Infinitely Many Solutions To Asymmetric, Polyharmonic Dirichlet Problems, 2018 The Graduate Center, City University of New York

#### Infinitely Many Solutions To Asymmetric, Polyharmonic Dirichlet Problems, Edger Sterjo

*All Dissertations, Theses, and Capstone Projects*

In this dissertation we prove new results on the existence of infinitely many solutions to nonlinear partial differential equations that are perturbed from symmetry. Our main theorems focus on polyharmonic Dirichlet problems with exponential nonlinearities, and are now published in Topol. Methods Nonlinear Anal. Vol. 50, No.1, (2017), 27-63. In chapter 1 we give an introduction to the problem, its history, and the perturbation argument itself. In chapter 2 we prove the variational principle of Bolle on the behavior of critical values under perturbation, and the variational principle of Tanaka on the existence of critical points of large augmented ...

From Convergence In Measure To Convergence Of Matrix-Sequences Through Concave Functions And Singular Values, 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 ...

Electromagnetic Resonant Scattering In Layered Media With Fabrication Errors, 2017 Louisiana State University and Agricultural and Mechanical College

#### Electromagnetic Resonant Scattering In Layered Media With Fabrication Errors, Emily Anne Mchenry

*LSU Doctoral Dissertations*

In certain layered electromagnetic media, one can construct a waveguide that supports a harmonic electromagnetic field at a frequency that is embedded in the continuous spectrum. When the structure is perturbed, this embedded eigenvalue moves into the complex plane and becomes a “complex resonance” frequency. The real and imaginary parts of this complex frequency have physical meaning. They lie behind anomalous scattering behaviors known collectively as “Fano resonance”, and people are interested in tuning them to specific values in optical devices. The mathematics involves spectral theory and analytic perturbation theory and is well understood [16], at least on a theoretical ...

Apathy And Concern Over The Future Habitability Of Earth: An Introductory College Assignment Of Forecasting Co2 In The Earth’S Atmosphere, 2017 Utah State University

#### Apathy And Concern Over The Future Habitability Of Earth: An Introductory College Assignment Of Forecasting Co2 In The Earth’S Atmosphere, Benjamin J. Burger

*Journal on Empowering Teaching Excellence*

Non-science, first year regional undergraduate students from rural Utah communities participated in an online introductory geology course and were asked to forecast the rise of CO_{2} in the Earth’s atmosphere. The majority of students predicted catastrophic rise to 5,000-ppm sometime over the next 3,100 years, resulting in an atmosphere nearly uninhabitable to human life. However, the level of concern the students exhibited in their answers was not directly proportional with their timing in their forecasted rise of CO_{2}. This study showcases the importance of presenting students with actual data and using data to develop student ...

Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, 2017 Cylance, Inc.

#### Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Gaussian Guesswork: Infinite Sequences And The Arithmetic-Geometric Mean, 2017 Colorado State University-Pueblo

#### Gaussian Guesswork: Infinite Sequences And The Arithmetic-Geometric Mean, Janet Heine Barnett

*Calculus*

No abstract provided.

Some Metric Properties Of The Teichmüller Space Of A Closed Set In The Riemann Sphere, 2017 The Graduate Center, City University of New York

#### Some Metric Properties Of The Teichmüller Space Of A Closed Set In The Riemann Sphere, Nishan Chatterjee

*All Dissertations, Theses, and Capstone Projects*

Let E be an infinite closed set in the Riemann sphere, and let T(E) denote its Teichmüller space. In this dissertation we study some metric properties of T(E). We prove Earle's form of Teichmüller contraction for T(E), holomorphic isometries from the open unit disk into T(E), extend Earle's form of Schwarz's lemma for classical Teichmüller spaces to T(E), and finally study complex geodesics and unique extremality for T(E).

