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Propagation Failure In Discrete Inhomogeneous Medium Using A Caricature Of The Cubic, Elizabeth Lydon
Propagation Failure In Discrete Inhomogeneous Medium Using A Caricature Of The Cubic, Elizabeth Lydon
Electronic Theses and Dissertations
Spatially discrete Nagumo equations have widespread physical applications, including modeling electrical impulses traveling through a demyelinated axon, an environment typical in multiple scle- rosis. We construct steady-state, single front solutions by employing a piecewise linear reaction term. Using a combination of Jacobi-Operator theory and the Sherman-Morrison formula we de- rive exact solutions in the cases of homogeneous and inhomogeneous diffusion. Solutions exist only under certain conditions outlined in their construction. The range of parameter values that satisfy these conditions constitutes the interval of propagation failure, determining under what circumstances a front becomes pinned in the media. Our exact solutions represent …
Modeling Network Worm Outbreaks, Evan Foley
Modeling Network Worm Outbreaks, Evan Foley
Electronic Theses and Dissertations
Due to their convenience, computers have become a standard in society and therefore, need the utmost care. It is convenient and useful to model the behavior of digital virus outbreaks that occur, globally or locally. Compartmental models will be used to analyze the mannerisms and behaviors of computer malware. This paper will focus on a computer worm, a type of malware, spread within a business network. A mathematical model is proposed consisting of four compartments labeled as Susceptible, Infectious, Treatment, and Antidotal. We shall show that allocating resources into treating infectious computers leads to a reduced peak of infections across …
The Subject Librarian Newsletter, Mathematics, Fall 2015, Patti Mccall
The Subject Librarian Newsletter, Mathematics, Fall 2015, Patti Mccall
Libraries' Newsletters
No abstract provided.
Integral Representations Of Positive Linear Functionals, Angela Siple
Integral Representations Of Positive Linear Functionals, Angela Siple
Electronic Theses and Dissertations
In this dissertation we obtain integral representations for positive linear functionals on commutative algebras with involution and semigroups with involution. We prove Bochner and Plancherel type theorems for representations of positive functionals and show that, under some conditions, the Bochner and Plancherel representations are equivalent. We also consider the extension of positive linear functionals on a Banach algebra into a space of pseudoquotients and give under conditions in which the space of pseudoquotients can be identified with all Radon measures on the structure space. In the final chapter we consider a system of integrated Cauchy functional equations on a semigroup, …
On The Theory Of Zeta-Functions And L-Functions, Almuatazbellah Awan
On The Theory Of Zeta-Functions And L-Functions, Almuatazbellah Awan
Electronic Theses and Dissertations
In this thesis we provide a body of knowledge that concerns Riemann zeta-function and its generalizations in a cohesive manner. In particular, we have studied and mentioned some recent results regarding Hurwitz and Lerch functions, as well as Dirichlet's L-function. We have also investigated some fundamental concepts related to these functions and their universality properties. In addition, we also discuss different formulations and approaches to the proof of the Prime Number Theorem and the Riemann Hypothesis. These two topics constitute the main theme of this thesis. For the Prime Number Theorem, we provide a thorough discussion that compares and contrasts …
Tiling With Polyominoes, Polycubes, And Rectangles, Michael Saxton
Tiling With Polyominoes, Polycubes, And Rectangles, Michael Saxton
Electronic Theses and Dissertations
In this paper we study the hierarchical structure of the 2-d polyominoes. We introduce a new infinite family of polyominoes which we prove tiles a strip. We discuss applications of algebra to tiling. We discuss the algorithmic decidability of tiling the infinite plane Z x Z given a finite set of polyominoes. We will then discuss tiling with rectangles. We will then get some new, and some analogous results concerning the possible hierarchical structure for the 3-d polycubes.
Calibration Of Option Pricing In Reproducing Kernel Hilbert Space, Lei Ge
Calibration Of Option Pricing In Reproducing Kernel Hilbert Space, Lei Ge
Electronic Theses and Dissertations
A parameter used in the Black-Scholes equation, volatility, is a measure for variation of the price of a financial instrument over time. Determining volatility is a fundamental issue in the valuation of financial instruments. This gives rise to an inverse problem known as the calibration problem for option pricing. This problem is shown to be ill-posed. We propose a regularization method and reformulate our calibration problem as a problem of finding the local volatility in a reproducing kernel Hilbert space. We defined a new volatility function which allows us to embrace both the financial and time factors of the options. …
Analysis And Simulation For Homogeneous And Heterogeneous Sir Models, Joseph Wilda
Analysis And Simulation For Homogeneous And Heterogeneous Sir Models, Joseph Wilda
Electronic Theses and Dissertations
In mathematical epidemiology, disease transmission is commonly assumed to behave in accordance with the law of mass action; however, other disease incidence terms also exist in the literature. A homogeneous Susceptible-Infectious-Removed (SIR) model with a generalized incidence term is presented along with analytic and numerical results concerning effects of the generalization on the global disease dynamics. The spatial heterogeneity of the metapopulation with nonrandom directed movement between populations is incorporated into a heterogeneous SIR model with nonlinear incidence. The analysis of the combined effects of the spatial heterogeneity and nonlinear incidence on the disease dynamics of our model is presented …