Browsing by Author "Huang, Huajun"

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Adjoint Orbits of Borel Subgroup on Maximal Nilpotent Subalgebra of Types A and C.

Bogale, Meaza (2021-11-18) ETD File Embargoed

We describe the adjoint orbits of a Borel subgroup on a maximal nilpotent algebra of Types A and C. In Chapter 1, we provide a historical background and motivation behind the study. We highlight the important works in ...

A Comparison of High School Students’ Development of Statistical Reasoning Outcomes in High and Low Statistical Reasoning Learning Environments

Conway, Basil, IV (2015-12-11)

The purpose of this study was to study the impact of conformity to Statistical Reasoning Learning Environment (SRLE) principles on students’ statistical reasoning in Advanced Placement statistics courses. The study encompassed ...

Derivations of subalgebras of the Lie algebra of block upper triangular matrices

Ghimire, Prakash (2016-07-22)

This dissertation studies the derivations of some subalgebras of the Lie algebra of block upper triangular matrices. Specifically, we study the derivations of the Lie algebra of strictly block upper triangular matrices ...

Differential geometry on matrix groups

Gan, Luyining (2020-03-20)

In this dissertation, we study the differential geometry of the matrix groups. In literatures, many authors proposed to compute matrix means using the geodesic distance defined by an invariant Riemannian metrics on the ...

Generalizations of Various Results in Quantum Computation Theory to Mixed-Dimensional Quantum Systems

Gay, Randall (2021-04-05)

The majority of the research in quantum computation theory is based on quantum mechanical systems consisting of quantum subsystems that are all of the same dimension. Following and expanding on the research conducted by ...

Geometric means inequalities and their extensions to Lie groups

Ahsani, Sima (2018-12-05)

This dissertation has two main parts. 1. After reviewing the Riemannian structure of the space of n n positive de nite matrices, Pn, and the geometric mean in terms of geodesic, t-geometric mean, we present some ...

Lower Bounds for Betti Numbers in Vietoris–Rips Complexes of Hypercubes

Wang, Zichao (2024-04-29)

This thesis serves as a comprehensive introduction and elucidation of Henry Adams and Žiga Virk's seminal work \cite{Lower bounds} on new lower bounds on the Betti numbers for Vietoris–Rips complexes of hypercube graphs ...

Measure-preserving dynamical systems on R3 with all trajectories bounded

Ford, Jeffrey (2017-11-16)

We present here constructions, both smooth and piecewise-linear, of non-singular, measure-preserving dynamical systems on R3, with each trajectory contained in a bounded set. In the smooth case, we use a sequence of nested ...

On O-Basis Groups and Generalizations

Ervin, Jason (2007-08-15)

A class of finite groups which we call o-basis groups is generalized and explored. One reason for interest in these groups lies with the concept's origins. The notion of o-basis group arose from the study of the existence, ...

On the derivation algebras of parabolic Lie algebras with applications to zero product determined algebras

Brice, Daniel (2014-07-11)

This dissertation builds upon and extends previous work completed by the author and his advisor in [5]. A Lie algebra g is said to be zero product determined if for each bilinear map φ: g × g → V that satisfies φ(x, y) = ...

Products of positive definite symplectic matrices

Granario, Daryl Quebrar (2020-07-15)

We show that every symplectic matrix is a product of five positive definite symplectic matrices and five is the best in the sense that there are symplectic matrices which are not product of less.

Progress on the Marcus-de Oliveira Determinantal Conjecture

Homadi, Khadejah (2017-04-12)

We discuss the well known conjecture of Marcus and de Oliveira of the determinant of the sum of normal matrices. We present the motivation of this conjecture, along with detailed history of its origin. Then we compile ...