# Analysis Commons™

## All Articles in Analysis

505 full-text articles. Page 1 of 16.

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 ...

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 CO2 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 CO2. This study showcases the importance of presenting students with actual data and using data to develop student ...

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.

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 ...

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.

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 ...

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

##### Analysis

No abstract provided.

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.

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 ...

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.

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.

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.

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.

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.

2017 Heinrich-Heine-Universität Düsseldorf

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

##### Communications on Stochastic Analysis

No abstract provided.