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Articles 1  30 of 39
FullText Articles in Education
High Cognitive Demand Examples In Precalculus: Examining The Work And Knowledge Entailed In Enactment, Erica R. Miller
High Cognitive Demand Examples In Precalculus: Examining The Work And Knowledge Entailed In Enactment, Erica R. Miller
Dissertations, Theses, and Student Research Papers in Mathematics
Historically, pass rates in undergraduate precalculus courses have been dismally low and the teaching practices and knowledge of university instructors have been understudied. To help improve teaching effectiveness and student outcomes in undergraduate precalculus courses, I have studied the cognitive demand of enacted examples. The purpose of this dissertation is to examine the pedagogical work and mathematical knowledge entailed in the enactment of high cognitive demand examples in a threepart study. To answer my research questions, I conducted classroom observations as well as pre and postobservation interviews with seven graduate student instructors at a large public R1 university in the ...
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.
Covariant Representations Of C*Dynamical Systems Involving Compact Groups, Firuz Kamalov
Covariant Representations Of C*Dynamical Systems Involving Compact Groups, Firuz Kamalov
Dissertations, Theses, and Student Research Papers in Mathematics
Given a C*dynamical system (A, G, σ) the crossed product C*algebra A x _{σ}G encodes the action of G on A. By the universal property of A x _{σ}G there exists a one to one correspondence between the set all covariant representations of the system (A, G, σ) and the set of all *representations of A x _{σ}G. Therefore, the study of representations of A x _{σ}G is equivalent to that of covariant representations of (A, G, σ).
We study induced covariant representations of systems involving compact groups. We prove that every irreducible (resp ...
On A Family Of Generalized Wiener Spaces And Applications, Ian Pierce
On A Family Of Generalized Wiener Spaces And Applications, Ian Pierce
Dissertations, Theses, and Student Research Papers in Mathematics
We investigate the structure and properties of a variety of generalized Wiener spaces. Our main focus is on Wienertype measures on spaces of continuous functions; our generalizations include an extension to multiple parameters, and a method of adjusting the distribution and covariance structure of the measure on the underlying function space.
In the second chapter, we consider singleparameter function spaces and extend a fundamental integration formula of Paley, Wiener, and Zygmund for an important class of functionals on this space. In the third chapter, we discuss measures on very general function spaces and introduce the specific example of a generalized ...
On Morrey Spaces In The Calculus Of Variations, Kyle Fey
On Morrey Spaces In The Calculus Of Variations, Kyle Fey
Dissertations, Theses, and Student Research Papers in Mathematics
We prove some global Morrey regularity results for almost minimizers of functionals of the form u → ∫_{Ω} f(x, u, ∇u)dx. This regularity is valid up to the boundary, provided the boundary data are sufficiently regular. The main assumption on f is that for each x and u, the function f(x, u, ·) behaves asymptotically like the function h(·)^{α(x)}, where h is an Nfunction.
Following this, we provide a characterization of the class of Young measures that can be generated by a sequence of functions {f_{j}} uniformly bounded in the Morrey space L^{p}^{, λ ...}
Homology Of Artinian Modules Over Commutative Noetherian Rings, Micah J. Leamer
Homology Of Artinian Modules Over Commutative Noetherian Rings, Micah J. Leamer
Dissertations, Theses, and Student Research Papers in Mathematics
This work is primarily concerned with the study of artinian modules over commutative noetherian rings.
We start by showing that many of the properties of noetherian modules that make homological methods work seamlessly have analogous properties for artinian modules. We prove many of these properties using Matlis duality and a recent characterization of Matlis reflexive modules. Since Matlis reflexive modules are extensions of noetherian and artinian modules many of the properties that hold for artinian and noetherian modules naturally follow for Matlis reflexive modules and more generally for minimax modules.
In the last chapter we prove that if the Betti ...
