Analyzing Cholera Dynamics In Homogeneous And Heterogeneous Environments,
2014
Old Dominion University
Analyzing Cholera Dynamics In Homogeneous And Heterogeneous Environments, Drew Posny
Mathematics & Statistics Theses & Dissertations
Cholera continues to be a serious public health concern in developing countries and the global increase in the number of reported outbreaks suggests that activities to control the diseases and surveillance programs to identify or predict the occurrence of the next outbreaks are not adequate. Mathematical models play a critical role in predicting and understanding disease mechanisms, and have long provided basic insights in the possible ways to control infectious diseases. This dissertation is concerned with mathematical modeling and analysis of cholera dynamics. First, we study an autonomous model in a homogeneous environment with added controls that involves both direct …
Adverse Impacts Of Furlough Programs On Employee Work Rate And Organizational Productivity,
2014
Air Force Institute of Technology
Adverse Impacts Of Furlough Programs On Employee Work Rate And Organizational Productivity, Adedeji B. Badiru
Faculty Publications
This article is primarily a research-provoking exposition against the management approach used in the 2013 government furlough program. It is intended to prompt potentially productive research investigations on the impact of personnel furloughs, particularly on defense acquisition programs. Defense acquisition programs are time-sensitive and systems oriented. What appears as a minor delay in one unit of an acquisition life cycle can lead to long-term encumbrances within the entire defense system, resulting in enormous cost escalation. Pertinent analytical techniques/methodologies are provided to illustrate potential pathways for further research studies of furloughs and how they adversely impact organizational productivity. The author’s intent …
One-Parameter Families Of Supersymmetric Isospectral Potentials From Riccati Solutions In Function Composition Form,
2014
Instituto Potosino de Investigacion Cientifica y Tecnologica
One-Parameter Families Of Supersymmetric Isospectral Potentials From Riccati Solutions In Function Composition Form, Haret C. Rosu, S.C. Mancas, Pisin Chen
Publications
In the context of supersymmetric quantum mechanics, we define a potential through a particular Riccati solution of the composition form (F∘f)(x)=F(f(x)) and obtain a generalized Mielnik construction of one-parameter isospectral potentials when we use the general Riccati solution. Some examples for special cases of F and f are given to illustrate the method. An interesting result is obtained in the case of a parametric double well potential generated by this method, for which it is shown that the parameter of the potential controls the heights of the localization probability in the two wells, and for certain values of the parameter …
Euler-Poincar´E Equations For G-Strands,
2014
Imperial College London
Euler-Poincar´E Equations For G-Strands, Darryl Holm, Rossen Ivanov
Conference papers
The G-strand equations for a map R×R into a Lie group G are associated to a G-invariant Lagrangian. The Lie group manifold is also the configuration space for the Lagrangian. The G-strand itself is the map g(t,s):R×R→G, where t and s are the independent variables of the G-strand equations. The Euler-Poincar'e reduction of the variational principle leads to a formulation where the dependent variables of the G-strand equations take values in the corresponding Lie algebra g and its co-algebra, g∗ with respect to the pairing provided by the variational derivatives of the Lagrangian. We review examples of different G-strand …
A Contagion Model Of Emergency Airplane Evacuations,
2014
Pepperdine University
A Contagion Model Of Emergency Airplane Evacuations, Junyuan Lin
Seaver College Research And Scholarly Achievement Symposium
Motivated by the Asiana Flight 214 crash in San Francisco this summer, this project focuses on modeling an emergency airplane evacuation. Our models are based on the Particle Swarm Optimization (PSO) algorithm, where each agent's position is compared to a fitness function that describes the current environment. Each agent moves according to its knowledge of its own previous best position and the group's current best position. The static environment is modeled by a potential function that describes the layout of the airplane that includes the exits and physical barriers such as the seats. We model the interactions within the swarm …
Existence And Uniqueness Of Solutions For A Fractional Boundary Value Problem On A Graph,
2014
Rowan University
Existence And Uniqueness Of Solutions For A Fractional Boundary Value Problem On A Graph, John R. Graef, Lingju Kong, Min Wang
College of Science & Mathematics Departmental Research
In this paper, the authors consider a nonlinear fractional boundary value problem defined on a star graph. By using a transformation, an equivalent system of fractional boundary value problems with mixed boundary conditions is obtained. Then the existence and uniqueness of solutions are investigated by fixed point theory.
