Physical Sciences and Mathematics Commons^™

New Eurasian Continental Bridgehead Lianyungang, Qiaoqiao Wu

World Maritime University Dissertations

No abstract provided.

An Application Of Armitage Trend Test To Genome-Wide Association Studies, Nigel A. Scott

Mathematics Theses

Genome-wide Association (GWA) studies have become a widely used method for analyzing genetic data. It is useful in detecting associations that may exist between particular alleles and diseases of interest. This thesis investigates the dataset provided from problem 1 of the Genetic Analysis Workshop 16 (GAW 16). The dataset consists of GWA data from the North American Rheumatoid Arthritis Consortium (NARAC). The thesis attempts to determine a set of single nucleotide polymorphisms (SNP) that are associated significantly with rheumatoid arthritis. Moreover, this thesis also attempts to address the question of whether the one-sided alternative hypothesis that the minor allele is …

Multistability In Bursting Patterns In A Model Of A Multifunctional Central Pattern Generator., Matthew Bryan Brooks

Mathematics Theses

A multifunctional central pattern generator (CPG) can produce bursting polyrhythms that determine locomotive activity in an animal: for example, swimming and crawling in a leech. Each rhythm corresponds to a specific attractor of the CPG. We employ a Hodgkin-Huxley type model of a bursting leech heart interneuron, and connect three such neurons by fast inhibitory synapses to form a ring. This network motif exhibits multistable co-existing bursting rhythms. The problem of determining rhythmic outcomes is reduced to an analysis of fixed points of Poincare mappings and their attractor basins, in a phase plane defined by the interneurons' phase differences along …

Asymptotic Dynamics Of Attractive-Repulsive Swarms, Andrew J. Leverentz '08, Chad M. Topaz, Andrew J. Bernoff

All HMC Faculty Publications and Research

We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the density with a kernel describing attractive-repulsive social interactions. The kernel’s first moment and its limiting behavior at the origin determine whether the population asymptotically spreads, contracts, or reaches steady state. For the spreading case, the dynamics approach those of the porous medium equation. The widening, compactly supported population has edges that behave like traveling waves whose speed, density, and slope we calculate. …

Two Problems On Bipartite Graphs, Albert Bush

Mathematics Theses

Erdos proved the well-known result that every graph has a spanning, bipartite subgraph such that every vertex has degree at least half of its original degree. Bollobas and Scott conjectured that one can get a slightly weaker result if we require the subgraph to be not only spanning and bipartite, but also balanced. We prove this conjecture for graphs of maximum degree 3.

The majority of the paper however, will focus on graph tiling. Graph tiling (or sometimes referred to as graph packing) is where, given a graph H, we find a spanning subgraph of some larger graph G that …

Advanced Statistical Methodologies In Determining The Observation Time To Discriminate Viruses Using Ftir, Shan Luo

Mathematics Theses

Fourier transform infrared (FTIR) spectroscopy, one method of electromagnetic radiation for detecting specific cellular molecular structure, can be used to discriminate different types of cells. The objective is to find the minimum time (choice among 2 hour, 4 hour and 6 hour) to record FTIR readings such that different viruses can be discriminated. A new method is adopted for the datasets. Briefly, inner differences are created as the control group, and Wilcoxon Signed Rank Test is used as the first selecting variable procedure in order to prepare the next stage of discrimination. In the second stage we propose either partial …

Almost Avoiding Permutations, Robert Brignall, Shalosh B. Ekhad, Rebecca Smith, Vincent Vatter

Dartmouth Scholarship

The permutation π of length n, written in one-line notation as π (1)π (2)· · · π (n), is said to contain the permutation σ if π has a subsequence that is order isomorphic to σ, and each such subsequence is said to be an occurrence of σ in π or simply a σ pattern. For example, π = 491867532 contains σ = 51342 because of the subsequence π (2)π (3)π (5)π (6)π (9) = 91672. Permutation containment is easily seen to be a partial order on the set of all (finite) permutations, which we simply denote by ≤. If …

The Expectation Of Transition Events On Finite-State Markov Chains, Jeremy Michael West

