# Gallery — Math

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LEYES DE NEWTON
Preinforme guia de laboratorio L4.
Yeimi Johana Blanco Santos
Newton's Method Cycles
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.
Edgara Vanoye & MacKay Martin
E6 Übungsblatt 11
Experimentalphysik 6: Festkörperphysik
Tarea 5
larry061198
CS 155 HW 9
CS 155 HW 9
Gabe
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
The Chaos of Damped-driven Pendulum System
We will study some aspects of the damped driven pendulum. We will see that the trajectory of damped driven pendulum is unpredictable under certain ranges of parameters. Under some conditions, the trajectory behaves like random. A perturbation of initial condition will lead to different result. Several mathematical tools will be introduced in this study.
zev
The Parallelization and Optimization of the N-Body Problem using OpenMP and Cuda
This research paper aims at exploiting efficient ways of implementing the N-Body problem. The N-Body problem, in the field of physics, predicts the movements and planets and their gravitational interactions. In this paper, the efficient execution of heavy computational work through usage of different cores in CPU and GPU is looked into; achieved by integrating the OpenMP parallelization API and the Nvidia CUDA into the code. The paper also aims at performance analysis of various algorithms used to solve the same problem. This research not only aids as an alternative to complex simulations but also for bigger data that requires work distribution and computationally expensive procedures.
Tushaar Gangarapu