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  <title>Looking4U</title>
  
  <subtitle>编程学习笔记</subtitle>
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  <updated>2026-05-16T12:06:33.778Z</updated>
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  <author>
    <name>张嘉译</name>
    
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  <generator uri="https://hexo.io/">Hexo</generator>
  
  <entry>
    <title>重庆大学校园网多设备检测对抗实战（OpenWrt + ua3f）</title>
    <link href="https://lucky-z.fun/p/1e43e556.html"/>
    <id>https://lucky-z.fun/p/1e43e556.html</id>
    <published>2026-05-16T12:00:00.000Z</published>
    <updated>2026-05-16T12:06:33.778Z</updated>
    
    <content type="html"><![CDATA[<blockquote><p>声明：本文仅记录在<strong>本人自有账号、自有路由器</strong>上的网络配置实践，用于多设备共享自用，不涉及破解计费、不针对他人。文中所有账号 / 密码 / token / 公网 IP 均已打码。请遵守所在学校的网络管理规定，风险自负。</p></blockquote><h2 id="背景"><a class="markdownIt-Anchor" href="#背景"></a> 背景</h2><p>重庆大学校园网认证端点迁移到了 <code>login.cqu.edu.cn</code>（旧的固定 IP 认证作废），同时上线了<strong>多设备共享检测</strong>：一个账号下若被识别出多台设备，会提示&quot;检测到共享 / 请勿使用代理&quot;并冻结一段时间。</p><p>我的方案是一台 OpenWrt 路由器做主路由：</p><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">客户端 → nftables(TPROXY拦截) → hev-socks5-tproxy → ua3f(UA改写) → 校园网</span><br></pre></td></tr></table></figure><p>认证部分用了一个自己 fork 改造的 LuCI 插件（适配 <code>login.cqu.edu.cn</code> 的新 JSONP 协议，账号 <code>2025********</code>、密码均在路由器本地配置，不外泄）。本文不讲认证，只讲<strong>怎么尽量不被多设备检测，同时还能用</strong>。</p><h2 id="一个核心认知"><a class="markdownIt-Anchor" href="#一个核心认知"></a> 一个核心认知</h2><p>ua3f 是个 <strong>SOCKS5 终结点</strong>：hev-socks5-tproxy 把 TPROXY 拦下的流量交给它，它<strong>关闭客户端 TCP、用路由器自己的协议栈重新发起一条新连接</strong>。</p><p>所以——凡是<strong>进了代理</strong>的流量，对外的 L3/L4 指纹（TTL、IP-ID、TCP options/时间戳、源端口行为）统一成路由器这一台，再叠加 HTTP UA 改写，对外等效&quot;一台主机&quot;。</p><blockquote><p>结论：检测能抓到的，只有<strong>漏出代理</strong>的流量。加固 = 让尽量多的流量进代理 + 抑制进不了代理的流量。</p></blockquote><p>下面按&quot;检测维度 → 处理&quot;组织。环境示例：LAN <code>192.168.1.0/24</code>、WAN 口 <code>eth0.1</code>、WAN 地址 <code>10.244.x.x</code>。</p><h2 id="p0关掉-ipv6最关键"><a class="markdownIt-Anchor" href="#p0关掉-ipv6最关键"></a> P0：关掉 IPv6（最关键）</h2><p>TPROXY 规则只处理 IPv4（<code>tproxy ip to</code>）。客户端只要有全局 IPv6 地址，就绕过 NAT 和代理，<strong>每台设备的 v6 地址直接暴露</strong>，前面所有努力白费。</p><figure class="highlight bash"><table><tr><td class="code"><pre><span class="line">uci <span class="built_in">set</span> dhcp.lan.ra_slaac=<span class="string">&#x27;0&#x27;</span></span><br><span class="line">uci <span class="built_in">set</span> dhcp.lan.ra=<span class="string">&#x27;disabled&#x27;</span></span><br><span class="line">uci <span class="built_in">set</span> dhcp.lan.dhcpv6=<span class="string">&#x27;disabled&#x27;</span></span><br><span class="line">uci -q delete network.wan6</span><br><span class="line">uci commit</span><br><span class="line">grep -q disable_ipv6 /etc/sysctl.conf || &#123;</span><br><span class="line">  <span class="built_in">echo</span> <span class="string">&#x27;net.ipv6.conf.all.disable_ipv6=1&#x27;</span>     &gt;&gt; /etc/sysctl.conf</span><br><span class="line">  <span class="built_in">echo</span> <span class="string">&#x27;net.ipv6.conf.default.disable_ipv6=1&#x27;</span> &gt;&gt; /etc/sysctl.conf</span><br><span class="line">&#125;</span><br><span class="line">sysctl -p</span><br><span class="line">/etc/init.d/odhcpd restart; /etc/init.d/network reload</span><br></pre></td></tr></table></figure><blockquote><p><code>network reload</code> 会瞬断 WAN，校园门户掉线几十秒后认证守护会自动重连。</p></blockquote><h2 id="p1拦截范围从端口白名单改成几乎全部-tcp"><a class="markdownIt-Anchor" href="#p1拦截范围从端口白名单改成几乎全部-tcp"></a> P1：拦截范围从&quot;端口白名单&quot;改成&quot;几乎全部 TCP&quot;</h2><p>很多教程的 TPROXY 只拦 <code>{80,8080,...}</code> 几个端口。实测发现：任意端口的明文 HTTP（例如某服务跑在 <code>:8000</code>）会<strong>整条漏出去</strong>，真实 UA 直达服务器。</p><p>把规则改成&quot;除 443 和 LAN 本地外的全部 TCP 都进代理&quot;（<code>/etc/nfts/100-tproxy.nft</code>）：</p><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">table inet tproxy_table &#123;</span><br><span class="line">    chain prerouting &#123;</span><br><span class="line">        type filter hook prerouting priority -100; policy accept;</span><br><span class="line">        iifname &quot;br-lan&quot; ip daddr != 192.168.1.0/24 tcp dport != 443 \</span><br><span class="line">            tproxy ip to 127.0.0.1:1088 mark set 1</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure><ul><li>排除 <code>192.168.1.0/24</code>：不劫持本机 SSH/管理页和内网互访（<strong>防把自己锁外面</strong>，按自己 LAN 段改）。</li><li>排除 <code>dport 443</code>：HTTPS 直连，避免把 TLS 大流量全压到弱 CPU（性价比折中）。</li><li><strong>不要</strong>排除 <code>10.0.0.0/8</code>：校园认证 / 内网就是 <code>10.x</code>，得继续走代理改写。</li><li>代价：443 仍直连 → 它的 TLS 指纹（见后文残留）改不掉。</li></ul><h2 id="p2统一-ttl-以及那个最容易踩的坑"><a class="markdownIt-Anchor" href="#p2统一-ttl-以及那个最容易踩的坑"></a> P2：统一 TTL —— 以及那个最容易踩的坑</h2><p>多种客户端 OS 的初始 TTL 不同（Windows 128 / Linux·Android·iOS 64），经路由器再 -1，服务器看到一组离散 TTL 就知道你后面挂了多台不同系统。</p><p>新增 <code>/etc/nfts/110-cqu-hardening.nft</code>：</p><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">table inet cqu_hardening &#123;</span><br><span class="line">    chain cqu_post &#123;</span><br><span class="line">        type filter hook postrouting priority mangle; policy accept;</span><br><span class="line">        oifname &quot;eth0.1&quot; ip ttl set 64</span><br><span class="line">    &#125;</span><br><span class="line">    chain cqu_forward &#123;</span><br><span class="line">        type filter hook forward priority -10; policy accept;</span><br><span class="line">        iifname &quot;br-lan&quot; oifname &quot;eth0.1&quot; udp dport 443 reject   # P3: 封 QUIC</span><br><span class="line">        iifname &quot;br-lan&quot; meta nfproto ipv6 counter drop          # P0 兜底</span><br><span class="line">    &#125;</span><br><span class="line">    chain cqu_nat &#123;</span><br><span class="line">        type nat hook prerouting priority dstnat; policy accept;</span><br><span class="line">        iifname &quot;br-lan&quot; udp dport 123 redirect to :123          # NTP 收敛</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure><blockquote><p>小坑：nft 里 chain 不能命名为 <code>fwd</code>，那是保留字。</p></blockquote><h3 id="️-关键坑不关-flow-offloadttl-改写是假的"><a class="markdownIt-Anchor" href="#️-关键坑不关-flow-offloadttl-改写是假的"></a> ⚠️ 关键坑：不关 flow offload，TTL 改写是假的</h3><p>OpenWrt 默认开 <strong>软件/硬件流量卸载（flow offloading）</strong>。被卸载的连接走 fastpath 快速转发，<strong>直接跳过 netfilter 的 postrouting hook</strong>——也就是说上面的 <code>ip ttl set 64</code> 对这些连接<strong>根本没执行</strong>。</p><p>实测：开着 offload 时 <code>conntrack</code> 里大量连接带 <code>[OFFLOAD]</code> 标记，那条 <code>ttl set</code> 规则的计数远小于真实流量；关掉后单核负载从 <code>0.07</code> 直接飙到 <code>1.16</code>（流量全部回到协议栈）。</p><p>所以必须关：</p><figure class="highlight bash"><table><tr><td class="code"><pre><span class="line">uci <span class="built_in">set</span> firewall.@defaults[0].flow_offloading=<span class="string">&#x27;0&#x27;</span></span><br><span class="line">uci <span class="built_in">set</span> firewall.@defaults[0].flow_offloading_hw=<span class="string">&#x27;0&#x27;</span></span><br><span class="line">uci commit firewall</span><br><span class="line">/etc/init.d/firewall restart</span><br></pre></td></tr></table></figure><blockquote><p>同理 <code>fullcone</code>（全锥 NAT）在部分实现里也会绕 hook，介意可一并关，代价是 P2P/游戏 NAT 类型变差。</p></blockquote><p>这一步是好多人&quot;配了 TTL 还是被检测&quot;的根因。</p><h2 id="p3封-quic"><a class="markdownIt-Anchor" href="#p3封-quic"></a> P3：封 QUIC</h2><p>浏览器默认机会性走 HTTP/3（QUIC over UDP 443），它带类 TLS 指纹、流量大，且<strong>完全绕过 TCP 代理链路</strong>。上面 <code>cqu_forward</code> 里 <code>udp dport 443 reject</code> 一句把它打掉，浏览器会自动回落到 TCP（再被 ua3f 处理）。<code>reject</code> 比 <code>drop</code> 回落更快。</p><h2 id="ntp被忽略的强特征"><a class="markdownIt-Anchor" href="#ntp被忽略的强特征"></a> NTP：被忽略的强特征</h2><p>不同设备默认 NTP 服务器、对时频率都不一样，<code>udp/123</code> 直连出去就是一组多设备特征。处理方式：路由器自己当 NTP server，把客户端的 123 全部重定向到本地（上面 <code>cqu_nat</code> 已含 redirect）：</p><figure class="highlight bash"><table><tr><td class="code"><pre><span class="line">uci <span class="built_in">set</span> system.ntp.enable_server=<span class="string">&#x27;1&#x27;</span></span><br><span class="line">uci commit system</span><br><span class="line">/etc/init.d/sysntpd restart</span><br></pre></td></tr></table></figure><p>效果：客户端以为在和公网 NTP 对话，其实被路由器本地应答；对外只剩路由器一个 NTP client 同步上游，多设备 NTP 特征收敛成一个。</p><h2 id="ua伪装值本身别穿帮"><a class="markdownIt-Anchor" href="#ua伪装值本身别穿帮"></a> UA：伪装值本身别穿帮</h2><p>ua3f 的 <code>-f</code> 一定要是<strong>真实存在、当前主流</strong>的 UA。我接手时它被设成了带 <code>CoolMarket/14.2.3-...</code>（某 App 尾巴）的串——桌面 Chrome 不可能带这种尾巴，所有设备统一成这个<strong>不存在的客户端组合</strong>，本身就是个显眼特征。换成干净的：</p><figure class="highlight bash"><table><tr><td class="code"><pre><span class="line">uci <span class="built_in">set</span> ua3f.main.ua=<span class="string">&#x27;Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/124.0.0.0 Safari/537.36&#x27;</span></span><br><span class="line">uci commit ua3f</span><br><span class="line">/etc/init.d/ua3f restart</span><br></pre></td></tr></table></figure><h2 id="自检脚本"><a class="markdownIt-Anchor" href="#自检脚本"></a> 自检脚本</h2><p>在路由器上跑，逐项确认而不是凭感觉（节选）：</p><figure class="highlight sh"><table><tr><td class="code"><pre><span class="line">NF=/proc/net/nf_conntrack</span><br><span class="line"><span class="comment"># P0: 应为 0</span></span><br><span class="line">grep -c <span class="string">&#x27;^ipv6&#x27;</span> <span class="variable">$NF</span></span><br><span class="line"><span class="comment"># P2: 应为 0（还有 OFFLOAD 说明 TTL 没真生效）</span></span><br><span class="line">grep -c -i offload <span class="variable">$NF</span></span><br><span class="line"><span class="comment"># P3: 应为 0</span></span><br><span class="line">grep -cE <span class="string">&#x27;udp .*(dport=443|sport=443)&#x27;</span> <span class="variable">$NF</span></span><br><span class="line"><span class="comment"># NTP: 客户端 123 应被本地(网关 IP)应答；src=WAN 的是路由器自身同步，正常</span></span><br><span class="line">grep <span class="string">&#x27;dport=123&#x27;</span> <span class="variable">$NF</span></span><br><span class="line"><span class="comment"># UA: 取最新一行启动日志确认伪装值</span></span><br><span class="line">grep <span class="string">&#x27;User-Agent:&#x27;</span> /var/log/ua3f/ua3f.<span class="built_in">log</span> | <span class="built_in">tail</span> -1</span><br></pre></td></tr></table></figure><p>客户端侧再配一个多 UA / 多端口探测脚本（思路同经典的 <code>ua_test.sh</code>：用不同 UA、不同端口请求一个回显服务，看服务器实际收到什么），就能定位还有哪一维在漏。<strong>测的时候记得关掉客户端自己的代理软件</strong>，否则流量绕过路由器，结果不可信。</p><h2 id="诚实的残留路由器侧改不掉"><a class="markdownIt-Anchor" href="#诚实的残留路由器侧改不掉"></a> 诚实的残留（路由器侧改不掉）</h2><table><thead><tr><th>维度</th><th>状态</th></tr></thead><tbody><tr><td>HTTPS/443 的 UA（在 TLS 里）、JA3/JA4</td><td>不做中间人解密就改不了；现代浏览器 JA3 已随机化弱化，JA4 仍可区分</td></tr><tr><td>IP-ID（Windows 全局递增）</td><td>经代理的已统一；直连转发的要彻底解决得编 <code>kmod-rkp-ipid</code>（重编固件）</td></tr><tr><td>TCP 时间戳 / options</td><td>经代理的统一；直连泄露</td></tr><tr><td>并发连接数 / 账号行为</td><td>任何方案都藏不住&quot;一个号大量并发&quot;</td></tr></tbody></table><p>思路是：把能收敛的都收敛掉，让单一残留维度难以单独定位到&quot;多设备&quot;。</p><h2 id="性能取舍"><a class="markdownIt-Anchor" href="#性能取舍"></a> 性能取舍</h2><p>关 flow offload + 几乎全部 TCP 进 ua3f，对<strong>弱硬件</strong>（入门级单核 + 64MB 内存那种）是实打实的负担：实测关 offload 瞬间单核负载就上 1.1（≈满载），高带宽 / 多设备 / 测速会明显降速、延迟抖动、偶发卡顿，内存也吃紧。</p><p>可选：</p><ul><li><strong>接受</strong>：日常网页 / IM / 文档够用。</li><li><strong>折中</strong>：P1 退回只代理少数明文 HTTP 端口，网速回升，但重新暴露非标端口明文（取舍）。</li><li><strong>换硬件</strong>（双核及以上 / x86 软路由）：根本解，强烈建议——弱核跑这套本就勉强。</li></ul><h2 id="致谢"><a class="markdownIt-Anchor" href="#致谢"></a> 致谢</h2><ul><li>认证插件 fork 自 <a href="https://github.com/lurenjiamax/luci-app-cquauth">lurenjiamax/luci-app-cquauth</a>，协议参考 <a href="https://github.com/haowang02/cqu-net-auth">haowang02/cqu-net-auth</a></li><li>UA 改写 <a href="https://github.com/SunBK201/UA3F">SunBK201/UA3F</a>，TPROXY <a href="https://github.com/heiher/hev-socks5-tproxy">heiher/hev-socks5-tproxy</a></li><li>检测原理参考：褐瞳《校园网防止多设备检测指北》、SunBK201《某大学校园网共享上网检测机制研究》及若干博客园文章</li></ul>]]></content>
    
