2023-05-20 收到小米平板，感觉很好

Recamán’s sequence Sound representation This is not a permutation of the integers: the first repeated term is {\displaystyle 42=a_{24}=a_{20}}. Another one is {\displaystyle 43=a_{18}=a_{26}}. Neil Sloane has conjectured that every number eventually appears,but it has not been proved. Even though 10＃230 terms have been calculated (in 2018), the number 852,655 has not appeared on the list.

https://github.com/mushan0x0/AI0x0.com

### 2023-07-18

Of course, P3 is not an induced subgraph of K3, though:

``````k3 = graphs.CompleteGraph(3); p3 = graphs.PathGraph(3)
k3.relabel(list('abc'))
k3.subgraph_search(p3, induced=True) is None
#True
``````

The genus of a graph is the minimal integer n such that the graph can be drawn without crossing itself on a sphere with n handles (i.e. an oriented surface of the genus n). Thus, a planar graph has genus 0, because it can be drawn on a sphere without self-crossing.

The smallest cubic graphs with crossing numbers 1–8 and 11 are known (sequence A110507 in the OEIS). The smallest 1-crossing cubic graph is the complete bipartite graph K3,3, with 6 vertices. The smallest 2-crossing cubic graph is the Petersen graph, with 10 vertices. The smallest 3-crossing cubic graph is the Heawood graph, with 14 vertices. The smallest 4-crossing cubic graph is the Möbius-Kantor graph, with 16 vertices. The smallest 5-crossing cubic graph is the Pappus graph, with 18 vertices. The smallest 6-crossing cubic graph is the Desargues graph, with 20 vertices. None of the four 7-crossing cubic graphs, with 22 vertices, are well known. The smallest 8-crossing cubic graphs include the Nauru graph and the McGee graph or (3,7)-cage graph, with 24 vertices. The smallest 11-crossing cubic graphs include the Coxeter graph with 28 vertices.

In 2009, Pegg and Exoo conjectured that the smallest cubic graph with crossing number 13 is the Tutte–Coxeter graph and the smallest cubic graph with crossing number 170 is the Tutte 12-cage.

There has been much research on Hamiltonicity of cubic graphs. In 1880, P.G. Tait conjectured that every cubic polyhedral graph has a Hamiltonian circuit. William Thomas Tutte provided a counter-example to Tait’s conjecture, the 46-vertex Tutte graph, in 1946. In 1971, Tutte conjectured that all bicubic graphs are Hamiltonian. However, Joseph Horton provided a counterexample on 96 vertices, the Horton graph. Later, Mark Ellingham constructed two more counterexamples: the Ellingham–Horton graphs. Barnette’s conjecture, a still-open combination of Tait’s and Tutte’s conjecture, states that every bicubic polyhedral graph is Hamiltonian. When a cubic graph is Hamiltonian, LCF notation allows it to be represented concisely.

### 2023-07-19

Gauss-Bonnet formula 高斯一波涅公式

### 2023-07-28

《诗》云：“靡不有初，鲜克有终”。故莫要一鼓作气再衰三竭，当有恒心毅力，须知飞瀑之下，必有深潭。一曝十寒，易生之物弗长；揠苗助长，良苗成槁也。

https://www.sciencemag.org/ https://www.nature.com/ https://www.sciencedirect.com/ https://onlinelibrary.wiley.com/ http://www.chinaxiv.org/home.htm 中科院科技论文预发布 ais.cn Tex live 2023

https://media.mit.edu/ mit媒体实验室

https://xueqiu.com/ 聪明的投资者都在这里

NFT的全称是Non-Fungible Tokens，中文常翻译为“不可同质化代币/不可替代代币”。简单地说，NFT是区块链的一个条目，而区块链是类似于比特币等加密货币的去中心化数字账本技术。 因为NFT不可替代的特性，这意味着它可以用来代表独一无二的东西，比如博物馆里的蒙娜丽莎原画，或者一块土地的所有权。

https://github.com/mouse484/jupyterlab-gitpod

Chat2DB 是一款有开源免费的多数据库客户端工具，支持windows、mac本地安装，也支持服务器端部署，web网页访问。阿里出品。和传统的数据库客户端软件Navicat、DBeaver 相比Chat2DB集成了AIGC的能力，能够将自然语言转换为SQL，也可以将SQL转换为自然语言

moviepy​ 是一个 Python 库，用于视频编辑和处理。

LiteDB是类似于MongoDB的轻量级嵌入式数据库。它完全使用C#开发。

win12网页版网址：http://www.does5.cn/
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