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Articles 1  8 of 8
FullText Articles in Education
Boundary Value Problems For Discrete Fractional Equations, Khulud Alyousef
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 socalled Liapunov inequality will be given.
Commutative Rings Graded By Abelian Groups, Brian P. Johnson
Commutative Rings Graded By Abelian Groups, Brian P. Johnson
Dissertations, Theses, and Student Research Papers in Mathematics
Rings graded by Z and Z^{d} 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 propertiessuch as chain conditions, dimension, and CohenMacaulayness. We then study the ...
Prime Ideals In TwoDimensional Noetherian Domains And Fiber Products And Connected Sums, Ela Celikbas
Prime Ideals In TwoDimensional 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 twodimensional quotients of mixed power seriespolynomial 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
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 integerorder 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 wellknown rightfocal 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 integerorder 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
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
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
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 wellposedness of the coupled nonlinear wave equations
u_{tt} – Δu + g_{1}(u_{t}) = f_{1}(u, v)
v_{tt} – Δv + g_{2}(v_{t}) = f_{2}(u, v);
in a bounded domain Ω subset of the real numbers (R^{n}) with a nonlinear Robin boundary condition on u and a zero boundary conditions on v. The nonlinearities f_{1}(u, v) and f_{2}(u, v) are with supercritical exponents representing strong sources, while g_{1}(u_{t}) and g_{2}(v_{t}) act as damping. It is wellknown that the ...
Combinatorics Using Computational Methods, Derrick Stolee
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 spacebounded computational complexity are also presented.