BC%80%E8%8D%AF">开药</a></li>
</ul>
</li>
</ul>
<h2>梳理症状</h2>
<ul>
<li>找出具体不适的部位和症状表现</li>
<li>梳理症状出现的时间 (可以日记记录)</li>
<li>症状具体的特点
<ul>
<li>难受的表现 <code>刺痛</code> <code>持续痛</code></li>
<li>加重/缓解的因素 <code>昨天吃了西瓜后比今天更难受</code></li>
</ul>
</li>
<li>整理既往病史 (不知道<strong>一定要和爸妈问</strong>)</li>
</ul>
<h2>挂号</h2>
<p>分为<a href="#%E7%BA%BF%E4%B8%8A%E6%8C%82%E5%8F%B7">线上挂号</a>和<a href="#%E7%BA%BF%E4%B8%8B%E6%8C%82%E5%8F%B7">线下挂号</a>两种方式</p>
<h3>线上挂号</h3>
<ul>
<li>绝大多数医院都可以直接通过<strong>微信</strong>搜索<strong>医院名字</strong>进行挂号</li>
</ul>
<figure><img src="/image/IMG-20251018 215536046-4.1 医院看病流程.png" alt="450" tabindex="0" loading="lazy"><figcaption>450</figcaption></figure>
<ul>
<li>挂号完成后，可以得到一个预约记录:</li>
</ul>
<figure><img src="/image/IMG-20251018 215536651-4.1 医院看病流程.png" alt="IMG-20251018 215536651-4.1 医院看病流程.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536651-4.1 医院看病流程.png</figcaption></figure>

<details class="callout" data-callout="note" data-callout-fold="+" open="">
<summary class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-pencil"><path d="M17 3a2.85 2.83 0 1 1 4 4L7.5 20.5 2 22l1.5-5.5Z"></path><path d="m15 5 4 4"></path></svg>
</div>
<div class="callout-title-inner">优缺点分析</div>
<div class="callout-fold"></div>
</summary>
<div class="callout-content"><p></p>
<ul>
<li>比<a href="#%E7%BA%BF%E4%B8%8B%E6%8C%82%E5%8F%B7">线下挂号</a>更好挂<strong>指定医生</strong>的号</li>
</ul>
<blockquote>
<p>例如，你想挂某个特别厉害的医生，在线上就可以很方便看他的出诊时间，来选择合适的挂号时间。</p>
</blockquote>
<ul>
<li>但是，需要知道你要挂的科的名字，例如你最好清楚的知道你要挂的是 <code>呼吸内科</code>，不然有时间的话还是优先选择<a href="#%E7%BA%BF%E4%B8%8B%E6%8C%82%E5%8F%B7">线下挂号</a></li>
</ul>
</div></details><h3>线下挂号</h3>
<ul>
<li>不清楚挂什么的话就选择<a href="#%E7%AA%97%E5%8F%A3%E6%8C%82%E5%8F%B7">窗口挂号</a>或者<a href="#%E5%AF%BC%E5%8C%BB%E5%8F%B0">导医台</a>去问一下</li>
<li>费用: 几元 ~ 十几元 专家会有少许上升</li>
</ul>
<h4>窗口挂号</h4>
<p>去写了<strong>挂号</strong>的窗口直接问<br>
注意区分<strong>收费</strong>和<strong>挂号</strong>窗口</p>
<figure><img src="/image/IMG-20251018 215548602-4.1 医院看病流程.png" alt="IMG-20251018 215548602-4.1 医院看病流程.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215548602-4.1 医院看病流程.png</figcaption></figure>
<h4>自助机器挂号</h4>
<p>需要<strong>证件</strong> <code>身份证</code> / <code>医保卡（实体/电子卡）</code></p>
<h4>导医台</h4>
<figure><img src="/image/IMG-20251018 215548833-4.1 医院看病流程.png" alt="IMG-20251018 215548833-4.1 医院看病流程.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215548833-4.1 医院看病流程.png</figcaption></figure>
<h2>诊治</h2>
<ul>
<li>前往<strong>对应的科室</strong>就诊</li>
</ul>
<blockquote>
<p>一般来说，挂单号上面会写位置<br>
<img src="/image/IMG-20251018 215550967-4.1 医院看病流程.png" alt="IMG-20251018 215550967-4.1 医院看病流程.png" loading="lazy"></p>
</blockquote>
<ul>
<li>在科室门口签到排队 <code>注意别把病历单丢了，留着，要用的</code>
<ul>
<li>线上的把 <code>预约挂号二维码</code>、条形码、身份证</li>
<li>线下直接用挂号单上面的条形码</li>
</ul>
</li>
<li>签到叫号之后，进去，和医生说症状</li>
</ul>
<blockquote>
<p>有的医生会带学生，不用尴尬</p>
</blockquote>
<h2>检查</h2>
<p><a href="#%E8%AF%8A%E6%B2%BB">诊治</a>结束后，可能需要一些检查</p>
<blockquote>
<p>例如验血、拍片子</p>
</blockquote>
<ul>
<li>拿着医生给的单子去缴费窗口(机器也可以)缴费</li>
