Site updated: 2024-11-25 21:23:45

Birkhoff-ergodic-theorem/index.html

@@ -312,7 +312,9 @@ <h1>Birkhoff 遍历定理</h1>
 
 
 
-
+                                    <div class="toc pink-link-context hide-on-med-and-down">
+    <ol class="section table-of-contents"><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E5%87%86%E5%A4%87%E5%B7%A5%E4%BD%9C"><span class="section table-of-contents-text">准备工作</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#birkhoff-%E9%81%8D%E5%8E%86%E5%AE%9A%E7%90%86"><span class="section table-of-contents-text">Birkhoff 遍历定理</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#birkhoff-%E9%81%8D%E5%8E%86%E5%AE%9A%E7%90%86%E7%9A%84%E8%AF%81%E6%98%8E"><span class="section table-of-contents-text">Birkhoff 遍历定理的证明</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E6%9E%81%E5%A4%A7%E9%81%8D%E5%8E%86%E5%AE%9A%E7%90%86%E7%9A%84%E8%AF%81%E6%98%8E"><span class="section table-of-contents-text">极大遍历定理的证明</span></a></li></ol>
+</div>
 
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Marden-theorem/index.html

@@ -306,7 +306,9 @@ <h1>静电场与 Marden 定理</h1>
 
 
 
-
+                                    <div class="toc pink-link-context hide-on-med-and-down">
+
+</div>
 
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Pfaffian-and-chessboard-tiling/index.html

@@ -312,7 +312,9 @@ <h1>国际象棋棋盘的多米诺骨牌密铺</h1>
 
 
 
-
+                                    <div class="toc pink-link-context hide-on-med-and-down">
+    <ol class="section table-of-contents"><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E5%8F%8D%E5%AF%B9%E7%A7%B0%E7%9F%A9%E9%98%B5%E7%9A%84-pfaffian"><span class="section table-of-contents-text">反对称矩阵的 Pfaffian</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E5%B9%B3%E9%9D%A2%E5%9B%BE%E7%9A%84-pfaffian-%E5%AE%9A%E5%90%91"><span class="section table-of-contents-text">平面图的 Pfaffian 定向</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E6%A3%8B%E7%9B%98%E7%9A%84%E5%A4%9A%E7%B1%B3%E8%AF%BA%E9%AA%A8%E7%89%8C%E5%AF%86%E9%93%BA%E7%9A%84%E8%AE%A1%E6%95%B0"><span class="section table-of-contents-text">棋盘的多米诺骨牌密铺的计数</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E6%9C%AA%E5%B0%BD%E7%9A%84%E8%AE%A8%E8%AE%BA"><span class="section table-of-contents-text">未尽的讨论</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E9%99%84%E5%BD%95"><span class="section table-of-contents-text">附录</span></a><ol class="section table-of-contents-child"><li class="section table-of-contents-item section table-of-contents-level-2"><a class="section table-of-contents-link" href="#%E6%B1%82%E9%82%BB%E6%8E%A5%E7%9F%A9%E9%98%B5-lmn-%E7%9A%84%E5%85%B7%E4%BD%93%E6%AD%A5%E9%AA%A4"><span class="section table-of-contents-text">求邻接矩阵 \(L(m,n)\) 的具体步骤</span></a></li><li class="section table-of-contents-item section table-of-contents-level-2"><a class="section table-of-contents-link" href="#%E6%B1%82-b_n-%E5%92%8C-c_m-%E7%9A%84%E7%89%B9%E5%BE%81%E5%80%BC"><span class="section table-of-contents-text">求 \(B_n\) 和 \(C_m\) 的特征值</span></a></li></ol></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#bibliography"><span class="section table-of-contents-text">References</span></a></li></ol>
+</div>
 
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Rouche-theorem-winding-number/index.html

@@ -305,7 +305,9 @@ <h1>遛狗中的数学：曲线的环绕数、Rouché 定理和开映射定理</
 
 
 
-
+                                    <div class="toc pink-link-context hide-on-med-and-down">
+    <ol class="section table-of-contents"><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#bibliography"><span class="section table-of-contents-text">References</span></a></li></ol>
+</div>
 
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Todd-Coxeter-and-uniform-polytopes/index.html

@@ -306,7 +306,11 @@ <h1>Todd-Coxeter 算法和 3D/4D 均匀多胞体</h1>
 
 
 
