## Archive of posts in 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.

• ### 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.

何为手纸本?

• ### 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.

• ### 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).

• ### 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.

• ### 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.

• ### 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!