Hello World: A First Research Post

This is a sample research post demonstrating the full feature set.

Code blocks

Here is some Python with syntax highlighting:

import numpy as np

def fibonacci(n: int) -> list[int]:
    """Generate the first n Fibonacci numbers."""
    fib = [0, 1]
    for i in range(2, n):
        fib.append(fib[i-1] + fib[i-2])
    return fib[:n]

print(fibonacci(10))

And some TypeScript:

function greet(name: string): string {
  return `Hello, ${name}!`;
}

LaTeX Math

Inline math: The Euler identity $e^{i\pi} + 1 = 0$ is beautiful.

Display math — the Gaussian integral:

$$\int_{-\infty}^{\infty} e^{-x^2} \, dx = \sqrt{\pi}$$

A matrix:

$$\mathbf{A} = \begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix}$$

Tables

Method	Accuracy	Speed
Baseline	78.3%	120 ms
Our Method	91.2%	85 ms

中文数学公式测试

设 $f(x)$ 为连续函数，则有：

$$\lim_{n \to \infty} \sum_{i=1}^{n} f(x_i) \Delta x = \int_a^b f(x) \, dx$$

这是中文环境下的数学公式渲染测试。标点符号：「引号」、逗号，句号。

繁體中文測試

設 $g(x)$ 為可微函數，根據泰勒展開：

$$g(x) = \sum_{n=0}^{\infty} \frac{g^{(n)}(a)}{n!}(x-a)^n$$

以上是繁體中文與數學公式的混排測試。

Citations

This result builds on prior work ¹ and extends the framework proposed in ².

Footnotes

1. Smith, J. “On the Theory of Everything.” Journal of Examples, 2023. ↩

2. 张三，李四．「关于某问题的研究」．《示例期刊》，2024年． ↩