Subdifferentials Of Value Functions In Nonconvex Dynamic Programming For Nonstationary Stochastic Processes, 2019 Department of Mathematics, Wayne State University, Detroit, MI 48202, USA

#### Subdifferentials Of Value Functions In Nonconvex Dynamic Programming For Nonstationary Stochastic Processes, Boris S. Mordukhovich, Nobusumi Sagara

*Communications on Stochastic Analysis*

No abstract provided.

Hybrid Models And Switching Control With Constraints, 2019 Wayne State University

#### Hybrid Models And Switching Control With Constraints, Jose L. Menaldi, Maurice Robin

*Communications on Stochastic Analysis*

No abstract provided.

Non-Nested Monte Carlo Dual Bounds For Multi-Exercisable Options, 2019 Centre for Actuarial Studies, Department of Economics, The University of Melbourne, VIC 3010, Australia

#### Non-Nested Monte Carlo Dual Bounds For Multi-Exercisable Options, Xiang Cheng, Zhuo Jin

*Communications on Stochastic Analysis*

No abstract provided.

Totalitarian Random Tug-Of-War Games In Graphs, 2019 Universitat Politècnica de Catalunya, Departament de Matemàtiques, Diagonal 647, 08028 Barcelona, Spain

#### Totalitarian Random Tug-Of-War Games In Graphs, Marcos Antón, Fernando Charro, Peiyong Wang

*Communications on Stochastic Analysis*

No abstract provided.

Analysis Of Feast Spectral Approximations Using The Dpg Discretization, 2019 Portland State University

#### Analysis Of Feast Spectral Approximations Using The Dpg Discretization, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall, Benjamin Q. Parker

*Jeffrey S. Ovall*

A filtered subspace iteration for computing a cluster of eigenvalues and its accompanying eigenspace, known as “FEAST”, has gained considerable attention in recent years. This work studies issues that arise when FEAST is applied to compute part of the spectrum of an unbounded partial differential operator. Specifically, when the resolvent of the partial differential operator is approximated by the discontinuous Petrov Galerkin (DPG) method, it is shown that there is no spectral pollution. The theory also provides bounds on the discretization errors in the spectral approximations. Numerical experiments for simple operators illustrate the theory and also indicate the value of ...

Polynomial And Rational Convexity Of Submanifolds Of Euclidean Complex Space, 2019 The University of Western Ontario

#### Polynomial And Rational Convexity Of Submanifolds Of Euclidean Complex Space, Octavian Mitrea

*Electronic Thesis and Dissertation Repository*

The goal of this dissertation is to prove two results which are essentially independent, but which do connect to each other via their direct applications to approximation theory, symplectic geometry, topology and Banach algebras. First we show that every smooth totally real compact surface in complex Euclidean space of dimension 2 with finitely many isolated singular points of the open Whitney umbrella type is locally polynomially convex. The second result is a characterization of the rational convexity of a general class of totally real compact immersions in complex Euclidean space of dimension n..

Analysis Of Feast Spectral Approximations Using The Dpg Discretization, 2019 Portland State University

#### Analysis Of Feast Spectral Approximations Using The Dpg Discretization, Jay Gopalakrishnan, Luka Grubišić, Jeffrey S. Ovall, Benjamin Q. Parker

*Jay Gopalakrishnan*

A filtered subspace iteration for computing a cluster of eigenvalues and its accompanying eigenspace, known as “FEAST”, has gained considerable attention in recent years. This work studies issues that arise when FEAST is applied to compute part of the spectrum of an unbounded partial differential operator. Specifically, when the resolvent of the partial differential operator is approximated by the discontinuous Petrov Galerkin (DPG) method, it is shown that there is no spectral pollution. The theory also provides bounds on the discretization errors in the spectral approximations. Numerical experiments for simple operators illustrate the theory and also indicate the value of ...

General Nonlinear-Material Elasticity In Classical One-Dimensional Solid Mechanics, 2019 University of New Orleans

#### General Nonlinear-Material Elasticity In Classical One-Dimensional Solid Mechanics, Ronald Joseph Giardina Jr

*University of New Orleans Theses and Dissertations*

We will create a class of generalized ellipses and explore their ability to define a distance on a space and generate continuous, periodic functions. Connections between these continuous, periodic functions and the generalizations of trigonometric functions known in the literature shall be established along with connections between these generalized ellipses and some spectrahedral projections onto the plane, more specifically the well-known multifocal ellipses. The superellipse, or Lam\'{e} curve, will be a special case of the generalized ellipse. Applications of these generalized ellipses shall be explored with regards to some one-dimensional systems of classical mechanics. We will adopt the Ramberg-Osgood ...

Krylov Subspace Spectral Methods With Non-Homogenous Boundary Conditions, 2019 University of Southern Mississippi

#### Krylov Subspace Spectral Methods With Non-Homogenous Boundary Conditions, Abbie Hendley

*Master's Theses*

For this thesis, Krylov Subspace Spectral (KSS) methods, developed by Dr. James Lambers, will be used to solve a one-dimensional, heat equation with non-homogenous boundary conditions. While current methods such as Finite Difference are able to carry out these computations efficiently, their accuracy and scalability can be improved. We will solve the heat equation in one-dimension with two cases to observe the behaviors of the errors using KSS methods. The first case will implement KSS methods with trigonometric initial conditions, then another case where the initial conditions are polynomial functions. We will also look at both the time-independent and time-dependent ...