<li>缴费后拿着<strong>凭证</strong>去检查科室坐检查</li>
<li>接着再拿着报告去诊室</li>
</ul>
<h2>开药</h2>
<ul>
<li><a href="#%E8%AF%8A%E6%B2%BB">诊治</a>完后，医生会让你去开药，给你一个<strong>药单</strong></li>
<li>把药单缴费后，前往<strong>取药窗口</strong>签到扫码，等叫号</li>
<li>拿药，走，根据医嘱吃</li>
</ul>

<details class="callout" data-callout="note" data-callout-fold="+" open="">
<summary class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-pencil"><path d="M17 3a2.85 2.83 0 1 1 4 4L7.5 20.5 2 22l1.5-5.5Z"></path><path d="m15 5 4 4"></path></svg>
</div>
<div class="callout-title-inner">输液(感冒/发烧可能需要)</div>
<div class="callout-fold"></div>
</summary>
<div class="callout-content"><p></p>
<ul>
<li>拿药后，去输液室输液</li>
</ul>
</div></details>
<details class="callout" data-callout="note" data-callout-fold="+" open="">
<summary class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-pencil"><path d="M17 3a2.85 2.83 0 1 1 4 4L7.5 20.5 2 22l1.5-5.5Z"></path><path d="m15 5 4 4"></path></svg>
</div>
<div class="callout-title-inner">中医取药</div>
<div class="callout-fold"></div>
</summary>
<div class="callout-content"><p></p>
<ul>
<li>可以选择自己回家煎药 <code>你觉得你会吗.jpg</code></li>
<li>找医院<strong>代煎</strong>（取药的时候直接说）</li>
<li>会给你一张取药单，一段时间后（例如第二天）让你来取</li>
</ul>
</div></details><h1>参考链接</h1>
<p><a href="https://www.bilibili.com/video/BV1eWxneME3Q" target="_blank" rel="noopener noreferrer">真的有大学开了《成年人社会常识课》【看病&amp;医保篇】</a></p>
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      <title>4.1a 如何使用医保</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/4.1a%20%E5%A6%82%E4%BD%95%E4%BD%BF%E7%94%A8%E5%8C%BB%E4%BF%9D.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/4.1a%20%E5%A6%82%E4%BD%95%E4%BD%BF%E7%94%A8%E5%8C%BB%E4%BF%9D.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">4.1a 如何使用医保</source>
      <description>如何使用医保 医保的概念 俗称的医保分为: 城市职工基本医疗保险 企业和你签订劳动合同的时候一定缴的 城乡居民基本医疗保险 取决你个人 想缴就缴 确认是否有医保 打开微信/支付宝 搜索 电子医保 会出现一个二维码，那么这就是你的医保 650650 报销范围 药品费、诊疗费、住院费等，依据医保种类定 需要在定点医疗机构就诊，并且符合医保目录 使用 直接搜...</description>
      <category>卡片/普通</category>
      <pubDate>Sat, 16 Nov 2024 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<hr>
<h1>如何使用医保</h1>
<h2>医保的概念</h2>
<p>俗称的医保分为:</p>
<ul>
<li><a href="%E5%9F%8E%E5%B8%82%E8%81%8C%E5%B7%A5%E5%9F%BA%E6%9C%AC%E5%8C%BB%E7%96%97%E4%BF%9D%E9%99%A9">城市职工基本医疗保险</a> 企业和你签订劳动合同的时候一定缴的</li>
<li><a href="%E5%9F%8E%E4%B9%A1%E5%B1%85%E6%B0%91%E5%9F%BA%E6%9C%AC%E5%8C%BB%E7%96%97%E4%BF%9D%E9%99%A9">城乡居民基本医疗保险</a> 取决你个人 想缴就缴</li>
</ul>
<h2>确认是否有医保</h2>
<ul>
<li>打开微信/支付宝</li>
<li>搜索 <code>电子医保</code></li>
<li>会出现一个二维码，那么这就是你的医保</li>
</ul>
<figure><img src="/image/IMG-20251018 215536048-4.1a 如何使用医保.png" alt="650" tabindex="0" loading="lazy"><figcaption>650</figcaption></figure>
<h2>报销范围</h2>
<ul>
<li>药品费、诊疗费、住院费等，依据医保种类定</li>
<li>需要在<strong>定点医疗机构</strong>就诊，并且符合<strong>医保目录</strong></li>
</ul>
<h2>使用</h2>
<ul>
<li>直接搜索电子医保</li>
<li>在<strong>所有缴费环节</strong>说明使用<strong>医保支付</strong>即可 <code>机器也可以用</code></li>
</ul>

<details class="callout" data-callout="tip" data-callout-fold="+" open="">