Theses and Dissertations

Markov chains are a fundamental subject of study in mathematical probability and have found wide application in nearly every branch of science. Of particular interest are finite-state Markov chains; the representation of finite-state Markov chains by a transition matrix facilitates detailed analysis by linear algebraic methods. Previous methods of analyzing finite-state Markov chains have emphasized state events. In this thesis we develop the concept of a transition event and define two types of transition events: cumulative events and time-average events. Transition events generalize state events and provide a more flexible framework for analysis. We derive computable, closed-form expressions for the …

Submodular Percolation, Graham R. Brightwell, Peter Winkler

Dartmouth Scholarship

Let $f:{\cal L}\to\mathbb{R}$ be a submodular function on a modular lattice ${\cal L}$; we show that there is a maximal chain ${\cal C}$ in ${\cal L}$ on which the sequence of values of f is minimal among all paths from 0 to 1 in the Hasse diagram of ${\cal L}$, in a certain well-behaved partial order on sequences of reals. One consequence is that the maximum value of f on ${\cal C}$ is minimized over all such paths—i.e., if one can percolate from 0 to 1 on lattice points X with $f(X)\le b$, then one can do so along a …

The Orbifold Landau-Ginzburg Conjecture For Unimodal And Bimodal Singularities, Natalie Wilde Bergin

Theses and Dissertations

The Orbifold Landau-Ginzburg Mirror Symmetry Conjecture states that for a quasihomogeneous singularity W and a group G of symmetries of W, there is a dual singularity WT and dual group GT such that the orbifold A-model of W/G is isomorphic to the orbifold B-model of WT/GT. The Landau-Ginzburg A-model is the Frobenius algebra HW,G constructed by Fan, Jarvis, and Ruan, and the B-model is the Orbifold Milnor ring of WT . The unorbifolded conjecture has been verified for Arnol'd's list of simple, unimodal and bimodal quasi-homogeneous singularities with G the maximal diagonal symmetry group by Priddis, Krawitz, Bergin, Acosta, et …

Development Of Scoring Rubrics And Pre-Service Teachers Ability To Validate Mathematical Proofs, Timothy J. Middleton

Mathematics & Statistics ETDs

The basic aim of this exploratory research study was to determine if a specific instructional strategy, that of developing scoring rubrics within a collaborative classroom setting, could be used to improve pre-service teachers facility with proofs. During the study, which occurred in a course for secondary mathematics teachers, the primary focus was on creating and implementing a scoring rubric, rather than on direct instruction about proofs. In general, the study had very mixed results. Statistically, the quantitative data indicated no significant improvement occurred in participants' ability to validate proofs. However, the qualitative results and the considerable improvement by some participants …

Some Congruence Properties Of Pell's Equation, Nathan C. Priddis

Theses and Dissertations

In this thesis I will outline the impact of Pell's equation on various branches of number theory, as well as some of the history. I will also discuss some recently discovered properties of the solutions of Pell's equation.

Evans Function Computation, Blake H. Barker

Theses and Dissertations

In this thesis, we review the stability problem for traveling waves and discuss the Evans function, an emerging tool in the stability analysis of traveling waves. We describe some recent developments in the numerical computation of the Evans function and discuss STABLAB, an interactive MATLAB based tool box that we developed. In addition, we verify the Evans function for shock layers in Burgers equation and the p-system with and without capillarity, as well as pulses in the generalized Kortweg-de Vries (gKdV) equation. We conduct a new study of parallel shock layers in isentropic magnetohydrodynamics (MHD) obtaining results consistent with stability.

Numerical Solutions For Stochastic Differential Equations And Some Examples, Yi Luo

Theses and Dissertations

In this thesis, I will study the qualitative properties of solutions of stochastic differential equations arising in applications by using the numerical methods. It contains two parts. In the first part, I will first review some of the basic theory of the stochastic calculus and the Ito-Taylor expansion for stochastic differential equations (SDEs). Then I will discuss some numerical schemes that come from the Ito-Taylor expansion including their order of convergence. In the second part, I will use some schemes to solve the stochastic Duffing equation, the stochastic Lorenz equation, the stochastic pendulum equation, and the stochastic equations which model …

