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Tiling with Polyominoes, Polycubes, and Rectangles
Title
Tiling with Polyominoes, Polycubes, and Rectangles.
Creator
Saxton, Michael, Reid, Michael, Lee, Junho, Han, Deguang, University of Central Florida
Abstract / Description
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
Integral Representations of Positive Linear Functionals
Title
Integral Representations of Positive Linear Functionals.
Creator
Siple, Angela, Mikusinski, Piotr, Atanasiu, Dragu, Dutkay, Dorin, Han, Deguang, Lee, Junho, Brennan, Joseph, Huo, Qun, University of Central Florida
Abstract / Description
In this dissertation we obtain integral representations for positive linear functionals on commutative algebras with involution and semigroups with involution. We prove Bochner and Plancherel type theorems for representations of positive functionals and show that, under some conditions, the Bochner and Plancherel representations are equivalent. We also consider the extension of positive linear functionals on a Banach algebra into a space of pseudoquotients and give under conditions in which...
Show moreIn this dissertation we obtain integral representations for positive linear functionals on commutative algebras with involution and semigroups with involution. We prove Bochner and Plancherel type theorems for representations of positive functionals and show that, under some conditions, the Bochner and Plancherel representations are equivalent. We also consider the extension of positive linear functionals on a Banach algebra into a space of pseudoquotients and give under conditions in which the space of pseudoquotients can be identified with all Radon measures on the structure space. In the final chapter we consider a system of integrated Cauchy functional equations on a semigroup, which generalizes a result of Ressel and offers a different approach to the proof.
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Date Issued
2015
Identifier
CFE0005713, ucf:50144
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0005713