<summary class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-flame"><path d="M8.5 14.5A2.5 2.5 0 0 0 11 12c0-1.38-.5-2-1-3-1.072-2.143-.224-4.054 2-6 .5 2.5 2 4.9 4 6.5 2 1.6 3 3.5 3 5.5a7 7 0 1 1-14 0c0-1.153.433-2.294 1-3a2.5 2.5 0 0 0 2.5 2.5z"></path></svg>
</div>
<div class="callout-title-inner">Tip</div>
<div class="callout-fold"></div>
</summary>
<div class="callout-content"><p></p>
<ul>
<li>不是所有的药店都可以用医保支付，见<a href="#%E6%8A%A5%E9%94%80%E8%8C%83%E5%9B%B4">报销范围</a>，需要<strong>定点医疗机构</strong></li>
<li>善用地图搜索</li>
</ul>
</div></details><figure><img src="/image/IMG-20251018 215536653-4.1a 如何使用医保.png" alt="600" tabindex="0" loading="lazy"><figcaption>600</figcaption></figure>
<h3>挂号医保报销</h3>
<ul>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/4.1%20%E5%8C%BB%E9%99%A2%E7%9C%8B%E7%97%85%E6%B5%81%E7%A8%8B.html#%E7%BA%BF%E4%B8%8A%E6%8C%82%E5%8F%B7" target="_blank">线上挂号</a>有时候会直接缴费，需要用绑定的就诊卡挂号才能报销 <code>可能无法报销</code></li>
<li>医院现场刷的时候，如果是居民医保需要缴纳个人部分，职工医保会自动从个人账户里面扣除</li>
</ul>

<details class="callout" data-callout="note" data-callout-fold="+" open="">
<summary class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-pencil"><path d="M17 3a2.85 2.83 0 1 1 4 4L7.5 20.5 2 22l1.5-5.5Z"></path><path d="m15 5 4 4"></path></svg>
</div>
<div class="callout-title-inner">缴纳的是完全没有报销的金额</div>
<div class="callout-fold"></div>
</summary>
<div class="callout-content"><p></p>
<ul>
<li>年度累计门诊费用未达到起付线</li>
<li>部分地区挂号费不支持医保报销</li>
<li>部分地区线上挂号无法报销（尽量<a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/4.1%20%E5%8C%BB%E9%99%A2%E7%9C%8B%E7%97%85%E6%B5%81%E7%A8%8B.html#%E7%BA%BF%E4%B8%8B%E6%8C%82%E5%8F%B7" target="_blank">线下挂号</a>，用医保卡、电子医保表明身份）</li>
</ul>
</div></details><h3>买药医保报销</h3>
<p>所有缴费环节均出示<code>医保卡</code>/<code>电子医保</code></p>
<h3>住院医保报销</h3>
<ul>
<li>需要提前<strong>预存住院金</strong></li>
<li>发生的费用根据医保信息自动扣除，其他的走预存金</li>
<li>出院的时候没用完的预存金会退费</li>
</ul>
<h1>参考链接</h1>
<p><a href="https://www.bilibili.com/video/BV1eWxneME3Q" target="_blank" rel="noopener noreferrer">真的有大学开了《成年人社会常识课》【看病&amp;医保篇】</a></p>
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      <title>6.2 Better Export PDF的一些问题</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/6.2%20Better%20Export%20PDF%E7%9A%84%E4%B8%80%E4%BA%9B%E9%97%AE%E9%A2%98.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/6.2%20Better%20Export%20PDF%E7%9A%84%E4%B8%80%E4%BA%9B%E9%97%AE%E9%A2%98.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">6.2 Better Export PDF的一些问题</source>
      <description>前言 很好的插件，但是有些问题实在是有点大 导出 此问题在Github Issue亦有记载 在导出单个文件的时候，需要等待左边渲染出来后，才能导出，不然就是空白的 IMG-20251018 215536051-6.2 Better Export PDF的一些问题.pngIMG-20251018 215536051-6.2 Better Export P...</description>
      <category>卡片/普通</category>
      <pubDate>Sun, 09 Feb 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p>很好的插件，但是有些问题实在是有点大</p>
</div></div><h2>导出</h2>
<blockquote>
<p>此问题在<a href="https://github.com/l1xnan/obsidian-better-export-pdf/issues/373" target="_blank" rel="noopener noreferrer">Github Issue</a>亦有记载</p>
