Physical Sciences and Mathematics Commons^™

On Some Aspects Of The Arens-Hoffman Extension Of Banach Algebras, David Brown

David C. Brown

In this dissertation, we will refer to any commutative algebra over the complex field which possesses an identity e simply as an algebra... This dissertaion deals primarily with algebraic aspects of the Arens-Hoffman extension of a Banach Algebra A and thus builds upon the work of G. A. Heuer, J.A. Lindberg, and Heuer and Lidberg...

Construction Of Nonlinear Expression For Recursive Number Sequences, Tian-Xiao He

Tian-Xiao He

Collaboration And Health Care Diagnostics: An Agent Based Model Simulation, Sebastian Linde, George K. Thiruvathukal

George K. Thiruvathukal

This paper presents a simple ABM simulation that seeks to provide insight into the public health benefits that derive from greater collaboration among health care professionals. In particular, the paper compares the efficiency, delivery and timeliness of health care diagnostics under two contrasting paradigms–one in which collaboration is encouraged, and an- other where it is not. The preliminary results of this study suggest that while the effect of cooperation on aggregate public health depends on the patient search algorithm employed, its effect on overall efficiency and timeliness of health care diagnostics and treatment is significant and pos- itive. Since the …

Coarsening In High Order, Discrete, Ill-Posed Diffusion Equations, Catherine Kublik

Catherine Kublik

We study the discrete version of a family of ill-posed, nonlinear diffusion equations of order 2n. The fourth order (n=2) version of these equations constitutes our main motivation, as it appears prominently in image processing and computer vision literature. It was proposed by You and Kaveh as a model for denoising images while maintaining sharp object boundaries (edges). The second order equation (n=1) corresponds to another famous model from image processing, namely Perona and Malik's anisotropic diffusion, and was studied in earlier papers. The equations studied in this paper are high order analogues of the Perona-Malik equation, and like the …

Algorithms For Area Preserving Flows, Catherine Kublik, Selim Esedoglu, Jeffrey A. Fessler

Catherine Kublik

We propose efficient and accurate algorithms for computing certain area preserving geometric motions of curves in the plane, such as area preserving motion by curvature. These schemes are based on a new class of diffusion generated motion algorithms using signed distance functions. In particular, they alternate two very simple and fast operations, namely convolution with the Gaussian kernel and construction of the distance function, to generate the desired geometric flow in an unconditionally stable manner. We present applications of these area preserving flows to large scale simulations of coarsening.

An Implicit Interface Boundary Integral Method For Poisson’S Equation On Arbitrary Domains, Catherine Kublik, Nicolay M. Tanushev, Richard Tsai

Catherine Kublik

We propose a simple formulation for constructing boundary integral methods to solve Poisson’s equation on domains with smooth boundaries defined through their signed distance function. Our formulation is based on averaging a family of parameterizations of an integral equation defined on the boundary of the domain, where the integrations are carried out in the level set framework using an appropriate Jacobian. By the coarea formula, the algorithm operates in the Euclidean space and does not require any explicit parameterization of the boundaries. We present numerical results in two and three dimensions.

Lyapunov Functionals That Lead To Exponential Stability And Instability In Finite Delay Volterra Difference Equations, Catherine Kublik, Youssef Raffoul

Catherine Kublik

We use Lyapunov functionals to obtain sufficient conditions that guarantee exponential stability of the zero solution of the finite delay Volterra difference equation. Also, by displaying a slightly different Lyapunov functional, we obtain conditions that guarantee the instability of the zero solution. The highlight of the paper is the relaxing of the condition |a(t)| < 1. Moreover, we provide examples in which we show that our theorems provide an improvement of some recent results.

Chaotic Behavior In Monetary Systems: Comparison Among Different Types Of Taylor Rule, Reza Moosavi Mohseni Dr., Wenjun Zhang Dr., Jiling Cao Prof.

Reza Moosavi Mohseni

The aim of the present study is to detect the chaotic behavior in the monetary economic relevant dynamical system. The study employs three different forms of Taylor rules: current, forward and backward looking. The result suggests the existence of the chaotic behavior in all three systems. In addition, the results strongly represent that using expectations in policy rule especially rational expectation hypothesis can increase the complexity of the system and leads to more chaotic behavior.

Chaotic Behavior In Monetary Systems: Comparison Among Different Types Of Taylor Rule, Reza Moosavi Mohseni Dr., Wenjun Zhang, Jiling Cao

Reza Moosavi Mohseni

The aim of the present study is to detect the chaotic behavior in monetary economic relevant dynamical system. The study employs three different forms of Taylor rules: current, forward, and backward looking. The result suggests the existence of the chaotic behavior in all three systems. In addition, the results strongly represent that using expectations in policy rule especially rational expectation hypothesis can increase complexity of the system and leads to more chaotic behavior.

Pixley-Roy Hyperspaces Of Ω-Graphs, Joe Mashburn

Joe D. Mashburn

The techniques developed by Wage and Norden are used to show that the Pixley-Roy hyperspaces of any two ω-graphs are homeomorphic. The Pixley-Roy hyperspaces of several subsets of Rn are also shown to be homeomorphic.

