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Integral Closure and the Generalized Multiplicity Sequence
(North Dakota State University, 2015)
See Dissertation Document for Full Abstract (Mathematical Symbols Included)
Gorenstein Dimension over Some Rings of the Form R [0 plus]C
(North Dakota State University, 2015)
Commutative algebra is the study of commutative rings and other abstract structures based on commutative rings. Modules can be viewed as a common generalization of several of those structures, and some invariants, e.g. ...
Semidualizing DG Modules over Tensor Products
(North Dakota State University, 2015)
In this dissertation, we study rings: sets with addition, subtraction, and multiplication. One way to study a ring is by studying its modules: the algebraic objects the ring acts on. Since it is impractical to study all ...
Modeling Swap and Geophysical Analysis using Barndorff-Nielson and Shephard Model
(North Dakota State University, 2015)
Video summarizing Ph.D. dissertation for a non-specialist audience.
L1 Approximation in De Branges Spaces
(North Dakota State University, 2015)
In this thesis we study bandlimited approximations to various functions. Bandlimited functions
have compactly supported Fourier transforms, which is a desirable feature in many applications.
In particular, we address the ...
Modeling Financial Swaps and Geophysical data Using the Barndorff-Nielsen and Shephard Model
(North Dakota State University, 2015)
This dissertation uses Barndoff-Nielsen and Shephard (BN-S) models to model swap, a type of financial derivative, and analyze geophysical data for estimation of major earthquakes. From empirical observation of the stock ...
Homological Dimensions with Respect to a Semidualizing Complex
(North Dakota State University, 2015)
See Dissertation Document for Full Abstract (Mathematical Symbols Included)