    
      
      
    <summary type="html">&lt;blockquote&gt;
&lt;p&gt;声明：本文仅记录在&lt;strong&gt;本人自有账号、自有路由器&lt;/strong&gt;上的网络配置实践，用于多设备共享自用，不涉及破解计费、不针对他人。文中所有账号 / 密码 / token / 公网 IP 均已打码。请遵守所在学校的网络管理规定，风险自负。</summary>
      
    
    
    
    <category term="网络" scheme="https://lucky-z.fun/categories/%E7%BD%91%E7%BB%9C/"/>
    
    
    <category term="OpenWrt" scheme="https://lucky-z.fun/tags/OpenWrt/"/>
    
    <category term="校园网" scheme="https://lucky-z.fun/tags/%E6%A0%A1%E5%9B%AD%E7%BD%91/"/>
    
    <category term="多设备检测" scheme="https://lucky-z.fun/tags/%E5%A4%9A%E8%AE%BE%E5%A4%87%E6%A3%80%E6%B5%8B/"/>
    
    <category term="nftables" scheme="https://lucky-z.fun/tags/nftables/"/>
    
    <category term="ua3f" scheme="https://lucky-z.fun/tags/ua3f/"/>
    
  </entry>
  
  <entry>
    <title>微信降级</title>
    <link href="https://lucky-z.fun/p/108f9a46.html"/>
    <id>https://lucky-z.fun/p/108f9a46.html</id>
    <published>2025-10-07T02:16:28.000Z</published>
    <updated>2025-10-07T02:27:38.633Z</updated>
    
    <content type="html"><![CDATA[<h2 id="微信降级教程"><a class="markdownIt-Anchor" href="#微信降级教程"></a> 微信降级教程</h2><h3 id="适用于安卓"><a class="markdownIt-Anchor" href="#适用于安卓"></a> 适用于安卓</h3><figure class="highlight bash"><table><tr><td class="code"><pre><span class="line">adb shell pm uninstall -k com.tencent.mm</span><br><span class="line">adb reboot</span><br><span class="line">adb install wechat.apk</span><br></pre></td></tr></table></figure>]]></content>
    
