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- Title
- Tiling the Integers.
- Creator
-
Li, Shasha, Dutkay, Dorin, Han, Deguang, Sun, Qiyu, University of Central Florida
- Abstract / Description
-
A set tiles the integers if and only if the integers can be written as a disjoint union of translates of that set. Counterexamples based on ?nite Abelian groups show that Fuglede conjecture is false inhigh dimensions. A solution for the Fuglede conjecture in Z or all the groups ZN would provide a solution for the Fuglede conjecture in R. Focusing on tiles in dimension one, we will concentrate on the analysis of tiles in the ?nite groups ZN. Based on the Coven- Meyerowitz conjecture, it has...
Show moreA set tiles the integers if and only if the integers can be written as a disjoint union of translates of that set. Counterexamples based on ?nite Abelian groups show that Fuglede conjecture is false inhigh dimensions. A solution for the Fuglede conjecture in Z or all the groups ZN would provide a solution for the Fuglede conjecture in R. Focusing on tiles in dimension one, we will concentrate on the analysis of tiles in the ?nite groups ZN. Based on the Coven- Meyerowitz conjecture, it has been proved that if any spectral set in Z satis?es the the Coven-Meyerowitz properties, then everyspectral set in R is a tile. We will present some of the main results related to integer tiles and give a self-contained description of the theory with detailed proofs.
Show less - Date Issued
- 2014
- Identifier
- CFE0005199, ucf:50642
- Format
- Document (PDF)
- PURL
- http://purl.flvc.org/ucf/fd/CFE0005199
- Title
- Tiling properties of spectra of measures.
- Creator
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Haussermann, John, Dutkay, Dorin, Han, Deguang, Sun, Qiyu, Dogariu, Aristide, University of Central Florida
- Abstract / Description
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We investigate tiling properties of spectra of measures, i.e., sets ? in R with an orthogonal basis in L2 with respect to some finite Borel measure on R. Such measures include Lebesgue measure on bounded Borel subsets, finite atomic measures and some fractal Hausdorff measures. We show that various classes of such spectra of measures have translational tiling properties. This lead to some surprising tiling properties for spectra of fractal measures, the existence of complementing sets and...
Show moreWe investigate tiling properties of spectra of measures, i.e., sets ? in R with an orthogonal basis in L2 with respect to some finite Borel measure on R. Such measures include Lebesgue measure on bounded Borel subsets, finite atomic measures and some fractal Hausdorff measures. We show that various classes of such spectra of measures have translational tiling properties. This lead to some surprising tiling properties for spectra of fractal measures, the existence of complementing sets and spectra for finite sets with the Coven-Meyerowitz property, the existence of complementing Hadamard pairs in the case ofHadamard pairs of size 2,3,4 or 5. In the context of the Fuglede conjecture, we prove that any spectral set is a tile, if the period of the spectrum is 2,3,4 or 5.
Show less - Date Issued
- 2014
- Identifier
- CFE0005182, ucf:50656
- Format
- Document (PDF)
- PURL
- http://purl.flvc.org/ucf/fd/CFE0005182
- Title
- Tiling with Polyominoes, Polycubes, and Rectangles.
- Creator
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Saxton, Michael, Reid, Michael, Lee, Junho, Han, Deguang, University of Central Florida
- Abstract / Description
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In this paper we study the hierarchical structure of the 2-d polyominoes. We introduce a new infinite family of polyominoes which we prove tiles a strip. We discuss applications of algebra to tiling. We discuss the algorithmic decidability of tiling the infinite plane Z x Z given a finite set of polyominoes. We will then discuss tiling with rectangles. We will then get some new, and some analogous results concerning the possible hierarchical structure for the 3-d polycubes.
- Date Issued
- 2015
- Identifier
- CFE0005995, ucf:50791
- Format
- Document (PDF)
- PURL
- http://purl.flvc.org/ucf/fd/CFE0005995
- Title
- EVALUATION OF SPACE SHUTTLE TILE SUBNOMINAL BONDS.
- Creator
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Snapp, Cooper, Moslehy, Faissal, University of Central Florida
- Abstract / Description
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This study researched the history of Space Shuttle Reusable Surface Insulation which was designed and developed for use on the United States Orbiter fleet to protect from the high heating experienced during reentry through Earth's atmosphere. Specifically the tile system which is attached to the structure by the means of an RTV adhesive has experienced situations where the bonds are identified as subnominal. The history of these subnominal conditions is presented along with a recent...
Show moreThis study researched the history of Space Shuttle Reusable Surface Insulation which was designed and developed for use on the United States Orbiter fleet to protect from the high heating experienced during reentry through Earth's atmosphere. Specifically the tile system which is attached to the structure by the means of an RTV adhesive has experienced situations where the bonds are identified as subnominal. The history of these subnominal conditions is presented along with a recent identification of a subnominal bond between the Strain Isolation Pad and the tile substrate itself. Tests were run to identify the cause of these subnominal conditions and also to show how these conditions were proved to be acceptable for flight. The study also goes into cases that could be used to identify subnominal conditions on tile as a non-destructive test prior to flight. Several options of non-destructive testing were identified and recommendations are given for future research into this topic. A recent topic is also discussed in the instance where gap fillers were identified during the STS-114 mission that did not properly adhere to the substrate. The gap fillers were found protruding past the Outer Mold Line of the vehicle which required an unprecedented spacewalk to remove them to allow for a safe reentry through the atmosphere.
Show less - Date Issued
- 2006
- Identifier
- CFE0000947, ucf:46754
- Format
- Document (PDF)
- PURL
- http://purl.flvc.org/ucf/fd/CFE0000947