Non-Continuous Double Barrier Reflected Bsdes With Jumps Under A Stochastic Lipschitz Coefficient, 2018 Laboratory of Analysis and Applied Mathematics (LAMA), Faculty of sciences Agadir, Ibn Zohr University, Morocco

#### Non-Continuous Double Barrier Reflected Bsdes With Jumps Under A Stochastic Lipschitz Coefficient, Mohamed Marzougue, Mohamed El Otmani

*Communications on Stochastic Analysis*

No abstract provided.

Stochastic Differential Equations With Anticipating Initial Conditions, 2018 Louisiana State University, Baton Rouge, USA

#### Stochastic Differential Equations With Anticipating Initial Conditions, Hui-Hsiung Kuo, Sudip Sinha, Jiayu Zhai

*Communications on Stochastic Analysis*

No abstract provided.

On A Stochastic 2d Simplified Liquid Crystal Model Driven By Jump Noise, 2018 Department Mathematics and Statistics, Florida International University, MMC, Miami, FL, 33199, USA

#### On A Stochastic 2d Simplified Liquid Crystal Model Driven By Jump Noise, T. Tachim Medjo

*Communications on Stochastic Analysis*

No abstract provided.

New Filters For The Calibration Of Regime Switching Beta Dynamics, 2018 University of Calgary

#### New Filters For The Calibration Of Regime Switching Beta Dynamics, Robert J. Elliott, Carlton Osakwe

*Communications on Stochastic Analysis*

No abstract provided.

Invariant Subspaces Of Compact Operators And Related Topics, 2018 California Polytechnic State University, San Luis Obispo

#### Invariant Subspaces Of Compact Operators And Related Topics, Weston Mckay Grewe

*Mathematics*

The invariant subspace problem asks if every bounded linear operator on a Banach space has a nontrivial closed invariant subspace. Per Enflo has shown this is false in general, however it is known that every compact operator has an invariant subspace. The purpose of this project is to explore introductory results in functional analysis. Specifically we are interested in understanding compact operators and the proof that all compact operators on a Hilbert space have an invariant subspace. In the process of doing this we build up many examples and theorems relating to operators on a Hilbert or Banach space. Continuing ...

Catalytic Deoxygenation Of Model And Realistic Feeds To Fuel-Like Hydrocarbons Over Supported Nickel-Copper Catalysts, 2018 Kentucky State University

#### Catalytic Deoxygenation Of Model And Realistic Feeds To Fuel-Like Hydrocarbons Over Supported Nickel-Copper Catalysts, Deyshon Ward, Kazi Javed

*Posters-at-the-Capitol*

The goal was to make a renewable fuel by using catalysts to remove oxygen molecules from fats. This is a current issue that society faces today because nonrenewable fossil fuels hurt the environment more than they help it. There are two components that make up a heterogeneous catalyst, a support and a reduced metal active phase. The active metal phases Nickel, Palladium, Platinum have been studied in the past on an alumina and carbon supports. We were investigating other supports using Nickel as the active phase component to determine the effect the support has on the catalyst removing oxygen of ...

Global Well-Posedness And Scattering For The Defocusing Quintic Nonlinear Schrödinger Equation In Two Dimensions, 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 H^{1/2}.

We show that if a solution remains bounded in dot H^{1/2} in its maximal time interval of existence, then the time interval is infinite and the solution scatters.

Well-Posedness For The Cubic Nonlinear Schrödinger Equations On Tori, 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)}

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

A Decomposition Of A Space Of Multiple Wiener Integrals By The Difference Of Two Independent Lévy Processes In Terms Of The Lévy Laplacian, 2018 Mitsubishi Electric Mechatronics Software Corporation, Nagoya, Japan

#### A Decomposition Of A Space Of Multiple Wiener Integrals By The Difference Of Two Independent Lévy Processes In Terms Of The Lévy Laplacian, Atsushi Ishikawa

*Communications on Stochastic Analysis*

No abstract provided.

Parametric Family Of Sdes Driven By Lévy Noise, 2018 Indian Institute of Technology Kanpur, India

#### Parametric Family Of Sdes Driven By Lévy Noise, Suprio Bhar, Barun Sarkar

*Communications on Stochastic Analysis*

No abstract provided.

