Gait Transition Dynamics Are Modulated By Experimental Protocol, 2015 University of Connecticut - Storrs

#### Gait Transition Dynamics Are Modulated By Experimental Protocol, Mohammad Abdolvahab, Jason Gordon

*Mohammad Abdolvahab*

No abstract provided.

Castelnuovo–Mumford Regularity And Arithmetic Cohen–Macaulayness Of Complete Bipartite Subspace Arrangements, 2015 Boise State University

#### Castelnuovo–Mumford Regularity And Arithmetic Cohen–Macaulayness Of Complete Bipartite Subspace Arrangements, Zach Teitler, Douglas A. Torrence

*Mathematics Faculty Publications and Presentations*

We give the Castelnuovo–Mumford regularity of arrangements of (n−2)-planes in P^{n} whose incidence graph is a sufficiently large complete bipartite graph, and determine when such arrangements are arithmetically Cohen–Macaulay.

The Dirichlet Spectral Radius Of Trees, 2015 Qingdao University of Science and Technology

#### The Dirichlet Spectral Radius Of Trees, Guang-Jun Zhang, Wei-Xia Li

*Electronic Journal of Linear Algebra*

In this paper, the trees with the largest Dirichlet spectral radius among all trees with a given degree sequence are characterized. Moreover, the extremal graphs having the largest Dirichlet spectral radius are obtained in the sets ofall trees of order n with a given number of pendant vertices.

Video Event Understanding With Pattern Theory, 2015 University of South Florida

#### Video Event Understanding With Pattern Theory, Fillipe Souza, Sudeep Sarkar, Anuj Srivastava, Jingyong Su

*MODVIS Workshop*

We propose a combinatorial approach built on Grenander’s pattern theory to generate semantic interpretations of video events of human activities. The basic units of representations, termed generators, are linked with each other using pairwise connections, termed bonds, that satisfy predefined relations. Different generators are specified for different levels, from (image) features at the bottom level to (human) actions at the highest, providing a rich representation of items in a scene. The resulting configurations of connected generators provide scene interpretations; the inference goal is to parse given video data and generate high-probability configurations. The probabilistic structures are imposed using energies ...

Non-Orientable Objects As Gaming Surfaces, 2015 Portland State University

#### Non-Orientable Objects As Gaming Surfaces, Haley P. Bourke, Paul Latiolais

*Student Research Symposium*

Developed in Python, Klein Space Fighter is an interactive learning tool and mathematically themed arcade game that allows the player to combat on different mathematical surfaces including a 2D Klein bottle. The app is available for Android and desktop devices, and will be made available for iOS in the future.

To receive an invitation to download the app through Google Play, contact me at HaleyoBourke@yahoo.com

Second Hamiltonian Cycles In Claw-Free Graphs, 2015 Georgia Southern University

#### Second Hamiltonian Cycles In Claw-Free Graphs, Hossein Esfandiari, Colton Magnant, Pouria Salehi Nowbandegani, Shirdareh Haghighi

*Theory and Applications of Graphs*

Sheehan conjectured in 1975 that every Hamiltonian regular simple graph of even degree at least four contains a second Hamiltonian cycle. We prove that most claw-free Hamiltonian graphs with minimum degree at least 3 have a second Hamiltonian cycle and describe the structure of those graphs not covered by our result. By this result, we show that Sheehan’s conjecture holds for claw-free graphs whose order is not divisible by 6. In addition, we believe that the structure that we introduce can be useful for further studies on claw-free graphs.

Student Understanding Of Function And Success In Calculus, 2015 Boise State University

#### Student Understanding Of Function And Success In Calculus, Daniel I. Drlik

*Boise State University Theses and Dissertations*

The purpose of this study was to determine if there is a relationship between student success in calculus and student understanding of function. Student understanding of function was measured using two questionnaires, one of which is a modification of an existing measure based on APOS theory. The other I developed with items from the concept image literature. The participants of this study were 116 high school students who were enrolled in a first-year calculus course. The results of the questionnaires were aligned to course exam scores to determine connections between function understanding and rate of success in calculus.

