Physics Elliptical Motion in Classical Mechanics
This article consider elliptical motion in three-dimensional space. Typically, it would be the motion of a planet orbiting a large star such as the Sun.
kaname.hirano
Physics 
Analysis Bessel Functions
Here is a brief summary of the properties of Bessel functions. They will be necessary when considering Kepler's equations (equations of elliptical motion) and the motion of electrons bound to atomic nuclei.
Physics Uniform Circular Motion in the Theory of Relativity
This article explain the theory of uniform circular motion in classical mechanics and extend it to the case of the theory of relativity.
Physics Free Fall in the Theory of Relativity
The falling motion caused only by gravity, ignoring the effects of air resistance and friction, is called free fall. Find the equation of motion for free fall in the theory of relativity.
Probability The Kelly Criterion in Gambling: Implementation
Some readers may want to try using the Kelly Criterion, so I have included the source code in VBA and python. This will probably be the last in "The Kelly Criterion in Gambling" series.
Probability The Probability Distribution of Composites of Normal Random Numbers
For two random numbers that follow a normal distribution, the probability distribution that their sum, product, ratio, etc. follow is shown.
Probability Extension of the Kelly Criterion in Gambling: Mean-Variance Utility Function
As another variant of the Kelly criterion, we define the utility function in terms of the mean and variance of the assets and consider the problem of maximizing it.
Analysis Complex Functions and Schrödinger Equation
A short story about the title of the author's book "Complex Functions and the Schrödinger Equation".
Economics Extension of the Kelly Criterion in Gambling: CRRA-type Utility Function
In this article, we extend the Kelly criterion to a more general utility function (CRRA-type utility function) and explain how to determine a betting portfolio based on a gambler's risk aversion.
Physics Harmonic Oscillator and Schrödinger Equation
This article explains what kind of probability distribution the Schrödinger equation for the harmonic oscillator expresses, and presents an interpretation of the solution.