Mathematics Commons^™

Up Congruences Of Modular Functions Modulo Powers Of Primes, Michael Griffin, Dr. Paul Jenkins

Journal of Undergraduate Research

Modular forms are constructs of complex analysis that possess many intricate connections to widely-separated branches of mathematics. In the most well-known application of these functions, Andrew Wiles established a connection between the Fourier coefficients of modular forms and elliptic curves–objects of analytic geometry–in order to prove Fermat’s Last Theorem, a classical number theory problem that had resisted proof for more than 350 years. Modular forms have also found applications ranging from cryptography to the million-dollar Birch and Swinerton-Dyer conjecture.

Investigation Of Investor-Manager Conflict In Mutual Funds Using Dynamic Models, Jeremiah Bejarano, Dr. Jeffrey Humpherys

Journal of Undergraduate Research

In this project, my goal was to analyze the relation between marketshare incentives and risk taking in the hedge fund industry. Using the techniques of stochastic optimal control or dynamic programming, as applied in the typical Continuous-Time Consumption and Portfolio Choice model, I worked to develop a mathematical model to explore the effects of management fees and performance bonuses as well as the effects of changing market share on the fund manager’s implicit aversion towards high-risk portfolios. My continuing hypothesis is that due to fundamental differences between the investors and managers incentives, (essentially profit maximization vs. commission maximization) a fund …

Qcd Vs. The Centrifugal Barrier: A New Qcd Effect, Tamar Friedmann

Mathematics Sciences: Faculty Publications

We propose an extended schematic model for hadrons in which quarks and diquarks alike serve as building blocks. The outcome is a reclassification of the hadron spectrum in which there are no radially excited hadrons: all mesons and baryons previously believed to be radial excitations are orbitally excited states involving diquarks. Also, there are no exotic hadrons: all hadrons previously believed to be exotic are states involving diquarks and are an integral part of the model. We discuss the implications of this result for a new understanding of confinement and its relation to asymptotic freedom, as well as its implications …

The Fundamental Principle Of Productivity: What They Don't Teach You In Graduate School, Gizem Karaali

Pomona Faculty Publications and Research

But through the years, I have read many books, ranging from self-help guides to creative writing manuals, attended workshops, frequented relevant websites, and reflected upon my own personal experiences. As a result, I have collected together a few ideas and tools on productivity and time management that have been working well for me. In this post I want to share with you the most basic of these principles, with the hope that it may assist you in your life, at whatever stage you are. Whether you are a graduate student, a postdoctoral researcher, a junior mathematician on the tenure track, …

Prognostic Value Of Choline And Betaine Depends On Intestinal Microbiota-Generated Metabolite Trimethylamine-N-Oxide, Zeneng Wang, W.H. Wilson Tang, Jennifer A. Buffa, Xiaoming Fu, Earl B. Britt, Robert A. Koeth, Bruce S. Levison, Yiying Fan, Yuping Wu, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

Aims: Recent metabolomics and animal model studies show trimethylamine-N-oxide (TMAO), an intestinal microbiota-dependent metabolite formed from dietary trimethylamine-containing nutrients such as phosphatidylcholine (PC), choline, and carnitine, is linked to coronary artery disease pathogenesis. Our aim was to examine the prognostic value of systemic choline and betaine levels in stable cardiac patients. Methods and Results: We examined the relationship between fasting plasma choline and betaine levels and risk of major adverse cardiac events (MACE = death, myocardial infraction, stroke) in relation to TMAO over 3 years of follow-up in 3903 sequential stable subjects undergoing elective diagnostic coronary angiography. In our study …

Analysis Of Resource Allocation Through Game Theory, Brittney L. Benzio

Honors College Theses

Game theory presents a set of decision-makers in a model in order to simulate how they will interact according to a set of rules. The game is set up with a set of players, actions, and preferences. The model allows each player to, in some way, be affected by the actions of all players. Nash equilibrium illustrates that the best action for any given player depends on the other players’ actions, and so, each player must make some assumption about what the competition will do. The goal of this project is to model situations of different car companies to improve …

A Maximum Principle In The Engel Group, James Klinedinst

USF Tampa Graduate Theses and Dissertations

In this thesis, we will examine the properties of subelliptic jets in the Engel group of step 3. Step-2 groups, such as the Heisenberg group, do not provide insight into the general abstract calculations. This thesis then, is the first explicit non-trivial computation of the abstract results.

