Digital Commons Network^™

Alpha-Representability Of Vector Lattices, Matthew Judson Stephenson

Honors Theses

The primary topic of this thesis is representation of vector lattices. The related theory of Boolean algebras is used as a tool to this end. In [1], Brown and Nakano present a theorem that establishes what we will call cr-representabihty for vector lattices in this thesis. We cast their proof in the light of the Boolean algebra of bands. Consequently, we show that it is the Loomis-Sikorski Theorem which makes their proof work. We then exploit this insight to study a-representability for greater cardinal numbers a. A primary goal of this thesis is to be self-contadned. As a result of …

Development Of A Laser-Induced Breakdown Spectrometer For Lead-Free Gunshot Residue Analysis, Ryan Alexander Gregg

Honors Theses

Research has demonstrated that Laser‐Induced Breakdown Spectroscopy (LIBS) can be used as an effective method of screening for the common elemental components in gunshot residue. Barium (Ba), lead (Pb), and antimony (Sb) make up the primer cap of most ammunition involved in forensic gunshot residue analysis. Recently, ammunition manufacturers have started producing and popularizing ammunition with zinc (Zn), titanium (Ti), and gadolinium (Gd) primer components that are non‐toxic to the environment. This paper discusses the development of the Ole Miss Department of Chemistry and Biochemistry's first LIBS instrument for forensic analysis of lead‐free using Gd as a tracer element for …

Developing The Techniques For Raman, Surface-Enhanced Raman Scattering (Sers), And Fluorescence Spectroscopies Of Organic Molecules In Isolation, Jonathan Wolfe

Honors Theses

The nature of matter and light has been a subject of philosophical debate since antiquity. However, by the end of the nineteenth century, much of the scientific community believed that most of the significant principles that govern the natural world had been discovered. Classical physics was able to explain complex phenomena such as planetary motions, elasticity, and hydrodynamics. The field of thermodynamics had been developed nearly to completion by James Joule, Sadi Carnot, Josiah Gibbs, et al. The magnetic and electronic nature of light had been demonstrated by James Clerk Maxwell's famous equations. In the neighboring field of chemistry, a …

I'M Not A Math Person: An Examination Of How Parents And Peers Affect The Ways In Which Students Engage With Mathematics, Samantha Jean Grey

Honors Theses

Culture plays an important role in influencing the ways in which students engage '^ith mathematics. This study sought to examine the ways in which the culture of the home influences the mathematics identities that students bring to the classroom. The researcher recruited participants from a college algebra class taught at a public university. The researcher interviewed four participants from the sample to collect their narratives for analysis. The results of this study indicate that parents and peers influence students’ mathematics identities in powerful and unexpected ways, especially when there is disagreement between the explicit and implicit messages that they communicate …

Newspaper Coverage And Its Effect On Public Opinion: An Analysis Of Media Coverage: Sonia Sotomayor's Nomination And Confirmation To The United States Supreme Court, Courtney Ann Jackson

Honors Theses

No abstract provided.

Estimation Of Charge Transfers By Individual Lightning Return Strokes, Lauren Elizabeth Vickers

Honors Theses

LAUREN ELIZABETH VICKERS: Estimation ofCharge Transfers by Individual Lightning Return Strokes (Under the direction of Dr. Thomas Marshall)

The ultimate purpose ofthis project is to estimate the charge transfers of individual return strokes of cloud-to-ground lightning flashes. The data were collected using a sensor that measures and records changes in electric field during storms. The graphical displays ofthe these data show the field changes associated with the return strokes and other related events of a storm’s activity, specifically ofthe cloud-to-ground flashes relevant to this project. These data were used in collaboration with four other data acquisition systems to estimate charge …

The Effect Of Mood On Short Term Memory, Amy Vitell

Honors Theses

ABSTRACT AMY VITELL: The Effect of Mood on Short Term Memory

Eighty-four undergraduate students (13 males and 71 females) from the University of Mississippi were tested on the effect of mood on short term memory. The participants, with a mean age of 19, were made up of 61 Caucasians, 21 African American, and 2 Asians. The participants took part in a free recall task involving 25 neutral words. Next, a film clip was shown to induce a particular mood (either positive or negative, depending on assigned condition). Following the mood manipulation the participants took part in a second recall task …

Rebirth Of Roth : A Cpa's Ultimate Guide For Client Care, Robert S. Keebler, American Institute Of Certified Public Accountants. Personal Financial Planning Division

Guides, Handbooks and Manuals

No abstract provided.

