Physical Sciences and Mathematics Commons^™

The Remedy That's Killing: Cuny, Laguardia, And The Fight For Better Math Policy, Rachel A. Oppenheimer

Dissertations, Theses, and Capstone Projects

Nationwide, there is a crisis in math learning and math achievement at all levels of education. Upwards of 80% of students who enter the City University of New York’s community colleges from New York City’s Department of Education high schools fail to meet college level math proficiencies and as a result, are funneled into the system’s remedial math system. Once placed into pre-college remedial arithmetic, pre-algebra, and elementary algebra courses, students fail at alarming rates and research indicates that students’ failure in remedial math has negative ripple effects on their persistence and degree completion. CUNY is not alone in facing …

An Averaging Method For Advection-Diffusion Equations, Nicholas Spizzirri

Dissertations, Theses, and Capstone Projects

Many models for physical systems have dynamics that happen over various different time scales. For example, contrast the everyday waves in the ocean with the larger, slowly moving global currents. The method of multiple scales is an approach for approximating the solutions of differential equations by separating out the dynamics at slower and faster time scales. In this work, we apply the method of multiple scales to generic advection-diffusion equations (both linear and non-linear, and in arbitrary spatial dimensions) and develop a method for 'averaging out' the faster scale phenomena, giving us an 'effective' solution for the slower scale dynamics. …

Data-Driven Synthesis And Evaluation Of Syntactic Facial Expressions In American Sign Language Animation, Hernisa Kacorri

Dissertations, Theses, and Capstone Projects

Technology to automatically synthesize linguistically accurate and natural-looking animations of American Sign Language (ASL) would make it easier to add ASL content to websites and media, thereby increasing information accessibility for many people who are deaf and have low English literacy skills. State-of-art sign language animation tools focus mostly on accuracy of manual signs rather than on the facial expressions. We are investigating the synthesis of syntactic ASL facial expressions, which are grammatically required and essential to the meaning of sentences. In this thesis, we propose to: (1) explore the methodological aspects of evaluating sign language animations with facial expressions, …

Suppression Of High Transverse Momentum Charged Hadrons In Au+Au Collisions At 200 Gev Nucleon-Nucleon Center Of Mass Energy, Jason B. Bryslawskyj

Dissertations, Theses, and Capstone Projects

The dynamical properties of quark gluon plasma are studied in heavy ion collisions. Gold ions are accelerated with the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory and collided at energies up to 200 GeV per nucleon. Collision products and their properties are detected and measured with the PHENIX detector. At these energies the colliding ions may form a thermalized distribution of quarks and gluons called the Quark-Gluon Plasma. The suppression of single hadrons still provides one of the strongest constraints on energy loss mechanisms in the Quark-Gluon Plasma. Presently, neutral pions provide the best measurement at RHIC of …

Model For The Electrolysis Of Water And Its Use For Optimization, Roger Lascorz, Javier E. Hasbun Dr

Georgia Journal of Science

The goal of this research was to study the optimization of the electrolysis of water both theoretically and experimentally. For accuracy, 3 hr experiments were made with measurements recorded every 15 min. The results show that a better model than the classical one is needed for water electrolysis. A new model that fits experimental data better is proposed. The results of this new model not only predict hydrogen production in electrolysis of water better, but show a way to predict gas production of any liquid as well as what voltage to use to optimize it.

Dendrochronological Analysis Of The Bixler House

Historic Structures

Dating historical structures using dendrochronology. The Historical Structures collection consists of reports that are the result of dendochronological analysis of timbers from structures in Pennsylvania and Ohio. Contributors: AlBashaireh, Amineh; Jimerson, Cole; Luna, Eduardo; Wiesenberg, Nicholas; Wiles, Greg

Method Of Lines Transpose: High Order L-Stable {O}(N) Schemes For Parabolic Equations Using Successive Convolution, Matthew F. Causley, Hana Cho, Andrew J. Christlieb, David C. Seal

Mathematics Publications

We present a new solver for nonlinear parabolic problems that is L-stable and achieves high order accuracy in space and time. The solver is built by first constructing a one-dimensional heat equation solver that uses fast $\mathcal O(N)$ convolution. This fundamental solver has arbitrary order of accuracy in space and is based on the use of the Green's function to invert a modified Helmholtz equation. Higher orders of accuracy in time are then constructed through a novel technique known as successive convolution (or resolvent expansions). These resolvent expansions facilitate our proofs of stability and convergence, and permit us to construct …

