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.

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 ...

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.

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

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.

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 ...

Solving Ordinary Differential Equations Using Differential Forms And Lie Groups, 2015 Liberty University

#### Solving Ordinary Differential Equations Using Differential Forms And Lie Groups, Richard M. Shumate

*Senior Honors Theses*

Differential equations have bearing on practically every scientific field. Though they are prevalent in nature, they can be challenging to solve. Most of the work done in differential equations is dependent on the use of many methods to solve particular types of equations. Sophus Lie proposed a modern method of solving ordinary differential equations in the 19th century along with a coordinate free variation of finding the infinitesimal generator by combining the influential work of Élie Cartan among others in the field of differential geometry. The driving idea behind using symmetries to solve differential equations is that there exists a ...

From The High Seas To Life Insurance: The Mathematics Of Nathaniel Bowditch, 2015 Keene State College

#### From The High Seas To Life Insurance: The Mathematics Of Nathaniel Bowditch, Maureen Moran

*Academic Excellence Conference*

Nathaniel Bowditch (1773-1838) was an American mathematician who pulled himself out of a life of poverty through self-education. Fulfilling an early passion for mathematics, he taught himself advanced topics by reading the works of the masters; he learned Latin, French, and German on his own to read mathematical texts. He became an influential mathematician, influencing future generations of research mathematicians. Bowditch corrected the mathematical tables of existing navigational references and the mathematical work of such luminaries as Newton and Laplace. In this talk we discuss how Bowditch was influenced by predecessors and in turn influenced future generations. He explained mathematics ...

Stochastic Comparisons Of Weighted Sums Of Arrangement Increasing Random Variables, 2015 University of Science and Technology of China

#### Stochastic Comparisons Of Weighted Sums Of Arrangement Increasing Random Variables, Xiaoqing Pan, Min Yuan, Subhash C. Kochar

*Mathematics and Statistics Faculty Publications and Presentations*

Assuming that the joint density of random variables X1,X2, . . . ,Xn is arrangement increasing (AI), we obtain some stochastic comparison results on weighted sums of Xi’s under some additional conditions. An application to optimal capital allocation is also given.

Mathematical Analysis Of Uniform Polyhedron (Trapezohedron) Having 2n Congruent Right Kite Faces, 4n Edges & 2n+2 Vertices Lying On A Spherical Surface By H.C. Rajpoot), 2015 M.M.M. University of Technology, Gorakhpur-273010 (UP) India

#### Mathematical Analysis Of Uniform Polyhedron (Trapezohedron) Having 2n Congruent Right Kite Faces, 4n Edges & 2n+2 Vertices Lying On A Spherical Surface By H.C. Rajpoot), Harish Chandra Rajpoot Rajpoot Hcr

*Harish Chandra Rajpoot H.C. Rajpoot*

The generalized formula are applicable on any uniform polyhedron having 2n congruent right kite faces, 4n edges & 2n+2 vertices lying on a spherical surface with a certain radius. These formula have been derived by the author Mr H.C. Rajpoot to analyse infinite no. of the uniform polyhedrons having congruent right kite faces simply by setting n=3,4,5,6,7,………………upto infinity, to calculate all the important parameters such as ratio of unequal edges, outer radius, inner radius, mean radius, surface area, volume, solid angles subtended by the polyhedron at its vertices, dihedral angles between the adjacent ...

Table Of Solid Angles Subtended By All 13 Archimedean Solids At Their Vertices, 2015 M.M.M. University of Technology, Gorakhpur-273010 (UP) India

#### Table Of Solid Angles Subtended By All 13 Archimedean Solids At Their Vertices, Harish Chandra Rajpoot Rajpoot Hcr

*Harish Chandra Rajpoot H.C. Rajpoot*

Table of the solid angles subtended at the vertices by all 13 Archimedean solids (uniform polyhedrons) calculated by the author Mr H.C. Rajpoot by using standard formula of solid angle & formula of tetrahedron. These are the standard values of solid angles which are useful for the analysis of all 13 Archimedean solids truncated tetrahedron, truncated hexahedron (cube), truncated octahedron, truncated dodecahedron, truncated icosahedron, cuboctahedron, icosidodecahedron, small rhombicuboctahedron, small rhombicosidodecahedron, snub cube, snub dodecahedron, great rhombicuboctahedron & great rhombicosidodecahedron.

