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phyzk committed Oct 6, 2024
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19 changes: 11 additions & 8 deletions 2023/09/10/first/index.html
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<meta name="author" content="liu19">
<meta name="keywords" content="">

<meta name="description" content="这是一篇测试文章 今天是10月 :smile: h1 标题 h2 标题引擎可以选择 mathjax 或 katex，下面使用的 mathjax $$ \int f(x)^2 &#x3D;\begin{pmatrix} \hbar &amp; \not\gamma \ 0 &amp; 0\end{pmatrix}\\Set{ x\in\mathbf{R}^2 | 0&amp;l">
<meta name="description" content="这是一篇测试文章 今天是10月 😄 h1 标题 h2 标题引擎可以选择 mathjax 或 katex，下面使用的 mathjax $$ \int f(x)^2 &#x3D;\begin{pmatrix} \hbar &amp; \not\gamma \ 0 &amp; 0\end{pmatrix}\\Set{ x\in\mathbf{R}^2 | 0&lt;{|x|}&amp;lt">
<meta property="og:type" content="article">
<meta property="og:title" content="first">
<meta property="og:url" content="http://example.com/2023/09/10/first/index.html">
<meta property="og:site_name" content="Liu19">
<meta property="og:description" content="这是一篇测试文章 今天是10月 :smile: h1 标题 h2 标题引擎可以选择 mathjax 或 katex，下面使用的 mathjax $$ \int f(x)^2 &#x3D;\begin{pmatrix} \hbar &amp; \not\gamma \ 0 &amp; 0\end{pmatrix}\\Set{ x\in\mathbf{R}^2 | 0&amp;l">
<meta property="og:description" content="这是一篇测试文章 今天是10月 😄 h1 标题 h2 标题引擎可以选择 mathjax 或 katex，下面使用的 mathjax $$ \int f(x)^2 &#x3D;\begin{pmatrix} \hbar &amp; \not\gamma \ 0 &amp; 0\end{pmatrix}\\Set{ x\in\mathbf{R}^2 | 0&lt;{|x|}&amp;lt">
<meta property="og:locale" content="zh_CN">
<meta property="og:image" content="https://github.githubassets.com/images/icons/emoji/unicode/1f604.png?v8">
<meta property="og:image" content="http://example.com/2023/09/10/first/ocean.jpg">
<meta property="og:image" content="http://example.com/images/ocean.jpg">
<meta property="article:published_time" content="2023-09-10T07:07:16.000Z">
<meta property="article:modified_time" content="2023-10-12T02:47:17.079Z">
<meta property="article:author" content="liu19">
<meta property="article:tag" content="test">
<meta name="twitter:card" content="summary_large_image">
<meta name="twitter:image" content="http://example.com/2023/09/10/first/ocean.jpg">
<meta name="twitter:image" content="https://github.githubassets.com/images/icons/emoji/unicode/1f604.png?v8">



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<meta name="generator" content="Hexo 7.3.0"></head>
<meta name="generator" content="Hexo 7.3.0">
<style>.github-emoji { position: relative; display: inline-block; width: 1.2em; min-height: 1.2em; overflow: hidden; vertical-align: top; color: transparent; } .github-emoji > span { position: relative; z-index: 10; } .github-emoji img, .github-emoji .fancybox { margin: 0 !important; padding: 0 !important; border: none !important; outline: none !important; text-decoration: none !important; user-select: none !important; cursor: auto !important; } .github-emoji img { height: 1.2em !important; width: 1.2em !important; position: absolute !important; left: 50% !important; top: 50% !important; transform: translate(-50%, -50%) !important; user-select: none !important; cursor: auto !important; } .github-emoji-fallback { color: inherit; } .github-emoji-fallback img { opacity: 0 !important; }</style>
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<span class="post-meta mr-2">
<i class="iconfont icon-chart"></i>

76 字
73 字

</span>

Expand Down Expand Up @@ -302,15 +305,15 @@ <h1 id="seo-header">first</h1>
<div class="markdown-body">

