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Homogenization In Perforated Domains And With Soft Inclusions, Brandon C. Russell 2018 University of Kentucky

Homogenization In Perforated Domains And With Soft Inclusions, Brandon C. Russell

Theses and Dissertations--Mathematics

In this dissertation, we first provide a short introduction to qualitative homogenization of elliptic equations and systems. We collect relevant and known results regarding elliptic equations and systems with rapidly oscillating, periodic coefficients, which is the classical setting in homogenization of elliptic equations and systems. We extend several classical results to the so called case of perforated domains and consider materials reinforced with soft inclusions. We establish quantitative H1-convergence rates in both settings, and as a result deduce large-scale Lipschitz estimates and Liouville-type estimates for solutions to elliptic systems with rapidly oscillating periodic bounded and measurable coefficients. Finally ...


W1,P Regularity Of Eigenfunctions For The Mixed Problem With Nonhomogeneous Neumann Data, Kohei Miyazaki 2018 Murray State University

W1,P Regularity Of Eigenfunctions For The Mixed Problem With Nonhomogeneous Neumann Data, Kohei Miyazaki

Murray State Theses and Dissertations

We consider an eigenvalue problem with a mixed boundary condition, where a second-order differential operator is given in divergence form and satisfies a uniform ellipticity condition. We show that if a function u in the Sobolev space W1,pD is a weak solution to the eigenvalue problem, then u also belongs to W1,pD for some p>2. To do so, we show a reverse Hölder inequality for the gradient of u. The decomposition of the boundary is assumed to be such that we get both Poincaré and Sobolev-type inequalities up to the boundary.


Essays On Financial Information In Text, Gustaf Bellstam 2018 University of Colorado at Boulder

Essays On Financial Information In Text, Gustaf Bellstam

Business Administration Graduate Theses & Dissertations

In the first essay, I study how analysts' performance depends on their incentives and access to information using a regulatory shock and the textual content of analyst reports. My results focus on two aspects of performance, informativeness and bias. After incentives and access to information are reduced, analyst reports become less informative but also less biased. My identification strategy uses the Global Research Settlement as a shock that affected analysts at investment banks, but not other analysts, in a difference-in-difference design. I find that analyst reports become more similar to one another after the shock, an indication of less information ...


I’M Being Framed: Phase Retrieval And Frame Dilation In Finite-Dimensional Real Hilbert Spaces, Jason L. Greuling 2018 University of Central Florida

I’M Being Framed: Phase Retrieval And Frame Dilation In Finite-Dimensional Real Hilbert Spaces, Jason L. Greuling

Honors Undergraduate Theses

Research has shown that a frame for an n-dimensional real Hilbert space offers phase retrieval if and only if it has the complement property. There is a geometric characterization of general frames, the Han-Larson-Naimark Dilation Theorem, which gives us the necessary and sufficient conditions required to dilate a frame for an n-dimensional Hilbert space to a frame for a Hilbert space of higher dimension k. However, a frame having the complement property in an n-dimensional real Hilbert space does not ensure that its dilation will offer phase retrieval. In this thesis, we will explore and provide what necessary and sufficient ...


Foreword By Guest Editors Maa 2018 Volume 18 Issue 4, Frank Prendergast, A. César González-García, Gary Wells, Juan Antonio Belmonte 2018 Dublin Institute of Technology

Foreword By Guest Editors Maa 2018 Volume 18 Issue 4, Frank Prendergast, A. César González-García, Gary Wells, Juan Antonio Belmonte

Conference Papers

MAA SPECIAL ISSUE VOL 18 ISSUE 4:

Sixty-three (63) Selected (peer reviewed) Papers of the INSAP X – Oxford XI – SEAC 25th Joint Conference ‘ROAD TO THE STARS’, held in Santiago de Compostela, Spain, 18th–22nd September 2017

Mediterranean Archaeology and Archaeometry (MAA) is an Open Access Journal published since 2001 by The University of the Aegean, Department of Mediterranean Studies, Rhodes, Greece.

It covers the dual nature of archaeology and cultural heritage with science which includes, amongst others, natural science applied to archaeology (physics, chemistry, biology, geology, geophysics, astronomy), archaeology, ancient history, cultural sustainability, astronomy in culture, physical anthropology, digital ...