Model Uncertainty And Test Of A Segmented Mirror Telescope,
2014
Air Force Institute of Technology
Model Uncertainty And Test Of A Segmented Mirror Telescope, Luke C. Dras
Theses and Dissertations
The future of large aperture telescopes relies heavily on the development of segmented array designs. Today's monolithic mirror technology has reached a barrier, particularly for space-based telescopes. These large diameter, dense mirrors allow stable high-resolution imaging but are incompatible with optimized space launch. Segmented mirror telescopes are designed to balance lightweight with compact stowage. The structure necessary to support the flexible mirror array often combines isogrid geometry and complex actuation hardware. High-fidelity finite element models are commonly used to economically predict how the optics will perform under different environmental conditions. The research detailed herein integrates superelement partitioning and complexity simplifying …
Airborne Wireless Communication Modeling And Analysis With Matlab,
2014
Air Force Institute of Technology
Airborne Wireless Communication Modeling And Analysis With Matlab, Matthew J. Vincie
Theses and Dissertations
Over the past decade, there has been a dramatic increase in the use of unmanned aerial vehicles (UAV) for military, commercial, and private applications. Critical to maintaining control and a use for these systems is the development of wireless networking systems [1]. Computer simulation has increasingly become a key player in airborne networking developments though the accuracy and credibility of network simulations has become a topic of increasing scrutiny [2-5]. Much of the inaccuracies seen in simulation are due to inaccurate modeling of the physical layer of the communication system. This research develops a physical layer model that combines antenna …
A Generalization Of Aztec Diamond Theorem, Part I,
2014
Indiana University Bloomington
A Generalization Of Aztec Diamond Theorem, Part I, Tri Lai
Department of Mathematics: Faculty Publications
We consider a new family of 4-vertex regions with zigzag boundary on the square lattice with diagonals drawn in. By proving that the number of tilings of the new regions is given by a power 2, we generalize both Aztec diamond theorem and Douglas’ theorem. The proof extends an idea of Eu and Fu for Aztec diamonds, by using a bijection between domino tilings and non-intersecting Schr¨oder paths, then applying Lindstr¨om-Gessel-Viennot methodology.
For Each Mathematical Statement, Only Finitely Many Of Its Generalizations Are Useful: A Formal Proof Of E. Bishop's Idea,
2014
The University of Texas at El Paso
For Each Mathematical Statement, Only Finitely Many Of Its Generalizations Are Useful: A Formal Proof Of E. Bishop's Idea, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Generalization is one of the main mathematical activities. Some generalizations turn out to be useful for working mathematics, while many other generalizations have so far been not very useful. E. Bishop believed that most fruitless-so-far generalizations are hopeless, that every mathematical statement has only a few useful generalizations. In this paper, we show that, under a natural definition of the notion of useful generalization, Bishop's belief can be proven -- moreover, it turns out that for each mathematical statement, only finitely many of its generalizations are useful.
Deep Mathematical Results Are The Ones That Connect Seemingly Unrelated Areas: Towards A Formal Proof Of Gian-Carlo Rota's Thesis,
2014
The University of Texas at El Paso
Deep Mathematical Results Are The Ones That Connect Seemingly Unrelated Areas: Towards A Formal Proof Of Gian-Carlo Rota's Thesis, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
When is a mathematical result deep? At first glance, the answer to this question is subjective: what is deep for one mathematician may not sound that deep for another. A renowned mathematician Gian-Carlo Rota expressed an opinion that the notion of deepness is more objective that we may think: namely, that a mathematical statement is deep if and only if it connects two seemingly unrelated areas of mathematics. In this paper, we formalize this thesis, and show that in this formalization, Gian Carlo Rota's thesis becomes a provable mathematical result.
Ua66 Ogden College Of Science & Engineering Newsletter,
2014
Western Kentucky University
Ua66 Ogden College Of Science & Engineering Newsletter, Cheryl Stevens, Dean
Ogden College of Science & Engineering Publications
No abstract provided.
Conditional Tests On Basins Of Attraction With Finite Fields,
2014
Portland State University
Conditional Tests On Basins Of Attraction With Finite Fields, Ian H. Dinwoodie
Mathematics and Statistics Faculty Publications and Presentations
An iterative method is given for computing the polynomials that vanish on the basin of attraction of a steady state in discrete polynomial dynamics with finite field coefficients. The algorithm is applied to dynamics of a T cell survival network where it is used to compare transition maps conditional on a basin of attraction.
