When you are traveling in a place which is obviously different from your hometown, you may experience the traditional culture and enjoy a fabulous time there. After the long journey, you may become more energetic spiritually.
米兰大教堂
意大利·米兰·Duomo di Milano
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The note is mainly a summary of basic knowledge that the author learned in arithmetic geometry. One of the aims of this note is to provide a preliminary for Perfectoid geometry. Most contents are fundamental, but they are essential towards Perfectoid geometry. The ultimate goal of this note is to help readers to understand Peter Scholze's classic paper , where the notion of perfectoid spaces first appeared.
在网页上,有很多种方法可以渲染漂亮的数学公式。但是这些方法基本上不能直接应用于Vue.js或者Nuxt.js。在本文中,我们将分别说明如何在Vue.js或者Nuxt.js中使用katex和mathjax渲染数学公式。Katex想要自动渲染所有页面上的数学公式,你需要使用CDN来加载katex:<!-- index.html --> <!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8"> <link rel="icon" href="/poem-studio-favicon-black.svg"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> <link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.16.10/dist/ka ...
网站开发,需要前端与后端的开发。前端指用户端、浏览器端,是用户能看得到的部分。后端指服务器端,是用户看不到的部分。前端开发,需要用到CSS3和HTML5以及JavaScript。后端开发能用的编程语言则很多了,主流的有python、java等,只要我们电脑能够使用的编程语言,服务端都能使用。目前流行前后端分离,后端只需要提供好接口就行了,前端直接使用后端的接口。前端三大框架:Vue、react、AngularVue是目前中国使用比较多的框架,因为创造这个框架的是中国人——前谷歌员工Even You。React框架则是Meta公司(原Facebook公司)创造的框架,Angular是谷歌建立的框架。从最近GitHub的数据上看,Vue是目前全世界下载量最多的框架,第二大的为React,第三为Angular。前端框架建立的目的,其实是为了方便开发,提高开发效率,降低开发难度。本质上,最后到浏览器那里,都是转换为CSS3、HTML5、JavaScript的语言。前端的开发,代码实现前,还需要设计UI界面,提高用户体验。因此,网站前后端开发分别对应三个职位——前端工程师、后端工程师、UI设计师 ...
In this section, we focus on Section 2 in [Sch], following [Hu], [Hu1], and [Hu2]. Moreover, we need to compare Huber's adic spaces with Berkovich's analytic spaces and Tate's rigid analytic spaces. Hence, we will briefly introduce the notion of Berkovich's analytic spaces in §1.3 and the notion of rigid analytic varieties in §1.4.§1. Adic SpacesDefinition 1.1. A morphism $f:X\rightarrow Y$ of adic spaces is adic if, for every $x\in X$, there exist open affinoid subspaces $U,V$ of $X,Y$ wi ...
In How to render math in Vue or Nuxt?, we explain the way to use Mathjax to render beautiful math formula in Nuxt.js. However, using CDN to load Mathjax is easy, but it degrades the performance of our pages. In other words, Mathjax may load slow if it is loaded by CDN.One of the solutions is to load Mathjax locally. You can use npm to install Mathjax to your project. npm install mathjax@4.0.0-beta.6However, it is difficult to integrate with Mathjax in Nuxt. Not only because there is little infor ...
你也想像其他网站那样,可以高亮用户写的代码块吗?有两个Javascript库可以帮助你实现这一点,他们分别是Prism.js和highlight.js。在本教程中,我们将使用PrismJS来讲解如何实现代码块高亮。首先,使用npm安装PrismJS:npm install prismjs然后前往composables文件夹,并在里面新建文件prism.js,其内容如下:import Prism from 'prismjs' import 'prismjs/themes/prism-tomorrow.css' // You can choose other themes export default Prism就这样,PrismJS就安装并配置好了,你只需要每次需要高亮代码的时候调用highlightAll()函数就可以了。具体例子如下:<script lang="ts" setup> onMounted(()=>{ Prism.highlightAll() }) $fetch('https://www.example.com') .then((res)=& ...
