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Now showing items 11-20 of 53
Totally Reflected Groups
(2016-05-13)
A group G is totally reflected if it has a generating set S such that each edge in the Cayley graph Gamma(G,S) is inverted by some color-preserving reflection on the graph. For example, we will show that Coxeter groups and ...
Webs for Type Q Lie Superalgebras
(2017-12-15)
In the first part of this dissertation, we construct a monoidal supercategory whose morphism spaces are spanned by equivalence classes of diagrams called oriented type Q webs, modulo certain relations. We then prove a ...
Extensional Maps
(2014-05-09)
In a recent paper, Ziga Virk defined a type of continuous map which preserves extension properties. We generalize this notion and call such maps extensional maps. In this paper we will establish many of the basic properties ...
A Guided Reinvention of Ring, Integral Domain, and Field
(2012)
Abstract algebra enjoys a prestigious position in mathematics and the undergraduate mathematics curriculum. A typical abstract algebra course aims to provide students with a glimpse into the elegance of mathematics by ...
ON THE EXISTENCE OF KAM TORI FOR PRESYMPLECTIC VECTOR FIELDS
(2016-05)
We prove the existence of a torus that is invariant with respect to the flow of a presymplectic vector field found in a family of presymplectic vector fields. Moreover, the flow on this invariant torus is conjugate to a ...
Parameter Estimation for Damped Sine-Gordon Equation with Neumann Boundary Condition
(2010)
In this thesis we study an identification problem for physical parameters associated with damped sine-Gordon equation with Neumann boundary conditions. The existence, uniqueness, and continuous dependence of weak solution ...
Geodesic fibrations of elliptic 3-manifolds
(2013)
The well-known Hopf fibration of S3 is interesting in part because its fibers are geodesics, or great circles, of S3. However, this is not the only great circle fibration of S3. In 1983, Herman Gluck and Frank Warner ...
SEPARATION AND FENCHEL-TYPE DUALITY THEOREMS FOR FUNCTIONS WITH INTEGER AND REAL VARIABLES
(2011)
The concepts of convex and concave functions are of critical importance in optimization theory. These concepts arise for both functions of real (that is, continuous) variables and functions of integer variables (that is, ...
Differences in Beliefs and Teaching Practices between International and U.S. Domestic Mathematics Teaching Assistants
(2011)
International Mathematics Teaching Assistants (MTAs) and U.S. domestic MTAs are an indispensable part of mathematics departments regarding teaching a substantial portion of undergraduate students. Because MTAs' beliefs are ...
Some sharp inequalities related to Moser-Tridinger-Onofri inequality
(2014-05)
In this dissertation, we focus on the study of sharp inequalities of Moser-
Trudinger-Onofri type. We first establish the analog Bliss and Hardy inequal-
ities with sharp constant involving exponential weight function. ...