Zheng Chen
Southern university at New Orleans
March 2014
2014
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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)
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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
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))
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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
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Julia sets of iterations of a particular function
2
x
 ;
quadratic polynomial of form like
target is to dealing with rational function of
one complex variable of the form
ax  b a b
,
 0.
cx  d c d
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Mr. Gino, a advisee of mine, worked on it in
the course Math 400 (Math Seminar) in 2013.
• 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
n / 2, if n is even
f ( x)  
3n  1, if n is odd
Adjusted Collatz function:
n / 2, if n is even
f ( x)  
(3n  1) / 2, if n is odd
A holomorphic function:
1
4
(1  4 z  (1  2 z ) cos( z ))
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In this project, we will study and investigate how to
extract terminations and bifurcations points from a
fingerprint image by MATLAB operations.
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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.