    
      
      
    <summary type="html">&lt;h2 id=&quot;微信降级教程&quot;&gt;&lt;a class=&quot;markdownIt-Anchor&quot; href=&quot;#微信降级教程&quot;&gt;&lt;/a&gt; 微信降级教程&lt;/h2&gt;
&lt;h3 id=&quot;适用于安卓&quot;&gt;&lt;a class=&quot;markdownIt-Anchor&quot; href=&quot;#适用于安卓&quot;&gt;&lt;/a&gt; </summary>
      
    
    
    
    
  </entry>
  
  <entry>
    <title>【Windows】终端配置代理</title>
    <link href="https://lucky-z.fun/p/1aeba13e.html"/>
    <id>https://lucky-z.fun/p/1aeba13e.html</id>
    <published>2025-01-02T08:57:00.000Z</published>
    <updated>2026-05-15T10:02:14.224Z</updated>
    
    <content type="html"><![CDATA[<h2 id="windows-cmd-设置代理"><a class="markdownIt-Anchor" href="#windows-cmd-设置代理"></a> Windows cmd 设置代理</h2><h3 id="设置-http-代理"><a class="markdownIt-Anchor" href="#设置-http-代理"></a> 设置 HTTP 代理：</h3><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">set http_proxy=http://127.0.0.1:7890 &amp; set https_proxy=http://127.0.0.1:7890</span><br></pre></td></tr></table></figure><h3 id="socks5代理设置"><a class="markdownIt-Anchor" href="#socks5代理设置"></a> socks5代理设置：</h3><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">set http_proxy=socks5://127.0.0.1:7890</span><br><span class="line">set https_proxy=socks5://127.0.0.1:7890</span><br></pre></td></tr></table></figure><h3 id="取消代理"><a class="markdownIt-Anchor" href="#取消代理"></a> 取消代理：</h3><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">set http_proxy=</span><br><span class="line">set https_proxy=</span><br></pre></td></tr></table></figure><h2 id="windows-git-bash-设置代理"><a class="markdownIt-Anchor" href="#windows-git-bash-设置代理"></a> Windows git bash 设置代理</h2><h3 id="设置-http-代理-2"><a class="markdownIt-Anchor" href="#设置-http-代理-2"></a> 设置 HTTP 代理：</h3><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">git config --global http.proxy http://127.0.0.1:7890</span><br><span class="line">git config --global https.proxy http://127.0.0.1:7890</span><br></pre></td></tr></table></figure><h3 id="设置-socks5代理"><a class="markdownIt-Anchor" href="#设置-socks5代理"></a> 设置 socks5代理：</h3><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">git config --global http.proxy socks5://127.0.0.1:7890</span><br><span class="line">git config --global https.proxy socks5://127.0.0.1:7890</span><br></pre></td></tr></table></figure><h3 id="取消代理-2"><a class="markdownIt-Anchor" href="#取消代理-2"></a> 取消代理：</h3><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">git config --global --unset http.proxy</span><br><span class="line">git config --global --unset https.proxy</span><br></pre></td></tr></table></figure><h2 id="windows-powershell-设置代理"><a class="markdownIt-Anchor" href="#windows-powershell-设置代理"></a> Windows PowerShell 设置代理</h2><h3 id="设置-http-代理-3"><a class="markdownIt-Anchor" href="#设置-http-代理-3"></a> 设置 HTTP 代理：</h3><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">$Env:http_proxy=&quot;http://127.0.0.1:7890&quot;;$Env:https_proxy=&quot;http://127.0.0.1:7890&quot;</span><br></pre></td></tr></table></figure><h3 id="代理测试"><a class="markdownIt-Anchor" href="#代理测试"></a> <strong>代</strong>理测试:</h3><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">curl https://www.google.com</span><br></pre></td></tr></table></figure>]]></content>
    
    
      
      
    <summary type="html">&lt;h2 id=&quot;windows-cmd-设置代理&quot;&gt;&lt;a class=&quot;markdownIt-Anchor&quot; href=&quot;#windows-cmd-设置代理&quot;&gt;&lt;/a&gt; Windows cmd 设置代理&lt;/h2&gt;
&lt;h3 id=&quot;设置-http-代理&quot;&gt;&lt;a class=&quot;mar</summary>
      
    
    
    
    <category term="工具配置" scheme="https://lucky-z.fun/categories/%E5%B7%A5%E5%85%B7%E9%85%8D%E7%BD%AE/"/>
    
    
    <category term="Windows" scheme="https://lucky-z.fun/tags/Windows/"/>
    
    <category term="代理" scheme="https://lucky-z.fun/tags/%E4%BB%A3%E7%90%86/"/>
    
    <category term="Proxy" scheme="https://lucky-z.fun/tags/Proxy/"/>
    
    <category term="Git" scheme="https://lucky-z.fun/tags/Git/"/>
    
    <category term="PowerShell" scheme="https://lucky-z.fun/tags/PowerShell/"/>
    
  </entry>
  
  <entry>
    <title>数模算法集合(一)</title>
    <link href="https://lucky-z.fun/p/f618aec.html"/>
    <id>https://lucky-z.fun/p/f618aec.html</id>
    <published>2022-09-06T11:19:06.000Z</published>
    <updated>2022-09-19T15:35:17.087Z</updated>
    
    <content type="html"><![CDATA[<h3 id="写在前面"><a class="markdownIt-Anchor" href="#写在前面"></a> 写在前面</h3><p> 出于各种原因今年参加了一次“高教社”杯的数学建模比赛😆，说实话比赛题目挺难的，但是参加了比赛收获蛮多的。借此机会整理一下数学建模所有的学习资源。💇</p><p>  其次准备整理一下所有的算法以及思路种种。</p><h3 id="资源汇总"><a class="markdownIt-Anchor" href="#资源汇总"></a> 资源汇总</h3><p> 首先将资源整理如下:<a href="/download/%E6%95%B0%E5%AD%A6%E5%BB%BA%E6%A8%A1%E8%B5%84%E6%96%99.pdf">数学建模资料</a></p><h3 id="算法分类"><a class="markdownIt-Anchor" href="#算法分类"></a> 算法分类</h3><p>  数学建模常见的算法大体可分为两类，一类为传统经典算法，一类为现代算法以统计学运筹学为中心，以机器学习为中心。</p><ol><li>传统经典算法：</li><li>现代化算法：</li></ol><p>​另一种分类则是以算法的用途划分：</p><pre><code>1. 评价类算法1. 优化类算法</code></pre>]]></content>
    
    
      
      
    <summary type="html">&lt;h3 id=&quot;写在前面&quot;&gt;&lt;a class=&quot;markdownIt-Anchor&quot; href=&quot;#写在前面&quot;&gt;&lt;/a&gt; 写在前面&lt;/h3&gt;
&lt;p&gt; 出于各种原因今年参加了一次“高教社”杯的数学建模比赛😆，说实话比赛题目挺难的，但是参加了比赛收获蛮多的。借此机会整理一下数学建模</summary>
      
    
    
    
    
  </entry>
  
  <entry>
    <title>LaTex语法学习常用公式</title>
    <link href="https://lucky-z.fun/p/32167ff9.html"/>
    <id>https://lucky-z.fun/p/32167ff9.html</id>
    <published>2022-09-05T04:31:16.000Z</published>
    <updated>2022-09-05T05:51:17.934Z</updated>
    
    
    
    
    
  </entry>
  
  <entry>
    <title>LaTex语法学习</title>
    <link href="https://lucky-z.fun/p/4defbc1f.html"/>
    <id>https://lucky-z.fun/p/4defbc1f.html</id>
    <published>2022-09-04T15:48:43.000Z</published>
    <updated>2026-05-13T02:15:11.320Z</updated>
    