Properties Of The Zero Forcing Number, Kayla Denise Owens

Theses and Dissertations

The zero forcing number is a graph parameter first introduced as a tool for solving the minimum rank problem, which is: Given a simple, undirected graph G, and a field F, let S(F,G) denote the set of all symmetric matrices A=[a_{ij}] with entries in F such that a_{ij} doess not equal 0 if and only if ij is an edge in G. Find the minimum possible rank of a matrix in S(F,G). It is known that the zero forcing number Z(G) provides an upper bound for the maximum nullity of a graph. I investigate properties of the zero forcing number, …

Weighted Composition Operators From Logarithmic Bloch-Type Spaces To Bloch-Type Spaces, Stevo Stevic, Ravi P. Agarwal

Mathematics and System Engineering Faculty Publications

The boundedness and compactness of the weighted composition operators from to Bloch-type spaces are studied here. © 2009 S. Stević and R. P. Agarwal.

Section Abstracts: Astronomy, Mathematics, And Physics & Materials Science

Virginia Journal of Science

Abstracts of the Astronomy, Mathematics and Physics & Materials Science Section for the 87th Annual Meeting of the Virginia Academy of Science, May 27-29, 2009, Virginia Commonwealth University, Richmond VA.

Variational Analysis In Semi-Infinite And Infinite Programming, Ii: Necessary Optimality Conditions, M J. Cánovas, M A. Lopez, Boris S. Mordukhovich, J Parra

Mathematics Research Reports

This paper concerns applications of advanced techniques of variational analysis and generalized differentiation to problems of semi-infinite and infinite programming with feasible solution sets defined by parameterized systems of infinitely many linear inequalities of the type intensively studied in the preceding development [5] from our viewpoint of robust Lipschitzian stability. We present meaningful interpretations and practical examples of such models. The main results establish necessary optimality conditions for a broad class of semi-infinite and infinite programs, where objectives are generally described by nonsmooth and nonconvex functions on Banach spaces and where infinite constraint inequality systems are indexed by arbitrary sets. …

Pointed Trees Of Projective Spaces, Linda Chen, A. Gibney, D. Krashen

Mathematics & Statistics Faculty Works

We introduce a smooth projective variety T(d,n) which compactifies the space of configurations of it distinct points oil affine d-space modulo translation and homothety. The points in the boundary correspond to n-pointed stable rooted trees of d-dimensional projective spaces, which for d = 1, are (n + 1)-pointed stable rational curves. In particular, T(1,n) is isomorphic to ($) over bar (0,n+1), the moduli space of such curves. The variety T(d,n) shares many properties with (M) over bar (0,n+1). For example, as we prove, the boundary is a smooth normal crossings divisor whose components are products of T(d,i) for i < n and it has an inductive construction analogous to but differing from Keel's for (0,n+1). This call be used to describe its Chow groups and Chow motive generalizing [Trans. Airier. Math. Soc. 330 (1992), 545-574]. It also allows us to compute its Poincare polynomials, giving all alternative to the description implicit in [Progr. Math., vol. 129, Birkhauser, 1995, pp. 401-417]. We give a presentation of the Chow rings of T(d,n), exhibit explicit dual bases for the dimension I and codimension 1 cycles. The variety T(d,n) is embedded in the Fulton-MacPherson spaces X[n] for any smooth variety X, and we use this connection in a number of ways. In particular we give a family of ample divisors on T(d,n) and an inductive presentation of the Chow motive of X[n]. This also gives an inductive presentation of the Chow groups of X[n] analogous to Keel's presentation for (M) over bar (0,n+1), solving a problem posed by Fulton and MacPherson.

A Semilinear Wave Equation With Smooth Data And No Resonance Having No Continuous Solution, Jose F. Caicedo, Alfonso Castro

All HMC Faculty Publications and Research

We prove that a boundary value problem for a semilinear wave equation with smooth nonlinearity, smooth forcing, and no resonance cannot have continuous solutions. Our proof shows that this is due to the non-monotonicity of the nonlinearity.

Harmonic Functions On R-Covered Foliations And Group Actions On The Circle, Sergio Fenley, Renato Feres, Kamlesh Parwani

Faculty Research and Creative Activity

Let (M,F) be a compact codimension-one foliated manifold whose leaves are equipped with Riemannian metrics, and consider continuous functions on M that are harmonic along the leaves of F. If every such function is constant on leaves we say that (M,F) has the Liouville property. Our main result is that codimension-one foliated bundles over compact negatively curved manifolds satisfy the Liouville property. Related results for R-covered foliations, as well as for discrete group actions and discrete harmonic functions, are also established.