Aqueous Photochemistry Of Glyoxylic Acid, Alexis J. Eugene, Sha-Sha Xia, Marcelo I. Guzman

Chemistry Faculty Publications

Aerosols affect climate change, the energy balance of the atmosphere, and public health due to their variable chemical composition, size, and shape. While the formation of secondary organic aerosols (SOA) from gas phase precursors is relatively well understood, studying aqueous chemical reactions contributing to the total SOA budget is the current focus of major attention. Field measurements have revealed that mono-, di-, and oxo-carboxylic acids are abundant species present in SOA and atmospheric waters. This work explores the fate of one of these 2-oxocarboxylic acids, glyoxylic acid, which can photogenerate reactive species under solar irradiation. Additionally, the dark thermal aging …

Large Length Scale Capillary Fluidics: From Jumping Bubbles To Drinking In Space, Andrew Paul Wollman

Dissertations and Theses

In orbit, finding the "bottom" of your coffee cup is a non-trivial task. Subtle forces often masked by gravity influence the containment and transport of fluids aboard spacecraft, often in surprising non-intuitive ways. Terrestrial experience with capillary forces is typically relegated to the micro-scale, but engineering community exposure to large length scale capillary fluidics critical to spacecraft fluid management design is low indeed. Low-cost drop towers and fast-to-flight International Space Station (ISS) experiments are increasing designer exposure to this fresh field of study. This work first provides a wide variety of drop tower tests that demonstrate fundamental and applied capillary …

Investigating The Potential Of Land Use Modifications To Mitigate The Respiratory Health Impacts Of No2: A Case Study In The Portland-Vancouver Metropolitan Area, Meenakshi Rao

Dissertations and Theses

The health impacts of urban air pollution are a growing concern in our rapidly urbanizing world. Urban air pollutants show high intra-urban spatial variability linked to urban land use and land cover (LULC). This correlation of air pollutants with LULC is widely recognized; LULC data is an integral input into a wide range of models, especially land use regression models developed by epidemiologists to study the impact of air pollution on human health. Given the demonstrated links between LULC and urban air pollution, and between urban air pollution and health, an interesting question arises: what is the potential of LULC …

The Terroir Of Pinot Noir Wine In The Willamette Valley, Oregon : A Broad Analysis Of Vineyard Soils, Grape Juice And Wine Chemistry, Kathryn Nora Barnard

Dissertations and Theses

Terroir is determined by a combination of factors in the vineyard including the grape varietal, geology and soil, soil hydrology, physiography, and climate. Although most studies have examined regional differences in wine flavors and associated provenance of wine based on chemistry, few have examined the chemistry of the soil and the ability to trace that chemistry to grape juice and, finally, to the wine. This dissertation examines what soil physical and chemical differences specific to this region might influence grape juice chemistry and wine chemistry.

Wine-grapes in the Willamette Valley, Oregon, are grown on three major soil parent materials: volcanic, …

Photoemission Electron Microscopy For Analysis Of Dielectric Structures And The Goos-Hänchen Shift, Theodore Axel Stenmark

Dissertations and Theses

Photoemission Electron Microscopy (PEEM) is a versatile tool that relies on the photoelectric effect to produce high-resolution electron images. Ultrafast pulse lasers allow for multi-photon PEEM where multiple visible or IR photons excite a single electron in a nonlinear process. The photoelectron yield in both cases is related to the near-field region of electromagnetic fields at the surface of the sample. We use this ability here to analyze wave propagation in a linear dielectric waveguide with wavelengths of 410 nm and 780 nm. The propagation constant of the waveguide can be extracted from interference patterns created by light propagating in …

Statistical Modeling Of Carbon Dioxide And Cluster Analysis Of Time Dependent Information: Lag Target Time Series Clustering, Multi-Factor Time Series Clustering, And Multi-Level Time Series Clustering, Doo Young Kim

USF Tampa Graduate Theses and Dissertations

The current study consists of three major parts. Statistical modeling, the connection between statistical modeling and cluster analysis, and proposing new methods to cluster time dependent information.

