- 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 $n,k\to\infty$ 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.
- Apr 5, 2023
I summarized my methods for studying. This can be served as a guide for those who have started learning math and science.
- Mar 30, 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.
- Mar 25, 2023
There is a very neat relation between the core (the set of proposals that defeats every proposal) of a voting system and the Pareto sets of the voters. Suppose there is a voting system of quota $q$, then the core is the intersection of all such sets: the Pareto set of $q$ of the voters.
- Feb 6, 2023
Both the Gini coefficient and the variance are measures of statistical dispersion. We are then motivated to find the relationship between them. It turns out that there is a neat mathematical relationship between them.
- Feb 4, 2023
Personally, I have the demand of handwriting math/physics notes, but an annoying fact about this is that I usually cannot distinguish every letter that may be possibly used well enough. In this article, I will try to settle this problem.
- Feb 3, 2023
何为手纸本?