On Hopf Algebras Of Dimension 4p, 2010 Iowa State University

#### On Hopf Algebras Of Dimension 4p, Yi-Lin Cheng

*Graduate Theses and Dissertations*

Some progress on classification problems for finite dimensional Hopf algebras has been made recently. In this thesis, we look at 4p-dimensional Hopf algebras over an algebraically closed field of characteristic zero. We show that a non-semisimple Hopf algebra of dimension 4p with an odd prime p is pointed if, and only if, this Hopf algebra contains more than two group-like elements. Moreover, we prove that non-semisimple Hopf algebras of dimensions 20, 28 and 44 are either pointed or dual-pointed, and this completes the classification of Hopf algebras of dimension 20, 28,and 44.

Adsorbate-Enhanced Transport Of Metals On Metal Surfaces: Oxygen And Sulfur On Coinage Metals, 2010 Iowa State University

#### Adsorbate-Enhanced Transport Of Metals On Metal Surfaces: Oxygen And Sulfur On Coinage Metals, Patricia A. Thiel, Mingmin Shen, Da-Jiang Liu, James W. Evans

*Chemistry Publications*

Coarsening (i.e., ripening) of single-atom-high, metal homoepitaxial islands provides a useful window on the mechanism and kinetics of mass transport at metal surfaces. This article focuses on this type of coarsening on the surfaces of coinage metals (Cu, Ag, Au), both clean and with an adsorbed chalcogen (O, S) present. For the *clean* surfaces, three aspects are summarized: (1) the balance between the two major mechanisms—Ostwald ripening (the most commonly anticipated mechanism) and Smoluchowski ripening—and how that balance depends on island size; (2) the nature of the mass transport agents, which are metal adatoms in almost all ...

Variation Of Growth Morphology With Chemical Composition Of Terraces: Ag On A Twofold Surface Of A Decagonal Al-Cu-Co Quasicrystal, 2010 Institut Jean Lamour

#### Variation Of Growth Morphology With Chemical Composition Of Terraces: Ag On A Twofold Surface Of A Decagonal Al-Cu-Co Quasicrystal, T. Duguet, Barış Ünal, Yong Han, James W. Evans, J. Ledieu, Cynthia J. Jenks, J.-M. Dubois, V. Fournée, Patricia A. Thiel

*Chemistry Publications*

Growth of Ag thin films on the twofold surface of a decagonal Al-Cu-Co quasicrystal is characterized by scanning tunneling microscopy, at different temperatures, and for coverages ranging from submonolayer to 11 monolayers. From prior work, three types of clean surface terraces are known to exist. By correlation with a bulk structural model, the major difference between them lies in their transition-metal (TM) content, two being aluminum-rich (0 and 15 at. % TM) and one being TM-rich (40–50 at. % TM). The present article focuses on understanding the difference between Ag film morphologies on these terminations, in terms of their chemical content ...

Formation And Coarsening Of Ag(110) Bilayer Islands On Nial(110): Stm Analysis And Atomistic Lattice-Gas Modeling, 2010 Iowa State University

#### Formation And Coarsening Of Ag(110) Bilayer Islands On Nial(110): Stm Analysis And Atomistic Lattice-Gas Modeling, Yong Han, Barış Ünal, Dapeng Jing, Feili Qin, Cynthia J. Jenks, Da-Jiang Liu, Patricia A. Thiel, James W. Evans

*Chemistry Publications*

Scanning tunneling microscopy analysis of the initial stages of film growth during deposition of Ag on NiAl(110) reveals facile formation of bilayer Ag(110) islands at temperatures of 130 K and above. Annealing subsequent to deposition at 130 K induces coarsening of the bilayer island distribution. The thermodynamic driving force for bilayer island formation reflects a lower relative surface energy for films of even layer thicknesses. This feature derives from quantum size effects due to electron confinement in the Ag film. The kinetics of island formation and relaxation is controlled by terrace and edge-diffusion barriers, detachment barriers, interlayer diffusion ...

Homogenization Problems In Random Media, 2010 Iowa State University

#### Homogenization Problems In Random Media, Dimitrios Kontogiannis

*Graduate Theses and Dissertations*

we study homogenization problems of partial differential equations in random domains. We give an overview of the classical techniques that are used to obtain homogenized equations over simple microstructures (for instance, periodic or almost periodic structures) and we show how we can obtain averaging equations over some particular random configurations. As it will be seen, such methods require ergodic theory, percolation, stochastic processes, in addition to the compactness of solutions and the convergence process.