Sparse Estimation And Inference For Censored Median Regression, Justin Shows

Probability & Statistics Seminar

Censored median regression has proved useful for analyzing survival data in complicated situations, such as when the variance is heteroscedastic, or the data contain outliers. The sparse estimation for censored median regression is an important problem for high dimensional survival data analysis. A new procedure is proposed to minimize an inverse-censoringprobability weighted least absolute deviation loss subject to the adaptive LASSO penalty and result in a sparse and robust median estimator. With a proper choice of tuning parameter, the procedure can identify the underlying sparse model consistently and has desired large-sample properties including root-n consistency and asymptotic normality. The procedure …

Random Graphs: From Paul Erdős To The Internet, Michał Karoński

Dalrymple Lecture Series

Paul Erdős, one of the greatest mathematicians of the twentieth century, was a champion of applications of probabilistic methods in many areas of mathematics, such as a graph theory, combinatorics and number theory. He also, almost fifty years ago, jointly with another great Hungarian mathematician Alfred Rényi, laid out foundation of the theory of random graphs: the theory which studies how large and complex systems evolve when randomness of the relations between their elements is incurred. In my talk I will sketch the long journey of this theory from the pioneering Erdős era to modern attempts to model properties of …

The Riemann Hypothesis…, Micah Milinovich

Algebra/Number Theory Seminar

The Riemann Hypothesis is 150 years old. In the fall of 1859, G. F. B. Riemann communicated his now famous paper “Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse" - translated as ”On the number of primes less than a given magnitude" to the Berlin Academy. In this paper, he outlined a potential proof of what is now called the Prime Number Theorem. His idea was to explicitly relate sums over the zeros of a certain meromorphic function (now called the Riemann zeta-function) to sums over the prime numbers. He further conjectured that all the zeros of this function …

Multiplicity In Algebra And Geometry, Florian Enescu

Colloquium

The multiplicity of a root of a polynomial equals its order of vanishing. A point on an algebraic variety is a solution to a system of polynomial equations. For such a point, how is its multiplicity defined? We will discuss some of the historical approaches to this question. In relation to this, we will present a new multiplicity, called Hilbert-Kunz multiplicity, and discuss some open problems related to it that have algebraic-geometric as well as number-theoretical flavor.

Sums Of Two Squares And Almost Squares, Tsz Ho Chan

Algebra/Number Theory Seminar

Sums of two squares are integers of the form n = a2 + b2.Almost squares are integers of the form n = ab where a and b are close to each other. In this talk, we will discuss the following question: what are the nearest sums of two squares and almost squares to any given positive real number α? This turns out to be related to the distribution of n2α (mod 1).

Two-Scale Convergence And Applications In Homogenization, Part Ii, Aida Timofte

Analysis Seminar

The two-scale convergence is a very efficient homogenization method for partial differential equations with periodically oscillating coefficients. We introduce the notions of weak/strong two-scale convergence, periodic unfolding/folding operators, and discuss some related results. We also point out their applications in the homogenization of evolutionary variational inequalities and in the homogenization of a ferroelectric material model.

Maximal Class Numbers Of Cm Number Fields, Ryan Daleida

Algebra/Number Theory Seminar

Through the class number formula, the Generalized Riemann Hypothesis (GRH) can be used to formulate upper bounds for the class numbers of certain natural families of number fields. A natural question to ask is whether or not these bounds are sharp. While the answer is known to be positive for all natural families of quadratic and cubic number fields, it is actually negative for certain families of quartic number fields. More generally, it turns out that for any family of CM number fields the GRH conditional upper bound on the class number is never attainable. However, by subdividing these natural …

October 20, 2009, The Daily Mississippian

Daily Mississippian (all digitized issues)

No abstract provided.

Rational Approximation And Inverse Problems, Laurent Baratchart

Analysis Seminar

Given a function analytic in the plane except for finitely many branch points in the unit disk, we consider its best rational approximant of given degree in L² of the unit circle. We analyze the behavior of the poles of the approximant when its degree becomes large and discuss how it can be used to approach certain inverse source problems for the Laplacian.

Six Entering Freshmen Chosen As Lott Leadership Scholars, Admin

University of Mississippi News

No abstract provided.