Global WellPosedness For A Nonlinear Wave Equation With PLaplacian Damping, Zahava Wilstein
Global WellPosedness For A Nonlinear Wave Equation With PLaplacian Damping, Zahava Wilstein
Dissertations, Theses, and Student Research Papers in Mathematics
This dissertation deals with the global wellposedness of the nonlinear wave equation
u_{tt} − Δu − Δ_{p}u_{t} = f (u) in Ω × (0,T),
{u(0), u_{t}(0)} = {u_{0},u_{1}} ∈ H^{1}_{0} (Ω) × L^{ 2} (Ω),
u = 0 on Γ × (0, T ),
in a bounded domain Ω ⊂ ℜ ^{n} with Dirichlét boundary conditions. The nonlinearities f (u) acts as a strong source, which is allowed to have, in some cases, a supersupercritical exponent. Under suitable restrictions on the parameters and with careful analysis involving the theory of monotone operators, we prove the existence and ...
Groups And Semigroups Generated By Automata, David Mccune
Groups And Semigroups Generated By Automata, David Mccune
Dissertations, Theses, and Student Research Papers in Mathematics
In this dissertation we classify the metabelian groups arising from a restricted class of invertible synchronous automata over a binary alphabet. We give faithful, selfsimilar actions of Heisenberg groups and upper triangular matrix groups. We introduce a new class of semigroups given by a restricted class of asynchronous automata. We call these semigroups ``expanding automaton semigroups''. We show that this class strictly contains the class of automaton semigroups, and we show that the class of asynchronous automaton semigroups strictly contains the class of expanding automaton semigroups. We demonstrate that undecidability arises in the actions of expanding automaton semigroups and semigroups ...
HilbertSamuel And HilbertKunz Functions Of ZeroDimensional Ideals, Lori A. Mcdonnell
HilbertSamuel And HilbertKunz Functions Of ZeroDimensional Ideals, Lori A. Mcdonnell
Dissertations, Theses, and Student Research Papers in Mathematics
The HilbertSamuel function measures the length of powers of a zerodimensional ideal in a local ring. Samuel showed that over a local ring these lengths agree with a polynomial, called the HilbertSamuel polynomial, for sufficiently large powers of the ideal. We examine the coefficients of this polynomial in the case the ideal is generated by a system of parameters, focusing much of our attention on the second Hilbert coefficient. We also consider the HilbertKunz function, which measures the length of Frobenius powers of an ideal in a ring of positive characteristic. In particular, we examine a conjecture of Watanabe and ...
Packings And Realizations Of Degree Sequences With Specified Substructures, Tyler Seacrest
Packings And Realizations Of Degree Sequences With Specified Substructures, Tyler Seacrest
Dissertations, Theses, and Student Research Papers in Mathematics
This dissertation focuses on the intersection of two classical and fundamental areas in graph theory: graph packing and degree sequences. The question of packing degree sequences lies naturally in this intersection, asking when degree sequences have edgedisjoint realizations on the same vertex set. The most significant result in this area is Kundu's kFactor Theorem, which characterizes when a degree sequence packs with a constant sequence. We prove a series of results in this spirit, and we particularly search for realizations of degree sequences with edgedisjoint 1factors.
Perhaps the most fundamental result in degree sequence theory is the ErdosGallai Theorem ...
Extremal Trees And Reconstruction, Andrew Ray
Extremal Trees And Reconstruction, Andrew Ray
Dissertations, Theses, and Student Research Papers in Mathematics
Problems in two areas of graph theory will be considered.
First, I will consider extremal problems for trees. In these questions we examine the trees that maximize or minimize various invariants. For instance the number of independent sets, the number of matchings, the number of subtrees, the sum of pairwise distances, the spectral radius, and the number of homomorphisms to a fixed graph. I have two general approaches to these problems. To find the extremal trees in the collection of trees on n vertices with a fixed degree bound I use the certificate method. The certificate is a branch invariant ...
Annihilators Of Local Cohomology Modules, Laura Lynch
Annihilators Of Local Cohomology Modules, Laura Lynch
Dissertations, Theses, and Student Research Papers in Mathematics
In many important theorems in the homological theory of commutative local rings, an essential ingredient in the proof is to consider the annihilators of local cohomology modules. We examine these annihilators at various cohomological degrees, in particular at the cohomological dimension and at the height or the grade of the defining ideal. We also investigate the dimension of these annihilators at various degrees and we refine our results by specializing to particular types of rings, for example, Cohen Macaulay rings, unique factorization domains, and rings of small dimension.