A major ...

Projected Composition Operators On The Dirichlet Space, 2015 Washington University in St Louis

#### Projected Composition Operators On The Dirichlet Space, Patrick Lopatto

*Arts & Sciences Electronic Theses and Dissertations*

A projected composition operator is a composition operator composed with a projection. Rochberg has proven several results concerning projected composition operators on the Hardy space. Building on his work, I prove analogous results for projected composition operators on the Dirichlet space. This thesis features explicit examples, d-bar techniques, and probabilistic methods.

Distance-2 Domatic Numbers Of Graphs, 2015 East Tennessee State University

#### Distance-2 Domatic Numbers Of Graphs, Derek Kiser

*Electronic Theses and Dissertations*

The distance d(u, v) between two vertices u and v in a graph G equals the length of a shortest path from u to v. A set S of vertices is called a distance-2 dominating set if every vertex in V \S is within distance-2 of at least one vertex in S. The distance-2 domatic number is the maximum number of sets in a partition of the vertices of G into distance-2 dominating sets. We give bounds on the distance-2 domatic number of a graph and determine the distance-2 domatic number of selected classes of graphs.

Loewner Space-Filling Curves, 2015 University of Tennessee, Knoxville

#### Loewner Space-Filling Curves, Hannah Marie Clark

*University of Tennessee Honors Thesis Projects*

No abstract provided.

An Intuitionstic Fuzzy Meet Semi L- Filter, 2015 Innovative Research Publications

#### An Intuitionstic Fuzzy Meet Semi L- Filter, Innovative Research Publications Irp India, R. Arimalar, B. Anandh

*Innovative Research Publications IRP India*

In this Paper, Intuitionistic fuzzy meet semi L-filter and Intuitionistic fuzzy level meet semi L-filter are defined. Also some theorems are derived.Some examples are provided

A Hierarchical Graph For Nucleotide Binding Domain 2, 2015 East Tennessee State University

#### A Hierarchical Graph For Nucleotide Binding Domain 2, Samuel Kakraba

*Electronic Theses and Dissertations*

One of the most prevalent inherited diseases is cystic fibrosis. This disease is caused by a mutation in a membrane protein, the cystic fibrosis transmembrane conductance regulator (CFTR). CFTR is known to function as a chloride channel that regulates the viscosity of mucus that lines the ducts of a number of organs. Generally, most of the prevalent mutations of CFTR are located in one of two nucleotide binding domains, namely, the nucleotide binding domain 1 (NBD1). However, some mutations in nucleotide binding domain 2 (NBD2) can equally cause cystic fibrosis. In this work, a hierarchical graph is built for NBD2 ...

Exploring Ways Of Identifying Outliers In Spatial Point Patterns, 2015 East Tennessee State University

#### Exploring Ways Of Identifying Outliers In Spatial Point Patterns, Jie Liu

*Electronic Theses and Dissertations*

This work discusses alternative methods to detect outliers in spatial point patterns.

Outliers are defined based on location only and also with respect to associated variables. Throughout the thesis we discuss five case studies, three of them come from experiments with spiders and bees, and the other two are data from earthquakes in a certain region. One of the main conclusions is that when detecting outliers from the point of view of location we need to take into consideration both the degree of clustering of the events and the context of the study. When detecting outliers from the point of ...

Invariant Basis Number And Basis Types For C*-Algebras, 2015 University of Nebraska-Lincoln

#### Invariant Basis Number And Basis Types For C*-Algebras, Philip M. Gipson

*Dissertations, Theses, and Student Research Papers in Mathematics*

We develop the property of Invariant Basis Number (IBN) in the context of C*-algebras and their Hilbert modules. A complete K-theoretic characterization of C*- algebras with IBN is given. A scheme for classifying C*-algebras which do not have IBN is given and we prove that all such classes are realized. We investigate the invariance of IBN, or lack thereof, under common C*-algebraic construction and perturbation techniques. Finally, applications of Invariant Basis Number to the study of C*-dynamical systems and the classification program are investigated.