Predictive Diagnostic Analysis Of Mammographic Breast Tissue Microenvironment, 2019 University of Maine

#### Predictive Diagnostic Analysis Of Mammographic Breast Tissue Microenvironment, Dexter G. Canning

*Honors College*

Improving computer-aided early detection techniques for breast cancer is paramount because current technology has high false positive rates. Existing methods have led to a substantial number of false diagnostics, which lead to stress, unnecessary biopsies, and an added financial burden to the health care system. In order to augment early detection methodology, one must understand the breast microenvironment. The CompuMAINE Lab has researched computational metrics on mammograms based on an image analysis technique called the Wavelet Transform Modulus Maxima (WTMM) method to identify the fractal and roughness signature from mammograms. The WTMM method was used to color code the mammograms ...

Understanding Volume Transport In The Jordan River: An Application Of The Navier-Stokes Equations, 2019 University of Maine

#### Understanding Volume Transport In The Jordan River: An Application Of The Navier-Stokes Equations, Gwyneth E. Roberts

*Honors College*

This study aims to characterize the circulation patterns in short and narrow estuarine systems on various temporal scales to identify the controls of material transport. In order to achieve this goal, a combination of in situ collected data and analytical modeling was used. The model is based on the horizontal Reynolds Averaged Navier-Stokes equations in the shallow water limit with scaling parameters defined from the characteristics of the estuary. The in situ measurements were used to inform a case study, seeking to understand water level variations and tidal current velocity patterns in the Jordan River and to improve understanding of ...

Elements Of Functional Analysis And Applications, 2019 Missouri State University

#### Elements Of Functional Analysis And Applications, Chengting Yin

*MSU Graduate Theses*

Functional analysis is a branch of mathematical analysis that studies vector spaces with a limit structure (such as a norm or inner product), and functions or operators defined on these spaces. Functional analysis provides a useful framework and abstract approach for some applied problems in variety of disciplines. In this thesis, we will focus on some basic concepts and abstract results in functional analysis, and then demonstrate their power and relevance by solving some applied problems under the framework. We will give the definitions and provide some examples of some different spaces (such as metric spaces, normed spaces and inner ...

Oscillatory Integrals And Weierstrass Polynomials, 2019 National University of Uzbekistan

#### Oscillatory Integrals And Weierstrass Polynomials, Azimbay Sadullaev, Isroil Ikromov

*Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences*

In this work we consider some applications of the Weierstrass preparation theorem and Weierstrass pseudopolynomials to study of behavior of the oscillatory integrals and Fourier transforms with analytic and smooth phases with critical points.

Approximation Of Continuous Functions By Artificial Neural Networks, 2019 Union College - Schenectady, NY

#### Approximation Of Continuous Functions By Artificial Neural Networks, Zongliang Ji

*Honors Theses*

An artificial neural network is a biologically-inspired system that can be trained to perform computations. Recently, techniques from machine learning have trained neural networks to perform a variety of tasks. It can be shown that any continuous function can be approximated by an artificial neural network with arbitrary precision. This is known as the universal approximation theorem. In this thesis, we will introduce neural networks and one of the first versions of this theorem, due to Cybenko. He modeled artificial neural networks using sigmoidal functions and used tools from measure theory and functional analysis.

Increasing C-Additive Processes, 2019 Department of Mathematical Sciences, University of Indianapolis, Indianapolis, IN 46627, USA

#### Increasing C-Additive Processes, Nadjib Bouzar

*Communications on Stochastic Analysis*

No abstract provided.

Spectral Theorem Approach To The Characteristic Function Of Quantum Observables, 2019 Universitá di Roma Tor Vergata, Via di Torvergata, Roma, Italy

#### Spectral Theorem Approach To The Characteristic Function Of Quantum Observables, Andreas Boukas, Philip J. Feinsilver

*Communications on Stochastic Analysis*

No abstract provided.

A Limiting Process To Invert The Gauss-Radon Transform, 2019 Department of Mathematics and Statistics, Stephen F. Austin State University, Nacogdoches, Texas 75962-3040, USA

#### A Limiting Process To Invert The Gauss-Radon Transform, Jeremy J. Becnel

*Communications on Stochastic Analysis*

No abstract provided.

Smoothing Parameters For Recursive Kernel Density Estimators Under Censoring, 2019 Univ. Poitiers, Lab. Math. et Appl., Futuroscope Chasseneuil, France

#### Smoothing Parameters For Recursive Kernel Density Estimators Under Censoring, Yousri Slaoui

*Communications on Stochastic Analysis*

No abstract provided.

Strong Convergence Rate In Averaging Principle For The Heat Equation Driven By A General Stochastic Measure, 2019 Department of Mathematical Analysis, Taras Shevchenko National University of Kyiv, Kyiv 01601, Ukraine

#### Strong Convergence Rate In Averaging Principle For The Heat Equation Driven By A General Stochastic Measure, Vadym Radchenko

*Communications on Stochastic Analysis*

No abstract provided.

Extracting Signal From The Noisy Environment Of An Ecosystem, 2019 Harrisburg University of Science and Technology

#### Extracting Signal From The Noisy Environment Of An Ecosystem, Emily Wefelmeyer, Pranita Pramod Patil, Sridhar Reddy Ravula, Kevin M. Purcell, Ziyuan Huang, Igor Pilja

*Other Student Works*

The collection and storage of environmental and ecological data by researchers, government agencies and stewardship groups over the last decade has been remarkable. The proportional challenge to this data accretion lies in capitalizing on these resources for significant gain for both stewards and stakeholders. These trends highlight the role of data science as a critical component to the future of data-driven environmental management. Most critical are models of how data scientists can collaborate with policy makers and stewards to offer tools that leverage data and facilitate decisions. Our project aims to show how a successful collaboration between a management group ...