<p>这是一篇测试文章</p>
<p>今天是10月 :smile:</p>
<p>今天是10月 <span class="github-emoji"><span>😄</span><img src="https://github.githubassets.com/images/icons/emoji/unicode/1f604.png?v8" srcset="/img/loading.gif" lazyload aria-hidden="true" onerror="this.parent.classList.add('github-emoji-fallback')"></span></p>
<h1 id="h1-标题"><a href="#h1-标题" class="headerlink" title="h1 标题"></a>h1 标题</h1><img src="/2023/09/10/first/ocean.jpg" srcset="/img/loading.gif" lazyload class="" title="图片引用方法一">


<p><img src="/images/ocean.jpg" srcset="/img/loading.gif" lazyload alt="图片引用方法三"></p>
<h2 id="h2-标题"><a href="#h2-标题" class="headerlink" title="h2 标题"></a>h2 标题</h2><p>引擎可以选择 <code>mathjax</code> 或 <code>katex</code>，下面使用的 <a target="_blank" rel="noopener" href="https://docs.mathjax.org/en/latest/input/tex/extensions/centernot.html?highlight=slash#centernot">mathjax</a></p>
<p>$$<br> \int f(x)^2 &#x3D;<br>\begin{pmatrix}<br> \hbar &amp; \not\gamma<br> \<br> 0 &amp; 0<br>\end{pmatrix}<br>\<br>\Set{ x\in\mathbf{R}^2 | 0&lt;{|x|}&lt;5 }<br>$$</p>
<p>$$<br> \int f(x)^2 =<br>\begin{pmatrix}<br> \hbar &amp; \not\gamma<br> \<br> 0 &amp; 0<br>\end{pmatrix}<br>\<br>\Set{ x\in\mathbf{R}^2 | 0&lt;{|x|}&lt;5 }<br>$$</p>
<p>这是行内 $\Braket{ \phi | \frac{\partial^2}{\partial t^2} | \psi }$。</p>
<p>$$E&#x3D;mc^2\tag{1}$$</p>
<p>$$E=mc^2\tag{1}$$</p>


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14 changes: 8 additions & 6 deletions 2023/09/10/hello-world/index.html
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<meta name="generator" content="Hexo 7.3.0"></head>
<meta name="generator" content="Hexo 7.3.0">
<style>.github-emoji { position: relative; display: inline-block; width: 1.2em; min-height: 1.2em; overflow: hidden; vertical-align: top; color: transparent; } .github-emoji > span { position: relative; z-index: 10; } .github-emoji img, .github-emoji .fancybox { margin: 0 !important; padding: 0 !important; border: none !important; outline: none !important; text-decoration: none !important; user-select: none !important; cursor: auto !important; } .github-emoji img { height: 1.2em !important; width: 1.2em !important; position: absolute !important; left: 50% !important; top: 50% !important; transform: translate(-50%, -50%) !important; user-select: none !important; cursor: auto !important; } .github-emoji-fallback { color: inherit; } .github-emoji-fallback img { opacity: 0 !important; }</style>
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<span class="post-meta mr-2">
<i class="iconfont icon-chart"></i>

18 字
16 字

</span>

Expand Down Expand Up @@ -298,16 +300,16 @@ <h1 id="seo-header">Hello World</h1>
<div class="markdown-body">

<p>Welcome to <a target="_blank" rel="noopener" href="https://hexo.io/">Hexo</a>! This is your very first post. Check <a target="_blank" rel="noopener" href="https://hexo.io/docs/">documentation</a> for more info. If you get any problems when using Hexo, you can find the answer in <a target="_blank" rel="noopener" href="https://hexo.io/docs/troubleshooting.html">troubleshooting</a> or you can ask me on <a target="_blank" rel="noopener" href="https://github.com/hexojs/hexo/issues">GitHub</a>.</p>
<h2 id="Quick-Start"><a href="#Quick-Start" class="headerlink" title="Quick Start"></a>Quick Start</h2><h3 id="Create-a-new-post"><a href="#Create-a-new-post" class="headerlink" title="Create a new post"></a>Create a new post</h3><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><code class="hljs bash">$ hexo new <span class="hljs-string">&quot;My New Post&quot;</span><br></code></pre></td></tr></table></figure>
<h2 id="Quick-Start"><a href="#Quick-Start" class="headerlink" title="Quick Start"></a>Quick Start</h2><h3 id="Create-a-new-post"><a href="#Create-a-new-post" class="headerlink" title="Create a new post"></a>Create a new post</h3><figure class="highlight bash"><table><tbody><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><code class="hljs bash">$ hexo new <span class="hljs-string">"My New Post"</span><br></code></pre></td></tr></tbody></table></figure>