</blockquote>
<ul>
<li>在导出单个文件的时候，需要等待左边渲染出来后，才能导出，不然就是空白的</li>
</ul>
<figure><img src="/image/IMG-20251018 215536051-6.2 Better Export PDF的一些问题.png" alt="IMG-20251018 215536051-6.2 Better Export PDF的一些问题.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536051-6.2 Better Export PDF的一些问题.png</figcaption></figure>
<ul>
<li>批量导出PDF的时候，也需要等待左边渲染完，不然导出的是空白的</li>
</ul>
<h2>参见</h2>
<h2>脚注</h2>
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      <title>6.4 Thino索引不出来东西的解决办法</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/6.4%20Thino%E7%B4%A2%E5%BC%95%E4%B8%8D%E5%87%BA%E6%9D%A5%E4%B8%9C%E8%A5%BF%E7%9A%84%E8%A7%A3%E5%86%B3%E5%8A%9E%E6%B3%95.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/6.4%20Thino%E7%B4%A2%E5%BC%95%E4%B8%8D%E5%87%BA%E6%9D%A5%E4%B8%9C%E8%A5%BF%E7%9A%84%E8%A7%A3%E5%86%B3%E5%8A%9E%E6%B3%95.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">6.4 Thino索引不出来东西的解决办法</source>
      <description>问题描述 在我迁移Obsidian仓库位置+重新下载Thino后，Thino内就一条条目都没有了，全部消失了 并且，Thino似乎没有提供重新索引全库的按钮 截止到2.7.17 如何解决 最简单的办法就是把所有的文件重新打开一次，让Thino去扫。 但是一个一个手点速度过慢，可以使用下面的办法加速操作: 需要使用Better Export Pdf这一插...</description>
      <category>卡片/普通</category>
      <pubDate>Fri, 01 Aug 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>问题描述</h2>
<ul>
<li>在我迁移Obsidian仓库位置+重新下载<a href="Thino">Thino</a>后，Thino内就一条条目都没有了，全部消失了</li>
<li>并且，Thino似乎没有提供重新索引全库的按钮 <code>截止到2.7.17</code></li>
</ul>
<h2>如何解决</h2>
<p>最简单的办法就是把所有的文件重新打开一次，让Thino去扫。<br>
但是一个一个手点速度过慢，可以使用下面的办法加速操作:</p>
<blockquote>
<p>需要使用<a href="Better%20Export%20Pdf">Better Export Pdf</a>这一插件</p>
</blockquote>
<ol>
<li>找到你的Thino条目存在的笔记所处的文件夹（比如我的thino在日记里面，所以我打开了日记文件夹）</li>
<li>右键刚刚所提到的文件夹，点击 <code>Export each file to PDDF</code></li>
</ol>
<figure><img src="/image/IMG-20251018 215536052-6.4 Thino索引不出来东西的解决办法.png" alt="IMG-20251018 215536052-6.4 Thino索引不出来东西的解决办法.png" tabindex="0" loading="lazy"><figcaption>IMG-20251018 215536052-6.4 Thino索引不出来东西的解决办法.png</figcaption></figure>
<ol start="3">
<li>等待一段时间，直到所有的文件都被打开了一次</li>
<li>ok,你的Thino恢复了。</li>
</ol>
<h2>为什么这能奏效？</h2>
<ul>
<li><a href="Better%20Export%20Pdf">Better Export Pdf</a>为了导出PDF，需要打开每个markdown文件来渲染PDF</li>
<li>而打开markdown文件后，Thino会进行扫描。</li>
<li>所以，二者就可以互相配合，重新完成索引</li>
</ul>
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    <item>
      <title>7.2 电声乐器插拔卡农线最佳实践</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/7.2%20%E7%94%B5%E5%A3%B0%E4%B9%90%E5%99%A8%E6%8F%92%E6%8B%94%E5%8D%A1%E5%86%9C%E7%BA%BF%E6%9C%80%E4%BD%B3%E5%AE%9E%E8%B7%B5.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/7.2%20%E7%94%B5%E5%A3%B0%E4%B9%90%E5%99%A8%E6%8F%92%E6%8B%94%E5%8D%A1%E5%86%9C%E7%BA%BF%E6%9C%80%E4%BD%B3%E5%AE%9E%E8%B7%B5.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">7.2 电声乐器插拔卡农线最佳实践</source>
      <description>操作步骤 开机从音源到音响，关机从音响到音源 不要在音响有音量的时候插拔任何设备的音频线 如果一定要移动位置，就保持卡农线插着移动 开机 / 接线 确认音响电源关闭/音量在最小位置 调音台推子推到底也可以 接上卡农线 打开乐器电源 打开音响电源 或者打开声音/调音台推子推回正常水平 关机 / 拆线 确认音响电源关闭/音量在最小位置 关闭乐器电源 拔掉卡...</description>
      <category>卡片/普通</category>
