Abstract: In this paper, the Katz centrality and Neumann series are used to identify the station importance of Taipei metro system. First, node importance of complex network is computed by the Katz ...

New quantum mechanics research is introducing an advanced Pi formula, optimizing complex computations and reshaping ...

Physics and Python stuff. Most of the videos here are either adapted from class lectures or solving physics problems. I really like to use numerical calculations without all the fancy programming ...

Ready to unlock your full math potential? 🎓Follow for clear, fun, and easy-to-follow lessons that will boost your skills, ...

ChatGPT shocked researchers by solving Plato’s ancient puzzle in a new way, showing reasoning-like behavior when guided with ...

In 1971, German mathematicians Schönhage and Strassen predicted a faster algorithm for multiplying large numbers, but it ...

Abstract: Chebyshev interpolation polynomials exhibit the exponential approximation property to analytic functions on a cube. Based on the Chebyshev interpolation polynomial approximation, we propose ...

The graphs of \(y = 2x + 1\) and \(y = 2x - 2\) are shown below. The graph of \(y = 2x + 1\) crosses the \(y\)-axis at (0, 1). The graph of \(y = 2x - 2\) crosses the ...

Professor Aydin's "Problem of the Week" is a creative, challenging (and fun) way to solve math problems outside of class.

The Lights Out puzzle consists of an m×n grid of lights, each of which has two states: on and off. The goal of the puzzle is to turn all the lights off, with the caveat that whenever a light is ...

$$\Vert \nabla_r T(\textbf{x}_s, \textbf{x}_r) \Vert = \frac{1}{v(\textbf{x}_r)}$$ $$\Vert \nabla_s T(\textbf{x}_s, \textbf{x}_r) \Vert = \frac{1}{v(\textbf{x}_s ...