Clones In Representable Matroids Over A Finite Field, Xiangqian Zhou

Combinatorics Seminar

A matroid is a pair (E,I) where E is a finite set and I is a collection of subsets of E that satisfies the following axioms: 1) I; 2) if I I and I I, then I mathcalI; 3) if I,J I and|I| < |J|, thenthereexists x J\I suchthatI {x} I. Two elements x and y of a matroid M are clones if the map that interchanges x and y and that fixes all other elements is an automorphism of M. It is clear that if E is the set of columns of a matrix over a field and I is the collection of subsets of E that are linearly independent, then (E,I) is a matroid. Such a matroid is essentially a sub-structure of the projective space over that field. We study clones in matroids that arise from matrices over a finite field. This is joint work with Reid, Robbins, and Wu.

On The Shell Of Some Graphs, William Staton

Combinatorics Seminar

Let G be a graph such that each vertex of G is contained in a (k + 1)clique for a positive integer k. We de ne the shell of G, denoted by Sh(G) as follows: The vertex set of Sh(G) consists of all distinct (k + 1)-cliques of G and two vertices in Sh(G) are adjacent if and only if the corresponding (k +1)-cliques have k vertices in common. If k = 1, Sh(G) will be the line graph of G. If G is a k-tree with at least k + 1 vertices, each vertex of G is contained in …

Geometry Of L₁(Μ) For Vector-Valued Measure, Part Iii, Iwo Labuda

Analysis Seminar

Let μ be a measure from a σ-algebra of subsets of a set �� into a sequentially complete Hausdorff topological vector space ��. Assume that the convex hull of the range of μ is bounded in �� and denote by L₁(μ) the space of scalar-valued functions on �� that are integrable with respect to the vector measure μ. Sometimes a property of �� is inherited by L₁(μ). I will show that the bounded multiplier property passes from �� to L₁(μ). Answering a 1972 question of Erik Thomas, I will show that for a large class of F-spaces ��, the non-containment …

Engineering Majors Help High School Students Master Math, Prepare For Statewide Competition, Admin

University of Mississippi News

No abstract provided.

Ole Miss Engineer 2009

Ole Miss Engineer

No abstract provided.

Geometry Of L₁(Μ) For Vector-Valued Measure, Part Ii, Iwo Labuda

Analysis Seminar

Let μ be a measure from a σ-algebra of subsets of a set �� into a sequentially complete Hausdorff topological vector space ��. Assume that the convex hull of the range of μ is bounded in �� and denote by L₁(μ) the space of scalar-valued functions on �� that are integrable with respect to the vector measure μ. Sometimes a property of �� is inherited by L₁(μ). I will show that the bounded multiplier property passes from �� to L₁(μ). Answering a 1972 question of Erik Thomas, I will show that for a large class of F-spaces ��, the non-containment …

Geometry Of L₁(Μ) For Vector-Valued Measure, Part I, Iwo Labuda

Analysis Seminar

Let μ be a measure from a σ-algebra of subsets of a set �� into a sequentially complete Hausdorff topological vector space ��. Assume that the convex hull of the range of μ is bounded in �� and denote by L₁(μ) the space of scalar-valued functions on �� that are integrable with respect to the vector measure μ. Sometimes a property of �� is inherited by L₁(μ). I will show that the bounded multiplier property passes from �� to L₁(μ). Answering a 1972 question of Erik Thomas, I will show that for a large class of F-spaces ��, the non-containment …

Alumni Association To Honor Six At Homecoming For Achievement, Service, Admin

University of Mississippi News

No abstract provided.

September 18, 2009, The Daily Mississippian

Daily Mississippian (all digitized issues)

No abstract provided.

Two-Scale Convergence And Applications In Homogenization, Aida Timofte

Analysis Seminar

The two-scale convergence is a very efficient homogenization method for partial differential equations with periodically oscillating coefficients. We introduce the notions of weak/strong two-scale convergence, periodic unfolding/folding operators, and discuss some related results. We also point out their applications in the homogenization of evolutionary variational inequalities and in the homogenization of a ferroelectric material model.

September 15, 2009, The Daily Mississippian

Daily Mississippian (all digitized issues)

No abstract provided.

Career Week Sept. 14-17 Offers Students Interview Opportunities, Networking, Admin

University of Mississippi News

No abstract provided.