Zijie Wen

Zijie Wen

A curious apprentice

Blog posts

2025

1 minute read

Published:

2023

Dynkin_graph

less than 1 minute read

Published:

Def. Cartan matrix \(A_{ij} = 2 \frac{<\alpha _i, \alpha_j>}{<\alpha _i, \alpha_i>},i,j \in 1, \dots, l\)

群表示论 复习速览

3 minute read

Published:

group representation

Def. representation A representation of $G$ over $F$ is the homomorphism $\rho$ \(\rho : G \to GL(n,F)\) the degree of $\rho$ is the integer $n$

killing_form

1 minute read

Published:

$g$ a f.d. Lie algebra over $\mathbb C$ The adjoint representation \(\begin{eqnarray} g &\to& \mathrm{End(g)}\\ x& \mapsto& \mathrm{ad}_x : y \mapsto [x,y] \end{eqnarray}\)

动力系统 Sarkovski定理

1 minute read

Published:

title: ‘Sarkovski定理-三即混沌’ date: 2023-10-11 tags:

  • learning notes

  • dynamic system

topological entropy

3 minute read

Published:

（概要，待补充）

the growth of orbit

黎曼几何：流形和流形上的故事

10 minute read

Published:

补充一些基础的微分流形知识

Regular surface

regular surface on $\mathbb R^n$

在 $\mathbb R^n$ 有一些最直接的曲面，

Def. regular surface A subset $M \subset \mathbb R ^n$ is called a regular surface if for each point $p \in M$, there exists a neighborhood $V$ of $p$ in $\mathbb R^n$ and a map $x:U\to R^n$ of an open set $U subset R^2$ onto $V \cap U$ such that 1. $\mathbf x$ is differentiable, 2. $\mathbf x:U \to V \cap M$ is a homeomorphism, and 3. $(d \mathbf x)_q : \mathbb R^k \to \mathbb R^n$ is injective for all $q \in U$.

可解李代数表示的分解

5 minute read

Published:

本篇笔记中将会展示有限维复数空间可解李代数的表示的分解性

引言

为什么我们需要一个 bracket structure ？ 当我们试图去理解非交换性给我带来的变化的时候，我们会很自然的去考虑$XY-YX$.

实变函数：外测度

6 minute read

Published:

前言

1 傅里叶级数

\(f \sim \sum a_n e^{inx}\) \(a_n = \frac{1}{2\pi}\int_{-\pi}^{\pi} f(x)e^{-inx}dx\) 由此我们可以得到Parseval恒等式： \(\sum_{n=-\infty}^{+\infty} |a_n|^2 = \frac{1}{2\pi}\int_{-\pi}^\pi |f(x)|^2 dx\) 在常庚哲,史济怀的《数学分析》中也有相关论述： 但是这样得到的度量，并非完备

2022

‘高代上的一些不等式’

less than 1 minute read

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稍微简单的记录了一下高等代数课程中遇到的不等式，方便自己以后进行查阅

分离公理

less than 1 minute read

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分离公理整理笔记

欧拉计划25-40

10 minute read

Published:

所需包

import math
import time
import numpy as np

2021

数分1知识梳理

3 minute read

Published:

数学分析的复习笔记，可以当成数分的基础知识使用。

欧拉计划7-15

3 minute read

Published:

Problem 7 10001st prime

By listing the first six prime numbers:2,3,5,7,11, and 13, we can see that the 6th prime is 13.

What is the 10001st prime number?