A Note On Irreducibility And Weak Covering Properties, Joe Mashburn

Joe D. Mashburn

A space X is irreducible if every open cover of X has a minimal open refinement. Interest in irreducibility began when Arens and Dugendji used this property to show that metacompact countably compact spaces are compact. It was natural, then, to find out what other types of spaces would be irreducible and therefore compact in the presence of countable compactness or Lindelof in the presence of N1-compactness. … It is shown in this paper that T1 δθ -refinable spaces and T1 weakly δθ-refinable spaces are irreducible. Since examples of Lindelof spaces that are neither T1 nor irreducible can be easily …

Countable Covers Of Spaces By Migrant Sets, Zoltan Balogh, Joe Mashburn, Peter Nyikos

Joe D. Mashburn

The motivation for this note is a paper by Hidenori Tanaka in which he shows that the Pixley-Roy hyperspace of a metric space X is normal if and only if X is an almost strong q-set.

Sobriety In Delta Not Sober, Joe Mashburn

Joe D. Mashburn

We will show that the space delta not sober defined by Coecke and Martin is sober in the Scott topology, but not in the weakly way below topology.

Dissertation: The Least Fixed Point Property For Ω-Chain Continuous Functions, Joe Mashburn

Joe D. Mashburn

The basic definitions are given in the first section, including those for ω-chain continuity, ω-chain completeness, and the least fixed point property for ω-chain continuous functions. Some of the relations between completeness and fixed point properties in partially ordered sets are stated and it is briefly shown how the question basic to the dissertation arises. In the second section, two examples are given showing that a partially ordered set need not be ω-chain complete to have the least fixed point property for ω-chain continuous functions. Retracts are discussed in section 3, where it is seen that they are not sufficient …

On The Decomposition Of Order-Separable Posets Of Countable Width Into Chains, Gary Gruenhage, Joe Mashburn

Joe D. Mashburn

partially ordered set X has countable width if and only if every collection of pairwise incomparable elements of X is countable. It is order-separable if and only if there is a countable subset D of X such that whenever p, q ∈ X and p < q, there is r ∈ D such that p ≤ r ≤ q. Can every order-separable poset of countable width be written as the union of a countable number of chains? We show that the answer to this question is "no" if there is a 2-entangled subset of IR, and "yes" under the Open Coloring …

The Least Fixed Point Property For Ω-Chain Continuous Functions, Joe Mashburn

Joe D. Mashburn

A partially ordered set P is ω-chain complete if every countable chain (including the empty set) in P has a supremum. … Notice that an ω-chain continuous function must preserve order. P has the (least) fixed point property for ω-chain continuous functions if every ω-chain continuous function from P to itself has (least) fixed point. It has been shown that a partially ordered set does not have to be ω-chain complete to have the least fixed point property for ω-chain continuous functions. This answers a question posed by G. Plotkin in 1978. I.I. Kolodner has shown that an ω-chain complete …

Oif Spaces, Zoltan Balogh, Harold Bennett, Dennis Burke, Gary Gruenhage, David Lutzer, Joe D. Mashburn

Joe D. Mashburn

A base β of a space X is called an OIF base when every element of B is a subset of only a finite number of other elements of β. We will explore the fundamental properties of spaces having such bases. In particular, we will show that in T2 spaces, strong OIF bases are the same as uniform bases, and that in T3 spaces where all subspaces have OIF bases, compactness, countable compactness, or local compactness will give metrizability.

Linearly Ordered Topological Spaces And Weak Domain Representability, Joe Mashburn

Joe D. Mashburn

It is well known that domain representable spaces, that is topological spaces that are homeomorphic to the space of maximal elements of some domain, must be Baire. In this paper it is shown that every linearly ordered topological space (LOTS) is homeomorphic to an open dense subset of a weak domain representable space. This means that weak domain representable spaces need not be Baire.

A Spectral Order For Infinite Dimensional Quantum Spaces: A Preliminary Report, Joe Mashburn

Joe D. Mashburn

In 2002 Coecke and Martin created a Bayesian order for the finite dimensional spaces of classical states in physics and used this to define a similar order, the spectral order on the finite dimensional quantum states. These orders gave the spaces a structure similar to that of a domain. This allows for measuring information content of states and for determining which partial states are approximations of which pure states. In a previous paper the author extended the Bayesian order to infinite dimensional spaces of classical states. The order on infinite dimensional spaces retains many of the characteristics important to physics, …

Three Counterexamples Concerning Ω-Chain Continuous Functions And Fixed-Point Properties, Joe Mashburn

Joe D. Mashburn

A partially ordered set is ω-chain complete if, for every countable chain, or ω-chain, in P, the least upper bound of C, denoted by sup C, exists. Notice that C could be empty, so an ω-chain complete partially ordered set has a least element, denoted by 0.