      <pubDate>Mon, 30 Mar 2026 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>操作步骤</h2>
<p><strong>开机从音源到音响，关机从音响到音源</strong></p>
<blockquote>
<p><strong>不要</strong>在音响有音量的时候插拔<strong>任何设备</strong>的音频线<br>
如果一定要移动位置，就保持卡农线插着移动</p>
</blockquote>
<h3>开机 / 接线</h3>
<ol>
<li>确认音响电源关闭/音量在最小位置 <code>调音台推子推到底也可以</code></li>
<li>接上卡农线</li>
<li>打开乐器电源</li>
<li>打开音响电源 <code>或者打开声音/调音台推子推回正常水平</code></li>
</ol>
<h3>关机 / 拆线</h3>
<ol>
<li>确认音响电源关闭/音量在最小位置</li>
<li>关闭乐器电源</li>
<li>拔掉卡农线</li>
</ol>
<h3>中途换线</h3>
<ol>
<li>调音台静音/推子推到底</li>
<li>拆掉原来的线</li>
<li>换上新线</li>
<li>调音台/音响恢复到正常的位置</li>
</ol>
<h2>为什么？</h2>
<ul>
<li>参见<a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/7.2a%20%20%E4%B8%BA%E4%BB%80%E4%B9%88%E4%B8%8D%E5%85%B3%E9%9F%B3%E5%93%8D%E7%9B%B4%E6%8E%A5%E6%8F%92%E6%8B%94%E7%BA%BF%E4%BC%9A%E6%8D%9F%E5%AE%B3%E9%9F%B3%E5%93%8D.html" target="_blank">7.2a  为什么不关音响直接插拔线会损害音响</a></li>
</ul>
]]></content:encoded>
    </item>
    <item>
      <title>7.2a  为什么不关音响直接插拔线会损害音响</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/7.2a%20%20%E4%B8%BA%E4%BB%80%E4%B9%88%E4%B8%8D%E5%85%B3%E9%9F%B3%E5%93%8D%E7%9B%B4%E6%8E%A5%E6%8F%92%E6%8B%94%E7%BA%BF%E4%BC%9A%E6%8D%9F%E5%AE%B3%E9%9F%B3%E5%93%8D.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/7.2a%20%20%E4%B8%BA%E4%BB%80%E4%B9%88%E4%B8%8D%E5%85%B3%E9%9F%B3%E5%93%8D%E7%9B%B4%E6%8E%A5%E6%8F%92%E6%8B%94%E7%BA%BF%E4%BC%9A%E6%8D%9F%E5%AE%B3%E9%9F%B3%E5%93%8D.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">7.2a  为什么不关音响直接插拔线会损害音响</source>
      <description>在音响开启的状态下 拔出卡农线的时候，因为并不是同时完美断开的，会产生微小的电弧或接触不良 ==&amp;gt; 产生一股电压脉冲 电压脉冲进入音响，音响功放无差别放大电流 脉冲进入音响的物理发声部分 因电流过大 ==&amp;gt; 高音部分烧毁 因运动幅度过大 ==&amp;gt; 低音部分撕裂/卡死</description>
      <category>卡片/普通</category>
      <pubDate>Tue, 31 Mar 2026 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<blockquote>
<p>在音响开启的状态下</p>
</blockquote>
<ul>
<li>拔出卡农线的时候，因为并不是同时完美断开的，会产生微小的电弧或接触不良 ==&gt; 产生一股电压脉冲</li>
<li>电压脉冲进入音响，音响功放无差别放大电流</li>
<li>脉冲进入音响的物理发声部分
<ul>
<li>因电流过大 ==&gt; 高音部分烧毁</li>
<li>因运动幅度过大 ==&gt; 低音部分撕裂/卡死</li>
</ul>
</li>
</ul>
]]></content:encoded>
    </item>
    <item>
      <title>8.1 实验设计题评分</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/8.1%20%E5%AE%9E%E9%AA%8C%E8%AE%BE%E8%AE%A1%E9%A2%98%E8%AF%84%E5%88%86.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/8.1%20%E5%AE%9E%E9%AA%8C%E8%AE%BE%E8%AE%A1%E9%A2%98%E8%AF%84%E5%88%86.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">8.1 实验设计题评分</source>
      <description>前言 指让你设计一个实验的评分规则，做这种题的时候记得这样检查 原理 化学式等，最重要，错了就没分 仪器 烧杯、酒精灯... 操作 先干什么在干什么 现象 结论 若...则...否则... 控制变量 错别字 一个0.5分 参见 参考文献 脚注</description>
      <category>卡片/普通</category>
      <pubDate>Thu, 20 Mar 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p>指让你设计一个实验的评分规则，做这种题的时候记得这样检查</p>
</div></div><ul>
<li>原理 <code>化学式等，最重要，错了就没分</code></li>
<li>仪器 <code>烧杯、酒精灯...</code></li>
<li>操作 <code>先干什么在干什么</code></li>
<li>现象</li>
<li>结论 <code>若...则...否则...</code></li>
<li>控制变量</li>
<li>错别字 <code>一个0.5分</code></li>
</ul>
<h2>参见</h2>
<ul>