<p>More info: <a target="_blank" rel="noopener" href="https://hexo.io/docs/writing.html">Writing</a></p>
<h3 id="Run-server"><a href="#Run-server" class="headerlink" title="Run server"></a>Run server</h3><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><code class="hljs bash">$ hexo server<br></code></pre></td></tr></table></figure>
<h3 id="Run-server"><a href="#Run-server" class="headerlink" title="Run server"></a>Run server</h3><figure class="highlight bash"><table><tbody><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><code class="hljs bash">$ hexo server<br></code></pre></td></tr></tbody></table></figure>

<p>More info: <a target="_blank" rel="noopener" href="https://hexo.io/docs/server.html">Server</a></p>
<h3 id="Generate-static-files"><a href="#Generate-static-files" class="headerlink" title="Generate static files"></a>Generate static files</h3><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><code class="hljs bash">$ hexo generate<br></code></pre></td></tr></table></figure>
<h3 id="Generate-static-files"><a href="#Generate-static-files" class="headerlink" title="Generate static files"></a>Generate static files</h3><figure class="highlight bash"><table><tbody><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><code class="hljs bash">$ hexo generate<br></code></pre></td></tr></tbody></table></figure>

<p>More info: <a target="_blank" rel="noopener" href="https://hexo.io/docs/generating.html">Generating</a></p>
<h3 id="Deploy-to-remote-sites"><a href="#Deploy-to-remote-sites" class="headerlink" title="Deploy to remote sites"></a>Deploy to remote sites</h3><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><code class="hljs bash">$ hexo deploy<br></code></pre></td></tr></table></figure>
<h3 id="Deploy-to-remote-sites"><a href="#Deploy-to-remote-sites" class="headerlink" title="Deploy to remote sites"></a>Deploy to remote sites</h3><figure class="highlight bash"><table><tbody><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><code class="hljs bash">$ hexo deploy<br></code></pre></td></tr></tbody></table></figure>

<p>More info: <a target="_blank" rel="noopener" href="https://hexo.io/docs/one-command-deployment.html">Deployment</a></p>