Onsager Reciprocal Relations: Microscopic (Onsager) Or Macroscopic (Sliepcevich), R. E. "Buddy" Babcock 2018 University of Arkansas - Main Campus

Onsager Reciprocal Relations: Microscopic (Onsager) Or Macroscopic (Sliepcevich), R. E. "Buddy" Babcock

Chemical Engineering Faculty Publications and Presentations

This paper is a combination of the discussion of two nineteenth century theoretical giantsLars Onsager and C. M. Sliepcevich, their works in general, and specifically the famousreciprocal relations of Onsager with respect to irreversible thermodynamics. Emphasis isplaced on their penetrating depth and breadth of analysis so inherently necessary in theirproblem-solving endeavors. The landscape of their work will be laid out for the readerby a comparison of Onsager’s microscopic statistical mechanics derivation of the famousreciprocal relationships and a macroscopic thermodynamic derivation published by C. M.Sliepsevich that led to considerable discussion in the literature in the 1960’s. Somelabelled this ...


The Boundedness Of The Hardy-Littlewood Maximal Function And The Strong Maximal Function On The Space Bmo, Wenhao Zhang 2018 Claremont Colleges

The Boundedness Of The Hardy-Littlewood Maximal Function And The Strong Maximal Function On The Space Bmo, Wenhao Zhang

CMC Senior Theses

In this thesis, we present the space BMO, the one-parameter Hardy-Littlewood maximal function, and the two-parameter strong maximal function. We use the John-Nirenberg inequality, the relation between Muckenhoupt weights and BMO, and the Coifman-Rochberg proposition on constructing A1 weights with the Hardy- Littlewood maximal function to show the boundedness of the Hardy-Littlewood maximal function on BMO. The analogous statement for the strong maximal function is not yet understood. We begin our exploration of this problem by discussing an equivalence between the boundedness of the strong maximal function on rectangular BMO and the fact that the strong maximal function maps ...


Markushevich Bases And Auerbach Bases In Banach Spaces, Apala Mandal 2018 University of Windsor

Markushevich Bases And Auerbach Bases In Banach Spaces, Apala Mandal

Major Papers

This paper studies Markushevich bases and Auerbach bases in Banach spaces. Firstly, a countable 1-norming Markushevich basis is constructed for any infinite-dimensional separable Banach space. Secondly, an Auerbach basis is constructed for any finite-dimensional Banach space. Thirdly, a Markushevich basis is constructed for a class of non-separable Banach spaces by applying projectional generators and projectional resolution identities, and the transfinite induction on the density character of the space.


On The Growth Of Sobolev Norms For The Nonlinear Schrödinger Equation On Tori And Boundary Unique Continuation For Elliptic Pde, Michael Boratko 2018 University of Massachusetts Amherst

On The Growth Of Sobolev Norms For The Nonlinear Schrödinger Equation On Tori And Boundary Unique Continuation For Elliptic Pde, Michael Boratko

Doctoral Dissertations

This dissertation is composed of two parts. The first part applies techniques from Harmonic and nonlinear Fourier Analysis to the nonlinear Schrödinger equation, and therefore tools from the study of Dispersive Partial Differential Equations (PDEs) will also be employed. The dissertation will apply the $\ell^2$ decoupling conjecture, proved recently by Bourgain and Demeter, to prove polynomial bounds on the growth of Sobolev norms of solutions to polynomial nonlinear Schrödinger equations. The first bound which is obtained applies to the cubic nonlinear Schrödinger equation and yields an improved bound for irrational tori in dimensions 2 and 3. For the 4 ...