Computational And Theoretical Aspects Of N-E.C. Graphs, 2010 Wilfrid Laurier University

#### Computational And Theoretical Aspects Of N-E.C. Graphs, Alexandru Costea

*Theses and Dissertations (Comprehensive)*

We consider graphs with the *n*-existentially closed adjacency property. For a positive integer *n*, a graph is *n-existentially closed* (or *n*-e.c.) if for all disjoint sets of vertices *A* and *B* with \*A*∪ *B*\ = *n* (one of *A* or *B* can be empty), there is a vertex 2 not in *A*∪*B* joined to each vertex of *A* and no vertex of *B*. Although the *n*-e.c. property is straightforward to define, it is not obvious from the definition that graphs with the property exist. In 1963, Erdos and Rényi gave a non-explicit, randomized construction of ...

Mathematical Modeling And Control Of Nonlinear Oscillators With Shape Memory Alloys, 2010 Wilfrid Laurier University

#### Mathematical Modeling And Control Of Nonlinear Oscillators With Shape Memory Alloys, Mohamed Bendame

*Theses and Dissertations (Comprehensive)*

Shape memory alloys (SMAs) belong to an interesting type of materials that have attracted the attention of scientists and engineers over the last few decades. They have some interesting properties that made them the subject of extensive research to find the best ways to utilize them in different engineering, biomedical, and scientific applications. In this thesis, we develop a mathematical model and analyze the behavior of SMAs by considering a one degree of freedom nonlinear oscillator consisting of a mass connected to a fixed frame through a viscous damping and a shape memory alloy device. Due to the nonlinear and ...

On Finite-Dimensional Hopf Algebras And Their Classifications, 2010 Iowa State University

#### On Finite-Dimensional Hopf Algebras And Their Classifications, Michael John Hilgemann

*Graduate Theses and Dissertations*

In this thesis, we investigate the classification problem for finite-dimensional Hopf algebras. If p is an odd prime, we show that a non-semisimple Hopf algebra of dimension 2p^{2} over an algebraically closed field of characteristic zero must be pointed or isomorphic to the dual of a pointed Hopf algebra. Based on previously established classification results, this completes

the classification of Hopf algebras of these dimensions.

Mathematical Modeling Of Mhc Class Ii Mediated Immune Responses In Tissues, 2010 Iowa State University

#### Mathematical Modeling Of Mhc Class Ii Mediated Immune Responses In Tissues, Wen Zhou

*Graduate Theses and Dissertations*

In this thesis, we developed a spatial-temporal mathematical model to capture fundamental aspects of MHC Class II mediated immune responses, which plays an essential role in protecting the host from a broad range of pathogens. To capture its essential mechanisms, we have considered terms that broadly describe intercellular communication, cell movement, and effector function (activation or inhibition). By defining the pathogen based on the associated antigens±Pathogen Associated Molecular Patterns (PAMPs), a framework to model phenotypic characteristics of pathogens is introduced. It includes the initial dose, distribution at infection site, secretion rate of associated soluble antigens, replication rate of particulate ...

Coloring And Extremal Problems In Combinatorics, 2010 Iowa State University

#### Coloring And Extremal Problems In Combinatorics, Jacob Manske

*Graduate Theses and Dissertations*

Coloring problems concern partitions of structures. The classic problem of partitioning the set of integers into a finite number of pieces so that no one piece has an arithmetic progression of a fixed length was solved in 1927. Van der Waerden's Theorem shows that it is impossible to do so. The theorem states that if the set of positive integers is partitioned into finitely many pieces, then at least one of the pieces contains arbitrarily long arithmetic progressions.

Extremal problems focus on finding the largest (or smallest) structures which exhibit a certain property. For instance, we may wish to ...