Adviser: Thomas Marley
The Theory Of Discrete Fractional Calculus: Development And Application, Michael T. Holm
The Theory Of Discrete Fractional Calculus: Development And Application, Michael T. Holm
Dissertations, Theses, and Student Research Papers in Mathematics
The author's purpose in this dissertation is to introduce, develop and apply the tools of discrete fractional calculus to the arena of fractional difference equations. To this end, we develop the Fractional Composition Rules and the Fractional Laplace Transform Method to solve a linear, fractional initial value problem in Chapters 2 and 3. We then apply fixed point strategies of Krasnosel'skii and Banach to study a nonlinear, fractional boundary value problem in Chapter 4.
Adviser: Lynn Erbe and Allan Peterson
Formalizing Categorical And Algebraic Constructions In Operator Theory, William Benjamin Grilliette
Formalizing Categorical And Algebraic Constructions In Operator Theory, William Benjamin Grilliette
Dissertations, Theses, and Student Research Papers in Mathematics
In this work, I offer an alternative presentation theory for C*algebras with applicability to various other normed structures. Specifically, the set of generators is equipped with a nonnegativevalued function which ensures existence of a C*algebra for the presentation. This modification allows clear definitions of a "relation" for generators of a C*algebra and utilization of classical algebraic tools, such as Tietze transformations.
On The Betti Number Of Differential Modules, Justin Devries
On The Betti Number Of Differential Modules, Justin Devries
Dissertations, Theses, and Student Research Papers in Mathematics
Let R = k[x_{1}, ..., x_{n}] with k a field. A multigraded differential Rmodule is a multigraded Rmodule D with an endomorphism d such that d^{2} = 0. This dissertation establishes a lower bound on the rank of such a differential module when the underlying Rmodule is free. We define the Betti number of a differential module and use it to show that when the homology ker d/im d of D is nonzero and finite dimensional over k then there is an inequality rank_{R} D ≥ 2^{n}. This relates to a problem of Buchsbaum ...
The Cohomology Of Modules Over A Complete Intersection Ring, Jesse Burke
The Cohomology Of Modules Over A Complete Intersection Ring, Jesse Burke
Dissertations, Theses, and Student Research Papers in Mathematics
We investigate the cohomology of modules over commutative complete intersection rings. The first main result is that if M is an arbitrary module over a complete intersection ring R, and if one even selfextension module of M vanishes then M has finite projective dimension. The second main result gives a new proof of the fact that the support variety of a CohenMacaulay module whose completion is indecomposable is projectively connected.
Applications Of Linear Programming To Coding Theory, Nathan Axvig
Applications Of Linear Programming To Coding Theory, Nathan Axvig
Dissertations, Theses, and Student Research Papers in Mathematics
Maximumlikelihood decoding is often the optimal decoding rule one can use, but it is very costly to implement in a general setting. Much effort has therefore been dedicated to find efficient decoding algorithms that either achieve or approximate the errorcorrecting performance of the maximumlikelihood decoder. This dissertation examines two approaches to this problem.
In 2003 Feldman and his collaborators defined the linear programming decoder, which operates by solving a linear programming relaxation of the maximumlikelihood decoding problem. As with many modern decoding algorithms, is possible for the linear programming decoder to output vectors that do not correspond to codewords; such ...
Vanishing Of Ext And Tor Over Complete Intersections, Olgur Celikbas
Vanishing Of Ext And Tor Over Complete Intersections, Olgur Celikbas
Dissertations, Theses, and Student Research Papers in Mathematics
Let (R,m) be a local complete intersection, that is, a local ring whose madic completion is the quotient of a complete regular local ring by a regular sequence. Let M and N be finitely generated Rmodules. This dissertation concerns the vanishing of Tor(M, N) and Ext(M, N). In this context, M satisfies Serre's condition (S_{n}) if and only if M is an nth syzygy. The complexity of M is the least nonnegative integer r such that the nth Betti number of M is bounded by a polynomial of degree r1 for all sufficiently large n ...