An Alternate Proof Of The De Branges Theorem On Canonical Systems, Keshav R. Acharya

Publications

The aim of this paper is to show that, in the limit circle case, the defect index of a symmetric relation induced by canonical systems, is constant on ₵. This provides an alternative proof of the De Branges theorem that the canonical systems with trH1 imply the limit point case. To this end, we discuss the spectral theory of a linear relation induced by a canonical system.

Dynamics Of Phase Locking In Neuronal Networks In The Presence Of Synaptic Plasticity, Zeynep Akcay

Dissertations

The behavior generated by neuronal networks depends on the phase relationships of its individual neurons. Observed phases result from the combined effects of individual cells and synaptic connections whose properties change dynamically. The properties of individual cells and synapses can often be characterized by driving the cell or synapse with inputs that arrive at different phases or frequencies, thus producing a feed-forward description of these properties. In this study, a recurrent network of two oscillatory neurons that are coupled with reciprocal synapses is considered. Feed-forward descriptions of the phase response curves of the neurons and the short-term synaptic plasticity properties …

Internet Radio: An Analysis Of Pandora And Spotify, Corinne Loiacono

Honors Projects in Mathematics

Unlike traditional stations, internet radio stations try to complete the task of effectively

identifying the individual in their audience and then cater to their musical taste. The

effectiveness of these stations can be analyzed through popular music customization mediums,

such as Pandora and Spotify. This paper seeks to analyze Pandora and Spotify and research

why they are such popular mediums for their users and how effective each site is in satisfying

a need for personalized radio. Specifically, what medium used for internet radio best caters

to the needs of users in terms of website features (extent of personalization and social …

The Impact Of Professional Sports Franchises On Local Economies, Jeffrey Pierro

Honors Projects in Mathematics

There is no doubt that professional sports franchises and stadiums generate a significant amount of economic activity, but is the impact on the local economy positive, negative, or neutral? Studies have shown that, while franchises can give the economy a boost in the short term, there are little to no long-term positive effects. This capstone will examine the trend in public financing of stadiums, look at the impact of stadium location, explore the factors of the economy that are impacted by professional sports franchises, and determine if the effects vary by sport or by region. Several major case studies will …

Bytes Of Π, Spring 2014, Department Of Mathematics, Bridgewater State University

Department of Mathematics Newsletter

No abstract provided.

Guaranteed Sparse Signal Recovery With Highly Coherent Sensing Matrices, Guangliang Chen, Atul Divekar, Deanna Needell

CMC Faculty Publications and Research

Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling matrices such as Gaussian and Bernoulli matrices. In common physically feasible signal acquisition and reconstruction scenarios such as super-resolution of images, the sensing matrix has a non-random structure with highly correlated columns. Here we present a compressive sensing type recovery algorithm, called Partial Inversion (PartInv), that overcomes the correlations among the columns. We provide theoretical justification as well as empirical comparisons.

Mapcores 2013-2014 Assessment Report, Kristen Nairn, Pamela L. Bacon, Jim Crumley, Yu Zhang

MapCores Faculty Publications

This is a report showing the assessment results for the MapCores (MAthematics, Physics, COmputer science REsearch Scholars) program at the College of Saint Benedict. Started in 2009, MapCores is a cohort-based program designed to increase women's interest and achievement in mathematics, physics, computer science and engineering. The report was submitted for the National Science Foundation grant number 0965705.

Inequalities Of Generalized Matrix Functions Via Tensor Products, Vehbi Emrah Paksoy, Ramazan Turkmen, Fuzhen Zhang

Mathematics Faculty Articles

By an embedding approach and through tensor products, some inequalities for generalized matrix functions (of positive semidefinite matrices) associated with any subgroup of the permutation group and any irreducible character of the subgroup are obtained.

Reducing The Effects Of Unequal Number Of Games On Rankings, T. P. Chartier, J. Harris, K. R. Hutson, A. N. Langville, D. Martin, Charles D. Wessell

Math Faculty Publications

Ranking is an important mathematical process in a variety of contexts such as information retrieval, sports and business. Sports ranking methods can be applied both in and beyond the context of athletics. In both settings, once the concept of a game has been defined, teams (or individuals) accumulate wins, losses, and ties, which are then factored into the ranking computation. Many settings involve an unequal number of games between competitors. This paper demonstrates how to adapt two sports rankings methods, the Colley and Massey ranking methods, to settings where an unequal number of games are played between the teams. In …

Aftermath: Every Math Major Should Take A Public-Speaking Course, Rachel Levy

All HMC Faculty Publications and Research

Rachel Levy argues that all mathematics majors should learn the art of public speaking.