Harmonic Functions On R-Covered Foliations And Group Actions On The Circle, Sergio Fenley, Renato Feres, Kamlesh Parwani

Faculty Research and Creative Activity

Let (M,F) be a compact codimension-one foliated manifold whose leaves are equipped with Riemannian metrics, and consider continuous functions on M that are harmonic along the leaves of F. If every such function is constant on leaves we say that (M,F) has the Liouville property. Our main result is that codimension-one foliated bundles over compact negatively curved manifolds satisfy the Liouville property. Related results for R-covered foliations, as well as for discrete group actions and discrete harmonic functions, are also established.

The Journal (Wheel) Keeps On Turning, Bharath Sriraman

The Mathematics Enthusiast

No abstract provided.

Small Change - Big Difference, Ilana Lavy, Atara Shriki

The Mathematics Enthusiast

Starting in a well known theorem concerning medians of triangle and using the ‘What If Not?’ strategy, we describe an example of an activity in which some relations among segments and areas in triangle were revealed. Some of the relations were proved by means of Affine Geometry.

An Application Of Gröbner Bases, Shengxiang Xia, Gaoxiang Xia

The Mathematics Enthusiast

In this paper, we program a procedure using Maple's packages, with it we can realize mechanical proving of some theorems in elementary geometry.

Tme Volume 6, Number 3

The Mathematics Enthusiast

No abstract provided.

Who Can Solve 2x=1? An Analysis Of Cognitive Load Related To Learning Linear Equation Solving, Timo Tossavainen

The Mathematics Enthusiast

Using 2x = 1 as an example, we discuss the cognitive load related to learning linear equation solving. In the framework of the Cognitive Load Theory we consider especially the intrinsic cognitive load needed in arithmetical, geometrical and real analytical approach to linear equation solving. This will be done e.g. from the point of view of the conceptual and procedural knowledge of mathematics and the APOS Theory. Basing on our observations, in the end of the paper we design a setting for teaching linear equation solving.

Book Review: What's All The Commotion Over Commognition? A Review Of Anna Sfard's Thinking As Communicating, Bharath Sriraman

The Mathematics Enthusiast

If straight edge and compass constructions are the so-called “atoms” of Euclidean geometry, if sequences are the “atoms” of Analysis, then what are the “atoms” (if any) of mathematics education? Arguably mathematics education is a much wider field than Euclidean Geometry or Elementary Analysis, however there are several fundamental things that the field purports to study, chief among which is mathematical thinking or more generally “thinking”. The book under review, though it appears in a Cambridge University Press series entitled Learning in Doing: Social, Cognitive, and Computational Perspectives, is in my view situated at the intersection of Consciousness Studies, …

Helping Teachers Un-Structure: A Promising Approach, Eric Hsu, Judy Kysh, Katherine Ramage, Diane Resek

The Mathematics Enthusiast

The amount of overt structure in the presentation of a task affects students’ engagement, creativity, and willingness to tolerate frustration. In a professional development project, with algebra teachers from nine American schools, we tried to help teachers make judicious decisions in their use of structure by having them facilitate low-structure tasks, remove structure from overly structured tasks, and observe “at-risk” students engaged in learning through low-structure tasks. Project schools that worked on structuring generally improved their algebra passing rates, both overall and for African-American students.

Intuitions Of "Infinite Numbers": Infinite Magnitude Vs. Infinite Representation, Ami Mamolo

The Mathematics Enthusiast

This study examines undergraduate students’ emerging conceptions of infinity as manifested in their engagement with geometric tasks. Students’ attempts to reduce the level of abstraction of infinity and properties of infinite quantities are described. Their arguments revealed they perceive infinity as an ongoing process, rather than a completed one, and fail to notice conflicting ideas. In particular, confusion between the infinite magnitude of points on a line segment and the infinite representation of real numbers was observed. Furthermore, students struggled to draw a connection between real numbers and their representation on a number line.