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Full-Text Articles in Analysis

Symmetric Rigidity For Circle Endomorphisms With Bounded Geometry And Their Dual Maps, John Adamski Jun 2020

Symmetric Rigidity For Circle Endomorphisms With Bounded Geometry And Their Dual Maps, John Adamski

All Dissertations, Theses, and Capstone Projects

Let $f$ be a circle endomorphism of degree $d\geq2$ that generates a sequence of Markov partitions that either has bounded nearby geometry and bounded geometry, or else just has bounded geometry, with respect to normalized Lebesgue measure. We define the dual symbolic space $\S^*$ and the dual circle endomorphism $f^*=\tilde{h}\circ f\circ{h}^{-1}$, which is topologically conjugate to $f$. We describe some properties of the topological conjugacy $\tilde{h}$. We also describe an algorithm for generating arbitrary circle endomorphisms $f$ with bounded geometry that preserve Lebesgue measure and their corresponding dual circle endomorphisms $f^*$ as ...


Nonlocal Helmholtz Decompositions And Connections To Classical Counterparts, Andrew Haar, Petronela Radu May 2020

Nonlocal Helmholtz Decompositions And Connections To Classical Counterparts, Andrew Haar, Petronela Radu

UCARE Research Products

In recent years nonlocal models have been successfully introduced in a variety of applications, such as dynamic fracture, nonlocal diffusion, flocking, and image processing. Thus, the development of a nonlocal calculus theory, together with the study of nonlocal operators has become the focus of many theoretical investigations. Our work focuses on a Helmholtz decomposition in the nonlocal (integral) framework. In the classical (differential) setting the Helmholtz decomposition states that we can decompose a three dimensional vector field as a sum of an irrotational function and a solenoidal function. We will define new nonlocal gradient and curl operators that allow us ...


Combinatorial And Asymptotic Statistical Properties Of Partitions And Unimodal Sequences, Walter Mcfarland Bridges May 2020

Combinatorial And Asymptotic Statistical Properties Of Partitions And Unimodal Sequences, Walter Mcfarland Bridges

LSU Doctoral Dissertations

Our main results are asymptotic zero-one laws satisfied by the diagrams of unimodal sequences of positive integers. These diagrams consist of columns of squares in the plane; the upper boundary is called the shape. For various types of unimodal sequences, we show that, as the number of squares tends to infinity, 100% of shapes are near a certain curve---that is, there is a single limit shape. Similar phenomena have been well-studied for integer partitions, but several technical difficulties arise in the extension of such asymptotic statistical laws to unimodal sequences. We develop a widely applicable method for obtaining these limit ...


Gait Characterization Using Computer Vision Video Analysis, Martha T. Gizaw May 2020

Gait Characterization Using Computer Vision Video Analysis, Martha T. Gizaw

Undergraduate Honors Theses

The World Health Organization reports that falls are the second-leading cause of accidental death among senior adults around the world. Currently, a research team at William & Mary’s Department of Kinesiology & Health Sciences attempts to recognize and correct aging-related factors that can result in falling. To meet this goal, the members of that team videotape walking tests to examine individual gait parameters of older subjects. However, they undergo a slow, laborious process of analyzing video frame by video frame to obtain such parameters. This project uses computer vision software to reconstruct walking models from residents of an independent living retirement ...


On Quantum Effects Of Vector Potentials And Generalizations Of Functional Analysis, Ismael L. Paiva May 2020

On Quantum Effects Of Vector Potentials And Generalizations Of Functional Analysis, Ismael L. Paiva

Computational and Data Sciences (PhD) Dissertations

This is a dissertation in two parts. In the first one, the Aharonov-Bohm effect is investigated. It is shown that solenoids (or flux lines) can be seen as barriers for quantum charges. In particular, a charge can be trapped in a sector of a long cavity by two flux lines. Also, grids of flux lines can approximate the force associated with continuous two-dimensional distributions of magnetic fields. More, if it is assumed that the lines can be as close to each other as desirable, it is explained how the classical magnetic force can emerge from the Aharonov-Bohm effect. Continuing, the ...