Well-Posedness For The Cubic Nonlinear Schrödinger Equations On Tori, Haitian Yue 2018 University of Massachusetts Amherst

Well-Posedness For The Cubic Nonlinear Schrödinger Equations On Tori, Haitian Yue

Doctoral Dissertations

This thesis studies the cubic nonlinear Sch\"rodinger equation (NLS) on tori both from the deterministic and probabilistic viewpoints. In Part I of this thesis, we prove global-in-time well-posedness of the Cauchy initial value problem for the defocusing cubic NLS on 4-dimensional tori and with initial data in the energy-critical space $H^1$. Furthermore, in the focusing case we prove that if a maximal-lifespan solution of the cubic NLS \, $u: I\times\mathbb{T}^4\to \mathbb{C}$\, satisfies $\sup_{t\in I}\|u(t)\|_{\dot{H}^1(\mathbb{T}^4)}


Global Well-Posedness And Scattering For The Defocusing Quintic Nonlinear Schrödinger Equation In Two Dimensions, Xueying Yu 2018 University of Massachusetts Amherst

Global Well-Posedness And Scattering For The Defocusing Quintic Nonlinear Schrödinger Equation In Two Dimensions, Xueying Yu

Doctoral Dissertations

In this thesis we consider the Cauchy initial value problem for the defocusing quintic nonlinear Schrödinger equation in two dimensions. We take general data in the critical homogeneous Sobolev space dot H1/2.

We show that if a solution remains bounded in dot H1/2 in its maximal time interval of existence, then the time interval is infinite and the solution scatters.


Quantitative Conservation Of The Gray Wolf (Canis Lupus): Implications Of Monitoring And Modeling The Yellowstone Wolves, Michael Procko 2018 University of Colorado, Boulder

Quantitative Conservation Of The Gray Wolf (Canis Lupus): Implications Of Monitoring And Modeling The Yellowstone Wolves, Michael Procko

Undergraduate Honors Theses

The 1995 reintroduction of wolves to the Greater Yellowstone ecosystem had lasting effects on our understanding of reintroduction biology as a whole. However, continued study of a system as complex and intricately interwoven as this should be done with minimal human influence on the ecosystem. The states comprising the tri-state area surrounding Yellowstone National Park—Wyoming, Idaho, and Montana—have recently delisted wolves from the endangered species list. Here, I assess the greater implications in conservation that can be deduced from quantitative analysis of the Yellowstone wolves, and question whether the species is, in fact, stable enough for delisting in ...


Old English Character Recognition Using Neural Networks, Sattajit Sutradhar 2018 Georgia Southern University

Old English Character Recognition Using Neural Networks, Sattajit Sutradhar

Electronic Theses and Dissertations

Character recognition has been capturing the interest of researchers since the beginning of the twentieth century. While the Optical Character Recognition for printed material is very robust and widespread nowadays, the recognition of handwritten materials lags behind. In our digital era more and more historical, handwritten documents are digitized and made available to the general public. However, these digital copies of handwritten materials lack the automatic content recognition feature of their printed materials counterparts. We are proposing a practical, accurate, and computationally efficient method for Old English character recognition from manuscript images. Our method relies on a modern machine learning ...


Survey Of Results On The Schrodinger Operator With Inverse Square Potential, Richardson Saint Bonheur 2018 Georgia Southern University

Survey Of Results On The Schrodinger Operator With Inverse Square Potential, Richardson Saint Bonheur

Electronic Theses and Dissertations

In this paper we present a survey of results on the Schrodinger operator with Inverse ¨ Square potential, La= −∆ + a/|x|^2 , a ≥ −( d−2/2 )^2. We briefly discuss the long-time behavior of solutions to the inter-critical focusing NLS with an inverse square potential(proof not provided). Later we present spectral multiplier theorems for the operator. For the case when a ≥ 0, we present the multiplier theorem from Hebisch [12]. The case when 0 > a ≥ −( d−2/2 )^2 was explored in [1], and their proof will be presented for completeness. No improvements on the sharpness of their proof ...


On Spectral Theorem, Muyuan Zhang 2018 Colby College

On Spectral Theorem, Muyuan Zhang

Honors Theses

There are many instances where the theory of eigenvalues and eigenvectors has its applications. However, Matrix theory, which usually deals with vector spaces with finite dimensions, also has its constraints. Spectral theory, on the other hand, generalizes the ideas of eigenvalues and eigenvectors and applies them to vector spaces with arbitrary dimensions. In the following chapters, we will learn the basics of spectral theory and in particular, we will focus on one of the most important theorems in spectral theory, namely the spectral theorem. There are many different formulations of the spectral theorem and they convey the "same" idea. In ...


