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A Mathematical Exploration of Norton’s Dome and Determinism in Classical Mechanics
Chinese, Classical Mechanics, Differential Equation, Introduction, Latex, Mathematics, Paradox, PhysicsIn classical mechanics, the principle of determinism states that the motion of a system is fully predictable given its initial conditions. However, does this principle always hold?
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Why Use L2 Norm Instead of L1 Norm in Loss Functions?
Algebra, Computer Science, Deep Learning, Latex, Likelihood, Machine Learning, Mathematics, Optimization, Probability, Probability Theory, Regression Analysis, StatisticsHave you guys noticed that, in machine learning, MSE is often the preferred choice…
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Intro to Git, Github and VSCode
Hi, this is Louis Liu. In this tutorial, I will guide you through some basic operations in Git, GitHub, and VSCode.
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How is Diandian (点点) (A cat my family rescued 2 years ago) now?
On February 7, 2022, my family found this poor little kitten in a distressing condition during a heavy rainstorm…
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Cracking the Logic Gates Construction Using the Knowledge from Mathematical Logic
Coding, Computer Science, Introduction, Latex, Logic, Logic Gate, Mathematical Logic, Mathematics, Programming, PythonWhat if I tell you that every complex truth function can be meticulously constructed using just 1 type of logic gates!!??
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Using Raspberry Pi to Build a US VPN Server for My Family in China
Cloudflare, Coding, Computer Science, DDNS, DNS, Github, Great Firewall, Linux, Network, Programming, Raspberry Pi, Server, Software, SSH, Video, VPNAround December 2023, all ChatGPT access node IPs used by our ClashX VPN were blocked by OpenAI. This situation led me to seek alternative methods to restore unrestricted internet access for my family. In this blog post, I’m going to share my experience and detailed process of setting up a Raspberry Pi as a VPN server for my family in China.
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I Switched From Github Pages to WordPress…
Transitioning from one platform to another for your digital presence, especially a blog, is a decision that’s never made lightly. My journey from GitHub Pages to WordPress was guided by a series of revelations and requirements that I believe many content creators might resonate with. In this post, I’ll share why I made the switch, focusing on key aspects such as efficiency, user-friendliness, community support, and interactivity with the audience.
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Competitive Mathematics — Factorization
This article is based extensively on the content of 《数学奥林匹克小丛书》, supplemented by my own insights and reorganized to cover additional topics not addressed in the original text. Therefore, it should be regarded as a newly compiled set of notes rather than a completely original work.
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A guide for preparing for the William Lowell Putnam Mathematical Competition
Are you planning to participate in the Putnam Maths Competition in the future? Come and check it out!
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Why mathematicians choose “A linear subspace must have the additive identity” as one of the condition of the linear subspace but not “A linear subspace must be nonempty” ?
Actually they can do that, but why they don’t? Because from the perspective of modern algebra…
