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Filter Base Integration, Bradley Howell
Filter Base Integration, Bradley Howell
Electronic Theses and Dissertations
In this paper we seek to investigate and compare several Kurzweil-Henstock type integrals. We present these integrals as special cases of a more general construction and establish key properties required in order to create similar "well behaved" integrals. After establishing basic results (additivity, monotonicity, etc.) for these integrals, we shift our focus to more interesting questions about them. We consider mainly the following topics: additivity, their relationship to the Lebesgue integral, absolute integrability, their relationships with each other, their relationship with differentiation, possible convergence theorems and the establishment of a Fubini Theorem.
The Virasoro Algebra: Signatures Of Highest Weight Modules And The Modular Group Action, Byung Chun
The Virasoro Algebra: Signatures Of Highest Weight Modules And The Modular Group Action, Byung Chun
Electronic Theses and Dissertations
The Virasoro algebra (\emph{Vir}) has important applications to the study of infinite dimensional Lie algebras, and specifically to areas of theoretical physics modeled by conformal field theories. The positive-energy representations of \emph{Vir} play a key role in string theory. A vital piece of information is the signature of the positive-energy representations. The physicist Adrian Kent calculated the characters of the signatures of these positive-energy representations in his paper. In this thesis, we will provide mathematical proofs for Kent's signature formulas for all possible values of the central charge and lowest weight. Furthermore, we simplify Kent's formulas by adopting a different …
Multiplier Hopf Algebras And Duality, Menghong Sun
Multiplier Hopf Algebras And Duality, Menghong Sun
Electronic Theses and Dissertations
In this thesis, we study and apprehend Hopf algebras, multiplier Hopf algebras, and their dualities. A Hopf algebra A is a unital algebra with an comutiplication (A tensor A) &rarr A, which is the reverse of multiplication, and other structures. In the finite-dimensional case, we can construct the dual A' of A, which is also a Hopf algebra, and prove that A is isomorphic to its bidual A''. If we drop the assumption that A is unital and allow the comultiplication to have values in the multiplier algebra of (A tensor A), we end with a multiplier Hopf algebra. If …