<li><a href="/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/8.1b%20%E5%9B%BA%E4%BD%93%E3%80%81%E6%B6%B2%E4%BD%93%E7%9A%84%E6%8E%A7%E5%88%B6%E5%8F%98%E9%87%8F.html" target="_blank">8.1b 固体、液体的控制变量</a></li>
</ul>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
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    <item>
      <title>8.1a 探究目的</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/8.1a%20%E6%8E%A2%E7%A9%B6%E7%9B%AE%E7%9A%84.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/8.1a%20%E6%8E%A2%E7%A9%B6%E7%9B%AE%E7%9A%84.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">8.1a 探究目的</source>
      <description>依据题干回答（画出来） 例子 探究不同质量分数的NaOH溶液对“彩虹管”效果的影响 从文本中得到足够的信息 参见 参考文献</description>
      <category>卡片/普通</category>
      <pubDate>Fri, 30 May 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<ul>
<li>依据<strong>题干</strong>回答（画出来）</li>
</ul>
<h2>例子</h2>
<ul>
<li>探究不同质量分数的NaOH溶液对“彩虹管”效果的影响 <code>从文本中得到足够的信息</code></li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
]]></content:encoded>
    </item>
    <item>
      <title>8.1a1 判断工艺流程的产物</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/8.1a1%20%E5%88%A4%E6%96%AD%E5%B7%A5%E8%89%BA%E6%B5%81%E7%A8%8B%E7%9A%84%E4%BA%A7%E7%89%A9.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/8.1a1%20%E5%88%A4%E6%96%AD%E5%B7%A5%E8%89%BA%E6%B5%81%E7%A8%8B%E7%9A%84%E4%BA%A7%E7%89%A9.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">8.1a1 判断工艺流程的产物</source>
      <description>前言 fuck off 工艺流程题 判断方式 寻找实验目的 为了得到什么 用途 判断是否可以循环利用某种物质</description>
      <category>卡片/普通</category>
      <pubDate>Sun, 22 Jun 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">前言</div>
</div>
<div class="callout-content"><p>fuck off 工艺流程题</p>
</div></div><h2>判断方式</h2>
<ul>
<li>寻找实验目的 <code>为了得到什么</code></li>
</ul>
<h2>用途</h2>
<ul>
<li>判断是否可以循环利用某种物质</li>
</ul>
]]></content:encoded>
    </item>
    <item>
      <title>8.1a1a 工艺流程题的解题步骤</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/8.1a1a%20%E5%B7%A5%E8%89%BA%E6%B5%81%E7%A8%8B%E9%A2%98%E7%9A%84%E8%A7%A3%E9%A2%98%E6%AD%A5%E9%AA%A4.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/8.1a1a%20%E5%B7%A5%E8%89%BA%E6%B5%81%E7%A8%8B%E9%A2%98%E7%9A%84%E8%A7%A3%E9%A2%98%E6%AD%A5%E9%AA%A4.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">8.1a1a 工艺流程题的解题步骤</source>
      <description>看题 --&amp;gt; 寻找产物 背景 一般来说给出的背景都会用上 题目 化学式 和 名称 看清楚，不要写错 注意盐酸和硫酸 操作 --&amp;gt; 95%的概率是 过滤</description>
      <category>卡片/普通</category>
      <pubDate>Sun, 22 Jun 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<ul>
<li>看题 --&gt; 寻找产物</li>
<li>背景 <code>一般来说给出的背景都会用上</code></li>
<li>题目
<ul>
<li><code>化学式</code> 和 <code>名称</code> <strong>看清楚</strong>，不要写错</li>
<li>注意<strong>盐酸</strong>和<strong>硫酸</strong></li>
</ul>
</li>
<li>操作 --&gt; 95%的概率是 <strong>过滤</strong></li>
</ul>
]]></content:encoded>
    </item>
    <item>