    <content type="html"><![CDATA[<h3 id="latex简单介绍"><a class="markdownIt-Anchor" href="#latex简单介绍"></a> LaTex简单介绍</h3><p>LaTex是一种简单文件生成系统，文件后缀为.tex</p><h3 id="基本用法"><a class="markdownIt-Anchor" href="#基本用法"></a> 基本用法</h3><ul><li>新建一个文件，后缀名为.tex</li><li>输入基本语法框架</li></ul><figure class="highlight latex"><table><tr><td class="code"><pre><span class="line"><span class="keyword">\documentclass</span>&#123;article&#125;</span><br><span class="line"><span class="keyword">\begin</span>&#123;document&#125; </span><br><span class="line"></span><br><span class="line">Hello world! </span><br><span class="line"></span><br><span class="line"><span class="keyword">\end</span>&#123;document&#125;</span><br></pre></td></tr></table></figure><h3 id="基本语法"><a class="markdownIt-Anchor" href="#基本语法"></a> 基本语法</h3><ol><li>文档类型 ’ article ', 'book ',等等</li><li>注释使用%，转义使用\</li></ol><h3 id="由于时间仓促就不介绍其他参数了直接上用法"><a class="markdownIt-Anchor" href="#由于时间仓促就不介绍其他参数了直接上用法"></a> 由于时间仓促就不介绍其他参数了，直接上用法</h3><h3 id="字体设置"><a class="markdownIt-Anchor" href="#字体设置"></a> 字体设置</h3><p>使用fontspec包设置字体</p><figure class="highlight latex"><table><tr><td class="code"><pre><span class="line"><span class="keyword">\usepackage</span>&#123;fontspec&#125; </span><br><span class="line"><span class="keyword">\usepackage</span>&#123;amsmath&#125; </span><br><span class="line"><span class="keyword">\setmainfont</span>&#123;Times New Roman&#125;</span><br></pre></td></tr></table></figure><p>不过一般论文使用TNR差不多了🌊</p><h3 id="字体大小设置"><a class="markdownIt-Anchor" href="#字体大小设置"></a> 字体大小设置</h3><figure class="highlight latex"><table><tr><td class="code"><pre><span class="line"><span class="keyword">\tiny</span> </span><br><span class="line"><span class="keyword">\scriptsize</span> </span><br><span class="line"><span class="keyword">\footnotesize</span> </span><br><span class="line"><span class="keyword">\small</span> </span><br><span class="line"><span class="keyword">\normalsize</span> </span><br><span class="line"><span class="keyword">\large</span> </span><br><span class="line"><span class="keyword">\large</span> </span><br><span class="line"><span class="keyword">\LARGE</span> </span><br><span class="line"><span class="keyword">\huge</span> </span><br><span class="line"><span class="keyword">\Huge</span></span><br></pre></td></tr></table></figure><h3 id="一-公式部分"><a class="markdownIt-Anchor" href="#一-公式部分"></a> 一、公式部分</h3><ol><li><p>行内公式 $. . .$，独立成行使用$$…$$</p><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">Einstein &#x27;s $E=mc^2$.   %行内</span><br></pre></td></tr></table></figure><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>E</mi><mo>=</mo><mi>m</mi><msup><mi>c</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">E=mc^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.8141079999999999em;vertical-align:0em;"></span><span class="mord mathnormal">m</span><span class="mord"><span class="mord mathnormal">c</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><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">2</span></span></span></span></span></span></span></span></span></span></span></p><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>5</mn><mo>+</mo><msqrt><mi>x</mi></msqrt><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">x^2 + 2x + 5 + \sqrt x = 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.897438em;vertical-align:-0.08333em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><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">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">2</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.04em;vertical-align:-0.23972em;"></span><span class="mord sqrt"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8002800000000001em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal" style="padding-left:0.833em;">x</span></span><span style="top:-2.76028em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/></svg></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.23972em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span></span></span></span></p><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>F</mi><mo>=</mo><mi>G</mi><mfrac><mrow><msub><mi>m</mi><mn>1</mn></msub><msub><mi>m</mi><mn>2</mn></msub></mrow><msup><mi>R</mi><mn>2</mn></msup></mfrac></mrow><annotation encoding="application/x-tex">F=G \frac {m_{1}m_{2}}{R^{2}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.056492em;vertical-align:-0.345em;"></span><span class="mord mathnormal">G</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:0.7114919999999999em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7463142857142857em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></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:-3.4101em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 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:0.143em;"><span></span></span></span></span></span></span><span class="mord mtight"><span class="mord mathnormal mtight">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31731428571428577em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></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></p><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi><mi mathvariant="normal">ℏ</mi><mfrac><mrow><mi mathvariant="normal">∂</mi><mi>ψ</mi></mrow><mrow><mi mathvariant="normal">∂</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mo>−</mo><msup><mi mathvariant="normal">ℏ</mi><mn>2</mn></msup></mrow><mrow><mn>2</mn><mi>m</mi></mrow></mfrac><mrow><mo fence="true">(</mo><mfrac><msup><mi mathvariant="normal">∂</mi><mn>2</mn></msup><mrow><mi mathvariant="normal">∂</mi><msup><mi>x</mi><mn>2</mn></msup></mrow></mfrac><mo>+</mo><mfrac><msup><mi mathvariant="normal">∂</mi><mn>2</mn></msup><mrow><mi mathvariant="normal">∂</mi><msup><mi>y</mi><mn>2</mn></msup></mrow></mfrac><mo>+</mo><mfrac><msup><mi mathvariant="normal">∂</mi><mn>2</mn></msup><mrow><mi mathvariant="normal">∂</mi><msup><mi>z</mi><mn>2</mn></msup></mrow></mfrac><mo fence="true">)</mo></mrow><mi>ψ</mi><mo>+</mo><mi>V</mi><mi>ψ</mi></mrow><annotation encoding="application/x-tex">i\hbar\frac{\partial \psi}{\partial t} = \frac{-\hbar^2}{2m} \left(\frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial z^2} \right) \psi + V \psi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.277216em;vertical-align:-0.345em;"></span><span class="mord mathnormal">i</span><span class="mord">ℏ</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:0.9322159999999999em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight" style="margin-right:0.05556em;">∂</span><span class="mord mathnormal mtight">t</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:-3.446108em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight" style="margin-right:0.05556em;">∂</span><span class="mord mathnormal mtight" style="margin-right:0.03588em;">ψ</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="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.80002em;vertical-align:-0.65002em;"></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:1.01792em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span><span class="mord mathnormal mtight">m</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">−</span><span class="mord mtight"><span class="mord mtight">ℏ</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913142857142857em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></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="mspace" style="margin-right:0.16666666666666666em;"></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:1.01792em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight" style="margin-right:0.05556em;">∂</span><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7463142857142857em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></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"><span class="mord mtight" style="margin-right:0.05556em;">∂</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913142857142857em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></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="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></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:1.01792em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight" style="margin-right:0.05556em;">∂</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7463142857142857em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></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"><span class="mord mtight" style="margin-right:0.05556em;">∂</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913142857142857em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.481108em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></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:1.01792em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight" style="margin-right:0.05556em;">∂</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.04398em;">z</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7463142857142857em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></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"><span class="mord mtight" style="margin-right:0.05556em;">∂</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913142857142857em;"><span style="top:-2.931em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></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 size2">)</span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">ψ</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="mord mathnormal" style="margin-right:0.03588em;">ψ</span></span></span></span></p></li><li><p>行间公式 [ …]</p><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">[E=mc^2]   %行内</span><br><span class="line">\[ E=mc^2. \]</span><br></pre></td></tr></table></figure><p>[ E=mc^2]</p></li><li><p>一行插入多个公式环境为flalign</p><figure class="highlight latex"><table><tr><td class="code"><pre><span class="line"><span class="keyword">\begin</span>&#123;flalign&#125; </span><br><span class="line">S<span class="built_in">_</span>&#123;n+1&#125; = S<span class="built_in">_</span>&#123;n&#125; + S<span class="built_in">_</span>&#123;n&#125;,  </span><br><span class="line">S<span class="built_in">_</span>&#123;n&#125;=1=2<span class="built_in">^</span>&#123;n&#125; </span><br><span