Rigorous Debates Over Debatable Rigor: Monster Functions In Introductory Analysis, 2017 Colorado State University-Pueblo

#### Rigorous Debates Over Debatable Rigor: Monster Functions In Introductory Analysis, Janet Heine Barnett

*Analysis*

No abstract provided.

The Loewner Equation And Weierstrass' Function, 2017 University of Tennessee, Knoxville

#### The Loewner Equation And Weierstrass' Function, Gavin Ainsley Glenn

*University of Tennessee Honors Thesis Projects*

No abstract provided.

Observations On Convexity, 2017 Stephen F Austin State University

#### Observations On Convexity, Chad A. Huckaby

*Electronic Theses and Dissertations*

This thesis will explore convexity as it pertains to sets of complex-valued functions. These include preliminary looks at established linear and polynomially convex hulls, along with the development of new types of convex hulls. These types will include, but are not limited to the hulls determined by inversions, shift inversions, and Mobius transformations. A convex hull must be preceded by the set of functions involved. These hulls are the smallest convex sets that contain the original set. Justifications and precise definitions are included within the body of the work.

On Vector-Valued Automorphic Forms On Bounded Symmetric Domains, 2017 The University of Western Ontario

#### On Vector-Valued Automorphic Forms On Bounded Symmetric Domains, Nadia Alluhaibi

*Electronic Thesis and Dissertation Repository*

The objective of the study is to investigate the behaviour of the inner products of vector-valued Poincare series, for large weight, associated to submanifolds of a quotient of the complex unit ball and how vector-valued automorphic forms could be constructed via Poincare series. In addition, it provides a proof of that vector-valued Poincare series on an irreducible bounded symmetric domain span the space of vector-valued automorphic forms.

Self-Interlacing Polynomials Ii: Matrices With Self-Interlacing Spectrum, 2017 Shanghai Jiaotong University

#### Self-Interlacing Polynomials Ii: Matrices With Self-Interlacing Spectrum, Mikhail Tyaglov

*Electronic Journal of Linear Algebra*

An $n\times n$ matrix is said to have a self-interlacing spectrum if its eigenvalues $\lambda_k$, $k=1,\ldots,n$, are distributed as follows: $$ \lambda_1>-\lambda_2>\lambda_3>\cdots>(-1)^{n-1}\lambda_n>0. $$ A method for constructing sign definite matrices with self-interlacing spectrum from totally nonnegative ones is presented. This method is applied to bidiagonal and tridiagonal matrices. In particular, a result by O. Holtz on the spectrum of real symmetric anti-bidiagonal matrices with positive nonzero entries is generalized.

From Pythagoreans And Weierstrassians To True Infinitesimal Calculus, 2017 Bar-Ilan University

#### From Pythagoreans And Weierstrassians To True Infinitesimal Calculus, Mikhail Katz, Luie Polev

*Journal of Humanistic Mathematics*

In teaching infinitesimal calculus we sought to present basic concepts like continuity and convergence by comparing and contrasting various definitions, rather than presenting “the definition” to the students as a monolithic absolute. We hope that our experiences could be useful to other instructors wishing to follow this method of instruction. A poll run at the conclusion of the course indicates that students tend to favor infinitesimal definitions over epsilon-delta ones.

Abel And Cauchy On A Rigorous Approach To Infinite Series, 2017 Ursinus College

#### Abel And Cauchy On A Rigorous Approach To Infinite Series, Dave Ruch

*Analysis*

No abstract provided.

The Mean Value Theorem, 2017 Ursinus College

Investigations Into Bolzano's Proof Of Lub Existence: A Student Project With Primary Sources, 2017 Ursinus College

#### Investigations Into Bolzano's Proof Of Lub Existence: A Student Project With Primary Sources, Dave Ruch

*Analysis*

No abstract provided.

An Introduction To A Rigorous Definition Of Derivative, 2017 Ursinus College

#### An Introduction To A Rigorous Definition Of Derivative, Dave Ruch

*Analysis*

No abstract provided.

Investigations Into D'Alembert's Definition Of Limit: A Student Project With Primary Sources, 2017 Ursinus College

#### Investigations Into D'Alembert's Definition Of Limit: A Student Project With Primary Sources, Dave Ruch

*Analysis*

No abstract provided.

Convergence Analysis Of A Proximal Point Algorithm For Minimizing Differences Of Functions, 2017 Institute of Research and Development, Duy Tan University

#### Convergence Analysis Of A Proximal Point Algorithm For Minimizing Differences Of Functions, Thai An Nguyen, Mau Nam Nguyen

*Mathematics and Statistics Faculty Publications and Presentations*

Several optimization schemes have been known for convex optimization problems. However, numerical algorithms for solving nonconvex optimization problems are still underdeveloped. A significant progress to go beyond convexity was made by considering the class of functions representable as differences of convex functions. In this paper, we introduce a generalized proximal point algorithm to minimize the difference of a nonconvex function and a convex function. We also study convergence results of this algorithm under the main assumption that the objective function satisfies the Kurdyka– ᴌojasiewicz property.