On A Nonlocal Nonlinear Schrodinger Equation,
2014
Technological University Dublin
On A Nonlocal Nonlinear Schrodinger Equation, Tihomir Valchev
Conference papers
We consider a nonlocal nonlinear Schr\"odinger equation recently proposed by Ablowitz and Musslimani as a theoretical model for wave propagation in {\it PT}-symmetric coupled wave-guides and photonic crystals. This new equation is integrable by means of inverse scattering method, i. e. it possesses a Lax pair, infinite number of integrals of motion and exact solutions. We aim to describe here some of the basic properties of the nonlocal Schr\"odinger equation and its scattering operator. In doing this we shall make use of methods alternative to those applied by Ablowitz and Musslimani which seem to be better suited for treating possible …
Arnold Diffusion,
2014
University of Victoria
Arnold Diffusion, Florin Diacu
Journal of Humanistic Mathematics
No abstract provided.
An Introduction To Fourier Analysis With Applications To Music,
2014
Claremont McKenna College
An Introduction To Fourier Analysis With Applications To Music, Nathan Lenssen, Deanna Needell
Journal of Humanistic Mathematics
In our modern world, we are often faced with problems in which a traditionally analog signal is discretized to enable computer analysis. A fundamental tool used by mathematicians, engineers, and scientists in this context is the discrete Fourier transform (DFT), which allows us to analyze individual frequency components of digital signals. In this paper we develop the discrete Fourier transform from basic calculus, providing the reader with the setup to understand how the DFT can be used to analyze a musical signal for chord structure. By investigating the DFT alongside an application in music processing, we gain an appreciation for …
Students Ahead Of The Curve In Regional Mathematics Competition,
2014
Illinois Wesleyan University
Students Ahead Of The Curve In Regional Mathematics Competition, Tia Patsavas
News and Events (Discontinued Series)
No abstract provided.
A Simple Proof For The Number Of Tilings Of Quartered Aztec Diamonds,
2014
Indiana University Bloomington
A Simple Proof For The Number Of Tilings Of Quartered Aztec Diamonds, Tri Lai
Department of Mathematics: Faculty Publications
We get four quartered Aztec diamonds by dividing an Aztec diamond region by two zigzag cuts passing its center. W. Jockusch and J. Propp (in an unpublished work) found that the number of tilings of quartered Aztec diamonds is given by simple product formulas. In this paper we present a simple proof for this result.
A Fast Algorithm For The Inversion Of Quasiseparable Vandermonde-Like Matrices,
2014
Embry-Riddle Aeronautical University
A Fast Algorithm For The Inversion Of Quasiseparable Vandermonde-Like Matrices, Sirani M. Perera, Grigory Bonik, Vadim Olshevsky
Publications
The results on Vandermonde-like matrices were introduced as a generalization of polynomial Vandermonde matrices, and the displacement structure of these matrices was used to derive an inversion formula. In this paper we first present a fast Gaussian elimination algorithm for the polynomial Vandermonde-like matrices. Later we use the said algorithm to derive fast inversion algorithms for quasiseparable, semiseparable and well-free Vandermonde-like matrices having O(n2) complexity. To do so we identify structures of displacement operators in terms of generators and the recurrence relations(2-term and 3-term) between the columns of the basis transformation matrices for quasiseparable, semiseparable and well-free polynomials. Finally we …
Sixteen Years Of Collaborative Learning Through Active Sense-Making In Physics (Clasp) At Uc Davis,
2014
University of California, Davis
Sixteen Years Of Collaborative Learning Through Active Sense-Making In Physics (Clasp) At Uc Davis, Wendell Potter, David Webb, Cassandra Paul, Emily West, Mark Bowen, Brenda Weiss, Lawrence Coleman, Charles De Leone
Faculty Publications
This paper describes our large reformed introductory physics course at UC Davis, which bioscience students have been taking since 1996. The central feature of this course is a focus on sense-making by the students during the five hours per week discussion/labs in which the students take part in activities emphasizing peer-peer discussions, argumentation, and presentations of ideas. The course differs in many fundamental ways from traditionally taught introductory physics courses. After discussing the unique features of CLASP and its implementation at UC Davis, various student outcome measures are presented showing increased performance by students who took the CLASP course compared …
