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Boundary Value Problems For Discrete Fractional Equations, Khulud Alyousef Aug 2012

Boundary Value Problems For Discrete Fractional Equations, Khulud Alyousef

Dissertations, Theses, and Student Research Papers in Mathematics

In this dissertation we are interested in proving the existence of solutions for various fractional boundary value problems. Our technique will be to apply certain fixed point theorems. Also comparison theorems for fractional boundary problems and a so-called Liapunov inequality will be given.


Commutative Rings Graded By Abelian Groups, Brian P. Johnson Aug 2012

Commutative Rings Graded By Abelian Groups, Brian P. Johnson

Dissertations, Theses, and Student Research Papers in Mathematics

Rings graded by Z and Zd play a central role in algebraic geometry and commutative algebra, and the purpose of this thesis is to consider rings graded by any abelian group. A commutative ring is graded by an abelian group if the ring has a direct sum decomposition by additive subgroups of the ring indexed over the group, with the additional condition that multiplication in the ring is compatible with the group operation. In this thesis, we develop a theory of graded rings by defining analogues of familiar properties---such as chain conditions, dimension, and Cohen-Macaulayness. We then study the ...


Prime Ideals In Two-Dimensional Noetherian Domains And Fiber Products And Connected Sums, Ela Celikbas Aug 2012

Prime Ideals In Two-Dimensional Noetherian Domains And Fiber Products And Connected Sums, Ela Celikbas

Dissertations, Theses, and Student Research Papers in Mathematics

This thesis concerns three topics in commutative algebra:

1) The projective line over the integers (Chapter 2),

2) Prime ideals in two-dimensional quotients of mixed power series-polynomial rings (Chapter 3),

3) Fiber products and connected sums of local rings (Chapter 4),

In the first chapter we introduce basic terminology used in this thesis for all three topics.

In the second chapter we consider the partially ordered set (poset) of prime ideals of the projective line Proj(Z[h,k]) over the integers Z, and we interpret this poset as Spec(Z[x]) U Spec(Z[1/x]) with an appropriate ...


An Analysis Of Nonlocal Boundary Value Problems Of Fractional And Integer Order, Christopher Steven Goodrich Aug 2012

An Analysis Of Nonlocal Boundary Value Problems Of Fractional And Integer Order, Christopher Steven Goodrich

Dissertations, Theses, and Student Research Papers in Mathematics

In this work we provide an analysis of both fractional- and integer-order boundary value problems, certain of which contain explicit nonlocal terms. In the discrete fractional case we consider several different types of boundary value problems including the well-known right-focal problem. Attendant to our analysis of discrete fractional boundary value problems, we also provide an analysis of the continuity properties of solutions to discrete fractional initial value problems. Finally, we conclude by providing new techniques for analyzing integer-order nonlocal boundary value problems.

Adviser: Lynn Erbe and Allan Peterson


The Weak Discrepancy And Linear Extension Diameter Of Grids And Other Posets, Katherine Victoria Johnson Jul 2012

The Weak Discrepancy And Linear Extension Diameter Of Grids And Other Posets, Katherine Victoria Johnson

Dissertations, Theses, and Student Research Papers in Mathematics

A linear extension of a partially ordered set is simply a total ordering of the poset that is consistent with the original ordering. The linear extension diameter is a measure of how different two linear extensions could be, that is, the number of pairs of elements that are ordered differently by the two extensions. In this dissertation, we calculate the linear extension diameter of grids. This also gives us a nice characterization of the linear extensions that are the farthest from each other, and allows us to conclude that grids are diametrally reversing.

A linear extension of a poset might ...


Modeling And Mathematical Analysis Of Plant Models In Ecology, Eric A. Eager Jun 2012

Modeling And Mathematical Analysis Of Plant Models In Ecology, Eric A. Eager

Dissertations, Theses, and Student Research Papers in Mathematics

Population dynamics tries to explain in a simple mechanistic way the variations of the size and structure of biological populations. In this dissertation we use mathematical modeling and analysis to study the various aspects of the dynamics of plant populations and their seed banks.

In Chapter 2 we investigate the impact of structural model uncertainty by considering different nonlinear recruitment functions in an integral projection model for Cirsium canescens. We show that, while having identical equilibrium populations, these two models can elicit drastically different transient dynamics. We then derive a formula for the sensitivity of the equilibrium population to changes ...


Systems Of Nonlinear Wave Equations With Damping And Supercritical Sources, Yanqiu Guo Apr 2012

Systems Of Nonlinear Wave Equations With Damping And Supercritical Sources, Yanqiu Guo

Dissertations, Theses, and Student Research Papers in Mathematics

We consider the local and global well-posedness of the coupled nonlinear wave equations

utt – Δu + g1(ut) = f1(u, v)

vtt – Δv + g2(vt) = f2(u, v);

in a bounded domain Ω subset of the real numbers (Rn) with a nonlinear Robin boundary condition on u and a zero boundary conditions on v. The nonlinearities f1(u, v) and f2(u, v) are with supercritical exponents representing strong sources, while g1(ut) and g2(vt) act as damping. It is well-known that the ...


Combinatorics Using Computational Methods, Derrick Stolee Mar 2012

Combinatorics Using Computational Methods, Derrick Stolee

Dissertations, Theses, and Student Research Papers in Mathematics

Computational combinatorics involves combining pure mathematics, algorithms, and computational resources to solve problems in pure combinatorics. This thesis provides a theoretical framework for combinatorial search, which is then applied to several problems in combinatorics. Some results in space-bounded computational complexity are also presented.