class="line"><span class="keyword">\end</span>&#123;flalign&#125;</span><br></pre></td></tr></table></figure><p><span class='katex-error' title='ParseError: KaTeX parse error: No such environment: flalign at position 7: \begin{̲f̲l̲a̲l̲i̲g̲n̲}̲ S_{n+1} = S_{…'>\begin{flalign} S_{n+1} = S_{n} + S_{n}, S_{n}=1=2^{n} \end{flalign}</span></p></li><li><p>对行间公式编号</p><figure class="highlight latex"><table><tr><td class="code"><pre><span class="line"><span class="keyword">\begin</span>&#123;equation&#125; </span><br><span class="line">... </span><br><span class="line"><span class="keyword">\end</span>&#123;equation&#125;</span><br></pre></td></tr></table></figure><p><span class='katex-error' title='ParseError: KaTeX parse error: No such environment: equation at position 7: \begin{̲e̲q̲u̲a̲t̲i̲o̲n̲}̲ ... \end{equ…'>\begin{equation} ... \end{equation}</span></p></li><li><p>公式上下标</p><figure class="highlight latex"><table><tr><td class="code"><pre><span class="line"><span class="built_in">^</span>&#123;&#125; <span class="comment">%上标 </span></span><br><span class="line"><span class="built_in">_</span>&#123;&#125; <span class="comment">%下标</span></span><br></pre></td></tr></table></figure></li><li><p>分式</p><figure class="highlight latex"><table><tr><td class="code"><pre><span class="line"><span class="keyword">\frac</span>&#123;m&#125;&#123;n&#125; <span class="comment">%n分之m</span></span><br></pre></td></tr></table></figure></li><li><p>开方</p><figure class="highlight latex"><table><tr><td class="code"><pre><span class="line"><span class="keyword">\sqrt</span>&#123;&#125; <span class="comment">%开平方 </span></span><br><span class="line"><span class="keyword">\sqrt</span>[m]&#123;n&#125; <span class="comment">%n开m次方</span></span><br></pre></td></tr></table></figure></li><li><p>求和</p><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">\sum_&#123;i=m&#125;^&#123;n&#125;  %从m到n求和</span><br></pre></td></tr></table></figure><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mi>m</mi></mrow><mi>n</mi></msubsup></mrow><annotation encoding="application/x-tex">\sum_{i=m}^{n}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.104002em;vertical-align:-0.29971000000000003em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.804292em;"><span style="top:-2.40029em;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"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mathnormal mtight">m</span></span></span></span><span style="top:-3.2029em;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="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span></span></span></span></p></li><li><p>求积</p><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">\prod_&#123;i=m&#125;^&#123;n&#125; %从m到n求积</span><br></pre></td></tr></table></figure><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mo>∏</mo><mrow><mi>i</mi><mo>=</mo><mi>m</mi></mrow><mi>n</mi></msubsup></mrow><annotation encoding="application/x-tex">\prod_{i=m}^{n}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.104002em;vertical-align:-0.29971000000000003em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∏</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.804292em;"><span style="top:-2.40029em;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"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mathnormal mtight">m</span></span></span></span><span style="top:-3.2029em;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="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span></span></span></span> %从m到n求积</p></li><li><p>积分</p></li></ol><pre><code>\int_{i=m}^{n}  %从m到n积分</code></pre><p>​<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mo>∫</mo><mrow><mi>i</mi><mo>=</mo><mi>m</mi></mrow><mi>n</mi></msubsup></mrow><annotation encoding="application/x-tex">\int_{i=m}^{n}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.215112em;vertical-align:-0.35582em;"></span><span class="mop"><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0005599999999999772em;">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8592920000000001em;"><span style="top:-2.34418em;margin-left:-0.19445em;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="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mathnormal mtight">m</span></span></span></span><span style="top:-3.2579000000000002em;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="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.35582em;"><span></span></span></span></span></span></span></span></span></span>  %从m到n积分</p><ol start="11"><li><p>向量</p><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">\vec a  %a向量 </span><br><span class="line">\overrightarrow&#123;AB&#125; %A到B的向量</span><br></pre></td></tr></table></figure><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>a</mi><mo>⃗</mo></mover></mrow><annotation encoding="application/x-tex">\vec a</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.714em;vertical-align:0em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.714em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord mathnormal">a</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.2355em;"><span class="overlay" style="height:0.714em;width:0.471em;"><svg width='0.471em' height='0.714em' style='width:0.471em' viewBox='0 0 471 714' preserveAspectRatio='xMinYMin'><path d='M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 53.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 1110.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359c-16-25.333-24-45-24-59z'/></svg></span></span></span></span></span></span></span></span></span></span> %a向量<br /><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mrow><mi>A</mi><mi>B</mi></mrow><mo stretchy="true">→</mo></mover></mrow><annotation encoding="application/x-tex">\overrightarrow{AB}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.20533em;vertical-align:0em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:1.20533em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span></span></span><span class="svg-align" style="top:-3.6833299999999998em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="height:0.522em;min-width:0.888em;"><svg width='400em' height='0.522em' viewBox='0 0 400000 522' preserveAspectRatio='xMaxYMin slice'><path d='M0 241v40h399891c-47.3 35.3-84 78-110 128-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67 151.7 139 205zm0 0v40h399900v-40z'/></svg></span></span></span></span></span></span></span></span></span> %A到B的向量</p></li><li><p>省略号</p><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">a+b+\cdots+z    %a+b+…+z</span><br></pre></td></tr></table></figure><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mo>⋯</mo><mo>+</mo><mi>z</mi><mi mathvariant="normal">%</mi><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mo>…</mo><mo>+</mo><mi>z</mi></mrow><annotation encoding="application/x-tex">a+b+\cdots+z    \%a+b+…+z</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.08333em;"></span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span><span class="mord">%</span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="minner">…</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span></span></span></span></p></li><li><p>大括号</p><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">\underbrace&#123;a+b+\cdots+z&#125;_&#123;26&#125;  %a+b+…+z</span><br></pre></td></tr></table></figure><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><munder><munder><mrow><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mo>⋯</mo><mo>+</mo><mi>z</mi></mrow><mo stretchy="true">⏟</mo></munder><mn>26</mn></munder></mrow><annotation encoding="application/x-tex">\underbrace{a+b+\cdots+z}_{26}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.076878em;vertical-align:-1.382438em;"></span><span class="mord munder"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-1.617562em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">2</span><span class="mord mtight">6</span></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord munder"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span class="svg-align" style="top:-2.26867em;"><span class="pstrut" style="height:3em;"></span><span class="stretchy" style="height:0.548em;min-width:1.6em;"><span class="brace-left" style="height:0.548em;"><svg width='400em' height='0.548em' viewBox='0 0 400000 548' preserveAspectRatio='xMinYMin slice'><path d='M0 6l6-6h17c12.688 0 19.313.3 20 1 4 4 7.313 8.3 10 13 35.313 51.3 80.813 93.8 136.5 127.5 55.688 33.7 117.188 55.8 184.5 66.5.688 0 2 .3 4 1 18.688 2.7 76 4.3 172 5h399450v120H429l-6-1c-124.688-8-235-61.7-331-161C60.687 138.7 32.312 99.3 7 54L0 41V6z'/></svg></span><span class="brace-center" style="height:0.548em;"><svg width='400em' height='0.548em' viewBox='0 0 400000 548' preserveAspectRatio='xMidYMin slice'><path d='M199572 214c100.7 8.3 195.3 44 280 108 55.3 42 101.7 93 139 153l9 14c2.7-4 5.7-8.7 9-14 53.3-86.7 123.7-153 211-199 66.7-36 137.3-56.3 212-62h199568v120H200432c-178.3 11.7-311.7 78.3-403 201-6 8-9.7 12-11 12-.7.7-6.7 1-18 1s-17.3-.3-18-1c-1.3 0-5-4-11-12-44.7-59.3-101.3-106.3-170-141s-145.3-54.3-229-60H0V214z'/></svg></span><span class="brace-right" style="height:0.548em;"><svg width='400em' height='0.548em' viewBox='0 0 400000 548' preserveAspectRatio='xMaxYMin slice'><path d='M399994 0l6 6v35l-6 11c-56 104-135.3 181.3-238 232-57.3 28.7-117 45-179 50H-300V214h399897c43.3-7 81-15 113-26 100.7-33 179.7-91 237-174 2.7-5 6-9 10-13 .7-1 7.3-1 20-1h17z'/></svg></span></span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="minner">⋯</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.73133em;"><span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.382438em;"><span></span></span></span></span></span></span></span></span> %a+b+…+z</p></li><li><p>横杠</p><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">\overline&#123;m+n&#125;  %m+n公式上面加上横杠 </span><br><span class="line">\underline&#123;m+n&#125; %m+n公式下面加上横杠</span><br></pre></td></tr></table></figure><p><span class='katex-error' title='ParseError: KaTeX parse error: No such environment: flalign at position 7: \begin{̲f̲l̲a̲l̲i̲g̲n̲}̲\overline{m+n},…'>\begin{flalign}\overline{m+n},\ \underline{m+n}\end{flalign}</span></p></li></ol><h3 id="二-其他内容"><a class="markdownIt-Anchor" href="#二-其他内容"></a> 二、其他内容</h3>]]></content>
    
