Mathematics

The Sharkovsky ordering of the natural numbers is 3 ≻ 5 ≻ 7 ≻ ... ≻ 2·3 ≻ 2·5 ≻ 2·7 ≻ ...... ≻ 22·3 ≻ 22·5 ≻ 22·7 ≻ ... ≻ 23 ≻ 22 ≻ 2 ≻ 1. Sharkovsky proved that if m comes before n in this ordering and a continuous map f: R → R has a ... Read More

Motivated by applications as a kernel of nonlinear regression algorithms, the row-wise weighted total least squares regression problem is examined to find a consistent and accurate estimator. Specifically, the proposed estimator has a time complexity linear in the number of observations and a space complexity constant in the same value, as the number of observations can be quite large in ... Read More

For public sector jobs such as university professors, there are two types of available retirement plans for their retirement package: The Defined Contribution (DC) and Defined Benefit (DB) plan. We will discuss the key differences between these plans, including their structure, benefits, and risks. One critical factor to compare these two plans is the Net Present Value (NPV). NPV is ... Read More

In 1926, Cartan introduced the concept of real symmetric spaces as a class of homogeneous Riemannian manifolds, where a symmetric space is defined as the homogeneous space $G/H$ with $G$ a reductive group and $H=G^{\theta}=\{g\in G|\theta(g)=g\}$, the fixed-point group of an $n$-automorphism. Of special interest are automorphism of order 2, also called involutions. In this project we focused on classifying ... Read More