It is known that the homomorphisms between group preserve products. However, the anti-homomorphisms between groups invert products in contrast to the homomorphisms. In this article, we briefly introduce the notion of anti-homomorphisms of groups, and we will study anti-homomorphisms of rings in the next article.1. Anti-homomorphisms of groups.In this section, all groups are not necessarily abelian. For simplicity, we will simply call anti-homomorphism instead of anti-homomorphism of groups.Defin ...
1. nginx服务器Nginx与Apache为两大主流web服务器。而我的轻量级云服务器使用了nginx。因为nginx相比与apache更轻量,性能更好,不怎么占内存,适合中小型服务器。同时Nginx善于应对高并发场景,在多用户同时点击的情况下,服务器能负荷得住。又由于nginx的负载均衡,让多个用户打开网站没那么卡。nginx官网安装教程Installing NGINX Open Source | NGINX DocumentationDebian12安装nginx:sudo apt-get update sudo apt-get install nginx最后输入sudo nginx -v验证安装。2. Nginx服务器反向代理客户端对代理是无感知的,只需将请求发送到反向代理服务器,由反向代理服务器去选择目标服务器获取数据后,再返回给客户端,此时反向代理服务器和目标服务器对外就是一个服务器,暴露的是代理服务器地址,隐藏了真实服务器IP地址
1. Introduction代数几何是数学的核心领域,也是如今国际数学界的主流。代数几何与许多数学分支都存在广泛的联系,比如数论、微分几何、代数拓扑、复几何、表示论、同调代数、交换代数、偏微分方程等等,这些分支的发展同时也对代数几何起到促进作用。数学史上的许多重大的事件,比如,费马大定理、莫德尔猜想、韦伊猜想的证明都跟代数几何有关。同时,代数几何存在广泛的应用,比如密码学、弦理论、大数据、统计学习理论等等。代数几何之下有众多分支,比如复代数几何,热带几何,算术几何,远阿贝尔几何,$p$进霍奇理论(complex algebraic geometry, tropical geometry, arithmetic geometry, anabelian geometry, p-adic hodge theory),每个分支代表代数几何研究的一个大方向,而在每个大方向下,又有各种以不同的问题为导向的子方向。在这篇文章中,我们将会对代数几何,包括它的分支算术代数几何,做一个简短的介绍。2. An Introduction to Arithmetic Geometry算术几何是算术代数几何的简 ...
IntroductionThe rapid evolution of big data technologies and artificial intelligence has radically transformed many aspects of society, businesses, people and the environment, enabling individuals to manage, analyze and gain insights from large volumes of data (Dwivedi et al., 2023). The AI Spark Big Model is one effective technology that has played a critical role in addressing significant data challenges and sophisticated ML operations. For example, the adoption of Apache Spark in various indu ...
我使用的版本是Django 4.2,有一个模型里定义了ImageField,以下面这个为例:class Example(models.Model) image = models.ImageField( blank=True, upload_to=my_image_path, )当我上传图片的时候,django返回了这样一个错误:Ensure this filename has at most 100 characters (it has 107)。在django文档中,我们可以发现:FileField 实例在数据库中被创建为 varchar 列,默认最大长度为 100 个字符。与其他字段一样,你可以使用 max_length 参数改变最大长度。并且要知道ImageField是FileField的子类:继承 FileField 的所有属性和方法,但也验证上传的对象是有效的图像。ImageField 实例在数据库中创建为 varchar 列,默认最大长度为 100 个字符。与其他字段一样,你可以使用 max_length 参数改变 ...
问题描述:正常使用pip install xxx安装会弹出错误,导致下载失败。必须增加trust host字段,才能下载成功:pip --trusted-host pypi.python.org install在cmd运行python -c "import ssl; print(ssl.get_default_verify_paths())"在默认路径里没有找到ca证书,而在Lib\site-packages\certifi文件夹中,却发现了cacert.pem文件。故而认为原因是ca证书丢失或者寻找ca证书路径出错,因此尝试修改pip的默认ca证书路径。pip.ini文件中有大量的pip配置信息,因此需要先找到该文件。在cmd通过pip -v config list发现,在多个路径中,都没有找到pip.ini文件。且了解到,pip会有一个默认的pip.conf文件(其实就是pip.ini),因此断定默认pip.ini配置文件丢失。解决办法:在python根目录中,新建pip.ini,在里面写上[global] index-url = https://mirrors.aliyun.co ...