Outlines computer system reliability, including series, parallel components, and N-modular redundancy.

## ALL POSTS

### System Reliability Model

### Equivalence of Rectangular and Trapezoidal Approximations

Discusses the equivalence and error estimation in integrating piecewise continuous functions using rectangular and trapezoidal approximations.

### 我没有离去

### Let's Implement a Video Server with node.js and Ffmpeg

Node.js utilizes an event-driven and non-blocking I/O model, which enables it to efficiently handle a large number of I/O requests and concurrent connections. This is crucial for a streaming media server. Meanwhile, ffmpeg provides powerful functionality for video processing. We can leverage Node.js's powerful extension capabilities to integrate ffmpeg and create a video streaming media server.

### 汉字的前端字体体积优化方案

对于欧洲等基于字母文字的地区，字体优化简单，大小通常不超过 1MB。但对于东亚国家，字体尺寸是一个头疼的问题，可能会达到数兆字节甚至更多。

### Coding and Error Checking of Binary Data

Concepts of Sign-Magnitude, One's Complement, Two's Complement, and Excess-n Notation, along with Parity Check and Hamming Code Error Detection Methods for Binary Data

### Data Table Relation's Normalization

Introduces functional dependencies, and the database paradigms 1NF, 2NF, 3NF, BCNF, and 4NF. and use examples to explain their concepts and connections.

### Taylor Formula, Taylor Theorem, Taylor Series, Taylor Expansion

This article mainly introduces the content and connection between the four concepts of Taylor's formula, Taylor's theorem, Taylor series and Taylor's expansion.

### Proof of Faulhaber's Formula

Faulhaber's Formula, which provides a method to compute the sum of the p-th powers of the first n positive integers.

### The Catalan Series

The article discusses Catalan numbers, a sequence used in combinatorial problems. It covers their recurrence relation, closed form, and applications in path counting. It provides insights into problem-solving using Catalan numbers.