- Apr 13, 2020
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 (Z), which is not a field, so the algebraic structure of chemicals is not linear space. They actually live in a free Z-module. See how I formalize this idea in mathematical language.
/chemistry
#linear algebra
#abstract algebra
- Apr 12, 2020
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.
/chemistry
#calculus
#ode
#chemical reaction
#long paper
- Apr 11, 2020
O, ’tis too true!
/literature
#snippet
#chinese
- Apr 8, 2020
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.
/programming
#ruby
#javascript
#rgss
- Mar 27, 2020
This article explores the concept which I call the frequency assignment, which is a mapping from N (the set of notes) to R+ (the set of frequencies). Concepts such as octaves, intervals, and equal temperaments are introduced.
/music
#music theory
#number sequence
#long paper
#abstract algebra
- Mar 3, 2020
This article gives the formula for the normal vectors of a surface defined by a scalar field on Rn. The normal vector of the graph of the function y=f(x) at (x0,f(x0)) is (∇f(x0),−1). 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 −1, and then integrate the rest components.
/math
#calculus
#vector analysis
- Feb 29, 2020
It is Feb 29 today. The date appears once for as long as 4 years!
/update
#fooling around
- Feb 9, 2020
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).
/programming
#ruby
#meta programming
#long paper
- Jan 26, 2020
I have been using Siteleaf to manage my blog. It is just convenient and amazing.
/update
#update
#jekyll
- Jan 25, 2020
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.
/math
#linear algebra
#long paper