An Option-Theoretic Valuation Model For Residential Mortgages With Stochastic Conditions And Discount Factors, 2010 Iowa State University

#### An Option-Theoretic Valuation Model For Residential Mortgages With Stochastic Conditions And Discount Factors, Fernando Miranda-Mendoza

*Graduate Theses and Dissertations*

Standard mathematical mortgage valuation models consist of three components: the future promised payments, the financial option to default, and the financial option to prepay. In this thesis we propose and analyze new concepts introduced into the standard models. The new concepts include discount factors, coherent boundary conditions, and stochastic terms. In this framework, the value of a mortgage satisfies a Black-Scholes type stochastic PDE. The approximate solution to our model involves a numerical method based on the Wiener-Ito chaos expansion, which breaks the stochastic PDE into a sequence of deterministic PDEs. These PDEs involve a free boundary, are discretized by ...

Solving Distance Geometry Problems For Protein Structure Determination, 2010 Iowa State University

#### Solving Distance Geometry Problems For Protein Structure Determination, Atilla Sit

*Graduate Theses and Dissertations*

A well-known problem in protein modeling is the determination of the structure of a protein with a given set of interatomic distances obtained from either physical experiments or theoretical estimates. A more general form of this problem is known as the distance geometry problem in mathematics, which can be solved in polynomial time if a complete set of exact distances is given, but is generally intractable for a general sparse set of distance data. We investigate the solution of the problem within a geometric buildup framework. We propose a new geometric buildup algorithm for solving the problem using special least-squares ...

A Mathematical Model For Il6-Induced Differentiation Of Neural Progenitor Cells On A Micropatterned Polymer Substrate, 2010 Iowa State University

#### A Mathematical Model For Il6-Induced Differentiation Of Neural Progenitor Cells On A Micropatterned Polymer Substrate, Cory Howk

*Graduate Theses and Dissertations*

Neural progenitor cells (NPC) hold potential for repairing the injured and diseased central nervous system, and because of this we would like to better understand the mechanisms of NPC migration and differentiation. Previous *in vitro* research has shown that adult rat hippocampal progenitor cells (AHPC) differentiate into neurons in response to hippocampal astrocyte-secreted factors, including the cytokine IL6. This work is a mathematical study of a simple mechanism for IL6-induced AHPC differentiation. We show that all experimental results under consideration can be replicated by this model. A global sensitivity analysis is performed, demonstrating that the inhibitor of this pathway does ...

Discrete-Time Multi-Scale Systems, 2010 Chapman University

#### Discrete-Time Multi-Scale Systems, Daniel Alpay, Mamadou Mboup

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

We introduce multi-scale filtering by the way of certain double convolution systems. We prove stability theorems for these systems and make connections with function theory in the poly-disc. Finally, we compare the framework developed here with the white noise space framework, within which a similar class of double convolution systems has been defined earlier.

The Topology Of Incidence Pseudographs, 2010 Otterbein University

#### The Topology Of Incidence Pseudographs, Thomas R. James, Reinhard Klette

*Mathematics Faculty Scholarship*

Incidence pseudographs model a (re°exive and symmetric) inci- dence relation between sets of various dimensions, contained in a count- able family. Work by Klaus Voss in 1993 suggested that this general discrete model allows to introduce a topology, and some authors have done some studies into this direction in the past (also using alternative discrete models such as, for example, abstract complexes or orders on sets of cells). This paper provides a comprehensive overview about the topology of incidence pseudographs. This topology has various appli- cations, such as in modeling basic data in 2D or 3D digital picture analysis ...

Enumeration Schemes For Permutations Avoiding Barred Patterns, 2009 Valparaiso University

#### Enumeration Schemes For Permutations Avoiding Barred Patterns, Lara Pudwell

*Lara K. Pudwell*

No abstract provided.

Exit Frequency Matrices For Finite Markov Chains, 2009 Macalester College

#### Exit Frequency Matrices For Finite Markov Chains, Andrew Beveridge, László Lovász

*Andrew Beveridge*

No abstract provided.

Exponential Growth Rate Of Paths And Its Connection With Dynamics, 2009 Northwestern University

#### Exponential Growth Rate Of Paths And Its Connection With Dynamics, Pengfei Zhang

*Pengfei Zhang*

No abstract provided.

Q-Partition Algebra Combinatorics, 2009 Macalester College

#### Q-Partition Algebra Combinatorics, Thomas Halverson, N. Theim

*Thomas M. Halverson*

No abstract provided.

Enumeration Schemes For Words Avoiding Permutations, 2009 Valparaiso University

#### Enumeration Schemes For Words Avoiding Permutations, Lara Pudwell

*Lara K. Pudwell*

No abstract provided.