Articles — Math

The Schroeder-Bernstein theorem

A simple derivation of the relationship between dot products and cosines. I wrote this reacquaint myself with LaTeX.

The lecture notes are based on the number theory topics course on 3 Feb, 2016.

Based on the paper Sometimes Newton's Method Cycles, we first asked ourselves if there were any Newtonian Method Cycle functions which have non-trivial guesses. We encountered a way to create functions that cycle between a set number of points with any initial, non-trivial guesses when Newton's Method is applied. We exercised these possibilities through the methods of 2-cycles, 3-cycles and 4-cycles. We then generalized these cycles into k-cycles. After generalizing Newton's Method, we found the conditions that skew the cycles into a spiral pattern which will either converge, diverge or become a near-cycle. Once we obtained all this information, we explored additional questions that rose up from our initial exploration of Newton's Method.

A Statistics paper on Correlation and Linear Relationships.

A very quick and easy to understand introduction to Gram-Schmidt Orthogonalization (Orthonormalization) and how to obtain QR decomposition of a matrix using it.

Estudo de um sistema dinâmico.

Merge Sort vs. Bubble Sort

The objective is to study the effect of different experimental parameters on the reconstruction of the density of states (DoS) and to verify the viability of the 1D/2D simulation model developed at GeePs. Beside the calculation of the DoS through the modulated photo-current method (MPC), the ambipolar minority carrier diffusion length is measured through steady state photocarrier grating (SSPG) and the majority carrier lifetime / mobility product is measured through steady state photo-conductivity (SSPC). The measurements were observed to be in agreement with the theoretical simulations, but further experiments are needed to accurately conclude the need of a 2D simulation for the MPC experiment.