    
      
      
    <summary type="html">&lt;h3 id=&quot;latex简单介绍&quot;&gt;&lt;a class=&quot;markdownIt-Anchor&quot; href=&quot;#latex简单介绍&quot;&gt;&lt;/a&gt; LaTex简单介绍&lt;/h3&gt;
&lt;p&gt;LaTex是一种简单文件生成系统，文件后缀为.tex&lt;/p&gt;
&lt;h3 id=&quot;基本用法&quot;&gt;&lt;a cla</summary>
      
    
    
    
    
  </entry>
  
  <entry>
    <title>常见代码案例</title>
    <link href="https://lucky-z.fun/p/4092cb80.html"/>
    <id>https://lucky-z.fun/p/4092cb80.html</id>
    <published>2022-09-04T04:59:48.000Z</published>
    <updated>2022-09-05T05:51:17.934Z</updated>
    
    <content type="html"><![CDATA[<p>#外挂标签案例</p><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">1. 带 &#123;% u 下划线 %&#125; 的文本</span><br><span class="line">2. 带 &#123;% emp 着重号 %&#125; 的文本</span><br><span class="line">3. 带 &#123;% wavy 波浪线 %&#125; 的文本</span><br><span class="line">4. 带 &#123;% del 删除线 %&#125; 的文本</span><br><span class="line">5. 键盘样式的文本 &#123;% kbd command %&#125; + &#123;% kbd D %&#125;</span><br><span class="line">6. 密码样式的文本：&#123;% psw 这里没有验证码 %&#125;</span><br></pre></td></tr></table></figure><p>带 <u>下划线</u> 的文本<br />带 <emp>着重号</emp> 的文本<br />带 <wavy>波浪线</wavy> 的文本<br />带 <del>删除线</del> 的文本<br />键盘样式的文本 <kbd>command</kbd> + <kbd>D</kbd><br />密码样式的文本：<psw>这里没有验证码</psw></p><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">- 彩色文字</span><br><span class="line">在一段话中方便插入各种颜色的标签，包括：&#123;% span red, 红色 %&#125;、&#123;% span yellow, 黄色 %&#125;、&#123;% span green, 绿色 %&#125;、&#123;% span cyan, 青色 %&#125;、&#123;% span blue, 蓝色 %&#125;、&#123;% span gray, 灰色 %&#125;。</span><br><span class="line">- 超大号文字</span><br><span class="line">文档「开始」页面中的标题部分就是超大号文字。</span><br><span class="line">&#123;% span center logo large, Volantis %&#125;</span><br><span class="line">&#123;% span center small, A Wonderful Theme for Hexo %&#125;</span><br></pre></td></tr></table></figure><p>预览:</p><ul><li>彩色文字<br />在一段话中方便插入各种颜色的标签，包括：<span class='p red'>红色</span>、<span class='p yellow'>黄色</span>、<span class='p green'>绿色</span>、<span class='p cyan'>青色</span>、<span class='p blue'>蓝色</span>、<span class='p gray'>灰色</span>。</li><li>超大号文字<br />文档「开始」页面中的标题部分就是超大号文字。<span class='p center logo large'>Volantis</span><span class='p center small'>A Wonderful Theme for Hexo</span></li></ul><div class="note success simple"><p>success 提示块标签</p></div><p>复选列表</p><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">&#123;% checkbox 纯文本测试 %&#125;</span><br><span class="line">&#123;% checkbox checked, 支持简单的 [markdown](https://guides.github.com/features/mastering-markdown/) 语法 %&#125;</span><br><span class="line">&#123;% checkbox red, 支持自定义颜色 %&#125;</span><br><span class="line">&#123;% checkbox green checked, 绿色 + 默认选中 %&#125;</span><br><span class="line">&#123;% checkbox yellow checked, 黄色 + 默认选中 %&#125;</span><br><span class="line">&#123;% checkbox cyan checked, 青色 + 默认选中 %&#125;</span><br><span class="line">&#123;% checkbox blue checked, 蓝色 + 默认选中 %&#125;</span><br><span class="line">&#123;% checkbox plus green checked, 增加 %&#125;</span><br><span class="line">&#123;% checkbox minus yellow checked, 减少 %&#125;</span><br><span class="line">&#123;% checkbox times red checked, 叉 %&#125;</span><br></pre></td></tr></table></figure><p>预览:</p><div class='checkbox'><input type="checkbox" />            <p>纯文本测试</p>            </div><div class='checkbox checked'><input type="checkbox" checked="checked"/>            <p>支持简单的 <a href="https://guides.github.com/features/mastering-markdown/">markdown</a> 语法</p>            </div><div class='checkbox red'><input type="checkbox" />            <p>支持自定义颜色</p>            </div><div class='checkbox green checked'><input type="checkbox" checked="checked"/>            <p>绿色 + 默认选中</p>            </div><div class='checkbox yellow checked'><input type="checkbox" checked="checked"/>            <p>黄色 + 默认选中</p>            </div><div class='checkbox cyan checked'><input type="checkbox" checked="checked"/>            <p>青色 + 默认选中</p>            </div><div class='checkbox blue checked'><input type="checkbox" checked="checked"/>            <p>蓝色 + 默认选中</p>            </div><div class='checkbox plus green checked'><input type="checkbox" checked="checked"/>            <p>增加</p>            </div><div class='checkbox minus yellow checked'><input type="checkbox" checked="checked"/>            <p>减少</p>            </div><div class='checkbox times red checked'><input type="checkbox" checked="checked"/>            <p>叉</p>            </div><p>视频</p><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">&#123;% video https://github.com/volantis-x/volantis-docs/releases/download/assets/IMG_0341.mov %&#125;</span><br><span class="line"></span><br></pre></td></tr></table></figure><p>预览:</p><div class="video"><video controls preload><source src='https://github.com/volantis-x/volantis-docs/releases/download/assets/IMG_0341.mov' type='video/mp4'>Your browser does not support the video tag.</video></div><p>诗词标签</p><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">&#123;% poem 水调歌头,苏轼 %&#125;</span><br><span class="line">丙辰中秋，欢饮达旦，大醉，作此篇，兼怀子由。</span><br><span class="line">明月几时有？把酒问青天。</span><br><span class="line">不知天上宫阙，今夕是何年？</span><br><span class="line">我欲乘风归去，又恐琼楼玉宇，高处不胜寒。</span><br><span class="line">起舞弄清影，何似在人间？</span><br><span class="line"></span><br><span class="line">转朱阁，低绮户，照无眠。</span><br><span class="line">不应有恨，何事长向别时圆？</span><br><span class="line">人有悲欢离合，月有阴晴圆缺，此事古难全。</span><br><span class="line">但愿人长久，千里共婵娟。</span><br><span class="line">&#123;% endpoem %&#125;</span><br><span class="line"></span><br></pre></td></tr></table></figure><div class='poem'><div class='poem-title'>水调歌头</div><div class='poem-author'>苏轼</div><p>丙辰中秋，欢饮达旦，大醉，作此篇，兼怀子由。<br />明月几时有？把酒问青天。<br />不知天上宫阙，今夕是何年？<br />我欲乘风归去，又恐琼楼玉宇，高处不胜寒。<br />起舞弄清影，何似在人间？</p><p>转朱阁，低绮户，照无眠。<br />不应有恨，何事长向别时圆？<br />人有悲欢离合，月有阴晴圆缺，此事古难全。<br />但愿人长久，千里共婵娟。</p></div><p>math的使用</p><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">katex:</span><br><span class="line">  enable: true</span><br><span class="line">  # true 表示每一页都加载katex.js</span><br><span class="line">  # false 需要时加载，须在使用的Markdown Front-matter 加上 katex: true</span><br><span class="line">  per_page: false</span><br><span class="line">  hide_scrollbar: true</span><br></pre></td></tr></table></figure><p>文章制定插件<br />Npm部署方式</p><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">npm i hexo-swiper-bar --save</span><br><span class="line"></span><br><span class="line"># 或者</span><br><span class="line"></span><br><span class="line">cnpm i hexo-swiper-bar --save</span><br></pre></td></tr></table></figure><p>配置博客main_config</p><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">swiper:</span><br><span class="line">  enable: true</span><br><span class="line">  priority: 2</span><br><span class="line">  enable_page: /</span><br><span class="line">  layout:</span><br><span class="line">    type: id</span><br><span class="line">    name: recent-posts</span><br><span class="line">    index: 0</span><br><span class="line">  temple_html: &#x27;&lt;div class=&quot;recent-post-item&quot; style=&quot;height: auto;width: 100%&quot;&gt;&lt;div class=&quot;blog-slider swiper-container-fade swiper-container-horizontal&quot; id=&quot;swiper_container&quot;&gt;$&#123;temple_html_item&#125;&lt;/div&gt;&lt;/div&gt;&#x27;</span><br><span class="line">  plus_style: &quot;&quot;</span><br></pre></td></tr></table></figure><p>参考于<a href="https://zfe.space/post/hexo-swiper.html">hexo置顶组件</a></p>]]></content>
    
    
      
      
    <summary type="html">&lt;p&gt;#外挂标签案例&lt;/p&gt;
&lt;figure class=&quot;highlight plaintext&quot;&gt;&lt;table&gt;&lt;tr&gt;&lt;td class=&quot;code&quot;&gt;&lt;pre&gt;&lt;span class=&quot;line&quot;&gt;1. 带 &amp;#123;% u 下划线 %&amp;#125; 的文本&lt;/span&gt;</summary>
      
    
    
    
    
  </entry>
  
  <entry>
    <title>林业害虫识别项目需求设计</title>
    <link href="https://lucky-z.fun/p/a2204dfa.html"/>
    <id>https://lucky-z.fun/p/a2204dfa.html</id>
    <published>2022-09-04T03:49:46.000Z</published>
    <updated>2022-09-05T05:51:17.949Z</updated>
    