Improving The Accuracy For The Long-Term Hydrologic Impact Assessment (L-Thia) Model, 2017 Purdue University

#### Improving The Accuracy For The Long-Term Hydrologic Impact Assessment (L-Thia) Model, Anqi Zhang, Lawrence Theller, Bernard A. Engel

*The Summer Undergraduate Research Fellowship (SURF) Symposium*

Urbanization increases runoff by changing land use types from less impervious to impervious covers. Improving the accuracy of a runoff assessment model, the Long-Term Hydrologic Impact Assessment (L-THIA) Model, can help us to better evaluate the potential uses of Low Impact Development (LID) practices aimed at reducing runoff, as well as to identify appropriate runoff and water quality mitigation methods. Several versions of the model have been built over time, and inconsistencies have been introduced between the models. To improve the accuracy and consistency of the model, the equations and parameters (primarily curve numbers in the case of this model ...

Smirnov Class For Spaces With The Complete Pick Property, 2017 Washington University in St Louis

#### Smirnov Class For Spaces With The Complete Pick Property, Alexandru Aleman, Michael Hartz, John E. Mccarthy, Stefan Richter

*Mathematics Faculty Publications*

We show that every function in a reproducing kernel Hilbert space with a normalized complete Pick kernel is the quotient of a multiplier and a cyclic multiplier. This extends a theorem of Alpay, Bolotnikov and Kaptanoğlu. We explore various consequences of this result regarding zero sets, spaces on compact sets and Gleason parts. In particular, using a construction of Salas, we exhibit a rotationally invariant complete Pick space of analytic functions on the unit disc for which the corona theorem fails.

Approximation Of Invariant Subspaces, 2017 University of Tennessee, Knoxville

#### Approximation Of Invariant Subspaces, Faruk Yilmaz

*Doctoral Dissertations*

For a real number α [alpha] the Dirichlet-type spaces 𝔇_{α} [script D sub alpha] are the family of Hilbert spaces consisting of all analytic functions f(z) = ∑_{n=0}^{∞}[sum over n equals zero to infinity] ˆf(n) [f hat of n] z^{n} [z to the n] defined on the open unit disc 𝔻 [unit disc] such that

∑_{n=0}^{∞} (n+ 1)^{α} |ˆf(n )|^{2}

is finite.

For α < 0, the spaces 𝔇_{α} are known as weighted Bergman spaces. When α= 0, then 𝔇_{0}= H^{2}, the well known and much studied Hardy space. For α > 0, the 𝔇 ...

Residuated Maps, The Way-Below Relation, And Contractions On Probabilistic Metric Spaces., 2017 University of Louisville

#### Residuated Maps, The Way-Below Relation, And Contractions On Probabilistic Metric Spaces., M. Ryan Luke

*Electronic Theses and Dissertations*

In this dissertation, we will examine residuated mappings on a function lattice and how they behave with respect to the way-below relation. In particular, which residuated $\phi$ has the property that $F$ is way-below $\phi(F)$ for $F$ in appropriate sets. We show the way-below relation describes the separation of two functions and how this corresponds to contraction mappings on probabilistic metric spaces. A new definition for contractions is considered using the way-below relation.

An Analysis Of The Application Of Simplified Silhouette To The Evaluation Of K-Means Clustering Validity, 2017 Dublin Institute of Technology

#### An Analysis Of The Application Of Simplified Silhouette To The Evaluation Of K-Means Clustering Validity, Fei Wang, Hector-Hugo Franco-Penya, John D. Kelleher, John Pugh, Robert Ross

*Conference papers*

Silhouette is one of the most popular and effective internal measures for the evaluation of clustering validity. Simplified Silhouette is a computationally simplified version of Silhouette. However, to date Simplified Silhouette has not been systematically analysed in a specific clustering algorithm. This paper analyses the application of Simplified Silhouette to the evaluation of k-means clustering validity and compares it with the k-means Cost Function and the original Silhouette from both theoretical and empirical perspectives. The theoretical analysis shows that Simplified Silhouette has a mathematical relationship with both the k-means Cost Function and the original Silhouette, while empirically, we show that ...