An Analysis Of The First Passage To The Origin (Fpo) Distribution, Aradhana Soni May 2020

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 ...


On The Application Of Multidimensional Logarithmic Residue To Systems Of Non-Algebraic Equations, Barlikbay Prenov Apr 2020

On The Application Of Multidimensional Logarithmic Residue To Systems Of Non-Algebraic Equations, Barlikbay Prenov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

In this paper, the residue integrals over cycles associated with a system of non-algebraic equations and formulas for their calculation are given. Their connection with the power sums of the roots of the system is established. Some examples are considered.


Investigations Into D'Alembert's Definition Of Limit (Real Analysis Version), Dave Ruch Apr 2020

Investigations Into D'Alembert's Definition Of Limit (Real Analysis Version), Dave Ruch

Analysis

No abstract provided.


Memory-Modulated Cir Process With Discrete Delay Coefficients, Pathiranage Lochana Siriwardena, Harry Randolph Hughes, D. G. Wilathgamuwa Mar 2020

Memory-Modulated Cir Process With Discrete Delay Coefficients, Pathiranage Lochana Siriwardena, Harry Randolph Hughes, D. G. Wilathgamuwa

Journal of Stochastic Analysis

No abstract provided.


Some Exit Time Estimates For Super-Brownian Motion And Fleming-Viot Process, Parisa Fatheddin Mar 2020

Some Exit Time Estimates For Super-Brownian Motion And Fleming-Viot Process, Parisa Fatheddin

Journal of Stochastic Analysis

No abstract provided.


An Improved Uniqueness Result For A System Of Sde Related To The Stochastic Wave Equation, Carl Mueller, Eyal Neuman, Michael Salins, Giang Truong Mar 2020

An Improved Uniqueness Result For A System Of Sde Related To The Stochastic Wave Equation, Carl Mueller, Eyal Neuman, Michael Salins, Giang Truong

Journal of Stochastic Analysis

No abstract provided.


Collaboration (Reacting To The Past/Math/History/Writing), James Hayashi Feb 2020

Collaboration (Reacting To The Past/Math/History/Writing), James Hayashi

Q2S Enhancing Pedagogy

This is an assignment for a Freshman level course in the College of Natural Science. By the end students will have an understanding of valid research, collaboration and communication skills. Faculty that chooses to use this assignment will be preparing students for an active learning environment, and understanding a “Big Idea”, valid research, technology and communication skills.

Faculty should give an example of what is valid research. As students are completing this assignment mini deadlines (check-ins) shall be set. With the check-ins for this assignment focus on how the group will communicate the check point and the collaboration.

The focus ...


Large And Moderate Deviation Principles For Recursive Kernel Estimators For Spatial Data, Salim Bouzebda, Yousri Slaoui Feb 2020

Large And Moderate Deviation Principles For Recursive Kernel Estimators For Spatial Data, Salim Bouzebda, Yousri Slaoui

Journal of Stochastic Analysis

No abstract provided.


Closed Quantum Black-Scholes: Quantum Drift And The Heisenberg Equation Of Motion, Will Hicks Feb 2020

Closed Quantum Black-Scholes: Quantum Drift And The Heisenberg Equation Of Motion, Will Hicks

Journal of Stochastic Analysis

No abstract provided.


Jump Theorems For The Bochner-Martinelli Integral In Domains With A Piecewise Smooth Boundary, Alexander Kytmanov, Davlatbay Dzhumabaev, Bayrambay Utemuratov, Barlikbay Prenov Feb 2020

Jump Theorems For The Bochner-Martinelli Integral In Domains With A Piecewise Smooth Boundary, Alexander Kytmanov, Davlatbay Dzhumabaev, Bayrambay Utemuratov, Barlikbay Prenov

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Jump theorems for the Bochner-Martinelli integral in domains with a piecewise smooth boundary are obtained. Moreover, theorem for the Bochner-Martinelli integral in domains with a piecewise smooth boundary is proved for continuous functions and also for functions from the class 𝓛p.


