Maps Preserving Norms Of Generalized Weighted Quasi-Arithmetic Means Of Invertible Positive Operators, 2019 Institute of Mathematics, University of Debrecen, H-4002 Debrecen, P.O. Box 400

#### Maps Preserving Norms Of Generalized Weighted Quasi-Arithmetic Means Of Invertible Positive Operators, Gergő Nagy, Patricia Szokol

*Electronic Journal of Linear Algebra*

In this paper, the problem of describing the structure of transformations leaving norms of generalized weighted quasi-arithmetic means of invertible positive operators invariant is discussed. In a former result of the authors, this problem was solved for weighted quasi-arithmetic means, and here the corresponding result is generalized by establishing its solution under certain mild conditions. It is proved that in a quite general setting, generalized weighted quasi-arithmetic means on self-adjoint operators are not monotone in their variables which is an interesting property. Moreover, the relation of these means with the Kubo-Ando means is investigated and it is shown that the ...

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 ...

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 ...

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 ...

Krylov Subspace Spectral Methods With Non-Homogenous Boundary Conditions, 2019 The 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 ...

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.

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.

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.

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.

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.

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.

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 ...

Survey Of Lebesgue And Hausdorff Measures, 2019 Missouri State University

#### Survey Of Lebesgue And Hausdorff Measures, Jacob N. Oliver

*MSU Graduate Theses*

Measure theory is fundamental in the study of real analysis and serves as the basis for more robust integration methods than the classical Riemann integrals. Measure theory allows us to give precise meanings to lengths, areas, and volumes which are some of the most important mathematical measurements of the natural world. This thesis is devoted to discussing some of the major proofs and ideas of measure theory. We begin with a study of Lebesgue outer measure and Lebesgue measurable sets. After a brief discussion of non-measurable sets, we define Lebesgue measurable functions and the Lebesgue integral. In the last chapter ...

Unbounded Derivations Of C*-Algebras And The Heisenberg Commutation Relation, 2019 University of Nebraska-Lincoln

#### Unbounded Derivations Of C*-Algebras And The Heisenberg Commutation Relation, Lara M. Ismert

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

This dissertation investigates the properties of unbounded derivations on C*-algebras, namely the density of their analytic vectors and a property we refer to as "kernel stabilization." We focus on a weakly-defined derivation δ_{D} which formalizes commutators involving unbounded self-adjoint operators on a Hilbert space. These commutators naturally arise in quantum mechanics, as we briefly describe in the introduction.

A first application of kernel stabilization for δ_{D} shows that a large class of abstract derivations on unbounded C*-algebras, defined by O. Bratteli and D. Robinson, also have kernel stabilization. A second application of kernel stabilization provides a ...

Admissibility Of C*-Covers And Crossed Products Of Operator Algebras, 2019 University of Nebraska-Lincoln

#### Admissibility Of C*-Covers And Crossed Products Of Operator Algebras, Mitchell A. Hamidi

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

In 2015, E. Katsoulis and C. Ramsey introduced the construction of a non-self-adjoint crossed product that encodes the action of a group of automorphisms on an operator algebra. They did so by realizing a non-self-adjoint crossed product as the subalgebra of a C*-crossed product when dynamics of a group acting on an operator algebra by completely isometric automorphisms can be extended to self-adjoint dynamics of the group acting on a C*-algebra by ∗-automorphisms. We show that this extension of dynamics is highly dependent on the representation of the given algebra and we define a lattice structure for an ...

Minimal Principal Series Representations Of Sl(3,R), 2019 William & Mary

#### Minimal Principal Series Representations Of Sl(3,R), Jacopo Gliozzi

*Undergraduate Honors Theses*

We discuss the properties of principal series representations of SL(3,R) induced from a minimal parabolic subgroup. We present the general theory of induced representations in the language of fiber bundles, and outline the construction of principal series from structure theory of semisimple Lie groups. For SL(3,R), we show the explicit realization a novel picture of principal series based on the nonstandard picture introduced by Kobayashi, Orsted, and Pevzner for symplectic groups. We conclude by studying the K-types of SL(3,R) through Frobenius reciprocity, and evaluate prospects in developing simple intertwiners between principal series representations.

An Alternative Almost Sure Construction Of Gaussian Stochastic Processes In The L2([0,1]) Space, 2019 Bowdoin College

#### An Alternative Almost Sure Construction Of Gaussian Stochastic Processes In The L2([0,1]) Space, Kevin Chen

*Honors Projects*

No abstract provided.