# Gallery — Math

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induced subgraphs
induced subgraphs question
Jimmy Cao
Gilbert and Porter Chapter 2.3: Rewrite of the proof of the Dual State Lemma
The proof of the Dual State Lemma in Chapter 2.3 of Gilbert and Porter's Knots and Surfaces has some problems with the exposition and a critical typo. This document reworks the proof to make it more correct and comprehensible. (This material starts on page 33.)
Sean Raleigh
Markowitz Portfolio Optimization Theory and Application
Suppose you have a data matrix comprised of several stock options over a set period of time. How do you choose the optimal collection of stocks such that you maximize your returns for a given level of risk? What Markowitz found was an elegant equation. What we realized rather quickly is there does not exist a closed form solution to this problem. Instead we use the tried and tested linear approximation. By transforming this problem into Matrix multiplication, we are able to quickly and (with desired accuracy) approximate the optimal solution, using only linear algebra.
ymxu
Resonant enhancement of sensitivity in a Magnetic Tunnel Junction based Spin Torque Oscillator
In this work, we investigate the STO as a detector with in-plane geometry using field modulation Spin Torque ferromagnetic resonance (FM-STFMR), during which microwave signal is injected into the device and output response is measured in terms of RMS voltage across lock-in amplifier. The microwave signal injected externally to STO, efficiently synchronizes signal at two times the frequency of free oscillation of the nanomagnet (f0). The synchronization efficiently enhances signal sensitivity at 2f0 which opens other potential for development of spintronic devices. The effect of synchronization in STO under applied input RF power follows a consistent decrease in sensitivity with increasing power. Better synchronization at 2f0 is noticed above threshold current and shows good agreement with the results of numerical simulations.
Dhananjay Tiwari
Solutions to in-class problems
Solutions to in-class problems
Kathryn Bragwell
The Proofs We Know and Love
A simple proofs essay using basic theorems while trying to get a grasp on LaTeX
Michael Asper
OBU Abstract Algebra first draft homework template
This is the template for homework first drafts for Dr. Sykes's Abstract Algebra class. It is adapted from Dana Ernst's original weekly homework template.
Jeffery Sykes
Norma euclidiana
Prova da expressão da norma utilizando o teorema de pitágoras.
Rui Carneiro
a Wilson-tétel megfordítása
A Wilson-tétel megfordításának bizonyítása.
Tamás Waldhauser