Mathematics Commons^™

Second-Order Convex Splitting Schemes For Gradient Flows With Ehrlich-Schwoebel Type Energy: Application To Thin Film Epitaxy, Jie Shen, Cheng Wang, Xiaoming Wang, Steven M. Wise

Mathematics and Statistics Faculty Research & Creative Works

We construct unconditionally stable, unconditionally uniquely solvable, and second order accurate (in time) schemes for gradient flows with energy of the form {equation presented} dx. the construction of the schemes involves the appropriate combination and extension of two classical ideas: (i) appropriate convex-concave decomposition of the energy functional and (ii) the secant method. as an application, we derive schemes for epitaxial growth models with slope selection (F(y) = 1/4 (|y| 2 - 1) 2) or without slope selection (F(y) = -1/2 ln(1 + |y| 2)). Two types of unconditionally stable uniquely solvable second-order schemes are presented. the first type inherits …

Long Time Stability Of A Classical Efficient Scheme For Two-Dimensional Navier-Stokes Equations, S. Gottlieb, F. Tone, C. Wang, X. Wang, D. Wirosoetisno

Mathematics and Statistics Faculty Research & Creative Works

This paper considers the long-time stability property of a popular semi-implicit scheme for the two-dimensional incompressible Navier-Stokes equations in a periodic box that treats the viscous term implicitly and the nonlinear advection term explicitly. We consider both the semi discrete (discrete in time but continuous in space) and fully discrete schemes with either Fourier Galerkin spectral or Fourier pseudo spectral (collocation) methods. We prove that in all cases, the scheme is long time stable provided that the timestep is sufficiently small. the long-time stability in the L 2 and H 1 norms further leads to the convergence of the global …

Interactive Concept To Aid In Understanding Dimensional Analysis, Alicia Hicks

Symposium 2012

Many students struggle with learning how to utilize dimensional analysis. This confusion is due to not understanding the concept of dose per volume, leading to difficulty when starting the sequencing. This could be one of the contributing causes to medication errors in clinical practice. Does using models, such as Play-doh and pebbles, help students learn the concept of milligrams per milliliters when calculating dosages using dimensional analysis method? A series of pre- and post-tests are used to measure learning growth in each of the treatment groups. Three treatment groups were utilized: Control: one group had no intervention between the pre …

Development Of Nabla Fractional Calculus And A New Approach To Data Fitting In Time Dependent Cancer Therapeutic Study, Nihan Acar

Masters Theses & Specialist Projects

The aim of this thesis is to develop discrete fractional models of tumor growth for a given data and to estimate parameters of these models in order to have better data tting. We use discrete nabla fractional calculus because we believe the discrete counterpart of this mathematical theory will give us a better and more accurate outcome.

This thesis consists of ve chapters. In the rst chapter, we give the history of the fractional calculus, and we present some basic de nitions and properties that are used in this theory. We de ne nabla fractional exponential and then nabla fractional …

Quantitative Patterns Of Stylistic Influence In The Evolution Of Literature, James M. Hughes, Nicholas J. Foti, David C. Krakauer, Daniel N. Rockmore

Dartmouth Scholarship

Literature is a form of expression whose temporal structure, both in content and style, provides a historical record of the evolution of culture. In this work we take on a quantitative analysis of literary style and conduct the first large-scale temporal stylometric study of literature by using the vast holdings in the Project Gutenberg Digital Library corpus. We find temporal stylistic localization among authors through the analysis of the similarity structure in feature vectors derived from content-free word usage, nonhomogeneous decay rates of stylistic influence, and an accelerating rate of decay of influence among modern authors. Within a given time …

On A Problem Of Burnside, Matthew Mizuhara

Honors Theses

Burnside posed the question as to whether or not there exist groups having an external automorphism that behaves in a certain, specific way like an inner automorphism: we shall define such automorphisms to be nearly-inner.

NI-groups are fairly rare. With the aid of the computer algebra system Magma - in particular with the aid of its small group database - we set out to test this hypothesis.

