User contributions for Etone

26 March 2025

• 09:5609:56, 26 March 2025 diff hist +17,231 N 组合数学 (Fall 2025)/Cayley's formula Created page with "== Cayley's Formula == We now present a theorem of the number of labeled trees on a fixed number of vertices. It is due to [http://en.wikipedia.org/wiki/Arthur_Cayley Cayley] in 1889. The theorem is often referred by the name [http://en.wikipedia.org/wiki/Cayley's_formula Cayley's formula]. {{Theorem|Cayley's formula for trees| : There are <math>n^{n-2}</math> different trees on <math>n</math> distinct vertices. }} The theorem has several proofs, including the bijectio..." current
• 09:5609:56, 26 March 2025 diff hist +141 组合数学 (Spring 2025) →Lecture Notes
• 09:5509:55, 26 March 2025 diff hist +189 概率论与数理统计 (Spring 2025) →Lectures

21 March 2025

• 10:0310:03, 21 March 2025 diff hist 0 概率论与数理统计 (Spring 2025)/Average-case analysis of QuickSort →快速排序算法的平均复杂度分析 I（基于全期望法则） current
• 10:0310:03, 21 March 2025 diff hist +11,838 N 概率论与数理统计 (Spring 2025)/Average-case analysis of QuickSort Created page with "[http://en.wikipedia.org/wiki/Quicksort '''快速排序'''（'''Quicksort'''）]是由Tony Hoare发现的排序算法。该算法的伪代码描述如下（为方便起见，假设数组元素互不相同——更一般情况的分析易推广得到）： '''''QSort'''''(A): 输入A[1...n]是存有n个不同数字的数组 if n>1 then '''pivot''' = A[1]; 将A中<pivot的元素存于数组L，将A中>pivot的元素存于数组R; \\保持内部元素之..."
• 10:0210:02, 21 March 2025 diff hist +421 概率论与数理统计 (Spring 2025) →Lectures
• 09:5809:58, 21 March 2025 diff hist +19,696 N 组合数学 (Fall 2025)/Pólya's theory of counting Created page with "== Groups == A group <math>(G,\cdot)</math> is set <math>G</math> along with a binary operator <math>\cdot</math> which satisfies the following axioms: * ''closure'': <math>\forall g,h\in G, g\cdot h \in G</math>; * ''associativity'': <math>\forall f,g,h\in G, f\cdot(g\cdot h)=(f\cdot g)\cdot h</math>; * ''identity'': there exists a special element <math>e\in G</math>, called the '''identity''', such that <math>e\cdot g=g</math> for any <math>g\in G</math>; * ''inverse''..." current

16 March 2025

• 09:3109:31, 16 March 2025 diff hist +165 组合数学 (Spring 2025) →Lecture Notes

12 March 2025

• 16:0716:07, 12 March 2025 diff hist +33,970 N 组合数学 (Fall 2025)/Sieve methods Created page with "== Principle of Inclusion-Exclusion == Let <math>A</math> and <math>B</math> be two finite sets. The cardinality of their union is :<math>|A\cup B|=|A|+|B|-{\color{Blue}|A\cap B|}</math>. For three sets <math>A</math>, <math>B</math>, and <math>C</math>, the cardinality of the union of these three sets is computed as :<math>|A\cup B\cup C|=|A|+|B|+|C|-{\color{Blue}|A\cap B|}-{\color{Blue}|A\cap C|}-{\color{Blue}|B\cap C|}+{\color{Red}|A\cap B\cap C|}</math>. This is illu..." current
• 16:0716:07, 12 March 2025 diff hist +125 组合数学 (Spring 2025) →Lecture Notes