First, we perform a statistical modeling of the Carbon Dioxide (CO₂) emission in South Korea in order to identify the attributable variables including interaction effects. One of the hot issues in the earth in 21st century is Global warming which is caused by the marriage between atmospheric temperature and CO₂ in the atmosphere. When we confront this global problem, we first need to verify what causes the problem then we …

Chaotic Advection-Driven Mixing In Unsteady Three-Dimensional Mhd Flows In Microfluidic Devices, Fangping Yuan, Kakkattukuzhy M. Isaac

Collaborative Research: Actively Controllable Microfluidics with Film-Confined Redox-Magnetohydrodynamics -- Video and Data

No abstract provided.

Sensitivity Of The Advanced Ligo Detectors At The Beginning Of Gravitational Wave Astronomy, D. V. Martynov, E. D. Hall, B. P. Abbott, R. Abbott, T. D. Abbott, C. Adams, R. X. Adhikari, R. A. Anderson, Volker Quetschke, G. Valdes

Physics & Astronomy Faculty Publications

The Laser Interferometer Gravitational Wave Observatory (LIGO) consists of two widely separated 4 km laser interferometers designed to detect gravitational waves from distant astrophysical sources in the frequency range from 10 Hz to 10 kHz. The first observation run of the Advanced LIGO detectors started in September 2015 and ended in January 2016. A strain sensitivity of better than 10-23/Hz was achieved around 100 Hz. Understanding both the fundamental and the technical noise sources was critical for increasing the astrophysical strain sensitivity. The average distance at which coalescing binary black hole systems with individual masses of 30 M could be …

The Collatz Conjecture And Integers Of The Form 2KB−M And 3KB−1, Patrick Wiltrout, Eric Landquist

Furman University Electronic Journal of Undergraduate Mathematics

One of the more well-known unsolved problems in number theory is the Collatz (3n + 1) Conjecture. The conjecture states that iterating the map that takes even n ∈ N to n/2 and odd n to (3n+1)/2 will eventually yield 1. This paper is an exploration of this conjecture on positive integers of the form 2^kb−m and 3^kb−1, and stems from the work of the first author's Senior Seminar research. We take an elementary approach to prove interesting relationships and patterns in the number of iterations, called …

The Search For One As A Prime Number: From Ancient Greece To Modern Times, Angela Reddick, Yeng Xiong

Furman University Electronic Journal of Undergraduate Mathematics

It has often been asked if one is a prime number, or if there was a time when most mathematicians thought one was prime. Whether or not the number one is prime is simply a matter of definition, but definitions are often decided by the use of mathematics. In this paper we will survey the history of the definition of prime as applied to the number one, from the ancient Greeks to the modern times. For the Greeks the numbers (αριθμος) were multiples of the unit, and for this reason one did not fall into the category of …

On The Dead End Depth Of Thompson's Group F, Justin Halverson

Furman University Electronic Journal of Undergraduate Mathematics

Thompson’s group F was introduced by Richard Thompson in the 1960’s and has since found applications in many areas of mathematics including algebra, logic and topology. We focus on the dead end depth of F, which is the minimal integer N such that for any group element, g, there is guaranteed to exist a path of length at most N in the Cayley graph of F leading from g to a point farther from the identity than g is. By viewing F as a diagram group, we improve the greatest known lower bound for the dead end depth …

Relative Goldbach Partitions And Goldbach's Conjecture, Houston Hutchinson

Furman University Electronic Journal of Undergraduate Mathematics

In this note, we utilize techniques from discrete mathematics to develop first an inequality, and then second a counting formula that is connected to Goldbach's conjecture. In order to do this, we introduce the notion of a Relative Goldbach Partition.

Integers Of The Form A2±B2, Robert Zeman

Furman University Electronic Journal of Undergraduate Mathematics

This paper explores which integers can be expressed in the form a²±2b² by using rings of the form Z[√d], particularly when d = 2 and d = −2.

Paths And Circuits In G-Graphs Of Certain Non-Abelian Groups, A. Dewitt, A. Rodriguez, Jennifer Daniel

Furman University Electronic Journal of Undergraduate Mathematics

In [BJRTD08], necessary and suffcient conditions were given for the existence of Eulerian and Hamiltonian paths and circuits in the G-graph of the dihedral group D_n. In this paper, we consider the G-graphs of the quasihedral, modular, and generalized quaternion group. These groups are of rank 2 and we consider only the graphs Γ(G, S) where |S|= 2.

