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Articles 1 - 9 of 9
Full-Text Articles in Analysis
Enestr¨Om-Kakeya Type Results For Complex And Quaternionic Polynomials, Matthew Gladin
Enestr¨Om-Kakeya Type Results For Complex And Quaternionic Polynomials, Matthew Gladin
Electronic Theses and Dissertations
The well known Eneström-Kakeya Theorem states that: for P(z)=∑i=0n ai zi, a polynomial of degree n with real coefficients satisfying 0 ≤ a0 ≤ a1 ≤ ⋯≤ an, all zeros of P(z) lie in |z|≤1 in the complex plane. In this thesis, we will find inner and outer bounds in which the zeros of complex and quaternionic polynomials lie. We will do this by imposing restrictions on the real and imaginary parts, and on the moduli, of the complex and quaternionic coefficients. We also apply similar restrictions on complex polynomials with …
Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang
Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang
Electronic Theses and Dissertations
While the "path integral" formulation of quantum mechanics is both highly intuitive and far reaching, the path integrals themselves often fail to converge in the usual sense. Richard Feynman developed regularization as a solution, such that regularized path integrals could be calculated and analyzed within a strictly physics context. Over the past 50 years, mathematicians and physicists have retroactively introduced schemes for achieving mathematical rigor in the study and application of regularized path integrals. One such scheme was introduced in 2007 by the mathematicians Klaus Kirsten and Paul Loya. In this thesis, we reproduce the Kirsten and Loya approach to …
Constructions & Optimization In Classical Real Analysis Theorems, Abderrahim Elallam
Constructions & Optimization In Classical Real Analysis Theorems, Abderrahim Elallam
Electronic Theses and Dissertations
This thesis takes a closer look at three fundamental Classical Theorems in Real Analysis. First, for the Bolzano Weierstrass Theorem, we will be interested in constructing a convergent subsequence from a non-convergent bounded sequence. Such a subsequence is guaranteed to exist, but it is often not obvious what it is, e.g., if an = sin n. Next, the H¨older Inequality gives an upper bound, in terms of p ∈ [1,∞], for the the integral of the product of two functions. We will find the value of p that gives the best (smallest) upper-bound, focusing on the Beta and Gamma integrals. …
An Analysis Of The First Passage To The Origin (Fpo) Distribution, Aradhana Soni
An Analysis Of The First Passage To The Origin (Fpo) Distribution, Aradhana Soni
Electronic Theses and Dissertations
What is the probability that in a fair coin toss game (a simple random walk) we go bankrupt in n steps when there is an initial lead of some known or unknown quantity $m? What is the distribution of the number of steps N that it takes for the lead to vanish? This thesis explores some of the features of this first passage to the origin (FPO) distribution. First, we explore the distribution of N when m is known. Next, we compute the maximum likelihood estimators of m for a fixed n and also the posterior distribution of m when …
An Algorithm For The Machine Calculation Of Minimal Paths, Robert Whitinger
An Algorithm For The Machine Calculation Of Minimal Paths, Robert Whitinger
Electronic Theses and Dissertations
Problems involving the minimization of functionals date back to antiquity. The mathematics of the calculus of variations has provided a framework for the analytical solution of a limited class of such problems. This paper describes a numerical approximation technique for obtaining machine solutions to minimal path problems. It is shown that this technique is applicable not only to the common case of finding geodesics on parameterized surfaces in R3, but also to the general case of finding minimal functionals on hypersurfaces in Rn associated with an arbitrary metric.
The Complete Structure Of Linear And Nonlinear Deformations Of Frames On A Hilbert Space, Devanshu Agrawal
The Complete Structure Of Linear And Nonlinear Deformations Of Frames On A Hilbert Space, Devanshu Agrawal
Electronic Theses and Dissertations
A frame is a possibly linearly dependent set of vectors in a Hilbert space that facilitates the decomposition and reconstruction of vectors. A Parseval frame is a frame that acts as its own dual frame. A Gabor frame comprises all translations and phase modulations of an appropriate window function. We show that the space of all frames on a Hilbert space indexed by a common measure space can be fibrated into orbits under the action of invertible linear deformations and that any maximal set of unitarily inequivalent Parseval frames is a complete set of representatives of the orbits. We show …
The Number Of Zeros Of A Polynomial In A Disk As A Consequence Of Coefficient Inequalities With Multiple Reversals, Derek T. Bryant
The Number Of Zeros Of A Polynomial In A Disk As A Consequence Of Coefficient Inequalities With Multiple Reversals, Derek T. Bryant
Electronic Theses and Dissertations
In this thesis, we explore the effect of restricting the coefficients of polynomials on the bounds for the number of zeros in a given region. The results presented herein build on a body of work, culminating in the generalization of bounds among three classes of polynomials. The hypotheses of monotonicity on each class of polynomials were further subdivided into sections concerning r reversals among the moduli, real parts, and both real and imaginary parts of the coefficients.
Revised Model For Antibiotic Resistance In A Hospital, Ruhang Pei
Revised Model For Antibiotic Resistance In A Hospital, Ruhang Pei
Electronic Theses and Dissertations
In this thesis we modify an existing model for the spread of resistant bacteria in a hospital. The existing model does not account for some of the trends seen in the data found in literature. The new model takes some of these trends into account. For the new model, we examine issues relating to identifiability, sensitivity analysis, parameter estimation, uncertainty analysis, and equilibrium stability.
The Number Of Zeros Of A Polynomial In A Disk As A Consequence Of Restrictions On The Coefficients, Brett A. Shields Mr.
The Number Of Zeros Of A Polynomial In A Disk As A Consequence Of Restrictions On The Coefficients, Brett A. Shields Mr.
Electronic Theses and Dissertations
In this thesis, we put restrictions on the coefficients of polynomials and give bounds concerning the number of zeros in a specific region. Our results generalize a number of previously known theorems, as well as implying many new corollaries with hypotheses concerning monotonicity of the modulus, real, as well as real and imaginary parts of the coefficients separately. We worked with Enestr\"{o}m-Kakeya type hypotheses, yet we were only concerned with the number of zeros of the polynomial. We considered putting the same type of restrictions on the coefficients of three different types of polynomials: polynomials with a monotonicity``flip" at some …