User contributions for Etone

A user with 1,149 edits. Account created on 30 August 2022.
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1 April 2025

  • 10:3310:33, 1 April 2025 diff hist +5,139 N 概率论与数理统计 (Spring 2025)/Weierstrass Approximation Theorem Created page with "[https://en.wikipedia.org/wiki/Stone%E2%80%93Weierstrass_theorem '''魏尔施特拉斯逼近定理''']('''Weierstrass approximation theorem''')陈述了这样一个事实:闭区间上的连续函数总可以用多项式一致逼近。 {{Theorem|魏尔施特拉斯逼近定理| :设 <math>f:[a,b]\to\mathbb{R}</math> 为定义在实数区间 <math>[a,b]</math> 上的连续实值函数。对每个 <math>\epsilon>0</math>,存在一个多项式 <math>p</math> 使得对..." current
  • 10:3310:33, 1 April 2025 diff hist +7,005 N 概率论与数理统计 (Spring 2025)/Threshold of k-clique in random graph Created page with "在 Erdős-Rényi 随机图模型 <math>G(n,p)</math> 中,一个随机无向图 <math>G</math> 以如下的方式生成:图 <math>G</math> 包含 <math>n</math> 个顶点,每一对顶点之间都独立同地以概率 <math>p</math> 连一条无向边。如此生成的随机图记为 <math>G\sim G(n,p)</math>。 固定整数 <math>k\ge 3</math>,考虑随机图 <math>G\sim G(n,p)</math> 包含 <math>K_k</math>(<math>k</math>-团,<math>k</math>-clique)子图..." current
  • 10:3210:32, 1 April 2025 diff hist +8,968 N 概率论与数理统计 (Spring 2025)/Two-point sampling Created page with "= 利用线性同余方程构造两两独立的随机变量 = 令<math>p</math>为一质数。考虑模<math>p</math>余数构成的集合<math>[p]=\{0,1,\ldots,p-1\}=\mathbb{Z}_p</math>。众所周知,当<math>p</math>为质数时,<math>\mathbb{Z}_p</math>为对模<math>p</math>加法和乘法运算闭合的'''有限域'''。 我们现在构造一系列值域为<math>[p]</math>的'''两两独立'''('''pairwise Independent''')且'''均匀分布'''('''uniforml..." current
  • 10:3210:32, 1 April 2025 diff hist +325 概率论与数理统计 (Spring 2025) Lectures current

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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

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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

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