A Spectral Order For Infinite Dimensional Quantum Spaces, Joe Mashburn

Joe D. Mashburn

In this paper we extend the spectral order of Coecke and Martin to infinite-dimensional quantum states. Many properties present in the finite-dimensional case are preserved, but some of the most important are lost. The order is constructed and its properties analysed. Most of the useful measurements of information content are lost. Shannon entropy is defined on only a part of the model, and that part is not a closed subset of the model. The finite parts of the lattices used by Birkhoff and von Neumann as models for classical and quantum logic appear as subsets of the models for infinite …

An Order Model For Infinite Classical States, Joe Mashburn

Joe D. Mashburn

In 2002 Coecke and Martin (Research Report PRG-RR-02-07, Oxford University Computing Laboratory,2002) created a model for the finite classical and quantum states in physics. This model is based on a type of ordered set which is standard in the study of information systems. It allows the information content of its elements to be compared and measured. Their work is extended to a model for the infinite classical states. These are the states which result when an observable is applied to a quantum system. When this extended order is restricted to a finite number of coordinates, the model of Coecke and …

A Note On Reordering Ordered Topological Spaces And The Existence Of Continuous, Strictly Increasing Functions, Joe Mashburn

Joe D. Mashburn

The origin of this paper is in a question that was asked of the author by Michael Wellman, a computer scientist who works in artificial intelligence at Wright Patterson Air Force Base in Dayton, Ohio. He wanted to know if, starting with Rn and its usual topology and product partial order, he could linearly reorder every finite subset and still obtain a continuous function from Rn into R that was strictly increasing with respect to the new order imposed on Rn. It is the purpose of this paper to explore the structural characteristics of ordered topological spaces which have this …

A Comparison Of Three Topologies On Ordered Sets, Joe Mashburn

Joe D. Mashburn

We introduce two new topologies on ordered sets: the way below topology and weakly way below topology. These are similar in definition to the Scott topology, but are very different if the set is not continuous. The basic properties of these three topologies are compared. We will show that while domain representable spaces must be Baire, this is not the case with the new topologies.

Quasisymmetric (K; L)-Hook Schur Functions, Sarah K. Mason, Elizabeth Niese

Elizabeth Niese

We introduce a quasisymmetric generalization of Berele and Regev's (k,l)-hook Schur functions. These quasisymmetric hook Schur functions decompose the hook Schur functions in a natural way. The quasisymmetric hook Schur functions can be defined as the generating function for a certain set of composition tableaux on two alphabets. We will look at the combinatorics of the quasisymmetric hook Schur functions, including an analogue of the RSK algorithm and a generalized Cauchy Identity.

Rooted In Hell: Predicting Invasion Rates Of Phragmites Australis, Jacob P. Duncan

Jacob P Duncan

No abstract provided.

Propagating Lyapunov Functions To Prove Noise-Induced Stabilization, Tiffany Kolba, Avanti Athreya, Jonathan Mattingly

Tiffany N Kolba

No abstract provided.

Optimization And Simulation Of An Evolving Kidney Paired Donation (Kpd) Program, Yijiang Li, Jack Kalbfleisch, Peter Xuekun Song, Yan Zhou, Alan Leichtman, Michael Rees

Yan Zhou 周彦文档

The old concept of barter exchange has extended to the modern area of living-donor kidney transplantation, where one incompatible donor-candidate pair is matched to another pair with a complementary incompatibility, such that the donor from one pair gives an organ to a compatible candidate in the other pair and vice versa. Kidney paired donation (KPD) programs provide a unique and important platform for living incompatible donor-candidate pairs to exchange organs in order to achieve mutual benefit. We propose a novel approach to organizing kidney exchanges in an evolving KPD program with advantages, including (i) it allows for a more exible …

Predicting Invasion Rates For Phragmites Australis, Rachel Nydegger, Jacob Duncan, James A. Powell

Jacob P Duncan

In wetlands of Utah and southern Idaho as well as estuaries of the east coast, the ten-foot tall invasive grass Phragmites australis can be found near waterways, where it outcompetes native plants and degrades wildlife habitat. Phragmites australis is an obligate out-crossing plant that can spread sexually through seed disper- sal, or asexually via stolons and rhi- zomes (Kettenring and Mock 2012). Small patches are usually a single genetic individual, spreading vegetatively (and slowly) via runners; when patches become genetically diverse viable seeds are produced and invasion rates can be increase by an order of magnitude (Kettenring et al. 2011)

A Model For Mountain Pine Beetle Outbreaks In An Age-Structured Forest: Predicting Severity And Outbreak Recovery Cycle Period, Jacob P. Duncan

Jacob P Duncan

The mountain pine beetle (MPB, Dendroctonus ponderosae), a tree-killing bark beetle, has historically been part of the normal disturbance regime in lodgepole pine (Pinus contorta) forests. In recent years,warm winters and summers have allowed MPB populations to achieve synchronous emergence and successful attacks, resulting in widespread population outbreaks and resultant tree mortality across western North America. We develop an age-structured forest demographic model that incorporates temperature-dependent MPB infestations. Stability of fixed points is analyzed as a function of (thermally controlled) MPB population growth rates and indicates the existence of periodic outbreaks that intensify as growth rates increase. We devise analytical …