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<meta name="generator" content="Hexo 7.3.0"></head>
<meta name="generator" content="Hexo 7.3.0">
<style>.github-emoji { position: relative; display: inline-block; width: 1.2em; min-height: 1.2em; overflow: hidden; vertical-align: top; color: transparent; } .github-emoji > span { position: relative; z-index: 10; } .github-emoji img, .github-emoji .fancybox { margin: 0 !important; padding: 0 !important; border: none !important; outline: none !important; text-decoration: none !important; user-select: none !important; cursor: auto !important; } .github-emoji img { height: 1.2em !important; width: 1.2em !important; position: absolute !important; left: 50% !important; top: 50% !important; transform: translate(-50%, -50%) !important; user-select: none !important; cursor: auto !important; } .github-emoji-fallback { color: inherit; } .github-emoji-fallback img { opacity: 0 !important; }</style>
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<meta name="generator" content="Hexo 7.3.0"></head>
<meta name="generator" content="Hexo 7.3.0">
<style>.github-emoji { position: relative; display: inline-block; width: 1.2em; min-height: 1.2em; overflow: hidden; vertical-align: top; color: transparent; } .github-emoji > span { position: relative; z-index: 10; } .github-emoji img, .github-emoji .fancybox { margin: 0 !important; padding: 0 !important; border: none !important; outline: none !important; text-decoration: none !important; user-select: none !important; cursor: auto !important; } .github-emoji img { height: 1.2em !important; width: 1.2em !important; position: absolute !important; left: 50% !important; top: 50% !important; transform: translate(-50%, -50%) !important; user-select: none !important; cursor: auto !important; } .github-emoji-fallback { color: inherit; } .github-emoji-fallback img { opacity: 0 !important; }</style>
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<meta name="generator" content="Hexo 7.3.0"></head>
<meta name="generator" content="Hexo 7.3.0">
<style>.github-emoji { position: relative; display: inline-block; width: 1.2em; min-height: 1.2em; overflow: hidden; vertical-align: top; color: transparent; } .github-emoji > span { position: relative; z-index: 10; } .github-emoji img, .github-emoji .fancybox { margin: 0 !important; padding: 0 !important; border: none !important; outline: none !important; text-decoration: none !important; user-select: none !important; cursor: auto !important; } .github-emoji img { height: 1.2em !important; width: 1.2em !important; position: absolute !important; left: 50% !important; top: 50% !important; transform: translate(-50%, -50%) !important; user-select: none !important; cursor: auto !important; } .github-emoji-fallback { color: inherit; } .github-emoji-fallback img { opacity: 0 !important; }</style>
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<meta name="generator" content="Hexo 7.3.0"></head>
<meta name="generator" content="Hexo 7.3.0">
<style>.github-emoji { position: relative; display: inline-block; width: 1.2em; min-height: 1.2em; overflow: hidden; vertical-align: top; color: transparent; } .github-emoji > span { position: relative; z-index: 10; } .github-emoji img, .github-emoji .fancybox { margin: 0 !important; padding: 0 !important; border: none !important; outline: none !important; text-decoration: none !important; user-select: none !important; cursor: auto !important; } .github-emoji img { height: 1.2em !important; width: 1.2em !important; position: absolute !important; left: 50% !important; top: 50% !important; transform: translate(-50%, -50%) !important; user-select: none !important; cursor: auto !important; } .github-emoji-fallback { color: inherit; } .github-emoji-fallback img { opacity: 0 !important; }</style>
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<meta name="author" content="liu19">
<meta name="keywords" content="">

<meta name="description" content="$\delta$ 函数:apple: 如果函数 $f(x)$ 的实根 $x_i$ 全是单根，那么有关系$$\delta(f(x)) &#x3D; \sum_i \frac{\delta(x-x_i)}{\abs{f’(x_i)}}$$">
<meta name="description" content="$\delta$ 函数🍎 如果函数 $f(x)$ 的实根 $x_i$ 全是单根，那么有关系$$\delta(f(x)) &#x3D; \sum_i \frac{\delta(x-x_i)}{|f’(x_i)|}$$ 1⃣ 首先证明 $\delta(ax) &#x3D; \frac{\delta(x)}{|a|}$$$\begin{align*} \int^\infty_{-\infty} \mathrm{d}">
<meta property="og:type" content="article">
<meta property="og:title" content="备忘">
<meta property="og:url" content="http://example.com/2024/09/23/memo-math/index.html">
<meta property="og:site_name" content="Liu19">
<meta property="og:description" content="$\delta$ 函数:apple: 如果函数 $f(x)$ 的实根 $x_i$ 全是单根，那么有关系$$\delta(f(x)) &#x3D; \sum_i \frac{\delta(x-x_i)}{\abs{f’(x_i)}}$$">
<meta property="og:description" content="$\delta$ 函数🍎 如果函数 $f(x)$ 的实根 $x_i$ 全是单根，那么有关系$$\delta(f(x)) &#x3D; \sum_i \frac{\delta(x-x_i)}{|f’(x_i)|}$$ 1⃣ 首先证明 $\delta(ax) &#x3D; \frac{\delta(x)}{|a|}$$$\begin{align*} \int^\infty_{-\infty} \mathrm{d}">
<meta property="og:locale" content="zh_CN">
<meta property="og:image" content="https://github.githubassets.com/images/icons/emoji/unicode/1f34e.png?v8">
<meta property="og:image" content="https://github.githubassets.com/images/icons/emoji/unicode/0031-20e3.png?v8">
<meta property="og:image" content="https://github.githubassets.com/images/icons/emoji/unicode/0032-20e3.png?v8">
<meta property="article:published_time" content="2024-09-23T01:54:07.611Z">
<meta property="article:modified_time" content="2024-09-23T02:09:08.548Z">
<meta property="article:modified_time" content="2024-10-06T08:17:27.396Z">
<meta property="article:author" content="liu19">
<meta name="twitter:card" content="summary_large_image">
<meta name="twitter:image" content="https://github.githubassets.com/images/icons/emoji/unicode/1f34e.png?v8">