5 March 2025

• 05:4505:45, 5 March 2025 diff hist +179 概率论与数理统计 (Spring 2025) →Lectures

3 March 2025

• 07:3607:36, 3 March 2025 diff hist +72 组合数学 (Spring 2025) →Lecture Notes
• 07:3107:31, 3 March 2025 diff hist +32 概率论与数理统计 (Spring 2025)/Entropy and volume of Hamming balls No edit summary current
• 07:3007:30, 3 March 2025 diff hist +217 概率论与数理统计 (Spring 2025)/Entropy and volume of Hamming balls No edit summary
• 07:2707:27, 3 March 2025 diff hist +2,803 N 概率论与数理统计 (Spring 2025)/Entropy and volume of Hamming balls Created page with "在求解抛掷公平硬币（fair coin）的尾概率时，我们经常会需要分析如下二项式系数求和： :<math>\sum_{k=0}^r{n\choose k}</math>，对于某个<math>1\le r\le n</math> 这其实等价与求一个 <math>n</math> 维汉明空间中半径为 <math>r</math> 的球的体积。 :{|border="2" width="100%" cellspacing="4" cellpadding="3" rules="all" style="margin:1em 1em 1em 0; border:solid 1px #AAAAAA; border-collapse:collapse;empty-cells:show;" | :'..."
• 07:2607:26, 3 March 2025 diff hist +118 概率论与数理统计 (Spring 2025) →Lectures

25 February 2025

• 12:0912:09, 25 February 2025 diff hist +25,549 N 组合数学 (Fall 2025)/Generating functions Created page with "== Generating Functions == In Stanley's magnificent book ''Enumerative Combinatorics'', he comments the generating function as "the most useful but most difficult to understand method (for counting)". The solution to a counting problem is usually represented as some <math>a_n</math> depending a parameter <math>n</math>. Sometimes this <math>a_n</math> is called a ''counting function'' as it is a function of the parameter <math>n</math>. <math>a_n</math> can also be tre..." current
• 12:0912:09, 25 February 2025 diff hist +88 组合数学 (Spring 2025) →Lecture Notes

19 February 2025

• 08:5808:58, 19 February 2025 diff hist +69 组合数学 (Spring 2025) →Lecture Notes
• 08:5408:54, 19 February 2025 diff hist +77 Main Page →Home Pages for Courses and Seminars
• 08:5108:51, 19 February 2025 diff hist +125 概率论与数理统计 (Spring 2025) →Lectures

18 February 2025

• 08:5008:50, 18 February 2025 diff hist +75 Main Page →Home Pages for Courses and Seminars

16 February 2025

• 12:2012:20, 16 February 2025 diff hist 0 概率论与数理统计 (Spring 2025) →Lectures
• 12:1512:15, 16 February 2025 diff hist −75 Main Page →Home Pages for Courses and Seminars

20 December 2024

• 08:1708:17, 20 December 2024 diff hist 0 高级算法 (Fall 2024) →Lecture Notes
• 08:1608:16, 20 December 2024 diff hist +301 高级算法 (Fall 2024) →Lecture Notes

9 December 2024

• 01:4801:48, 9 December 2024 diff hist +2,459 N Assignment 4, Fall 2024 Created page with "在第四章中，我们从准地转近似下的纬向平均风场、温度场的趋势方程出发，定义了E-P通量。但是该定义下的E-P通量并没有考虑到大气湿过程的影响。如果从第三章介绍的水汽方程出发，我们可以按照以下步骤定义出一个包含大气大尺度运动中湿过程作用的广义的E-P通量。 1）在准地转近似下，如果我们按照对热力学方程的简化方法，将比湿（specific humidity..." current
• 01:4801:48, 9 December 2024 diff hist +54 General Circulation(Fall 2024) →Assignments current

10 November 2024

• 14:3814:38, 10 November 2024 diff hist +1,093 N Assignment 3, Fall 2024 Created page with "Held-Hou(1980) 讨论了当外部强迫的经向分布呈二次勒让德多项式，即<math>\dfrac{\Theta_E(\phi,z)}{\Theta_o}=1-\dfrac{2}{3}\Delta_H P_2(\sin \phi)+\Delta_v(\dfrac{z}{H}-\dfrac{1}{2})</math>的情况下，哈德莱环流内的风场、温度场、环流的空间范围等将怎样随纬度和外力强迫的强度而变化。 如果将外力强迫的空间分布改为<math>\dfrac{\Theta_E(\phi,z)}{\Theta_o}=1-\Delta_H(\sin^3 \phi - \dfrac{1}{4})+\Delta_v..." current
• 14:3714:37, 10 November 2024 diff hist +59 General Circulation(Fall 2024) →Assignments

