type
status
date
slug
summary
tags
category
icon
password
Last edited time
May 29, 2024 10:50 AM
这里我想尝试把LaTeX格式的文件导入到Notion，我采用的方法是给公式添加左右两边各添加两个美元符号，发现对于行内公式，需要重新输入最后一个美元符号才可以正常导入；对于行间公式，则需要手动将其转化为Notion的公式块。
示例
Q1. Consider the function defined by . Show that the sequence of iterates defined by
satisfies for . Show that every point on the unit circle is a limit point for .
Solution:
Given the function defined as , where for a vector , and a sequence of iterates , where
it can be noted that is
and since , it can be simplified to
To prove that the sequence is decreasing, the inequality must hold, which translates to:
As and are positive for all , taking square roots of both sides and rearranging yields:
This inequality is valid for all , thus confirming that the sequence is decreasing.
For the second part of the proof, to show that every point on the unit circle is a limit point for , a point on the unit circle can be parameterized as for some . Given the density of the set of angles in the interval , it follows that there exists a such that for every . As a result, for sufficiently large , the distance between and can be made arbitrarily small because tends to as tends to infinity. Therefore, every point on the unit circle is a limit point for the sequence .
项目
然后呢，我就找到一个项目，一个markdown to notion的项目，基于NodeJS。
使用该项目的简单步骤：
- 安装 Node.js：你可以从 Node.js 的官方网站下载和安装 Node.js。
- 创建一个新的 Node.js 项目：打开你的终端或命令行工具，然后转到你想创建项目的目录。然后输入以下命令来创建一个新的 Node.js 项目：
这将创建一个新的
package.json 文件。- 安装
@tryfabric/martian库：在你的项目目录下，输入以下命令来安装@tryfabric/martian：
这将下载
@tryfabric/martian 库并将其添加到你的 package.json 文件的依赖项中。- 创建一个新的 JavaScript 文件（例如
index.js）并打开它。将以下内容复制并粘贴到该文件中：
这段代码首先引入了
@tryfabric/martian 库中的 markdownToBlocks 和 markdownToRichText 函数，然后使用 markdownToRichText 函数将 Markdown 文本转换为富文本，并将结果输出到控制台。- 运行你的代码：回到你的终端或命令行工具，然后输入以下命令来运行你的代码：
- 作者:很久不是自己
- 链接:https://weibo.com/article/math-1
- 声明:本文采用 CC BY-NC-SA 4.0 许可协议，转载请注明出处。