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wright1308100597.pdf (617.96 KB)
ETD Abstract Container
Abstract Header
Intersections of Deleted Digits Cantor Sets With Their Translates
Author Info
Phillips, Jason D.
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=wright1308100597
Abstract Details
Year and Degree
2011, Master of Science (MS), Wright State University, Mathematics.
Abstract
We define a family of deleted digits Cantor sets which satisfy specific constraints on the generating set of digits. We explore the structure and dimension of the intersection of a deleted digits Cantor set with its translate by a real value t. These results apply directly to the traditional Middle Thirds Cantor set as well as regular and uniform Cantor sets. We show that this family includes certain irregular sets which have not been previously analyzed. Our methods not only reveal the upper and lower bounds for the Minkowski dimension, but also uncover a formula for calculating the dimension of these intersections when specific conditions are met.
Committee
Steen Pedersen, PhD (Committee Chair)
Jim Vance, PhD (Committee Member)
David Miller, PhD (Committee Member)
Pages
94 p.
Subject Headings
Mathematics
Keywords
deleted digits
;
Cantor sets
;
fractals
;
fractal dimension
;
fractional dimension
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Citations
Phillips, J. D. (2011).
Intersections of Deleted Digits Cantor Sets With Their Translates
[Master's thesis, Wright State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=wright1308100597
APA Style (7th edition)
Phillips, Jason.
Intersections of Deleted Digits Cantor Sets With Their Translates.
2011. Wright State University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=wright1308100597.
MLA Style (8th edition)
Phillips, Jason. "Intersections of Deleted Digits Cantor Sets With Their Translates." Master's thesis, Wright State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=wright1308100597
Chicago Manual of Style (17th edition)
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Document number:
wright1308100597
Download Count:
422
Copyright Info
© 2011, all rights reserved.
This open access ETD is published by Wright State University and OhioLINK.