The Relationships Between Cg, Bfgs, And Two Limited-Memory Algorithms, Zhiwei (Tony) Qin

Furman University Electronic Journal of Undergraduate Mathematics

For the solution of linear systems, the conjugate gradient (CG) and BFGS are among the most popular and successful algorithms with their respective advantages. The limited-memory methods have been developed to combine the best of the two. We describe and examine CG, BFGS, and two limited-memory methods (L-BFGS and VSCG) in the context of linear systems. We focus on the relationships between each of the four algorithms, and we present numerical results to illustrate those relationships.

Finding Prime Numbers: Miller Rabin And Beyond, Christina Mcintosh

Furman University Electronic Journal of Undergraduate Mathematics

This expository paper motivates and explains the Miller Rabin test and gives some generalizations of it. The Miller Rabin test is a standard probabilistic test used to find large prime numbers quickly.

Carolinas Mathematics Undergraduate Research Conference Abstracts, John Harris

Furman University Electronic Journal of Undergraduate Mathematics

On Friday, March 24, 2006, Furman University hosted the Carolinas Mathematics Undergraduate Research Conference. The conference was supported by the Mathematical Association of America (NSF Grant DMS-0241090). These are the abstracts for the eight undergraduate talks given on that day.

Notes On Gabriel's Horn, Joseph Krenicky, Jan Rychtář

Furman University Electronic Journal of Undergraduate Mathematics

A smooth bounded solid of finite volume and infinite surface is constructed. It is a variant of the classical Gabriel’s horn that is often taught in Calculus classes.

Derham Cohomology Of The Rectangular Torus, Eric M. Katerman

Furman University Electronic Journal of Undergraduate Mathematics

For the special case of a rectangular at torus, we present and prove DeRham's Theorem, which says that cohomology is given by closed differential forms modulo exact forms.

The University Of North Carolina At Greensboro Regional Undergraduate Mathematics Conference Abstracts, Jan Rychtář

Furman University Electronic Journal of Undergraduate Mathematics

It was a very chaotic day, says Kathryn Sikes. Indeed, mutants spread everywhere, according to Brian Stadler. Bacterial wars raged all over the place, adds Dan MacMartin. Everybody was stealing, reported Christian Sykes. There were no limits to it, witnessed by Samuel Grundman. Only the fittest survived and got out of the prison, noted by Joseph Krenicky. The group was set free by Steven Piantadosi. We almost got lost in cyclic paths, said Heather Allmond. At least, our weight was a perfect number, smiles Michael Shiver, because we were not oversized thanks to Martha Shott. Finally, a picture was taken …

On The Nonexistence Of Singular Equilibria In The Four-Vortex Problem, Marshall Hampton, Andrea Peterson, Heather Stoller, Albert Wang

Furman University Electronic Journal of Undergraduate Mathematics

In this paper we provide a partial answer to a question recently posed by Hassan Aref et. al. in their article Vortex Crystals, namely whether there are certain singular equilibria of point vortices. We prove that there are no such equilibria in the four-vortex case.

Properties Of The Iterates Of The Weierstrass-℘ Function, Walter H. Chen, Michael S. Willis

Furman University Electronic Journal of Undergraduate Mathematics

This paper discusses several properties of the Weierstrass-℘ function, as defined on the fundamental parallelogram C/Γ, where C is the complex plane and Γ is the lattice generated by ω1 and ω2. Using the addition formula for ℘(z₁ + z₂), we develop a reccurence relation for ℘(nz) in terms of ℘(z). We then examine the degree of this expression, some coefficients, and patterns concerning the poles of this function. We also consider the geometric interpretation of taking an arbitrary z₀ and adding it to itself, both in the fundamental parallelogram C/Γ and …

A Dynamical Programming Solution For Shortest Path Itineraries In Robotics, Martin Talbot

Furman University Electronic Journal of Undergraduate Mathematics

In robotics, more precisely Autonomous Mobile Robotics (AMR), robots, much like human beings, are confronted regularly with the problem of finding the best path to take from a source location to a destination location. This is an optimization concern, since the robot wants to minimize its cost in time or in energy while achieving its goal. Different algorithms exist for shortest path computation; the famous Dijkstra’s Shortest Path Algorithm will solve single-source shortest path problems in near linear time (O(mn log n)). However, for certain complex optimization path-planning problems, this algorithm alone is insufficient. We will …