Ulysses' trip

Latest post

Jan 8, 2026, 10:32:08

My bike just decided to fail me again today by completely cutting off the chain and having it drop to the ground while I was riding it. Fortunately, I have a second bike that I can use in this very occasion. To be honest, the maintenance work required for the bike is exceeding my expectations. I have to fix some parts of it every year.

Articles

Mar 25, 2023
The core of a voting system is the intersection of Pareto sets

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.
- Categories: economics
- Tags: voting system, preference relation, pareto efficiency
Feb 6, 2023
Relationship between the Gini coefficient and the variance

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.
- Categories: economics
- Tags: from zhihu, calculus, probability
Feb 4, 2023
Distinguishing all the letters in handwritten math/physics notes

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.
- Categories: misc
- Tags: from zhihu, font, tex, handwriting, long paper
Feb 3, 2023
手纸本

何为手纸本?
- Categories: literature
- Tags: from zhihu, literary composition, short story, chinese
Feb 3, 2023
Introducing bra–ket notation to math learners

Bra–ket notation is a good-looking notation! I am sad that it is not generally taught in math courses. Let me introduce it to you.
- Categories: math
- Tags: from zhihu, quantum mechanics
Feb 2, 2023
Even solutions to bound states in an odd number of $\delta$ potential wells

We try solving the even function solutions to the time-independent Schrödinger equation for the potential $V=-\alpha\sum_{j=-n}^n\delta(x-ja)$ such that $E<0$ (bound states).
- Categories: physics
- Tags: from zhihu, quantum mechanics
Feb 1, 2023
Defend our earth against aliens’ bullets!

The aliens intiated their attack to the earth! They shoot bullets with mass $m$ and speed $v$ from a far-awar planet. To defend, humans built a field $U=\alpha/r$ that can repel the bullets. What regions are safe? The answer turns out to be the interior of a circular paraboloid.
- Categories: physics
- Tags: calculus, classical mechanics, kepler problem, from zhihu
Jan 18, 2023
This is what will happen after you get a haircut

Denote the length distribution of one’s hair to be $f(l,t)$ , where $l$ is hair length, and $t$ is time. Considering that each hair may be lost naturally from time to time (there is a probability of $\lambda\,\mathrm dt$ for each hair to be lost within time range from $t$ to $t+\mathrm dt$ ) and then restart growing from zero length, how will the length distribution of hair evolve with time? It turns out that we may model it with a first-order PDE.
- Categories: math
- Tags: calculus, probability, pde
Jan 11, 2023
I want to invent a better way to read numbers

Reading numbers in English is a pain. I want to invent a better way to read numbers!
- Categories: language
- Tags: imagination
Dec 25, 2022
The longest all- $1$ substring of a random bit string

Given your probability of breaking the combo at each note, what is the probability distribution of your max combo in the rhythm game chart? I considered the problem seriously!
- Categories: math
- Tags: long paper, rhythm game, algorithm, probability, stochastic process