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 Graduate Works by Year: 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.

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 ...

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.

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.

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 ...

On Infinite Stochastic And Related Matrices, 2017 Volterra Center, Roma

#### On Infinite Stochastic And Related Matrices, Andreas Boukas, Philip Feinsilver, Anargyros Fellouris

*Communications on Stochastic Analysis*

No abstract provided.

Statistical Analysis Of The Non-Ergodic Fractional Ornstein–Uhlenbeck Process Of The Second Kind, 2017 Cadi Ayyad University

#### Statistical Analysis Of The Non-Ergodic Fractional Ornstein–Uhlenbeck Process Of The Second Kind, Brahim El Onsy, Khalifa Es-Sebaiy, Ciprian A. Tudor

*Communications on Stochastic Analysis*

No abstract provided.

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.

Stationary Solutions Of Stochastic Partial Differential Equations In The Space Of Tempered Distributions, 2017 Tata Institute of Fundamental Research

#### Stationary Solutions Of Stochastic Partial Differential Equations In The Space Of Tempered Distributions, Suprio Bhar

*Communications on Stochastic Analysis*

No abstract provided.

Poisson Approximation Of Rademacher Functionals By The Chen-Stein Method And Malliavin Calculus, 2017 Ruhr University Bochum

#### Poisson Approximation Of Rademacher Functionals By The Chen-Stein Method And Malliavin Calculus, Kai Kronkowski

*Communications on Stochastic Analysis*

No abstract provided.

Spatial Ergodicity Of The Harris Flows, 2017 Institute of Mathematics NAS of Ukraine

#### Spatial Ergodicity Of The Harris Flows, E.V. Glinyanaya

*Communications on Stochastic Analysis*

No abstract provided.

Fractal Behavior Of Multivariate Operator-Self-Similar Stable Random Fields, 2017 Heinrich-Heine-Universität Düsseldorf

#### Fractal Behavior Of Multivariate Operator-Self-Similar Stable Random Fields, Ercan Sönmez

*Communications on Stochastic 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.

Jet-Hadron Correlations Relative To The Event Plane Pb--Pb Collisions At The Lhc In Alice, 2017 University of Tennessee, Knoxville

#### Jet-Hadron Correlations Relative To The Event Plane Pb--Pb Collisions At The Lhc In Alice, Joel Anthony Mazer

*Doctoral Dissertations*

In relativistic heavy ion collisions at the Large Hadron Collider (LHC), a hot, dense and strongly interacting medium known as the Quark Gluon Plasma (QGP) is produced. Quarks and gluons from incoming nuclei collide to produce partons at high momenta early in the collisions. By fragmenting into collimated sprays of hadrons, these partons form 'jets'. Within the framework of perturbative Quantum Chromodynamics (pQCD), jet production is well understood in pp collisions. We can use jets measured in pp interactions as a baseline reference for comparing to heavy ion collision systems to detect and study jet quenching. The jet quenching mechanism ...