Numerical Simulation Of Hydrogen Absorption/Desorption Processes In Cylindrical Metal-Hydrogen Reactors For Hydrogen Storage, Fei Han

Doctoral Dissertations

Hydrogen is one of the best fuels because of its high calorific value and environmental friendliness. However, because of its low density, it has storage problems such as high pressure, large volume requirements, heavy weight and safely risks; this quality prevents its wide usage and commercialization.

Researchers have found that some metal/inter-metallic compounds/alloys, such as Mg, La, LaNi5, ZrV2, Mg2Ni and Ti 2Ni, can react with hydrogen and attain relatively large amounts of hydrogen at a relatively low pressure and near normal temperature. Under certain conditions, hydride can desorb hydrogen quickly. Thus, the metal- hydrogen reaction could be a practical …

New Combinatorial Formulations Of The Shuffle Conjecture, Nicholas A. Loehr, Elizabeth Niese

Mathematics Faculty Research

The shuffle conjecture (due to Haglund, Haiman, Loehr, Remmel, and Ulyanov) provides a combinatorial formula for the Frobenius series of the diagonal harmonics module DH_n, which is the symmetric function∇(e_n). This formula is a sum over all labeled Dyck paths of terms built from combinatorial statistics called area, dinv, and IDes. We provide three new combinatorial formulations of the shuffle conjecture based on other statistics on labeled paths, parking functions, and related objects. Each such reformulation arises by introducing an appropriate new definition of the inverse descent set. Analogous results are proved for the higher-order shuffle …

The Scientist–Reporter Collaboration: A Guide To Working With The Press, Rachel Levy, Flora Lichtman, David L. Hu

All HMC Faculty Publications and Research

Science, technology, engineering, and mathematics (STEM) to the public can be challenging. Often, the language that researchers use among themselves is technical and difficult for non-experts to decipher. But as you probably know, communicating your research to non-experts is becoming mandatory. In a direct sense, funding agencies often require outreach for grant fulfillment. There are indirect benefits as well: Conveying the joy of discovery and the relevance of scientific results builds scientific literacy among the public---which of course includes both students who will eventually do research of their own and people who elect the policy makers who allocate funding. How …

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

Virginia Journal of Science

Abstracts of the Astronomy, Mathematics, and Physics with Materials Science Section for the 92nd Annual Meeting of the Virginia Academy of Science, May 13-15, 2014, Virginia Commonwealth University, Richmond, Virginia

On The Sensitivity Of 3-D Thermal Convection Codes To Numerical Discretization: A Model Intercomparison, P.-A. Arrial, N. Flyer, G. B. Wright, L. H. Kellogg

Mathematics Faculty Publications and Presentations

Fully 3-D numerical simulations of thermal convection in a spherical shell have become a standard for studying the dynamics of pattern formation and its stability under perturbations to various parameter values. The question arises as to how does the discretization of the governing equations affect the outcome and thus any physical interpretation. This work demonstrates the impact of numerical discretization on the observed patterns, the value at which symmetry is broken, and how stability and stationary behavior is dependent upon it. Motivated by numerical simulations of convection in the Earth's mantle, we consider isoviscous Rayleigh-Bénard convection at infinite Prandtl number, …

Volume 06, Kristen Gains, Amanda Willis, Holly Backer, Monika Gutierrez, Cara O'Neal, Sara Nelson, Sasha Silberman, Jessica Beardsley, Jamie Gardner, Edward Peeples, Matthew Sakach, Tess Lione, Emily Wilkins, Kelsey Holt, Jessica Page, Jamie Clift, Charles Vancampen, Gilbert Hall, Jenny Nehrt, Kasey Dye, Amanda Tharp, Jamie Leeuwrik, Ashley Mcgee, Emily Poulin, Michael Kropf, Nick Pastore, Austin Polasky, Morgan Glasco, Laura L. Kahler, Melinda L. Edwards, Brandon C. Smith, Mariah Asbell, Cabell Edmunds, Amelia D. Perry, Alyssa Hayes, Irina Boothe, Perry Bason, James Early