Exit Problems For Jump-Diffusion Processes With Uniform Jumps, Mario Lefebvre Feb 2020

Exit Problems For Jump-Diffusion Processes With Uniform Jumps, Mario Lefebvre

Journal of Stochastic Analysis

No abstract provided.


Ogawa Integrability And A Condition For Convergence In The Multidimensional Case, Nicolò Cangiotti, Sonia Mazzucchi Feb 2020

Ogawa Integrability And A Condition For Convergence In The Multidimensional Case, Nicolò Cangiotti, Sonia Mazzucchi

Journal of Stochastic Analysis

No abstract provided.


Mixing Coefficient For Discrete-Time Stochastic Flow, E.V. Glinyanaya Feb 2020

Mixing Coefficient For Discrete-Time Stochastic Flow, E.V. Glinyanaya

Journal of Stochastic Analysis

No abstract provided.


On A Class Of Average Preserving Semi-Martingale Laws Optimization Problems, Rémi Lassalle Feb 2020

On A Class Of Average Preserving Semi-Martingale Laws Optimization Problems, Rémi Lassalle

Journal of Stochastic Analysis

No abstract provided.


The Semimartingale Dynamics And Generator Of A Continuous Time Semi-Markov Chain, Robert J. Elliott Feb 2020

The Semimartingale Dynamics And Generator Of A Continuous Time Semi-Markov Chain, Robert J. Elliott

Journal of Stochastic Analysis

No abstract provided.


The Isoperimetric Inequality: Proofs By Convex And Differential Geometry, Penelope Gehring Jan 2020

The Isoperimetric Inequality: Proofs By Convex And Differential Geometry, Penelope Gehring

Rose-Hulman Undergraduate Mathematics Journal

The Isoperimetric Inequality has many different proofs using methods from diverse mathematical fields. In the paper, two methods to prove this inequality will be shown and compared. First the 2-dimensional case will be proven by tools of elementary differential geometry and Fourier analysis. Afterwards the theory of convex geometry will briefly be introduced and will be used to prove the Brunn--Minkowski-Inequality. Using this inequality, the Isoperimetric Inquality in n dimensions will be shown.


Quantitative Analysis Of A Stochastic Seitr Epidemic Model With Multiple Stages Of Infection And Treatment, Olusegun M. Otunuga, Mobolaji O. Ogunsolu Jan 2020

Quantitative Analysis Of A Stochastic Seitr Epidemic Model With Multiple Stages Of Infection And Treatment, Olusegun M. Otunuga, Mobolaji O. Ogunsolu

Mathematics Faculty Research

We present a mathematical analysis of the transmission of certain diseases using a stochastic susceptible-exposed-infectious-treated-recovered (SEITR) model with multiple stages of infection and treatment and explore the effects of treatments and external fluctuations in the transmission, treatment and recovery rates. We assume external fluctuations are caused by variability in the number of contacts between infected and susceptible individuals. It is shown that the expected number of secondary infections produced (in the absence of noise) reduces as treatment is introduced into the population. By defining RT,n and ℛT,n as the basic deterministic and stochastic reproduction numbers, respectively ...


Elementary Hyperreal Analysis, Logan Cebula Jan 2020

Elementary Hyperreal Analysis, Logan Cebula

Williams Honors College, Honors Research Projects

This text explores elementary analysis through the lens of non-standard analysis. The hyperreals will be proven to be implied by the existence of the reals via the axiom of choice. The notion of a hyperextension will be defined, and the so-called Transfer Principle will be proved. This principle establishes equivalence between results in real and hyperreal analysis. Sequences, subsequences, and limit suprema/infima will then be explored. Finally, integration will be considered.