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<meta name="generator" content="Hexo 7.3.0"></head>
<meta name="generator" content="Hexo 7.3.0">
<style>.github-emoji { position: relative; display: inline-block; width: 1.2em; min-height: 1.2em; overflow: hidden; vertical-align: top; color: transparent; } .github-emoji > span { position: relative; z-index: 10; } .github-emoji img, .github-emoji .fancybox { margin: 0 !important; padding: 0 !important; border: none !important; outline: none !important; text-decoration: none !important; user-select: none !important; cursor: auto !important; } .github-emoji img { height: 1.2em !important; width: 1.2em !important; position: absolute !important; left: 50% !important; top: 50% !important; transform: translate(-50%, -50%) !important; user-select: none !important; cursor: auto !important; } .github-emoji-fallback { color: inherit; } .github-emoji-fallback img { opacity: 0 !important; }</style>
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35 字
146 字

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1 分钟
2 分钟

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Expand Down Expand Up @@ -297,7 +303,13 @@ <h1 id="seo-header">备忘</h1>

<div class="markdown-body">

<h1 id="delta-函数"><a href="#delta-函数" class="headerlink" title="$\delta$ 函数"></a>$\delta$ 函数</h1><p>:apple: 如果函数 $f(x)$ 的实根 $x_i$ 全是单根，那么有关系<br>$$<br>\delta(f(x)) &#x3D; \sum_i \frac{\delta(x-x_i)}{\abs{f’(x_i)}}<br>$$</p>
<h1 id="delta-函数"><a href="#delta-函数" class="headerlink" title="$\delta$ 函数"></a>$\delta$ 函数</h1><p><span class="github-emoji"><span>🍎</span><img src="https://github.githubassets.com/images/icons/emoji/unicode/1f34e.png?v8" srcset="/img/loading.gif" lazyload aria-hidden="true" onerror="this.parent.classList.add('github-emoji-fallback')"></span> 如果函数 $f(x)$ 的实根 $x_i$ 全是单根，那么有关系<br>$$<br>\delta(f(x)) = \sum_i \frac{\delta(x-x_i)}{|f’(x_i)|}<br>$$</p>
<p><span class="github-emoji"><span>1⃣</span><img src="https://github.githubassets.com/images/icons/emoji/unicode/0031-20e3.png?v8" srcset="/img/loading.gif" lazyload aria-hidden="true" onerror="this.parent.classList.add('github-emoji-fallback')"></span> 首先证明 $\delta(ax) = \frac{\delta(x)}{|a|}$<br>$$<br>\begin{align*}<br> \int^\infty_{-\infty} \mathrm{d}x \delta(ax) &amp;= \int^{\infty\cdot a}<em>{-\infty\cdot a} \mathrm{d}y \frac{\delta(y)}{a}<br> \<br> &amp;= \int^{\infty}</em>{-\infty} \mathrm{d}y \frac{\delta(y)}{|a|}<br>\end{align*}<br>$$<br><span class="github-emoji"><span>2⃣</span><img src="https://github.githubassets.com/images/icons/emoji/unicode/0032-20e3.png?v8" srcset="/img/loading.gif" lazyload aria-hidden="true" onerror="this.parent.classList.add('github-emoji-fallback')"></span> 将函数 $f(x)$ 在零点附近展开 $f(x) = f(x_i) + f’(x_i)(x-x_i) + \frac{1}{2}f’’(x_i)(x-x_i)^2$</p>
<p>$$<br>\begin{align}<br> \int^\infty_{-\infty} \delta(f(x)) \mathrm{d}x &amp;= \sum\lim_{\epsilon\rightarrow 0} \int^{x_i+\epsilon}_{x_i-\epsilon} \delta(f(x)) \mathrm{d}x<br>\end{align}<br>$$</p>

<script>
console.error("Error: [hexo-tag-aplayer] Meting support is disabled, cannot resolve the meting tags properly.");
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