Incite: The Journal of Undergraduate Scholarship

Introduction from Dean Dr. Charles Ross

Caught Between Folklore and the Cold War: The Americanization of Russian Children's Literature by Kristen Gains

Graphic Design by Amanda Willis

Graphic Design by Holly Backer

Prejudices in Swiss German Accents by Monika Gutierrez

Photography by Cara O'Neal

Photography by Sara Nelson

Edmund Tyrone's Long Journey through Night by Sasha Silberman

Photography by Jessica Beardsley

Photography by Jamie Gardner and Edward Peeples

The Republican Razor: The Guillotine as a Symbol of Equality by Jamie Clift

Graphic Design by Matthew Sakach

Genocide: The Lasting Effects of Gender Stratification in Rwanda By Tess Lione and Emily …

An Introduction To The Markov Chain Monte Carlo And Wang-Landau Algorithms, Jacob R. Desmond

Honors Capstones

No abstract provided.

Highly Sensitive Noninvasive Cardiac Transplant Rejection Monitoring Using Targeted Quantification Of Donor-Specific Cell-Free Deoxyribonucleic Acid, Mats Hidestrand, Aoy Tomita-Mitchell, Pip M. Hidestrand, Arnold Oliphant, Mary Goetsch, Karl D. Stamm, Huan-Ling Liang, Chesney Castleberry, D. Woodrow Benson, Gail Stendahl, Pippa Simpson, Stuart Berger, James S. Tweddell, Steven Zangwill, Michael E. Mitchell

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

2014 (Spring), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2014 Spring Colloquium.

An Analysis Of The Practical Dpg Method, Jay Gopalakrishnan, Weifeng Qiu

Mathematics and Statistics Faculty Publications and Presentations

We give a complete error analysis of the Discontinuous Petrov Galerkin (DPG) method, accounting for all the approximations made in its practical implementation. Specifically, we consider the DPG method that uses a trial space consisting of polynomials of degree p on each mesh element. Earlier works showed that there is a "trial-to-test" operator T, which when applied to the trial space, defines a test space that guarantees stability. In DPG formulations, this operator T is local: it can be applied element-by-element. However, an infinite dimensional problem on each mesh element needed to be solved to apply T. In practical computations, …

Micro-Environment Causes Reversible Changes In Dna Methylation And Mrna Expression Profiles In Patient-Derived Glioma Stem Cells, Mehmet Baysan, Kevin Woolard, Serdar Bozdag, Gregory Riddick, Svetlana Kotliarova, Margaret C. Cam, Galina I. Belova, Susie Ahn, Wei Zhang, Hua Song, Jennifer Walling, Holly Stevenson, Paul Meltzer, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

In vitro and in vivo models are widely used in cancer research. Characterizing the similarities and differences between a patient's tumor and corresponding in vitro and in vivo models is important for understanding the potential clinical relevance of experimental data generated with these models. Towards this aim, we analyzed the genomic aberrations, DNA methylation and transcriptome profiles of five parental tumors and their matched in vitro isolated glioma stem cell (GSC) lines and xenografts generated from these same GSCs using high-resolution platforms. We observed that the methylation and transcriptome profiles of in vitro GSCs were significantly different from their corresponding …

Decoding Quantitative Language, Steven Cosares, Evelyn Burg

Open Educational Resources

We all need some “quantitative literacy” in order to communicate effectively. This means being able to read, write or speak intelligently in a medium where some quantitative information is a part the discussion, proof, or argument. The readers of these materials are expected to have sufficient wherewithal to understand this language so as to draw appropriate conclusions. Developing this type of literacy requires practice. It means using everyday language to describe the ways in which quantities relate to one another.

Determining The Duration Of R&D Processes Through Monte Carlo Simulation, Florentin Smarandache, Moga Monika, Calefariu Gavrila, Sarbu Flavius Aurelian

Branch Mathematics and Statistics Faculty and Staff Publications

The research and development (R&D) processes influence the economic development of a company, because in an industry that is changing fast, firms must continually revise their projects and range of products. Therefore in order to determine the specific costs of research and development activity we have to highlight the efforts and effects of these activities and to calculate some indicators of economic efficiency. In the cost calculation process in R & D we have emphasized the identification of the components of cost and the duration of the R & D processes, as a component of the R&D cost, that is …