- May 9, 2023
Suppose there are n distinguishable boxes and k indistinguishable balls. Now, we randomly put the balls into the boxes. For each of the boxes, what is the probability that it contains m balls? This is a simple combanitorics problem that can be solved by the stars and bars method. It turns out that in the limit n,k→∞ with k/n fixed, the distribution tends to be a geometric distribution.
- May 7, 2023
Many languages support breaking out of nested loops, such as Perl, Java, JavaScript, C#, etc. Languages that have goto can also do this easily. However, in most other languages, it is not easy to break out of nested loops. I want to introduce a way to do this in Ruby.
- May 1, 2023
I set up a simple model to determine the production and consumption in free trade between nations.
- May 1, 2023
For sake of rigor and generalizability, I feel it necessary to try to have a mathematical formulation for statistical ensembles. I chose measure spaces as the underlying mathematical structure of thermal systems and tried to justify the method of statistical ensembles by deducing them from some axioms.