Mathematical Modeling Of Optimal Seasonal Reproductive Strategies And A Comparison Of LongTerm Viabilities Of Annuals And Perennials, Anthony Delegge
Mathematical Modeling Of Optimal Seasonal Reproductive Strategies And A Comparison Of LongTerm Viabilities Of Annuals And Perennials, Anthony Delegge
Dissertations, Theses, and Student Research Papers in Mathematics
In 1954, Lamont Cole posed a question which has motivated much ecological work in the past 50 years: When is the life history strategy of semelparity (organisms reproduce once, then die) favored, via evolution, over iteroparity (organisms may reproduce multiple times in their lifetime)? Although common sense should dictate that iteroparity would always be favored, we can observe that this is not always the case, since annual plants are not only prevalent, but can dominate an area. Also, certain plant species may be perennial in one region, but annual in another. Thus, in these areas, certain characteristics must be present ...
Properties Of The Generalized Laplace Transform And Transport Partial Dynamic Equation On Time Scales, Chris R. Ahrendt
Properties Of The Generalized Laplace Transform And Transport Partial Dynamic Equation On Time Scales, Chris R. Ahrendt
Dissertations, Theses, and Student Research Papers in Mathematics
In this dissertation, we first focus on the generalized Laplace transform on time scales. We prove several properties of the generalized exponential function which will allow us to explore some of the fundamental properties of the Laplace transform. We then give a description of the region in the complex plane for which the improper integral in the definition of the Laplace transform converges, and how this region is affected by the time scale in question. Conditions under which the Laplace transform of a power series can be computed termbyterm are given. We develop a formula for the Laplace transform for ...
A Computational Study Of The Effects Of Temperature Variation On Turtle Egg Development, Sex Determination, And Population Dynamics, Amy L. Parrott
A Computational Study Of The Effects Of Temperature Variation On Turtle Egg Development, Sex Determination, And Population Dynamics, Amy L. Parrott
Dissertations, Theses, and Student Research Papers in Mathematics
Climate change and its effects on ecosystems is a major concern. For certain animal species, especially those that exhibit what is known as temperaturedependent sex determination (TSD), temperature variations pose a possibly serious threat (Valenzuela and Lance, 2004). In these species, temperature, and not chromosomes, determines the sex of the animal (Valenzuela and Lance, 2004). It is conceivable therefore, that if the temperature changes to favor only one sex, then dire consequences for their populations could occur. In this dissertation, we examine possible effects that climate change may have upon Painted Turtles (Chrysemys picta), a species with TSD. We investigate ...
Fan Cohomology And Equivariant Chow Rings Of Toric Varieties, MuWan Huang
Fan Cohomology And Equivariant Chow Rings Of Toric Varieties, MuWan Huang
Dissertations, Theses, and Student Research Papers in Mathematics
Toric varieties are varieties equipped with a torus action and constructed from cones and fans. In the joint work with Suanne Au and Mark E. Walker, we prove that the equivariant Ktheory of an affine toric variety constructed from a cone can be identified with a group ring determined by the cone. When a toric variety X(Δ) is smooth, we interpret equivariant Kgroups as presheaves on the associated fan space Δ. Relating the sheaf cohomology groups to equivariant Kgroups via a spectral sequence, we provide another proof of a theorem of Vezzosi and Vistoli: equivariant K ...
Modeling And Analysis Of Biological Populations, Joan Lubben
Modeling And Analysis Of Biological Populations, Joan Lubben
Dissertations, Theses, and Student Research Papers in Mathematics
Asymptotic and transient dynamics are both important when considering the future population trajectory of a species. Asymptotic dynamics are often used to determine whether the longterm trend results in a stable, declining or increasing population and even provide possible directions for management actions. Transient dynamics are important for estimating invasion speed of nonindigenous species, population establishment after releasing biocontrol agents, or population management after a disturbance like fire. We briefly describe here the results in this thesis.
(1) We consider asymptotic dynamics using discrete time linear population models of the form n(t + 1) = An(t) where A is a ...