Utilizing Remote And Numerical Methods To Provide Constraints For The Seasonal Development And Topographic Profiles Of Rock Glaciers, 2017 University of Colorado, Boulder

#### Utilizing Remote And Numerical Methods To Provide Constraints For The Seasonal Development And Topographic Profiles Of Rock Glaciers, Brett Oliver

*Undergraduate Honors Theses*

**Rock glaciers represent the dynamic interaction between rock and ice in many alpine settings that lie below the Equilibrium Line Altitude (ELA). These periglacial systems are formed by avalanched snow and debris from an overlying headwall, and are adorned with distinct topographic lobes collectively known as rumples. The central rock glacier of Mount Sopris presents a clear expression of rumples, where the structures are well-defined throughout the 1.8 km long glacier. In addition to clearly-expressed rumples, the accumulation area is constrained to a narrow bowl at the base of the headwall that is easy to identify. To inform our ...**

Series Solutions Of Polarized Gowdy Universes, 2017 Virginia Commonwealth University

#### Series Solutions Of Polarized Gowdy Universes, Doniray Brusaferro

*Theses and Dissertations*

Einstein's field equations are a system of ten partial differential equations. For a special class of spacetimes known as Gowdy spacetimes, the number of equations is reduced due to additional structure of two dimensional isometry groups with mutually orthogonal Killing vectors. In this thesis, we focus on a particular model of Gowdy spacetimes known as the polarized T^{3} model, and provide an explicit solution to Einstein's equations.

Compactness Of Isoresonant Potentials, 2017 University of Kentucky

#### Compactness Of Isoresonant Potentials, Robert G. Wolf

*Theses and Dissertations--Mathematics*

Bruning considered sets of isospectral Schrodinger operators with smooth real potentials on a compact manifold of dimension three. He showed the set of potentials associated to an isospectral set is compact in the topology of smooth functions by relating the spectrum to the trace of the heat semi-group. Similarly, we can consider the resonances of Schrodinger operators with real valued potentials on Euclidean space of whose support lies inside a ball of fixed radius that generate the same resonances as some fixed Schrodinger operator, an ``isoresonant" set of potentials. This isoresonant set of potentials is also compact in the topology ...

Approximation Of Solutions To The Mixed Dirichlet-Neumann Boundary Value Problem On Lipschitz Domains, 2017 University of Kentucky

#### Approximation Of Solutions To The Mixed Dirichlet-Neumann Boundary Value Problem On Lipschitz Domains, Morgan F. Schreffler

*Theses and Dissertations--Mathematics*

We show that solutions to the mixed problem on a Lipschitz domain Ω can be approximated in the Sobolev space *H*^{1}(Ω) by solutions to a family of related mixed Dirichlet-Robin boundary value problems which converge in *H*^{1}(Ω), and we give a rate of convergence. Further, we propose a method of solving the related problem using layer potentials.

Euler's Rediscovery Of E With Instructor Notes, 2017 Ursinus College

#### Euler's Rediscovery Of E With Instructor Notes, Dave Ruch

*Analysis*

No abstract provided.

Bolzano's Definition Of Continuity, His Bounded Set Theorem, And An Application To Continuous Functions, 2017 Ursinus College

#### Bolzano's Definition Of Continuity, His Bounded Set Theorem, And An Application To Continuous Functions, Dave Ruch

*Analysis*

No abstract provided.

Elliptic Curve Cryptography And Quantum Computing, 2017 Ouachita Baptist University

#### Elliptic Curve Cryptography And Quantum Computing, Emily Alderson

*Honors Theses*

In the year 2007, a slightly nerdy girl fell in love with all things math. Even though she only was exposed to a small part of the immense field of mathematics, she knew that math would always have a place in her heart. Ten years later, that passion for math is still burning inside. She never thought she would be interested in anything other than strictly mathematics. However, she discovered a love for computer science her sophomore year of college. Now, she is graduating college with a double major in both mathematics and computer science.

This nerdy girl is me ...

The Fundamental Theorem Of Algebra Analysis, 2016 Lake Forest College

#### The Fundamental Theorem Of Algebra Analysis, William Braubach

*Senior Theses*

From our early years of education we learn that polynomials can be factored to ﬁnd their roots. In 1797 Gauss proved the Fundamental Theo-rem of Algebra, which states that every polynomial every polynomial can be factored into quadratic and linear products. Here we build up the necessary background in advanced complex analysis to prove a variant of the Fundamental Theorem of Algebra, namely that every polynomial has at least one complex root. The proof we show here uses Cauchy’s Integral Formula and Liouville’s Theorem, which we develop and prove. This leads us into the brilliant ideas of conforming ...