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 Definite Integrals Of Cauchy And Riemann, 2017 Ursinus College

#### The Definite Integrals Of Cauchy And Riemann, Dave Ruch

*Analysis*

Rigorous attempts to define the definite integral began in earnest in the early 1800's. One of the pioneers in this development was A. L. Cauchy (1789-1857). In this project, students will read from his 1823 study of the definite integral for continuous functions . Then students will read from Bernard Riemann's 1854 paper, in which he developed a more general concept of the definite integral that could be applied to functions with infinite discontinuities.

The Importance Of Inhaler Technique In Measuring And Calculating Inhaler Adherence, And Its Clinical Outcomes, 2017 Royal College of Surgeons in Ireland

#### The Importance Of Inhaler Technique In Measuring And Calculating Inhaler Adherence, And Its Clinical Outcomes, Imran Sulaiman

*PhD theses*

Depending on the population studied, cross-sectional observational studies suggest that between 14%-90% of patients do not use their pressurized metered dose inhaler correctly, while 50-60% misuse a dry powder inhaler. This means that unless incorrect technique is acounted for a significant underestimation of how much medication the person actually obtained may be made.

The aim of this thesis was to objectively determine the frequency and importance of inhaler technique errors and to combine these with inhaler use to provide an acurate method of calculating adherence. I then investigated different patterns of inhaler use, determinants of inhaler use and the ...

Solutions Of The System Of Operator Equations $Bxa=B=Axb$ Via The *-Order, 2017 Ferdowsi University of Mashhad

#### Solutions Of The System Of Operator Equations $Bxa=B=Axb$ Via The *-Order, Mehdi Vosough, Mohammad Sal Moslehian

*Electronic Journal of Linear Algebra*

In this paper, some necessary and sufficient conditions are established for the existence of solutions to the system of operator equations $BXA=B=AXB$ in the setting of bounded linear operators on a Hilbert space, where the unknown operator $X$ is called the inverse of $A$ along $B$. After that, under some mild conditions, it is proved that an operator $X$ is a solution of $BXA=B=AXB$ if and only if $B \stackrel{*}{ \leq} AXA$, where the $*$-order $C\stackrel{*}{ \leq} D$ means $CC^*=DC^*, C^*C=C^*D$. Moreover, the general solution of the equation above is obtained ...

Weak Factorizations Of The Hardy Space H1(RN) In Terms Of Multilinear Riesz Transforms, 2017 Washington University in St. Louis

#### Weak Factorizations Of The Hardy Space H1(RN) In Terms Of Multilinear Riesz Transforms, Ji Li, Brett D. Wick

*Mathematics Faculty Publications*

This paper provides a constructive proof of the weak factorization of the classical Hardy space in terms of multilinear Riesz transforms. As a direct application, we obtain a new proof of the characterization of (the dual of ) via commutators of the multilinear Riesz transforms.

Spaces Of Dirichlet Series With The Complete Pick Property, 2017 Washington University in St Louis

#### Spaces Of Dirichlet Series With The Complete Pick Property, John E. Mccarthy, Orr Moshe Shalit

*Mathematics Faculty Publications*

We consider reproducing kernel Hilbert spaces of Dirichlet series with kernels of the form k(s,u)=∑a_{n}n^{−s−u¯}, and characterize when such a space is a complete Pick space. We then discuss what it means for two reproducing kernel Hilbert spaces to be “the same”, and introduce a notion of weak isomorphism. Many of the spaces we consider turn out to be weakly isomorphic as reproducing kernel Hilbert spaces to the Drury–Arveson space H_{d}^{2} in *d* variables, where *d* can be any number in {1, 2,...,∞}, and in particular their multiplier algebras are ...

Mixed Strategies For Deterministic Differential Games, 2017 Brown University

#### Mixed Strategies For Deterministic Differential Games, Wendell H. Fleming, Daniel Hernandez-Hernandez

*Communications on Stochastic Analysis*

No abstract provided.

A Note On Evolution Systems Of Measures Of Stochastic Differential Equations In Infinite Dimensional Hilbert Spaces, 2017 University of Quynhon

#### A Note On Evolution Systems Of Measures Of Stochastic Differential Equations In Infinite Dimensional Hilbert Spaces, Thanh Tan Mai

*Communications on Stochastic Analysis*

No abstract provided.