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Surface Entropy Of Shifts Of Finite Type, Dennis Pace
Surface Entropy Of Shifts Of Finite Type, Dennis Pace
Electronic Theses and Dissertations
Let χ be the class of 1-D and 2-D subshifts. This thesis defines a new function, HS : χ x R → [0,∞] which we call the surface entropy of a shift. This definition is inspired by the topological entropy of a subshift and we compare and contrast several structural properties of surface entropy to entropy. We demonstrate that much like entropy, the finiteness of surface entropy is a conjugacy invariant and is a tool in the classification of subshifts. We develop a tiling algorithm related to continued fractions which allows us to prove a continuity result about surface …
T-De Vries Algebra, Nawal Alznad
T-De Vries Algebra, Nawal Alznad
Electronic Theses and Dissertations
The main point of this dissertation is to introduce the action on de Vries algebra by a topological monoid and we denoted the resulting category by dVT. In order to reach our goal, we started with introducing new proofs for some well known results in the category of flows. Then, we studied the Generalized Smirnov's Theorem for flows. After we studied the new category (dVT), we were able to provide a new way to construct the Čech-stone flow compactification of a given flow. Finally, we developed the co-free T-de Vries algebra for a special case.
Categories Of Residuated Lattices, Daniel Wesley Fussner
Categories Of Residuated Lattices, Daniel Wesley Fussner
Electronic Theses and Dissertations
We present dual variants of two algebraic constructions of certain classes of residuated lattices: The Galatos-Raftery construction of Sugihara monoids and their bounded expansions, and the Aguzzoli-Flaminio-Ugolini quadruples construction of srDL-algebras. Our dual presentation of these constructions is facilitated by both new algebraic results, and new duality-theoretic tools. On the algebraic front, we provide a complete description of implications among nontrivial distribution properties in the context of lattice-ordered structures equipped with a residuated binary operation. We also offer some new results about forbidden configurations in lattices endowed with an order-reversing involution. On the duality-theoretic front, we present new results on …