An Asymptotic Comparison Of Two Time-Homogeneous Pam Models, 2018 University of Southern California, Los Angeles, California USA

#### An Asymptotic Comparison Of Two Time-Homogeneous Pam Models, Hyun-Jung Kim, Sergey Vladimir Lototsky

*Communications on Stochastic Analysis*

No abstract provided.

Reversibility Checking For Markov Chains, 2018 University of Windsor, Windsor, Ontario

#### Reversibility Checking For Markov Chains, P. H. Brill, Chi Ho Cheung, Myron Hlynka, Q. Jiang

*Communications on Stochastic Analysis*

No abstract provided.

Nonlocal Diffusions And The Quantum Black-Scholes Equation: Modelling The Market Fear Factor, 2018 Investec Bank PLC, 30 Gresham Street, London EC2V 7QP, United Kingdom

#### Nonlocal Diffusions And The Quantum Black-Scholes Equation: Modelling The Market Fear Factor, Will Hicks

*Communications on Stochastic Analysis*

No abstract provided.

Directional Malliavin Derivatives: A Characterisation Of Independence And A Generalised Chain Rule, 2018 University of Mannheim, Germany

#### Directional Malliavin Derivatives: A Characterisation Of Independence And A Generalised Chain Rule, Stefan Koch

*Communications on Stochastic Analysis*

No abstract provided.

A Stochastic Integral By A Near-Martingale, 2018 Meijo University, Tenpaku,Nagoya, Japan

#### A Stochastic Integral By A Near-Martingale, Shinya Hibino, Hui-Hsiung Kuo, Kimiaki Saitô

*Communications on Stochastic Analysis*

No abstract provided.

Topological Vector Spaces, 2018 University of Windsor

#### Topological Vector Spaces, Chunqing Li

*Major Papers*

This major paper is a report on author’s study of some topics on topological vector spaces. We prove a well-known Hahn-Banach theorem and some important consequences, including several separation and extension theorems. We study the weak topology on a topological vector space X and the weak-star topology on the dual space X* of X. We also prove the Banach-Alaoglu theorem. Consequently, we characterize the closed convex hull and the closed linear span for sets in X and X* , identify the dual of a subspace of X with the quotient of its annihilator, and obtain the Goldstine theorem as well ...

Translation-Invariant Gibbs Measures Of A Model On Cayley Tree, 2018 National University of Uzbekistan

#### Translation-Invariant Gibbs Measures Of A Model On Cayley Tree, Golibjon Botirov

*Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences*

We consider a model where the spin takes values in the set [0,1]^{d}, and is assigned to the vertexes of the Cayley tree. We reduce the problem of describing the “splitting Gibbs measures” of the model to the description of the solutions of some non-linear integral equation. For a concrete form of the Kernel of the integral equation we show the uniqueness of solution.

Equivalent Constructions Of Cartan Pairs, 2018 University of New Mexico

#### Equivalent Constructions Of Cartan Pairs, Phung Thanh Tran

*Math Theses*

Feldman and Moore [4] introduce Cartan subalgebra of the von Neumann algebra M on a separable Hilbert space H from the natural subalgebra of M(R, sigma), the twisted algebra of matrices over the relation R on a Borel space (X, B, muy). They show that if M has a Cartan subalgebra A, then M is isomorphic to M(R, sigma) where A is the twisted algebra onto the diagonal subalgebra L^inf (X, muy). The relation R is unique to isomorphism and the orbit of the two-cohomology class on R in the torus T, which is the automorphism group ...

Yelp’S Review Filtering Algorithm, 2018 Southern Methodist University

#### Yelp’S Review Filtering Algorithm, Yao Yao, Ivelin Angelov, Jack Rasmus-Vorrath, Mooyoung Lee, Daniel W. Engels

*SMU Data Science Review*

In this paper, we present an analysis of features influencing Yelp's proprietary review filtering algorithm. Classifying or misclassifying reviews as *recommended* or *non-recommended* affects average ratings, consumer decisions, and ultimately, business revenue. Our analysis involves systematically sampling and scraping Yelp restaurant reviews. Features are extracted from review metadata and engineered from metrics and scores generated using text classifiers and sentiment analysis. The coefficients of a multivariate logistic regression model were interpreted as quantifications of the relative importance of features in classifying reviews as recommended or non-recommended. The model classified review recommendations with an accuracy of 78%. We found that ...