Symmetric Rigidity For Circle Endomorphisms With Bounded Geometry And Their Dual Maps, 2020 The Graduate Center, City University of New York

#### 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, 2020 University of Nebraska - Lincoln

#### 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, 2020 Louisiana State University and Agricultural and Mechanical College

#### 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, 2020 College of William and Mary

#### 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, 2020 Chapman University

#### 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, 2020 East Tennessee State University

#### 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, 2020 Nukus State Pedagogical Institute

#### 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), 2020 Ursinus College

#### 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, 2020 University of Indianapolis, Indianapolis, IN 46227, USA

#### 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, 2020 University of Pittsburgh, Pittsburgh, PA 15260, USA

#### 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, 2020 University of Rochester, Rochester, NY 14627, USA

#### 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), 2020 California State University, San Bernardino

#### 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, 2020 Alliance Sorbonne Universités, Université de Technologie de Compiègne, L.M.A.C., Compiègne, France

#### 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, 2020 Investec Bank PLC, 30 Gresham Street, London EC2V 7QP, United Kingdom

#### 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, 2020 Siberian Federal University

#### 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 𝓛^{p}.

Exit Problems For Jump-Diffusion Processes With Uniform Jumps, 2020 Polytechnique Montréal, Montréal, Québec H3C 3A7, Canada

#### 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, 2020 University of Trento, via Sommarive 14, 38123, Italy

#### 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, 2020 Institute of Mathematics NAS of Ukraine, Kyiv, Ukraine

#### 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, 2020 Université Paris-Dauphine, PSL, Place du Maréchal De Lattre De Tassigny, 75775 Paris Cedex 16, France

#### 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, 2020 University of Calgary, Calgary, AB, Canada

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

*Journal of Stochastic Analysis*

No abstract provided.