At The Interface Of Algebra And Statistics, 2020 The Graduate Center, City University of New York

#### At The Interface Of Algebra And Statistics, Tai-Danae Bradley

*All Dissertations, Theses, and Capstone Projects*

This thesis takes inspiration from quantum physics to investigate mathematical structure that lies at the interface of algebra and statistics. The starting point is a passage from classical probability theory to quantum probability theory. The quantum version of a probability distribution is a density operator, the quantum version of marginalizing is an operation called the partial trace, and the quantum version of a marginal probability distribution is a reduced density operator. Every joint probability distribution on a finite set can be modeled as a rank one density operator. By applying the partial trace, we obtain reduced density operators whose diagonals ...

Introductory Calculus: Through The Lenses Of Covariation And Approximation, 2020 University of Montana, Missoula

#### Introductory Calculus: Through The Lenses Of Covariation And Approximation, Caleb Huber

*Graduate Student Portfolios, Papers, and Capstone Projects*

Over the course of a year, I investigated reformative approaches to the teaching of calculus. My research revealed the substantial findings of two educators, Michael Oehrtman and Pat Thompson, and inspired me to design a course based upon two key ideas, covariation and approximation metaphors. Over a period of six weeks, I taught a course tailored around these ideas and documented student responses to both classroom activities and quizzes. Responses were organized intonarratives, covariation, rates of change, limits, and delta notation. Covariation with respect to rates of change was found to be incredibly complex, and students would often see it ...

Nonlinear Photonics In Twisted And Nonlocal Structures, 2020 Southern Methodist University

#### Nonlinear Photonics In Twisted And Nonlocal Structures, Austin Copeland

*Mathematics Theses and Dissertations*

We provide a theoretical framework for the observed confinement of light modes within a twisted coreless photonic crystal fiber. Asymptotic methods are applied through ray theory and field theory in both the linear and nonlinear regime. We find the modes have a radially symmetric chirp and the envelope will decay away from the axis of propagation. Secondly, we study the stability and singularity formation of unidirectional beams as described by the Schrodinger equation. We propose a novel extension to the modeling equation to include a fractional Laplacian in one spatial dimension and a standard second derivative in a second dimension ...

Exploring Pedagogical Empathy Of Mathematics Graduate Student Instructors, 2020 University of Nebraska-Lincoln

#### Exploring Pedagogical Empathy Of Mathematics Graduate Student Instructors, Karina Uhing

*Dissertations, Theses, and Student Research Papers in Mathematics*

Interpersonal relationships are central to the teaching and learning of mathematics. One way that teachers relate to their students is by empathizing with them. In this study, I examined the phenomenon of pedagogical empathy, which is defined as empathy that influences teaching practices. Specifically, I studied how mathematics graduate student instructors conceptualize pedagogical empathy and analyzed how pedagogical empathy might influence their teaching decisions. To address my research questions, I designed a qualitative phenomenological study in which I conducted observations and interviews with 11 mathematics graduate student instructors who were teaching precalculus courses at the University of Nebraska—Lincoln.

In ...

A Note On The Fine Structure Constant, 2020 University of Nebraska-Lincoln

#### A Note On The Fine Structure Constant, Bilal Khan, Irshadullah Khan

*CSE Technical reports*

We derive the numerical value of the fine structure constant in purely number-theoretic terms, under the assumption that in a system of charges between two parallel conducting plates, the Casimir energy and the mutual Coulomb interaction energy agree.

A Note On The Fine Structure Constant, 2020 University of Nebraska-Lincoln

#### A Note On The Fine Structure Constant, Bilal Khan, Irshadullah Khan

*Sociology Department, Faculty Publications*

We derive the numerical value of the fine structure constant $\alpha$ in purely number-theoretic terms, under the assumption that in a system of charges between two parallel conducting plates, the Casimir energy and the mutual Coulomb interaction energy agree.

A Note On The Fine Structure Constant, 2020 University of Nebraska-Lincoln

#### A Note On The Fine Structure Constant, Bilal Khan, Irshadullah Khan

*Sociology Department, Faculty Publications*

We derive the numerical value of the fine structure constant in purely number-theoretic terms, under the assumption that in a system of charges between two parallel conducting plates, the Casimir energy and the mutual Coulomb interaction energy agree.

Universal Vector Neural Machine Translation With Effective Attention, 2020 SMU

#### Universal Vector Neural Machine Translation With Effective Attention, Joshua Yi, Satish Mylapore, Ryan Paul, Robert Slater

*SMU Data Science Review*

Neural Machine Translation (NMT) leverages one or more trained neural networks for the translation of phrases. Sutskever intro- duced a sequence to sequence based encoder decoder model which be- came the standard for NMT based systems. Attention mechanisms were later introduced to address the issues with the translation of long sen- tences and improving overall accuracy. In this paper, we propose two improvements to the encoder decoder based NMT approach. Most trans- lation models are trained as one model for one translation. We introduce a neutral/universal model representation that can be used to predict more than one language depending ...

Homotopy Analysis Method For Nonlinear Ordinary Eigenvalue Problems, 2020 The University of Southern Mississippi

#### Homotopy Analysis Method For Nonlinear Ordinary Eigenvalue Problems, Subagya Perera

*Master's Theses*

In this thesis, we solve nonlinear differential equations by the homotopy analysis method (HAM), which is a semi-analytic method first introduced by Shijun Liao in 1992. The modified HAM can be viewed as a more generalized method that encloses many perturbation and non-perturbation methods. It is different from perturbation or other analytical methods in that it allows considerable freedomformanyvariables. Using the modified HAM, especially zero-order and higher-order deformation equations, we solve a nonlinear initial value problem and a nonlinear eigenvalue problem. We adjust the convergence region of a solution by modifying auxiliary parameter values. The results converge in very few ...

Written Reflections And Discussion Forums-- Math For Elementary School Teachers (Q2s-Ep: Math 301aqbr And Math 301bqbr ), 2020 California State University, San Bernardino

#### Written Reflections And Discussion Forums-- Math For Elementary School Teachers (Q2s-Ep: Math 301aqbr And Math 301bqbr ), Stephanie Creswell

*Q2S Enhancing Pedagogy*

Preparing for the transition from quarters to semesters, instructors of the mathematics sequence for future elementary teachers (Math 301ABC, Math 308 and their semester equivalents 3011, 3012 and 3013) applied research about best practices for online learning in mathematics to the quarter bridge courses Math 301AQBR and 301BQBR that each include 0.5 units of online activities. Successful activities piloted in the quarter bridge courses may be implemented in the 3011-3012-3013 semester sequence and their associated lab courses 3011L-3012L-3013L. This paper focuses on written reflections and group discussion forums associated with the class textbook Powerful Problem Solving by Max Ray.

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.

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.

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.