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Articles 1  12 of 12
FullText Articles in Education
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 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 ...}
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 ...
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 ...
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 ...
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 ...
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 ...