Latest post
The <input type="number"> is so evil. I thought that entering 1e309 will have its value return 1e309 and that converting it to a number will give me infinity. Nope, it will return an empty string, and converting it to a number gets me zero. Note that 1e309 IS A VALID FLOATING-POINT NUMBER according to the #HTML standard.
follow me on Mastodon
Articles
Algebraic structure of chemicals
Regarding balancing chemical equations, actually we are trying to find a non-trivial linear combination of some chemicals to get zero. The interesting thing is that the coefficients can only be integers (), which is not a field, so the algebraic structure of chemicals is not linear space. They actually live in a free -module. See how I formalize this idea in mathematical language.
- Categories: chemistry
- Tags: linear algebra, abstract algebra
The concentration change of gas in reversible reactions
A reversible elementary reaction takes place inside a closed, highly thermally conductive container of constant volume, whose reactants are all gases. Given the reaction equations and the reaction rate constants, a natural question to ask is how the concentration of each gas changes w.r.t. time. In this article, I will answer this question by proposing a general approach to solve it.
- Categories: chemistry
- Tags: calculus, ode, chemical reaction, long paper
Snippet: O, ’tis too true!
O, ’tis too true!
- Categories: literature
- Tags: snippet, chinese
The structure of a basic RM game
In this article, I present minimal examples of a RM game. They only illustrate the basic concepts of how a RM game is structured and what is the running logic of it.
- Categories: programming
- Tags: ruby, javascript, rgss
The frequency assignment of musical notes
This article explores the concept which I call the frequency assignment, which is a mapping from (the set of notes) to (the set of frequencies). Concepts such as octaves, intervals, and equal temperaments are introduced.
- Categories: music
- Tags: music theory, number sequence, long paper, abstract algebra
Normal vectors of a scalar field
This article gives the formula for the normal vectors of a surface defined by a scalar field on . The normal vector of the graph of the function at is . This also provides us a way to recover a scalar field from the normal vectors of its graph: normalizing the vectors so that the last component is , and then integrate the rest components.
- Categories: math
- Tags: calculus, vector analysis
It is Feb 29 today!
It is Feb 29 today. The date appears once for as long as 4 years!
- Categories: update
- Tags: fooling around
Monkey-patching graciously
Monkey-patching is a powerful tool in programming. In this article, I used techniques of Ruby metaprogramming to define a series of methods
def_after
,def_before
, etc. to help monkey-patching. They look graciously in that we can use it to shorten the codes for monkey-patching (avoiding aliasing and repeating codes).- Categories: programming
- Tags: ruby, meta programming, long paper
Amazing Siteleaf
I have been using Siteleaf to manage my blog. It is just convenient and amazing.
Hyperellipsoids in barycentric coordinates
In this article, I introduce the barycentric coordinates: it is an elegant way to represent geometric shapes related to a simplex. By using it, given a simplex, we can construct a hyperellipsoid with the properties: its surface passes every vertex of the simplex, and its tangent hyperplane at each vertex is parallel to the hyperplane containing all other vertices.
- Categories: math
- Tags: linear algebra, long paper
subscribe via RSS