-
+                                    <div class="toc pink-link-context hide-on-med-and-down">
+    <ol class="section table-of-contents"><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E4%BE%8B%E5%AD%90"><span class="section table-of-contents-text">例子</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E8%BF%99%E4%BA%9B%E5%9B%BE%E7%94%BB%E7%9A%84%E9%83%BD%E6%98%AF%E4%BB%80%E4%B9%88"><span class="section table-of-contents-text">这些图画的都是什么？</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E8%BF%99%E4%BA%9B%E5%9B%BE%E6%98%AF%E6%80%8E%E4%B9%88%E7%94%BB%E5%87%BA%E6%9D%A5%E7%9A%84"><span class="section table-of-contents-text">这些图是怎么画出来的？</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E6%9C%89%E9%99%90%E8%A1%A8%E7%8E%B0%E7%BE%A4%E5%92%8C-todd-coxeter-%E7%AE%97%E6%B3%95"><span class="section table-of-contents-text">有限表现群和 Todd-Coxeter
+算法</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E6%98%9F%E7%8A%B6%E5%A4%9A%E8%83%9E%E4%BD%93%E7%9A%84%E8%AE%A1%E7%AE%97"><span class="section table-of-contents-text">星状多胞体的计算</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#snub-cube-%E7%9A%84%E8%AE%A1%E7%AE%97"><span class="section table-of-contents-text">Snub cube 的计算</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E5%A4%9A%E9%9D%A2%E4%BD%93%E7%9A%84%E9%A1%B6%E7%82%B9%E6%8A%95%E5%BD%B1%E5%88%B0-coxeter-%E5%B9%B3%E9%9D%A2"><span class="section table-of-contents-text">多面体的顶点投影到 Coxeter
+平面</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E9%99%84%E5%BD%95%E6%89%8B%E7%AE%97-todd-coxeter"><span class="section table-of-contents-text">附录：手算 Todd-Coxeter</span></a></li></ol>
+</div>
 
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catacaustics/index.html

@@ -300,7 +300,11 @@ <h1>Catacaustics of a coffee cup</h1>
 
 
 
-
+                                    <div class="toc pink-link-context hide-on-med-and-down">
+    <ol class="section table-of-contents"><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#pov-ray-optical-experiment"><span class="section table-of-contents-text">POV-Ray Optical Experiment</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#catacaustics-of-parametric-curves"><span class="section table-of-contents-text">Catacaustics of parametric
+curves</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#catacaustics-of-polynomial-curves"><span class="section table-of-contents-text">Catacaustics of polynomial
+curves</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#some-notes"><span class="section table-of-contents-text">Some notes</span></a></li></ol>
+</div>
 
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central-simple-algebra/index.html

@@ -311,7 +311,9 @@ <h1>中心单代数的三个基本结论</h1>
 
 
 
-
+                                    <div class="toc pink-link-context hide-on-med-and-down">
+    <ol class="section table-of-contents"><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E4%B8%AD%E5%BF%83%E5%8D%95%E4%BB%A3%E6%95%B0%E5%AF%B9%E5%BC%A0%E9%87%8F%E7%A7%AF%E8%BF%90%E7%AE%97%E6%98%AF%E5%B0%81%E9%97%AD%E7%9A%84"><span class="section table-of-contents-text">中心单代数对张量积运算是封闭的</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#noether-skolem-%E5%AE%9A%E7%90%86"><span class="section table-of-contents-text">Noether-Skolem 定理</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E5%8F%8C%E9%87%8D%E4%B8%AD%E5%BF%83%E5%8C%96%E5%AD%90%E5%AE%9A%E7%90%86"><span class="section table-of-contents-text">双重中心化子定理</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#bibliography"><span class="section table-of-contents-text">References</span></a></li></ol>
+</div>
 
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coupling-from-the-past/index.html

@@ -310,7 +310,11 @@ <h1>Coupling from the past</h1>
 
 
 
