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Recent undergraduate research projects

Recent undergraduate research projects. Zheng Chen Southern university at New Orleans March 2014 2014. Projects (2010-2014). Lights Out Puzzle using SAGE (done) Reliability and risk analysis (c ooperated with Dr. Omojola) (done) Fractals using Matlab (done)

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Recent undergraduate research projects

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  1. Recent undergraduate research projects Zheng Chen Southern university at New Orleans March 2014 2014

  2. Projects (2010-2014) Lights Out Puzzle using SAGE (done) Reliability and risk analysis (cooperated with Dr. Omojola) (done) Fractals using Matlab (done) A holomorphic function “Collatz” problem (in progress) Fingerprints (cooperated with Dr. Tan, in progress)

  3. Project 1: Lights Out Puzzle using SAGE • Using Sage to find the conditions of solvability of Lights Out Puzzle • This research was conducted with funding by a grant from the National Science Foundation (HRD-0928797). • Mr. Gino Loverde, a math major, presented at the Emerging Researchers National (ERN) Conference and won 1st place in Feb. 2012

  4. Introduction to Lights Out Puzzle • Given an initial configuration of all lights on a board, turn off all of them Rules: each light has a button or switch, click one button, the light and its close neighbors will change. Each configuration can be viewed as a matrix with entries in Z(mod(2))

  5. Project 2: Reliability and risk analysis • Cooperated with Dr. Omojola • Supported by Louisiana Space Consortium (LaSPACE), Jan.10, 2011 • Ms. Brandy, a math major, joined this project and provided a poster in a local conference in Dillard University. • Three methods to calculate the reliability of a complicated system

  6. Project 3: Fractals using Matlab • Julia sets of iterations of a particular function quadratic polynomial of form like ; • target is to dealing with rational function of one complex variable of the form • Mr. Gino, a advisee of mine, worked on it in the course Math 400 (Math Seminar) in 2013.

  7. Project 4: A holomorphic function closely related to “Collatz” problem • Ms. Legendre, a math major, is working with me on it • The Collatz conjecture is an unsolved mathematical problem. • Collatz problem (or conjecture, or 3n+1 problem): after a finite iteration of the following function, any positive integer n will reach the number 1

  8. Two functions

  9. Image of unit circle under Collatz function under( 1st and 2nd iteration)

  10. Project 5 Fingerprints (in progress) • In this project, we will study and investigate how to extract terminations and bifurcations points from a fingerprint image by MATLAB operations.

  11. Cooperators • Dr. Tan, SUNO: on fingerprints, in progress, to be funded by Board of Regents in Louisiana, 2014. • Dr. Omojola, SUNO: on liability and risk analysis 2012.

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