      <title>8.1b 固体、液体的控制变量</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/8.1b%20%E5%9B%BA%E4%BD%93%E3%80%81%E6%B6%B2%E4%BD%93%E7%9A%84%E6%8E%A7%E5%88%B6%E5%8F%98%E9%87%8F.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/8.1b%20%E5%9B%BA%E4%BD%93%E3%80%81%E6%B6%B2%E4%BD%93%E7%9A%84%E6%8E%A7%E5%88%B6%E5%8F%98%E9%87%8F.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">8.1b 固体、液体的控制变量</source>
      <description>固体 --&amp;gt; 等量 液体 --&amp;gt; 等体积 液体一般都用体积 参见 参考文献</description>
      <category>卡片/普通</category>
      <pubDate>Sun, 08 Jun 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<ul>
<li>固体 --&gt; <strong>等量</strong></li>
<li>液体 --&gt; <strong>等体积</strong> <code>液体一般都用体积</code></li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
]]></content:encoded>
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    <item>
      <title>8.2 计算某种元素是否存在</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/8.2%20%E8%AE%A1%E7%AE%97%E6%9F%90%E7%A7%8D%E5%85%83%E7%B4%A0%E6%98%AF%E5%90%A6%E5%AD%98%E5%9C%A8.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/8.2%20%E8%AE%A1%E7%AE%97%E6%9F%90%E7%A7%8D%E5%85%83%E7%B4%A0%E6%98%AF%E5%90%A6%E5%AD%98%E5%9C%A8.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">8.2 计算某种元素是否存在</source>
      <description>问题描述 已知 4.02g 某物质与O2​发生了反应 生成了 2.7g H2​O 生成了 8.8g CO2​ 求该物质里面是否有氧元素 解答 根据质量守恒定律，计算出 其他 元素的质量 判断是否和消耗的质量相符，如果相等则说明没有其他元素，反之则有 计算出2.7g H2​O 中 H 的质量是 0.3g 计算出8.8g CO2​ 中 C 的质量是 2.4...</description>
      <category>卡片/普通</category>
      <pubDate>Thu, 17 Apr 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>问题描述</h2>
<ul>
<li>已知 4.02g 某物质与<span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>O</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">O_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>发生了反应</li>
<li>生成了 2.7g <span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>H</mi><mn>2</mn></msub><mi>O</mi></mrow><annotation encoding="application/x-tex">H_2O</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span></span></span></span></li>
<li>生成了 8.8g <span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><msub><mi>O</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">CO_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></li>
<li>求该物质里面是否有氧元素</li>
</ul>
<h2>解答</h2>
<blockquote>
<p>根据质量守恒定律，计算出 其他 元素的质量<br>
判断是否和消耗的质量相符，如果相等则说明没有其他元素，反之则有</p>
</blockquote>
<ul>
<li>计算出2.7g <span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>H</mi><mn>2</mn></msub><mi>O</mi></mrow><annotation encoding="application/x-tex">H_2O</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span></span></span></span> 中 <span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>H</mi></mrow><annotation encoding="application/x-tex">H</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.08125em;">H</span></span></span></span> 的质量是 0.3g</li>
<li>计算出8.8g <span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><msub><mi>O</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">CO_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> 中 <span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi></mrow><annotation encoding="application/x-tex">C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span></span></span></span> 的质量是 2.4g</li>