-
+                                    <div class="toc pink-link-context hide-on-med-and-down">
+    <ol class="section table-of-contents"><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#markov-%E9%93%BE%E7%9A%84%E9%9A%8F%E6%9C%BA%E5%8F%96%E6%A0%B7"><span class="section table-of-contents-text">Markov 链的随机取样</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#markov-%E9%93%BE%E7%9A%84%E9%9A%8F%E6%9C%BA%E6%98%A0%E5%B0%84%E8%A1%A8%E7%A4%BA"><span class="section table-of-contents-text">Markov 链的随机映射表示</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#coupling-from-the-past-%E7%AE%97%E6%B3%95"><span class="section table-of-contents-text">Coupling from the past 算法</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E7%AE%97%E6%B3%95%E4%B8%AD%E7%9A%84%E8%8B%A5%E5%B9%B2%E9%99%B7%E9%98%B1"><span class="section table-of-contents-text">算法中的若干陷阱</span></a><ol class="section table-of-contents-child"><li class="section table-of-contents-item section table-of-contents-level-2"><a class="section table-of-contents-link" href="#%E4%B8%BA%E4%BB%80%E4%B9%88%E6%9B%B4%E6%96%B0%E5%87%BD%E6%95%B0%E4%B8%8D%E8%83%BD%E6%98%AF%E4%BB%BB%E6%84%8F%E7%9A%84"><span class="section table-of-contents-text">为什么更新函数不能是任意的</span></a></li><li class="section table-of-contents-item section table-of-contents-level-2"><a class="section table-of-contents-link" href="#%E4%B8%BA%E4%BB%80%E4%B9%88-coupling-into-the-future-%E4%B8%8D%E8%A1%8C"><span class="section table-of-contents-text">为什么 Coupling into the
+future 不行</span></a></li><li class="section table-of-contents-item section table-of-contents-level-2"><a class="section table-of-contents-link" href="#%E4%B8%BA%E4%BB%80%E4%B9%88%E6%AF%8F%E6%AC%A1%E4%B8%8D%E8%83%BD%E9%87%8D%E6%96%B0%E7%94%9F%E6%88%90%E9%9A%8F%E6%9C%BA%E6%95%B0"><span class="section table-of-contents-text">为什么每次不能重新生成随机数</span></a></li></ol></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#monotone-coupling-from-the-past"><span class="section table-of-contents-text">Monotone coupling from the
+past</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE"><span class="section table-of-contents-text">参考文献</span></a></li></ol>
+</div>
 
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coxeter-element/index.html

@@ -320,7 +320,9 @@ <h1>Coxeter element</h1>
 
 
 
-
+                                    <div class="toc pink-link-context hide-on-med-and-down">
+    <ol class="section table-of-contents"><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#coxeter-%E5%85%83"><span class="section table-of-contents-text">Coxeter 元</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#coxeter-%E5%B9%B3%E9%9D%A2"><span class="section table-of-contents-text">Coxeter 平面</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E8%BF%9B%E4%B8%80%E6%AD%A5%E6%94%B9%E8%BF%9B"><span class="section table-of-contents-text">进一步改进</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#e_8-%E7%9A%84%E4%BE%8B%E5%AD%90"><span class="section table-of-contents-text">\(E_8\) 的例子</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#bibliography"><span class="section table-of-contents-text">References</span></a></li></ol>
+</div>
 
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e8-and-coxeter-plane/index.html

@@ -303,7 +303,9 @@ <h1>The E8 picture explained through code</h1>
 
 
 
-
+                                    <div class="toc pink-link-context hide-on-med-and-down">
+    <ol class="section table-of-contents"><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#the-structure-of-e_8"><span class="section table-of-contents-text">The Structure of \(E_8\)</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#coxeter-element"><span class="section table-of-contents-text">Coxeter Element</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#coxeter-plane"><span class="section table-of-contents-text">Coxeter Plane</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#further-improvement"><span class="section table-of-contents-text">Further Improvement</span></a></li></ol>
+</div>
 
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envelope-and-caustics/index.html

@@ -314,7 +314,9 @@ <h1>咖啡杯中的焦散线</h1>
 
 
 
-
+                                    <div class="toc pink-link-context hide-on-med-and-down">
+    <ol class="section table-of-contents"><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#pov-ray-%E5%85%89%E5%AD%A6%E5%AE%9E%E9%AA%8C"><span class="section table-of-contents-text">POV-Ray 光学实验</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E6%B1%82%E8%A7%A3%E5%8F%82%E6%95%B0%E6%9B%B2%E7%BA%BF%E7%9A%84%E7%84%A6%E6%95%A3"><span class="section table-of-contents-text">求解参数曲线的焦散</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E6%B1%82%E8%A7%A3%E5%A4%9A%E9%A1%B9%E5%BC%8F%E6%9B%B2%E7%BA%BF%E7%9A%84%E7%84%A6%E6%95%A3"><span class="section table-of-contents-text">求解多项式曲线的焦散</span></a></li><li class="section table-of-contents-item section table-of-contents-level-1"><a class="section table-of-contents-link" href="#%E6%B3%A8%E8%AE%B0"><span class="section table-of-contents-text">注记</span></a></li></ol>
+</div>
 
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gifmaze-cn/index.html

@@ -307,7 +307,9 @@ <h1>碉堡的小程序：用 Python 制作演示各种算法的 GIF 动画</h1>
 
 
 
-
+                                    <div class="toc pink-link-context hide-on-med-and-down">
+
+</div>
 
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