Mathematics Commons^™

Quasigroup Structures Arising From Partial Latin Squares, William Cocke, Dr. Rodney Forcade

Journal of Undergraduate Research

Latin squares represent one of the oldest elements of modern algebra, despite being over- shadowed by the structurally superior subclass of nite groups. Every nite group generates a Latin square, an n by n grid wherein n distinct element appear exactly once in each row and column. This grid is a Latin square

The Security Of Simplified Data Encryption Standard, Brandon Barker

College of Arts and Sciences Presentations

The Data Encryption Standard (DES) is the most widely used symmetric key cryptosystem in the commercial world. DES was published in 1975 by the National Bureau of Standards, and since then it and its variants have been commonly used. DES is utilized in many modern industries and products including the Blackberry, electronic financial transactions, and access cards to corporate offices. An efficient but secure cryptosystem is challenging to produce and even after it has been deemed “secure” new attacks and vulnerabilities are often discovered. By investigating the algebraic structure of a simplified version of DES we are able to analyze …

A Simplified Aes With Field Characteristic 7, Suzanne Craig

College of Arts and Sciences Presentations

Today the greatest challenge to the cyber world is security. Technology rapidly changes, making old methods obsolete and requiring new developments and advancements in information security. Cryptography, the science of preparing coded or protected communications, designs systems which make messages intelligible only to the person possessing a key. There are two types of key-based cryptosystems: symmetric key and asymmetric cryptosystem. Symmetric key encryption is a cryptographic technique that uses a shared secret key to encrypt and decrypt data. Symmetric encryption algorithms are very efficient in processing large amounts of information. There are two types of symmetric encryption algorithms: stream ciphers …

Packing Tree Factors In Random And Pseudo-Random Graphs, Deepak Bal, Alan Frieze, Michael Krivelevich, Po Shen Loh

Department of Mathematics Faculty Scholarship and Creative Works

For a fixed graph H with t vertices, an H-factor of a graph G with n vertices, where t divides n, is a collection of vertex disjoint (not necessarily induced) copies of H in G covering all vertices of G. We prove that for a fixed tree T on t vertices and ε > 0, the random graph Gn,p, with n a multiple of t, with high probability contains a family of edge-disjoint T-factors covering all but an ε-fraction of its edges, as long as ε4np ≫ log2 n. Assuming stronger divisibility conditions, the edge probability can be taken down to …

New Pod Error Expressions, Error Bounds, And Asymptotic Results For Reduced Order Model Of Parabolic Pdes, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

The derivations of existing error bounds for reduced order models of time varying partialdi erential equations (PDEs) constructed using proper orthogonal decomposition (POD) haverelied on bounding the error between the POD data and various POD projections of that data.Furthermore, the asymptotic behavior of the model reduction error bounds depends on theasymptotic behavior of the POD data approximation error bounds. We consider time varyingdata taking values in two di erent Hilbert spacesHandV, withVH, and prove exactexpressions for the POD data approximation errors considering four di erent POD projectionsand the two di erent Hilbert space error norms. Furthermore, the exact error expressions …

A Short Journey Through The Riemann Integral, Jesse Keyton

2014-2016 Undergraduate

An introductory-level theory of integration was studied, focusing primarily on the well-known Riemann integral and ending with the Lebesgue integral. An examination of the Riemann integral's basic properties and necessary conditions shows that this integral is not very strong. This conclusion leads to Lebesgue's necessary and sufficient condition for Riemann integrability, perhaps where the Riemann integral ends and the Lebesgue integral begins: a function defined on a closed integral [a, b] is Riemann integrable if and only if the function is discontinuous on a set of measure zero. The proof of this uses that the infinite union …

Arithmagons, Jose Franco

Mathematics Colloquium Series

Arithmagons are polygonal graphs whose vertices and edges are numbered by natural numbers in such a way that the product of the labels of two adjacent vertices equals the label on the edge that connects them. During the talk, Franco will briefly explore the conditions for solvability. The remainder of the talk will focus on counting the number of arithmagons that can be constructed so that the multiplication of all the values on the edges equals a fixed natural number.

Localized Quantum States, Francois Ziegler

Mathematical Sciences: Faculty Publications

Let X be a symplectic manifold and Aut(L) the automorphism group of a Kostant-Souriau line bundle on X. *Quantum states for X*, as defined by J.-M. Souriau in the 1990s, are certain positive-definite functions on Aut(L) or, less ambitiously, on any "large enough" subgroup G of Aut(L). This definition has two major drawbacks: when G=Aut(L) there are no known examples; and when G is a Lie subgroup the notion is, as we shall see, far from selective enough. In this paper we introduce the concept of a quantum state *localized at Y*, where Y is a coadjoint orbit of a …

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.