A Comparison Of Van Hiele Levels And Final Exam Grades Of Students At The University Of Southern Mississippi, Cononiah Watson

Honors Theses

This research analyzed students final exam scores in a college mathematics class with geometric components and their van Hiele levels upon entering the class. After the class was completed, each student’s final exam grade was calculated. The researcher used a Spearman correlation to compare the two; the result was a correlation coefficient of 0.742. The researcher then reported that the results of the van Hiele test are a major component in predicting a student’s success in such a class.

Unfolding Prismatoids As Convex Patches: Counterexamples And Positive Results, Joseph O'Rourke

Computer Science: Faculty Publications

We address the unsolved problem of unfolding prismatoids in a new context, viewing a “topless prismatoid” as a convex patch—a polyhedral subset of the surface of a convex polyhedron homeomorphic to a disk. We show that several natural strategies for unfolding a prismatoid can fail, but obtain a positive result for “petal unfolding” topless prismatoids. We also show that the natural extension to a convex patch consisting of a face of a polyhedron and all its incident faces, does not always have a nonoverlapping petal unfolding. However, we obtain a positive result by excluding the problematical patches. This then leads …

Computational Modeling And Numerical Methods For Spaciotemporal Calcium Cycling In Ventricular Myocytes, Robert Rovetti

Mathematics, Statistics and Data Science Faculty Works

Intracellular calcium (Ca) cycling dynamics in cardiac myocytes is regulated by a complex network of spatially distributed organelles, such as sarcoplasmic reticulum (SR), mitochondria, and myofibrils. In this study, we present a mathematical model of intracellular Ca cycling and numerical and computational methods for computer simulations. The model consists of a coupled Ca release unit (CRU) network, which includes a SR domain and a myoplasm domain. Each CRU contains 10 L-type Ca channels and 100 ryanodine receptor channels, with individual channels simulated stochastically using a variant of Gillespie’s method, modified here to handle time-dependent transition rates. Both the SR domain …

A Survey Of Line Graphs And Hamiltonian Paths, Meagan Field

Math Theses

In this paper, we are going to explore a survey of line graphs and hamiltonian paths. Research concerning line graphs and hamiltonian paths started in the 1960's. We will investigate some recent theorems and proofs covering this topic. At the end, we will prove a main result involving line graphs and hamiltonian paths.

Conformational Switching And Graph Grammar: Abstract Models Of Self-Assembly, Arnab Dutta

Math Theses

Abstract models of self-assembly are mathematical models that capture the behavior of natural or artificial self-assembling systems. In 1995, conformational switching in self-assembling mechanical systems was introduced and an abstract model of self-assembling systems, conformational switching model, was later developed where assembly instructions are written as rules representing the conformational changes of self-assembling components. In 2004, another abstract model named graph grammar was developed to self-assemble a prespecified graph structure by generating a grammar or a set of rules. We first provide the concepts related to the abstract models of self-assembly, followed by a brief history of the development of …

Item Response Models For Dichotomous And Polytomous Data In The Context Of Generalized Linear Models With Applications, Grant Campbell

Math Theses

Item response theory is a test theory, in contrast to classical test theory, that focuses on the individual items of an exam in order to analyze test accuracy amd reliability, and evaluate examinee ability levels. Developed in the mid 20th century, item response theory, or IRT, is consider superior in a number of ways to many other test theory approaches. Provided here is an overview of basic IRT models using the a test theory approach, as well as the development of IRT models in the context of generalized linear models. Binary, correct/incorrect, response and polytomous, or multiple, response items are …

Fundamentals Of Protein Structure Alignment, Allen Holder, Mark Brandt, Yosi Shibberu

Mathematical Sciences Technical Reports (MSTR)

The central dogma of molecular biology asserts a one way transfer of information from a cell’s genetic code to the expression of proteins. Proteins are the functional workhorses of a cell, and studying these molecules is at the foundation of much of computational biology. Our goal here is to present a succinct introduction to the biological, mathematical, and computational aspects of making pairwise comparisons between protein structures. The presentation is intended to be useful for those who are entering this research area. The chapter begins with a brief introduction to the biology of protein comparison, which is followed by a …