    <content type="html"><![CDATA[<h1 id="需求规格说明书及设计文档"><a class="markdownIt-Anchor" href="#需求规格说明书及设计文档"></a> 需求规格说明书及设计文档</h1><h2 id="项目场景"><a class="markdownIt-Anchor" href="#项目场景"></a> 项目场景</h2><blockquote><p>用户可以通过手机端APP拍照或者手动上传等方式提交林业有害生物图像照片，经预览，裁剪等操作处理后上传至服务器进行识别。反馈害虫种类、识别率、个数等信息。</p></blockquote><p>本团队自行设计并实现一客户端+前端到服务器进行信息交换实现项目场景。项目命名为Found Pest。消息队列开发完成后，为了维护害虫样本信息我们团队开发了一套基于Vue的前后端分离的害虫信息维护系统，下文简称“该项目”。该项目支持害虫信息识别维护等功能基本实现了项目应用场景的需求。</p><h2 id="实现思路"><a class="markdownIt-Anchor" href="#实现思路"></a> 实现思路</h2><blockquote><p>整体流程：选择图片==&gt;上传图片==&gt;识别图片==&gt;返回信息==&gt;接收信息==&gt;显示信息</p><p>​|能够显示害虫样本并管理样本</p><p>​|能够编辑用户上传的图片</p><p>信息维护==&gt;|能够在线识别</p><p>​ |与服务器后端进行数据交互</p><p>​ |能够被用户访问</p></blockquote><h2 id="功能"><a class="markdownIt-Anchor" href="#功能"></a> 功能</h2><h3 id="前端部分"><a class="markdownIt-Anchor" href="#前端部分"></a> 前端部分</h3><h4 id="用户管理员共有功能"><a class="markdownIt-Anchor" href="#用户管理员共有功能"></a> 用户/管理员共有功能</h4><ol><li>用户功能：<ol><li>包括用户注册和登录</li><li>查看害虫信息</li><li>忘记密码后找回密码</li></ol></li><li>害虫信息维护功能：<ol><li>浏览害虫样本信息等</li></ol></li><li>样本检索功能：<ol><li>可以检索害虫样本</li></ol></li><li>上传图片管理功能：<ol><li>管理移动端上传的图片</li></ol></li><li>数据集管理功能:</li><li>可视化展示功能</li><li>在线识别功能呢</li></ol><h2 id="技术访问服务器部分"><a class="markdownIt-Anchor" href="#技术访问服务器部分"></a> 技术–访问服务器部分</h2><h3 id="后端技术栈"><a class="markdownIt-Anchor" href="#后端技术栈"></a> 后端技术栈</h3><ul><li>开发工具：Pycharm</li><li>Vue：项目基础框架</li><li>html +CSS ：HTML5语言</li></ul><h3 id="前端技术栈"><a class="markdownIt-Anchor" href="#前端技术栈"></a> 前端技术栈</h3><ul><li>开发工具：IDEA</li><li>Vue：渐进式框架</li><li>Vue Router：VUE路由插件用来管理各个页面</li><li>VueX：VUE状态管理</li><li>Axios ：一个基于 promise 的 HTTP 库，用于GET/POST请求</li><li>Node.js+webpack：项目构建工具</li></ul><h3 id="移动端技术栈"><a class="markdownIt-Anchor" href="#移动端技术栈"></a> 移动端技术栈</h3><ul><li>开发工具：Hbuilder X</li><li>Uniapp:是一个使用 <a href="https://vuejs.org/">Vue.js (opens new window)</a>开发所有前端应用的框架，开发者编写一套代码，可发布到iOS、Android、Web（响应式）、以及各种小程序</li></ul><h3 id="技术介绍"><a class="markdownIt-Anchor" href="#技术介绍"></a> 技术介绍</h3><h4 id="技术规格及应用介绍"><a class="markdownIt-Anchor" href="#技术规格及应用介绍"></a> 技术规格及应用介绍</h4><p>本项目前端基于Vue渐进式框架开发，基本遵守HTML开发规范、Vue-Cli开发规范及Webpack开发规范；后端基于Python+flask框架开发。下面将从HTTP请求开始介绍本项目的技术特点。</p><ol><li><p>通过HTTP协议访问托管在服务器端的项目，通过Nginx集群，均衡负载返回页面</p></li><li><p>页面内通过Axios提供的request方式GET/POST请求页面内的数据</p></li><li><p>Nginx接收到请求地址后指向localhost:8090前端部分打开页面</p></li><li><p>App端与服务器交互，使用Base64压缩图片与服务器进行交互</p></li></ol><h4 id="数据库模型图"><a class="markdownIt-Anchor" href="#数据库模型图"></a> 数据库模型图</h4><h4 id="项目工程截图"><a class="markdownIt-Anchor" href="#项目工程截图"></a> 项目工程截图</h4><p>​前端部分</p><img src="C:\Users\LuckyEnough.z\AppData\Roaming\Typora\typora-user-images\image-20220430161809291.png" alt="image-20220430161809291" style="zoom: 50%;" /><p>​后端部分</p><img src="C:\Users\LuckyEnough.z\AppData\Roaming\Typora\typora-user-images\image-20220430161930231.png" alt="image-20220430161930231" style="zoom: 50%;" /><p>移动端</p><p>​<img src="C:\Users\LuckyEnough.z\AppData\Roaming\Typora\typora-user-images\image-20220430162034356.png" alt="image-20220430162034356" style="zoom:50%;" /></p><h2 id="技术害虫识别算法部分"><a class="markdownIt-Anchor" href="#技术害虫识别算法部分"></a> 技术–害虫识别算法部分</h2><p>基于YOLOV5算法实现的 害虫识别的功能，通过Flask框架接收数据与前端+App通信,前端通过Ajax.request与服务器进行交互，App端通过Uniapp原生API即uni.upload接口与服务器进行数据交互。</p><h3 id="支持害虫识别的种类"><a class="markdownIt-Anchor" href="#支持害虫识别的种类"></a> 支持害虫识别的种类</h3><ul><li><p>100类害虫在线样本检索</p><figure class="highlight html"><table><tr><td class="code"><pre><span class="line">黑蚱蝉蟪蛄蒙古寒蝉菜蝽茶翅蝽赤条蝽麻皮蝽硕蝽大皱蝽碧蛾蜡蝉大田鳖柿广翅蜡蝉透翅疏广蜡蝉斑衣蜡蝉草履蚧悬铃木方翅网蝽中华象蜡蝉大青叶蝉小绿叶蝉刺肩普缘蝽稻棘缘蝽点蜂缘蝽钝肩普缘蝽(钝角普缘蝽)虎斑蝶金斑蝶玉带斑蛾重阳木锦斑蛾大叶黄杨尺蛾四星尺蛾小蜻蜓尺蛾扁刺蛾褐边绿刺蛾黄刺蛾红尾大蚕蛾绿尾大蚕蛾八点灰灯蛾红缘灯蛾花布灯蛾美国白蛾强污灯蛾人纹污灯蛾优美苔蛾侧柏毒蛾盗毒蛾(黄尾毒蛾)柳毒蛾线茸毒蛾菜粉蝶碧凤蝶柑橘凤蝶金凤蝶蓝凤蝶麝凤蝶丝带凤蝶玉带凤蝶樟青凤蝶洋麻圆钩蛾桃小食心虫大红蛱蝶二尾蛱蝶黑脉蛱蝶黄钩蛱蝶柳紫闪蛱蝶马尾松毛虫黄杨绢野螟桃蛀螟樟巢螟缀叶丛螟豆天蛾甘薯天蛾红天蛾蓝目天蛾葡萄天蛾雀纹天蛾霜天蛾变色夜蛾臭椿皮蛾胡桃豹夜蛾斜纹夜蛾旋目夜蛾分月扇舟蛾核桃美舟蛾杨二尾舟蛾杨扇舟蛾杨小舟蛾白星花金龟黄粉鹿花金龟日本脊吉丁</span><br><span class="line">犀角粪金龟薄翅锯天牛(中华薄翅天牛) 中华大扁锹光肩星天牛桑天牛双条杉天牛松墨天牛桃红颈天牛星天牛锈色粒肩天牛云斑白条天牛柳蓝叶甲</span><br></pre></td></tr></table></figure></li><li><p>15类害虫的在线识别</p><figure class="highlight html"><table><tr><td class="code"><pre><span class="line">&quot;草履蚧&quot;, &quot;麻皮蝽&quot;, &quot;日本脊吉丁&quot;, &quot;星天牛&quot;, &quot;桑天牛&quot;, &quot;松墨天牛&quot;, &quot;柳蓝叶甲&quot;, &quot;黄刺蛾&quot;, &quot;褐边绿刺蛾&quot;, &quot;丝带凤蝶&quot;, &quot;人纹污灯蛾&quot;, &quot;霜天蛾&quot;,&quot;杨扇舟蛾&quot;, &quot;杨小舟蛾&quot;, &quot;美国白蛾&quot;</span><br></pre></td></tr></table></figure></li></ul><h3 id="接口对接实现样例"><a class="markdownIt-Anchor" href="#接口对接实现样例"></a> 接口对接实现样例</h3><p>前端识别接口调用样例</p><p>后端数据库</p><figure class="highlight python"><table><tr><td class="code"><pre><span class="line"><span class="keyword">class</span> <span class="title class_">Species</span>(db.Model):</span><br><span class="line">    <span class="comment"># 定义表名</span></span><br><span class="line">    __tablename__ = <span class="string">&#x27;t_species&#x27;</span></span><br><span class="line">    <span class="comment"># 定义列对象</span></span><br><span class="line">    <span class="built_in">id</span> = db.Column(db.Integer, primary_key=<span class="literal">True</span>, autoincrement=<span class="literal">True</span>)</span><br><span class="line">    name = db.Column(db.String(<span class="number">60</span>))</span><br><span class="line">    code = db.Column(db.String(<span class="number">60</span>), unique=<span class="literal">True</span>)</span><br><span class="line">    latin_name = db.Column(db.String(<span class="number">60</span>))</span><br><span class="line">    distribution_plants = db.Column(db.Text)</span><br><span class="line">    distribution_area = db.Column(db.Text)</span><br><span class="line">    sample_path = db.Column(db.String(<span class="number">60</span>))</span><br><span class="line"></span><br><span class="line">    genus_id = db.Column(db.Integer, db.ForeignKey(<span class="string">&#x27;t_genus.id&#x27;</span>, ondelete=<span class="string">&#x27;CASCADE&#x27;</span>))</span><br><span class="line">    genus = db.relationship(<span class="string">&quot;Genus&quot;</span>, backref=db.backref(<span class="string">&#x27;specieses&#x27;</span>, cascade=<span class="string">&quot;all, delete-orphan&quot;</span>))</span><br></pre></td></tr></table></figure><p>&lt;Scan.vue&gt;</p><figure class="highlight plaintext"><table><tr><td class="code"><pre><span class="line">&lt;Upload</span><br><span class="line">     :format=&quot;[&#x27;jpg&#x27;,&#x27;jpeg&#x27;,&#x27;png&#x27;]&quot; //规定图片格式，不一致就报错</span><br><span class="line">     :on-success=&quot;handleSuccess&quot;  //将图片选定后就执行上传方法</span><br><span class="line">     :on-format-error=&quot;handleFormatError&quot; //报错的方法</span><br><span class="line">     action=&quot;http://42.192.237.135:8090/FPIMS/detection_withFile/&quot;&gt; //请求的地址</span><br><span class="line">    &lt;Button type=&quot;primary&quot; icon=&quot;ios-cloud-upload-outline&quot;&gt;&lt;/Button&gt; //点击按钮会执行上传图片的方法</span><br><span class="line">&lt;/Upload&gt;</span><br><span class="line">&lt;script&gt;</span><br><span class="line">    method:&#123;</span><br><span class="line">        handleSuccess (res, file) &#123;//res :临时数组用来存储返沪的信息  file：上传的图片对象</span><br><span class="line">        this.$data.original_img_path = res.save_img_path;//接收临时图片地址</span><br><span class="line">        this.$data.detect_time = res.detect_time;//接收返回识别时间</span><br><span class="line">    &#125;</span><br><span class="line">&lt;/script&gt;</span><br></pre></td></tr></table></figure><p>后端接口返回信息</p><p><a href="http://app.py">app.py</a> —detection_withfile</p><figure class="highlight python"><table><tr><td class="code"><pre><span class="line"><span class="meta">@app.route(<span class="params"><span class="string">&#x27;/FPIMS/detection_withFile/&#x27;</span>, methods=[<span class="string">&#x27;GET&#x27;</span>, <span class="string">&#x27;POST&#x27;</span>]</span>)</span><span class="comment">#Get:接收待处理图片 #Post：将处理后的图片与识别结果返回前端</span></span><br><span class="line"><span class="keyword">def</span> <span class="title function_">detection_with_file</span>():  <span class="comment">#定义函数用来调用</span></span><br><span class="line">    file = request.files[<span class="string">&#x27;file&#x27;</span>]<span class="comment">#接收前端传来的</span></span><br><span class="line">    file.save(image_path)</span><br><span class="line">    <span class="comment"># 将保存的图片输入网络进行推测</span></span><br><span class="line">    processed_img, recognition_res = app.detect(cv2.imread(image_path),Species)</span><br><span class="line">    <span class="comment">#img_path：前端传来的的图片地址</span></span><br><span class="line">    <span class="comment">#Species:数据库对象用来查数据</span></span><br><span class="line">    <span class="comment"># 推测后的图片保存到processed目录</span></span><br><span class="line">    cv2.imwrite(<span class="string">&#x27;./picture_data/detect/processed/&#123;&#125;&#x27;</span>.<span class="built_in">format</span>(processed_filename), <span class="comment">#处理的图片)</span></span><br><span class="line">    <span class="comment"># 将“结果拼成字符串”和“推测后的图片的路径”一起传给前端</span></span><br><span class="line">    res = img_path_processed + <span class="string">&#x27;-&#x27;</span> + recognition_res <span class="comment">#结果数组</span></span><br><span class="line">    <span class="keyword">return</span> res</span><br></pre></td></tr></table></figure><h3 id="项目基本使用方式"><a class="markdownIt-Anchor" href="#项目基本使用方式"></a> 项目基本使用方式</h3><ol><li>运行后端app.py启动服务器</li><li>启动前端静态网页或者Vue项目 npm run server</li><li>启动手机端app</li></ol><figure class="highlight python"><table><tr><td class="code"><pre><span class="line"><span class="comment">#在后端服务器文件夹运行服务器</span></span><br><span class="line">python app.py</span><br><span class="line"><span class="comment">#在前端启动Vue项目文件</span></span><br><span class="line">npm run server</span><br></pre></td></tr></table></figure><h3 id="结果展示"><a class="markdownIt-Anchor" href="#结果展示"></a> 结果展示</h3>]]></content>
    