Global Holomorphic Functions In Several Noncommuting Variables, 2015 University of California - San Diego

#### Global Holomorphic Functions In Several Noncommuting Variables, Jim Agler, John E. Mccarthy

*Mathematics Faculty Publications*

We define a free holomorphic function to be a function that is locally, with respect to the free topology, a bounded nc-function. We prove that free holomorphic functions are the functions that are locally uniformly approximable by free polynomials. We prove a realization formula and an Oka-Weil theorem for free analytic functions.

Examining The Literature On “Networks In Space And In Time.” An Introduction, 2015 DED - University of Macerata - Italy

#### Examining The Literature On “Networks In Space And In Time.” An Introduction, Luca De Benedictis, Prosperina Vitale, Stanley Wasserman

*Luca De Benedictis*

The Network science special issue of “Networks in space and in time: methods and applications” contributes to the debate on contextual analysis in network science. It includes seven research papers that shed light on the analysis of network phenomena studied within geographic space and across temporal dimensions. In these papers, methodological issues as well as specific applications are described from different fields. We take the seven papers, study their citations and texts, and relate them to the broader literature. By exploiting the bibliographic information and the textual data of these seven documents, citation analysis and lexical correspondence analysis allow us ...

Bytes Of Π, Spring 2015, 2015 Bridgewater State University

#### Bytes Of Π, Spring 2015, Department Of Mathematics, Bridgewater State University

*Department of Mathematics Newsletter*

No abstract provided.

Sometimes, It Is Beneficial To Process Different Types Of Uncertainty Separately, 2015 Technical Educational Institute of Epirus

#### Sometimes, It Is Beneficial To Process Different Types Of Uncertainty Separately, Chrysostomos D. Stylios, Andrzej Pownuk, Vladik Kreinovich

*Departmental Technical Reports (CS)*

In many practical situations, we make predictions based on the measured and/or estimated values of different physical quantities. The accuracy of these predictions depends on the accuracy of the corresponding measurements and expert estimates. Often, for each quantity, there are several different sources of inaccuracy. Usually, to estimate the prediction accuracy, we first combine, for each input, inaccuracies from different sources into a single expression, and then use these expressions to estimate the prediction accuracy. In this paper, we show that it is often more computationally efficient to process different types of uncertainty separately, i.e., to estimate inaccuracies ...

Once We Know That A Polynomial Mapping Is Rectifiable, We Can Algorithmically Find A Rectification, 2015 University of Texas at El Paso

#### Once We Know That A Polynomial Mapping Is Rectifiable, We Can Algorithmically Find A Rectification, Julio Urenda, David Finston, Vladik Kreinovich

*Departmental Technical Reports (CS)*

It is known that some polynomial mappings φ: C^{k} --> C^{n} are *rectifiable* in the sense that there exists a polynomial mapping α: C^{n} --> C^{n} whose inverse is also polynomial and for which α(φ(z_{1}, ...,z_{k})) = (z_{1}, ...,z_{k}, 0, ..., 0) for all z_{1}, ...,z_{k}. In many cases, the existence of such a rectification is proven indirectly, without an explicit construction of the mapping α.

In this paper, we use Tarski-Seidenberg algorithm (for deciding the first order theory of real numbers) to design an algorithm that, given a polynomial mapping φ ...

When Can We Simplify Data Processing: An Algorithmic Answer, 2015 University of Texas at El Paso

#### When Can We Simplify Data Processing: An Algorithmic Answer, Julio Urenda, Olga Kosheleva, Vladik Kreinovich, Berlin Wu

*Departmental Technical Reports (CS)*

In many real-life situations, we are interested in the values of physical quantities x_{1}, ..., x_{n} which are difficult (or even impossible) to measure directly. To estimate these values, we measure easier-to-measure quantities y_{1}, ..., y_{m} which are related to the desired quantities by a known relation, and use these measurement results to estimate x_{i}. The corresponding data processing algorithms are sometimes very complex and time-consuming, so a natural question is: are simpler (and, thus, faster) algorithms possible for solving this data processing problem? In this paper, we show that by using the known Tarski-Seidenberg algorithm, we ...