Liar's Domination In Grid Graphs, Christopher Kent Sterling

Electronic Theses and Dissertations

As introduced by Slater in 2008, liar's domination provides a way of modeling protection devices where one may be faulty. Assume each vertex of a graph G is the possible location for an intruder such as a thief. A protection device at a vertex v is assumed to be able to detect the intruder at any vertex in its closed neighborhood N[v] and identify at which vertex in N[v] the intruder is located. A dominating set is required to identify any intruder's location in the graph G, and if any one device can fail to …

Preferential Arrangement Containment In Strict Superpatterns, Martha Louise Liendo

Electronic Theses and Dissertations

Most results on pattern containment deal more directly with pattern avoidance, or the enumeration and characterization of strings which avoid a given set of patterns. Little research has been conducted regarding the word size required for a word to contain all patterns of a given set of patterns. The set of patterns for which containment is sought in this thesis is the set of preferential arrangements of a given length. The term preferential arrangement denotes strings of characters in which repeated characters are allowed, but not necessary. Cardinalities for sets of all preferential arrangements of given lengths and alphabet sizes …

Computable Linear Orders And Turing Reductions, Whitney P. Turner

Master's Theses

This thesis explores computable linear orders through Turing Reductions and codes zero jump and zero double jump into linear orders using discrete, dense, and block linear relations.

Source Unfoldings Of Convex Polyhedra Via Certain Closed Curves, Jin-Ichi Itoh, Joseph O'Rourke, Costin Vîlcu

Computer Science: Faculty Publications

Abstract. We extend the notion of a source unfolding of a convex polyhedron P to be based on a closed polygonal curve Q in a particular class rather than based on a point. The class requires that Q “lives on a cone” to both sides; it includes simple, closed quasigeodesics. Cutting a particular subset of the cut locus of Q (in P) leads to a non-overlapping unfolding of the polyhedron. This gives a new general method to unfold the surface of any convex polyhedron to a simple, planar polygon

On Algorithmic Fractional Packings Of Hypergraphs, Jill Dizona

USF Tampa Graduate Theses and Dissertations

Let F₀ be a fixed k-uniform hypergraph, and let H be a given k-uniform hypergraph on n vertices. An F₀-packing of H is a family F of edge-disjoint copies of F₀ which are subhypergraphs in H. Let n_F0(H) denote the maximum size |F| of an F₀-packing F of H. It is well-known that computing n_F0(H) is NP-hard for nearly any choice of F₀.

In this thesis, we consider the special case when F₀ is a linear hypergraph, that is, when no two edges …

Wronskian, Grammian And Pfaffian Solutions To Nonlinear Partial Differential Equations, Alrazi Abdeljabbar

USF Tampa Graduate Theses and Dissertations

It is significantly important to search for exact soliton solutions to nonlinear partial differential equations (PDEs) of mathematical physics. Transforming nonlinear PDEs into bilinear forms using the Hirota differential operators enables us to apply the Wronskian and Pfaffian techniques to search for exact solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili (KP) equation with not only constant coefficients but also variable coefficients under a certain constraint

(u_t + α ₁(t)u_xxy + 3α ₂(t)u_xu_y)_x +α ₃ (t)u_ty -α ₄(t)u_zz + α ₅(t)(u_x + α ₃(t)u_y) = …

A Study Of Women Working In The Actuarial Field, Jillian Emberg

Honors Projects in Mathematics

The goal of this project is to examine how women fit into the actuarial career path and how cultural expectations, biological factors, and personal aspirations affect their experiences in the field. Dramatic changes in the profession have occurred since its emergence in the nineteenth century to become more welcoming to women who choose to enter the profession. However, despite the equalizing demographic shifts of the field, it is still a male-dominated profession. This paper attempts to analyze why some of the changes in the demographics of the field have occurred as well as explain what factors contribute to women’s underrepresentation …