Evaluating An Ordinal Output Using Data Modeling, Algorithmic Modeling, And Numerical Analysis, Martin Keagan Wynne Brown Jan 2020

Evaluating An Ordinal Output Using Data Modeling, Algorithmic Modeling, And Numerical Analysis, Martin Keagan Wynne Brown

Murray State Theses and Dissertations

Data and algorithmic modeling are two different approaches used in predictive analytics. The models discussed from these two approaches include the proportional odds logit model (POLR), the vector generalized linear model (VGLM), the classification and regression tree model (CART), and the random forests model (RF). Patterns in the data were analyzed using trigonometric polynomial approximations and Fast Fourier Transforms. Predictive modeling is used frequently in statistics and data science to find the relationship between the explanatory (input) variables and a response (output) variable. Both approaches prove advantageous in different cases depending on the data set. In our case, the data ...


Eigenvalue Statistics And Localization For Random Band Matrices With Fixed Width And Wegner Orbital Model, Benjamin Brodie Jan 2020

Eigenvalue Statistics And Localization For Random Band Matrices With Fixed Width And Wegner Orbital Model, Benjamin Brodie

Theses and Dissertations--Mathematics

We discuss two models from the study of disordered quantum systems. The first is the Random Band Matrix with a fixed band width and Gaussian or more general disorder. The second is the Wegner $n$-orbital model. We establish that the point process constructed from the eigenvalues of finite size matrices converge to a Poisson Point Process in the limit as the matrix size goes to infinity.

The proof is based on the method of Minami for the Anderson tight-binding model. As a first step, we expand upon the localization results by Schenker and Peled-Schenker-Shamis-Sodin to account for complex energies ...


Theory Of Lexicographic Differentiation In The Banach Space Setting, Jaeho Choi Dec 2019

Theory Of Lexicographic Differentiation In The Banach Space Setting, Jaeho Choi

Electronic Theses and Dissertations

Derivative information is useful for many problems found in science and engineering that require equation solving or optimization. Driven by its utility and mathematical curiosity, researchers over the years have developed a variety of generalized derivatives. In this thesis, we will first take a look at Clarke’s generalized derivative for locally Lipschitz continuous functions between Euclidean spaces, which roughly is the smallest convex set containing all nearby derivatives of a domain point of interest. Clarke’s generalized derivative in this setting possesses a strong theoretical and numerical toolkit, which is analogous to that of the classical derivative. It includes ...


A Generalization Of Schroter's Formula To George Andrews, On His 80th Birthday, James Mclaughlin Nov 2019

A Generalization Of Schroter's Formula To George Andrews, On His 80th Birthday, James Mclaughlin

Mathematics Faculty Publications

We prove a generalization of Schroter's formula to a product of an arbitrary number of Jacobi triple products. It is then shown that many of the well-known identities involving Jacobi triple products (for example the Quintuple Product Identity, the Septuple Product Identity, and Winquist's Identity) all then follow as special cases of this general identity. Various other general identities, for example certain expansions of (q; q)(infinity) and (q; q)(infinity)(k), k >= 3, as combinations of Jacobi triple products, are also proved.


Stochastic Process And Its Role In The Development Of The Financial Market: Celebrating Professor Chow's Long And Successful Career, Xisuo L. Liu Sep 2019

Stochastic Process And Its Role In The Development Of The Financial Market: Celebrating Professor Chow's Long And Successful Career, Xisuo L. Liu

Communications on Stochastic Analysis

No abstract provided.


Stochastic Partial Differential Equation Sis Epidemic Models: Modeling And Analysis, Nhu N. Nguyen, George Yin Sep 2019

Stochastic Partial Differential Equation Sis Epidemic Models: Modeling And Analysis, Nhu N. Nguyen, George Yin

Communications on Stochastic Analysis

No abstract provided.


Action Functionals For Stochastic Differential Equations With Lévy Noise, Shenglan Yuan, Jinqiao Duan Sep 2019

Action Functionals For Stochastic Differential Equations With Lévy Noise, Shenglan Yuan, Jinqiao Duan

Communications on Stochastic Analysis

No abstract provided.