21 October 2024

• 23:5923:59, 21 October 2024 diff hist +1 Namelist Assignment 1 2024 No edit summary current
• 23:5923:59, 21 October 2024 diff hist +1 Namelist Assignment 1 2024 No edit summary
• 23:5923:59, 21 October 2024 diff hist +27 Namelist Assignment 1 2024 No edit summary
• 23:5823:58, 21 October 2024 diff hist +690 N Namelist Assignment 1 2024 Created page with "姓名 学号 刘屹恒 211830104 袁世伟 211830113 刘倚帆 211830136 孙哲至 211840029 胡冰雁 211840036 罗常 211840226 陈晨 211840233 王道熙 211840324 鲍饴欣 502024280001 曹士豪 502024280003 冯亮 502024280007 顾也楠 502024280013 何鑫 502024280015 郎乐怡 502024280018 李子琦 502024280021 刘子辰 502024280024 潘玉洁 502024280028 宋辰 502024280030 唐永平 502024280032 王俊昌 502024280035..."
• 23:5523:55, 21 October 2024 diff hist +56 General Circulation(Fall 2024) →Assignments
• 01:1201:12, 21 October 2024 diff hist −2 Assignment 2, Fall 2024 No edit summary current
• 01:1101:11, 21 October 2024 diff hist +2 Assignment 2, Fall 2024 No edit summary
• 01:1001:10, 21 October 2024 diff hist +2,706 N Assignment 2, Fall 2024 Created page with "<font color="red" size="2">请在题目一和题目二中任选一题作为本章的作业题目。另外的一题可作为选做题。</font> ==Question 1== 假设在大气层顶（TOA），在多年全年平均的情况下，入射的太阳辐射随纬度的分布满足 <math>\begin{align} Q&=Q_o \cdot s(x), \\ s(x)&=s_o \cdot P_o(x)+ s_2 \cdot P_2(x), \end{align}</math> 其中，<math>P_o(x)=1</math>, <math>P_2(x)=\frac{1}{2}(3x^2-1)</math>, <math>s_o=1</math>, <..."
• 01:0901:09, 21 October 2024 diff hist +81 General Circulation(Fall 2024) →Assignments

11 October 2024

• 12:3712:37, 11 October 2024 diff hist +82 数据科学基础 (Fall 2024) →Lectures

9 October 2024

• 14:4614:46, 9 October 2024 diff hist +2,514 数据科学基础 (Fall 2024) →Concepts

30 September 2024

• 06:3106:31, 30 September 2024 diff hist −9 数据科学基础 (Fall 2024)/Average-case analysis of QuickSort No edit summary current
• 06:3106:31, 30 September 2024 diff hist +11,838 N 数据科学基础 (Fall 2024)/Average-case analysis of QuickSort Created page with "[http://en.wikipedia.org/wiki/Quicksort '''快速排序'''（'''Quicksort'''）]是由Tony Hoare发现的排序算法。该算法的伪代码描述如下（为方便起见，假设数组元素互不相同——更一般情况的分析易推广得到）： '''''QSort'''''(A): 输入A[1...n]是存有n个不同数字的数组 if n>1 then '''pivot''' = A[1]; 将A中<pivot的元素存于数组L，将A中>pivot的元素存于数组R; \\保持内部元素之..."
• 06:3006:30, 30 September 2024 diff hist +118 数据科学基础 (Fall 2024) →Lectures

29 September 2024

• 16:3216:32, 29 September 2024 diff hist +6 Assignment 1, Fall 2024 →Bonus Question current
• 16:2516:25, 29 September 2024 diff hist 0 Main Page No edit summary
• 16:2516:25, 29 September 2024 diff hist −103 Main Page No edit summary
• 16:2416:24, 29 September 2024 diff hist −2,322 Assignment 1, Fall 2024 No edit summary
• 16:2216:22, 29 September 2024 diff hist +2,498 Assignment 1, Fall 2024 →下载区
• 16:1916:19, 29 September 2024 diff hist +2,789 N Assignment 1, Fall 2024 Created page with "==Question #1== 请使用多年（>20年）的NCEP/NCAR月平均再分析资料，画出各季节（至少画出冬夏两季）纬向平均温度场、纬向平均纬向风场的高度－纬度剖面分布，并简述其分布特征和季节变化特征。 ==Question #2== 请使用多年（>20年）的NCEP/NCAR月平均再分析资料，画出各季节（至少画出冬夏两季）温度场、纬向风场在各高度（850、500、100 hPa， 对于温度场请再画..."