Adviser: David Pitts

Knörrer Periodicity And Bott Periodicity, 2015 University of Nebraska-Lincoln

#### Knörrer Periodicity And Bott Periodicity, Michael K. Brown

*Dissertations, Theses, and Student Research Papers in Mathematics*

The main goal of this dissertation is to explain a precise sense in which Knörrer periodicity in commutative algebra is a manifestation of Bott periodicity in topological K-theory. In Chapter 2, we motivate this project with a proof of the existence of an 8-periodic version of Knörrer periodicity for hypersurfaces defined over the real numbers. The 2- and 8-periodic versions of Knörrer periodicity for complex and real hypersurfaces, respectively, mirror the 2- and 8-periodic versions of Bott periodicity in *KU*- and *KO*-theory. In Chapter 3, we introduce the main tool we need to demonstrate the compatibility between Knörrer periodicity ...

Analysis Of Discrete Fractional Operators And Discrete Fractional Rheological Models, 2015 Western Kentucky University

#### Analysis Of Discrete Fractional Operators And Discrete Fractional Rheological Models, Meltem Uyanik

*Masters Theses & Specialist Projects*

This thesis is comprised of two main parts: Monotonicity results on discrete fractional operators and discrete fractional rheological constitutive equations. In the first part of the thesis, we introduce and prove new monotonicity concepts in discrete fractional calculus. In the remainder, we carry previous results about fractional rheological models to the discrete fractional case. The discrete method is expected to provide a better understanding of the concept than the continuous case as this has been the case in the past. In the first chapter, we give brief information about the main results. In the second chapter, we present some fundamental ...

Extremal Results For The Number Of Matchings And Independent Sets, 2015 University of Nebraska - Lincoln

#### Extremal Results For The Number Of Matchings And Independent Sets, Lauren Keough

*Dissertations, Theses, and Student Research Papers in Mathematics*

This dissertation answers several questions in extremal graph theory, each concerning the maximum or minimum number of certain substructures a graph can have, given that it must satisfy certain properties. In recent years there has been increased interest in such problems, which are extremal problems for "counting" parameters of graphs. The results in this dissertation focus on graphs that have *n* vertices and *e* edges and 3-uniform hypergraphs that have *n* vertices and *e* edges.

We first observe in the preliminaries chapter that for graphs with a fixed number of vertices and edges there is a threshold graph attaining the ...

Counting Convex Sets On Products Of Totally Ordered Sets, 2015 Western Kentucky University

#### Counting Convex Sets On Products Of Totally Ordered Sets, Brandy Amanda Barnette

*Masters Theses & Specialist Projects*

The main purpose of this thesis is to find the number of convex sets on a product of two totally ordered spaces. We will give formulas to find this number for specific cases and describe a process to obtain this number for all such spaces. In the first chapter we briefly discuss the motivation behind the work presented in this thesis. Also, the definitions and notation used throughout the paper are introduced here The second chapter starts with examining the product spaces of the form {1; 2; : : : ;n} × {1; 2}. That is, we begin by analyzing a two-row by n-column ...

The Apprentices' Tower Of Hanoi, 2015 East Tennessee State University

#### The Apprentices' Tower Of Hanoi, Cory Bh Ball

*Electronic Theses and Dissertations*

The Apprentices' Tower of Hanoi is introduced in this thesis. Several bounds are found in regards to optimal algorithms which solve the puzzle. Graph theoretic properties of the associated state graphs are explored. A brief summary of other Tower of Hanoi variants is also presented.

Teaching Algebra: A Comparison Of Scottish And American Perspectives, 2015 East Tennessee State University

#### Teaching Algebra: A Comparison Of Scottish And American Perspectives, Brittany Munro

*Undergraduate Honors Theses*

A variety of factors influence what teaching strategies an educator uses. I analyze survey responses from algebra teachers in Scotland and Appalachia America to discover how a teacher's perception of these factors, particularly their view of mathematics itself, determines the pedagogical strategies employed in the classroom.