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THE ENUMERATION PROBLEM ON NUMERICAL MONOIDS
(2019-05-10)
Even though the problem of counting points with integer coordinates on a (rational) polytope has connections to sophisticated mathematical topics like Algebraic K-Theory, Fourier-Dedekind Sums, Heegard-Floer Homology, ...
Estimation and Analysis of Atmospheric Vortices
(2013)
ESTIMATION AND ANALYSIS OF ATMOSPHERIC VORTICES
SOME LOCAL AND GLOBAL ASPECTS OF MATHEMATICAL DIGITAL SIGNAL PROCESSING
(2010)
We propose to use L^p norm of a given digital signal to identify the location where the dramatic chang occurs. The theory is based on Sobolev type inequalities on one dimensional intervals.
Categorizing Students' Difficulties with Mathematical Proofs: Developing a Model of the Structure of Proof Construction
(2015-08-14)
Studies have shown that proof construction is a challenging task for students at all levels. The purposes of my study were to examine students' difficulties with proof construction and to explore a practical method to help ...
Equivariant Piecewise-Linear Topology and Combinatorial Applications
(2011)
For G a finite group, we develop some theory of G-equivariant piecewise-linear topology and prove characterization theorems for G-equivariant regular neighborhoods. We use these results to prove a conjecture of Csorba ...
Irreducible non-cuspidal characters of GSp(4,Fq)
(2011)
Admissible non--supercuspidal representations of GSp(4,F), where F is a local field of characteristic zero with an odd-ordered residue field Fq, have finite dimensional spaces of fixed vectors under the action of principal ...
Generating Simulation Relations for Certain Nonlinear Control Systems
(2011)
In this dissertation, we introduce a new algorithm for generating simulation relations between nonlinear control systems that are affine in inputs and disturbances and provide precise mathematical conditions ensuring that ...
ELLIPTIC CURVES AND PARAMODULAR FORMS
(2019-08-01)
There is a lifting from a non-CM elliptic curve $E/\mathbb{Q}$ to a cuspidal paramodular newform $f$ of degree $2$ and weight $3$ given by the symmetric cube map. We find a description of the level of $f$ in terms of the ...
Invariant vectors and level raising operators in representations of the p-adic group GL(3)
(2012)
Each irreducibel, admissible representation (&pi,V) of GL(n) over a non-archimedean local field F has associated fixed vector spaces VK(m), for K(m) a compact-open subgroup of GL(n). It is known that there exists some ...
Dynamics and Stability of Buoyancy-Induced Flows
(2019-05-10)
The present dissertation tackles two different problems in fluid mechanics. In the first problem, we study the stability of free or natural convection of a compressible fluid over a heated plate underlying a semi-infinite ...