I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips.

Abstract: Catalytic cracking unit is a highly dynamic industrial process involving complex chemical reactions, catalyst circulation, temperature and pressure changes, and control system regulation. To ...

Covid-19 broke the charts. Decades from now, the pandemic will be visible in the historical data of nearly anything measurable today: an unmistakable spike, dip or jolt that officially began for ...

While retrieval-augmented generation is effective for simpler queries, advanced reasoning questions require deeper connections between information that exist across documents. They require a knowledge ...

The original version of this story appeared in Quanta Magazine. Much of mathematics is driven by intuition, by a deep-rooted sense of what should be true. But sometimes instinct can lead a ...

School of Mathematics and Statistics, Shandong Normal University, Jinan, China. In the next section, a statement of the problem is introduced. Afterwards, the proof of the main results is established.

Much of mathematics is driven by intuition, by a deep-rooted sense of what should be true. But sometimes instinct can lead a mathematician astray. Early evidence might not represent the bigger picture ...

I know that for chordal graphs, Sage has a function to recognize a perfect elimination ordering. This problem is somewhat similar, identifying chordal bipartite graphs. The following theorem is ...