Scalable And Timely Detection Of Cyberbullying In Online Social Networks, Rahat Ibn Rafiq 2018 University of Colorado at Boulder

Scalable And Timely Detection Of Cyberbullying In Online Social Networks, Rahat Ibn Rafiq

Computer Science Graduate Theses & Dissertations

The exponential growth of popularity of online social networks in the last decade has unfortunately paved the way for the threat of cyberbullying to rise to an unprecedented level. So a research that provides insights into the analysis of cyberbullying incidents and building a system that is highly scalable and responsive is of unparalleled need. This dissertation gathers insights into cyberbullying incidents in video and image-based social networks (Vine and Instagram respectively) and then presents a system solution that makes use of the gained insights to improve efficiency and efficacy of cyberbullying detection. First, it presents detailed analyses of cyberbullying ...


From Convergence In Measure To Convergence Of Matrix-Sequences Through Concave Functions And Singular Values, Giovanni Barbarino, Carlo Garoni 2017 Scuola Normale Superiore, Pisa, Italy

From Convergence In Measure To Convergence Of Matrix-Sequences Through Concave Functions And Singular Values, Giovanni Barbarino, Carlo Garoni

Electronic Journal of Linear Algebra

Sequences of matrices with increasing size naturally arise in several areas of science, such as, for example, the numerical discretization of differential and integral equations. An approximation theory for sequences of this kind has recently been developed, with the aim of providing tools for computing their asymptotic singular value and eigenvalue distributions. The cornerstone of this theory is the notion of approximating classes of sequences (a.c.s.), which is also fundamental to the theory of generalized locally Toeplitz (GLT) sequences, and hence to the spectral analysis of PDE discretization matrices. Drawing inspiration from measure theory, here it is introduced ...


Weighted Inequalities For Dyadic Operators Over Spaces Of Homogeneous Type, David Edward Weirich 2017 University of New Mexico

Weighted Inequalities For Dyadic Operators Over Spaces Of Homogeneous Type, David Edward Weirich

Mathematics & Statistics ETDs

A so-called space of homogeneous type is a set equipped with a quasi-metric and a doubling measure. We give a survey of results spanning the last few decades concerning the geometric properties of such spaces, culminating in the description of a system of dyadic cubes in this setting whose properties mirror the more familiar dyadic lattices in R^n . We then use these cubes to prove a result pertaining to weighted inequality theory over such spaces. We develop a general method for extending Bellman function type arguments from the real line to spaces of homogeneous type. Finally, we uses this ...


Statistical Analysis Of Momentum In Basketball, Mackenzi Stump 2017 Bowling Green State University

Statistical Analysis Of Momentum In Basketball, Mackenzi Stump

Honors Projects

The “hot hand” in sports has been debated for as long as sports have been around. The debate involves whether streaks and slumps in sports are true phenomena or just simply perceptions in the mind of the human viewer. This statistical analysis of momentum in basketball analyzes the distribution of time between scoring events for the BGSU Women’s Basketball team from 2011-2017. We discuss how the distribution of time between scoring events changes with normal game factors such as location of the game, game outcome, and several other factors. If scoring events during a game were always randomly distributed ...


Infinite-Dimensional Measure Spaces And Frame Analysis, Palle Jorgensen, Myung-Sin Song 2017 The University of Iowa

Infinite-Dimensional Measure Spaces And Frame Analysis, Palle Jorgensen, Myung-Sin Song

SIUE Faculty Research, Scholarship, and Creative Activity

We study certain infinite-dimensional probability measures in connection with frame analysis. Earlier work on frame-measures has so far focused on the case of finite-dimensional frames. We point out that there are good reasons for a sharp distinction between stochastic analysis involving frames in finite vs. infinite dimensions. For the case of infinite-dimensional Hilbert space ℋ, we study three cases of measures. We first show that, for ℋ infinite dimensional, one must resort to infinite dimensional measure spaces which properly contain ℋ. The three cases we consider are: (i) Gaussian frame measures, (ii) Markov path-space measures, and (iii) determinantal measures.


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