    
      
      
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&lt;h2 id=&quot;项目场景&quot;&gt;&lt;a class=&quot;markdownIt-Anchor&quot; hr</summary>
      
    
    
    
    
  </entry>
  
  <entry>
    <title>数学建模学习历程</title>
    <link href="https://lucky-z.fun/p/8bfd4855.html"/>
    <id>https://lucky-z.fun/p/8bfd4855.html</id>
    <published>2022-09-03T15:16:36.000Z</published>
    <updated>2026-05-13T07:21:16.312Z</updated>
    
    <content type="html"><![CDATA[<img src="/images/math_birds.jpg" alt="birds-g7ef62656c_1920" style="zoom: 25%;" /><h2 id="综述"><a class="markdownIt-Anchor" href="#综述"></a> 综述</h2><p>每年数学建模比赛有许多，具体可百度，但是，目前来看只有国赛的认可度最高，由此参加国赛想碰碰运气</p><h3 id="比赛需要干什么"><a class="markdownIt-Anchor" href="#比赛需要干什么"></a> 比赛需要干什么？</h3><p>1.写论文</p><p>2.绘图</p><p>3.对实际的问题进行建模解决</p><p>代码不查重</p>]]></content>
    
    
    <summary type="html">关于数学建模的学习</summary>
    
    
    
    
    <category term="学习" scheme="https://lucky-z.fun/tags/%E5%AD%A6%E4%B9%A0/"/>
    
  </entry>
  
  <entry>
    <title>教材选购</title>
    <link href="https://lucky-z.fun/p/c42187b7.html"/>
    <id>https://lucky-z.fun/p/c42187b7.html</id>
    <published>2022-09-03T14:29:09.000Z</published>
    <updated>2022-09-05T05:51:17.944Z</updated>
    
    <content type="html"><![CDATA[<h4 id="教材选购"><a class="markdownIt-Anchor" href="#教材选购"></a> 教材选购</h4><p><i class="iconfont icon-shu">待采购列表</i></p><table><thead><tr><th>书名</th><th>IBSN</th></tr></thead><tbody><tr><td>零基础学Android全彩版</td><td>9787569208542</td></tr><tr><td>人工智能</td><td>9787302572541</td></tr><tr><td>OpenCV计算机视觉基础教程（Python版）</td><td>9787115561770</td></tr><tr><td>管理信息系统实践教程</td><td>9787302551140</td></tr></tbody></table><p><i class="iconfont icon--">已采购列表</i></p><table><thead><tr><th>书名</th><th>资源</th></tr></thead><tbody><tr><td>计算机网络</td><td><a href="/download/%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%BD%91%E7%BB%9C%EF%BC%88%E7%AC%AC8%E7%89%88%EF%BC%89.pdf">计算机网络（第8版）.pdf</a></td></tr><tr><td>商务智能</td><td><a href="/download/%E5%95%86%E5%8A%A1%E6%99%BA%E8%83%BD%E4%B8%8E%E6%95%B0%E6%8D%AE%E6%8C%96%E6%8E%98%EF%BC%88%E7%AC%AC2%E7%89%88%EF%BC%89.pdf">商务智能与数据挖掘（第2版）.pdf</a></td></tr><tr><td>计算机组成原理</td><td><a href="/download/%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%BB%84%E6%88%90%E5%8E%9F%E7%90%86%E7%AC%AC3%E7%89%88.pdf">计算机组成原理第3版.pdf</a></td></tr><tr><td>操作系统原理</td><td><a href="/download/%E8%AE%A1%E7%AE%97%E6%9C%BA%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F%EF%BC%88%E7%AC%AC%E5%9B%9B%E7%89%88%EF%BC%89.pdf">计算机操作系统（第四版）.pdf</a></td></tr></tbody></table>]]></content>
    
    
      
      
    <summary type="html">&lt;h4 id=&quot;教材选购&quot;&gt;&lt;a class=&quot;markdownIt-Anchor&quot; href=&quot;#教材选购&quot;&gt;&lt;/a&gt; 教材选购&lt;/h4&gt;
&lt;p&gt;&lt;i class=&quot;iconfont icon-shu&quot;&gt;待采购列表&lt;/i&gt;&lt;/p&gt;
&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;t</summary>
      
    
    
    
    
    <category term="日常" scheme="https://lucky-z.fun/tags/%E6%97%A5%E5%B8%B8/"/>
    
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  <entry>
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    <link href="https://lucky-z.fun/p/d0725f51.html"/>
    <id>https://lucky-z.fun/p/d0725f51.html</id>
    <published>2022-09-02T14:57:43.000Z</published>
    <updated>2022-09-05T05:51:17.944Z</updated>
    
    <content type="html"><![CDATA[<p>置顶链接</p><p>经过一段时间的折腾终于用 Hexo + GitHub 搭建起了一个个人博客站点🌈，第一时间边学边写，弄出了这第一篇博客，心里甚是欢喜。</p><p>Hexo 是一款“快速、简洁且高效的博客框架”，支持 Markdown 的所有功能。所以，写出一篇博客必须学习 Hexo 和 Markdown 的使用规则。</p><p>H<sub>2</sub>O 💧</p><p>臣亮言：<mark class="hl-label default">先帝</mark>创业未半，而<mark class="hl-label blue">中道崩殂</mark>。今天下三分，<mark class="hl-label pink">益州疲敝</mark>，此诚<mark class="hl-label red">危急存亡之秋</mark>也！然侍衞之臣，不懈于内；<mark class="hl-label purple">忠志之士</mark>，忘身于外者，盖追先帝之殊遇，欲报之于陛下也。诚宜开张圣听，以光先帝遗德，恢弘志士之气；不宜妄自菲薄，引喻失义，以塞忠谏之路也。<br />宫中、府中，俱为一体；陟罚臧否，不宜异同。若有<mark class="hl-label orange">作奸</mark>、<mark class="hl-label green">犯科</mark>，及为忠善者，宜付有司，论其刑赏，以昭陛下平明之治；不宜偏私，使内外异法也。</p>]]></content>
    
    
      
      
    <summary type="html">&lt;p&gt;置顶链接&lt;/p&gt;
&lt;p&gt;经过一段时间的折腾终于用 Hexo + GitHub 搭建起了一个个人博客站点🌈，第一时间边学边写，弄出了这第一篇博客，心里甚是欢喜。&lt;/p&gt;
&lt;p&gt;Hexo 是一款“快速、简洁且高效的博客框架”，支持 Markdown 的所有功能。所以，写出一篇</summary>
      
    
    
    
    
    <category term="经验分享" scheme="https://lucky-z.fun/tags/%E7%BB%8F%E9%AA%8C%E5%88%86%E4%BA%AB/"/>
    
  </entry>
  
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