<li>2.4g + 0.3g = 2.7g</li>
<li>2.7g &lt; 4.02g，所以该物质里面一定有氧元素</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
<h2>脚注</h2>
]]></content:encoded>
    </item>
    <item>
      <title>8.2a 用和水的溶解现象来判断物质</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/8.2a%20%E7%94%A8%E5%92%8C%E6%B0%B4%E7%9A%84%E6%BA%B6%E8%A7%A3%E7%8E%B0%E8%B1%A1%E6%9D%A5%E5%88%A4%E6%96%AD%E7%89%A9%E8%B4%A8.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/8.2a%20%E7%94%A8%E5%92%8C%E6%B0%B4%E7%9A%84%E6%BA%B6%E8%A7%A3%E7%8E%B0%E8%B1%A1%E6%9D%A5%E5%88%A4%E6%96%AD%E7%89%A9%E8%B4%A8.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">8.2a 用和水的溶解现象来判断物质</source>
      <description>判断内容 溶/不溶 颜色 (比如 CuSO4​ ) 温度 (上升/下降) 参见 参考文献</description>
      <category>卡片/普通</category>
      <pubDate>Wed, 04 Jun 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[<h2>判断内容</h2>
<ul>
<li>溶/不溶</li>
<li>颜色 (比如 <span v-pre="" class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>u</mi><mi>S</mi><msub><mi>O</mi><mn>4</mn></msub></mrow><annotation encoding="application/x-tex">CuSO_4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">u</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> )</li>
<li>温度 (上升/下降)</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
]]></content:encoded>
    </item>
    <item>
      <title>8.2a1 各物质溶液互相鉴别的解题步骤</title>
      <link>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/8.2a1%20%E5%90%84%E7%89%A9%E8%B4%A8%E6%BA%B6%E6%B6%B2%E4%BA%92%E7%9B%B8%E9%89%B4%E5%88%AB%E7%9A%84%E8%A7%A3%E9%A2%98%E6%AD%A5%E9%AA%A4.html</link>
      <guid>https://blog.erduotong.com/60%20%E5%8D%A1%E7%89%87%E7%AC%94%E8%AE%B0/%E4%B8%BB%E5%8D%A1%E7%89%87/8.2a1%20%E5%90%84%E7%89%A9%E8%B4%A8%E6%BA%B6%E6%B6%B2%E4%BA%92%E7%9B%B8%E9%89%B4%E5%88%AB%E7%9A%84%E8%A7%A3%E9%A2%98%E6%AD%A5%E9%AA%A4.html</guid>
      <source url="https://blog.erduotong.com/rss.xml">8.2a1 各物质溶液互相鉴别的解题步骤</source>
      <description>识别 给你四个选项，每个选项有四个物质 问: 下列那个选项中的四个物质都能被鉴别出来 判断颜色 判断碱 判断酸 其他 参见 参考文献</description>
      <category>卡片/普通</category>
      <pubDate>Wed, 04 Jun 2025 00:00:00 GMT</pubDate>
      <content:encoded><![CDATA[
<div class="callout" data-callout="quote">
<div class="callout-title">
<div class="callout-title-icon">
<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-quote"><path d="M3 21c3 0 7-1 7-8V5c0-1.25-.756-2.017-2-2H4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2 1 0 1 0 1 1v1c0 1-1 2-2 2s-1 .008-1 1.031V20c0 1 0 1 1 1z"></path><path d="M15 21c3 0 7-1 7-8V5c0-1.25-.757-2.017-2-2h-4c-1.25 0-2 .75-2 1.972V11c0 1.25.75 2 2 2h.75c0 2.25.25 4-2.75 4v3c0 1 0 1 1 1z"></path></svg>
</div>
<div class="callout-title-inner">识别</div>
</div>
<div class="callout-content"><p>给你四个选项，每个选项有四个物质<br>
问: 下列那个选项中的四个物质都能被鉴别出来</p>
</div></div><ul>
<li>判断颜色</li>
<li>判断碱</li>
<li>判断酸</li>
<li>其他</li>
</ul>
<h2>参见</h2>
<h2>参考文献</h2>
]]></content:encoded>
    </item>
  </channel>
</rss>