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432 full-text articles. Page 1 of 13.

Rigorous Debates Over Debatable Rigor: Monster Functions In Introductory Analysis, Janet Heine Barnett 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, Gavin Ainsley Glenn 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, Chad A. Huckaby 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, Nadia Alluhaibi 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, Mikhail Tyaglov 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, Mikhail Katz, Luie Polev 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, Dave Ruch 2017 Ursinus College

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

Analysis

No abstract provided.


The Mean Value Theorem, Dave Ruch 2017 Ursinus College

The Mean Value Theorem, Dave Ruch

Analysis

No abstract provided.


Investigations Into Bolzano's Proof Of Lub Existence: A Student Project With Primary Sources, Dave Ruch 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, Dave Ruch 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, Dave Ruch 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, Thai An Nguyen, Mau Nam Nguyen 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, Brett Oliver 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, Doniray Brusaferro 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 T3 model, and provide an explicit solution to Einstein's equations.


Compactness Of Isoresonant Potentials, Robert G. Wolf 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, Morgan F. Schreffler 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 H1(Ω) by solutions to a family of related mixed Dirichlet-Robin boundary value problems which converge in H1(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, Dave Ruch 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, Dave Ruch 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, Emily Alderson 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, William Braubach 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 ...


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