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Model Order Reduction
(2014-11-24)
Model Order Reduction (MOR) is a wide area, and it has many techniques. In this thesis, we focus on Krylov subspaces method and Proper Orthogonal Decomposition (POD).We show some details about these two methods. A MATLAB ...
Nonlocal Dispersal Equations and Convergence to Random Dispersal Equations
(2014-05-15)
This dissertation is devoted to the study of the dynamics of nonlocal and random dispersal evolution equations.
Dispersal evolution equations are widely used to model the diffusions of organisms or individuals in many ...
On the derivation algebras of parabolic Lie algebras with applications to zero product determined algebras
(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) = ...
The Stone-Čech Compactification and the Number of Pairwise Nonhomeomorphic Subcontinua of β[0,∞)\[0,∞)
(2014-05-02)
An introduction to the Stone-Čech compactification $\beta X$ of a normal topological space $X$ is given. The method of invariantly embedding linear orders into ultrapowers is used to find $2^{\mathfrak{c}}$ pairwise ...
Path and Cycle Decompositions
(2008-09-09)
A $G$-design is a partition of edge set of K_v in which each element induces a copy of G. The existence of G-designs with the additional property that they contain no proper subsystems has been
previously settled when G ...
The Intersection Problem for Latin Squares with Holes of Size 2 and 3
(2009-04-28)
In this dissertation we give complete solutions for the intersection problem of latin
squares with holes of size 2 and 3. For a pair of 2n x 2n latin squares with holes of size 2
to have k entries in common outside of ...
3-Cycle Systems and Structure within Graph Decompositions
(2014-07-24)
An $H$-decomposition of a graph $G$ is a partition of the edge set $E(G)$ such that each element of the partition induces a subgraph isomorphic to $H$. A packing or cover of $\lambda K_n$ (with triples) is an ordered pair ...
4-cycles systems of line graphs of complete multipartite graphs
(2008-09-09)
Here we investigate the necessary and sufficient conditions for the existence of 4 - cycle systems of the line graphs of complete multipartite graphs.
Discrete sets, free sequences and cardinal properties of topological spaces
(2009-07-01)
We study the influence of discrete sets and free sequences on cardinal properties of topological spaces. We focus mainly on the minimum number of discrete sets needed to cover a space X (denoted by dis(X)) and on reflection ...
Integral closures
(2010-07-06)
The q^th-power algorithm from Leonard [3], [4], and Leonard and Pellikaan [1] is a
recent and efficient method of computing the integral closure of a ring in its field of fractions.
Previously, the q^th-power algorithm ...