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 ...

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 ...

Positive Solutions Of The System Of Operator Equations $A_1x=C_1,Xa_2=C_2, A_3xa^*_3=C_3, A_4xa^*_4=C_4$ In Hilbert $C^*$-Modules, 2018 Ferdowsi University of Mashhad

#### Positive Solutions Of The System Of Operator Equations $A_1x=C_1,Xa_2=C_2, A_3xa^*_3=C_3, A_4xa^*_4=C_4$ In Hilbert $C^*$-Modules, Rasoul Eskandari, Xiaochun Fang, Mohammad Sal Moslehian, Qingxiang Xu

*Electronic Journal of Linear Algebra*

Necessary and sufficient conditions are given for the operator system $A_1X=C_1$, $XA_2=C_2$, $A_3XA^*_3=C_3$, and $A_4XA^*_4=C_4$ to have a common positive solution, where $A_i$'s and $C_i$'s are adjointable operators on Hilbert $C^*$-modules. This corrects a published result by removing some gaps in its proof. Finally, a technical example is given to show that the proposed investigation in the setting of Hilbert $C^*$-modules is different from that of Hilbert spaces.

Three Examples Of Mondoromy Groups, 2018 alice.wise

#### Three Examples Of Mondoromy Groups, Alice A. Wise

*Electronic Theses and Dissertations*

This thesis illustrates the notion of the Monodromy group of a global analytic function through three examples. One is a relatively simple finite example; the others are more complicated infinite cases, one abelian and one non-abelian, which show connections to other parts of mathematics.

The Hilbert-Huang Transform: A Theoretical Framework And Applications To Leak Identification In Pressurized Space Modules, 2018 University of Maine

#### The Hilbert-Huang Transform: A Theoretical Framework And Applications To Leak Identification In Pressurized Space Modules, Kenneth R. Bundy

*Electronic Theses and Dissertations*

Any manned space mission must provide breathable air to its crew. For this reason, air leaks in spacecraft pose a danger to the mission and any astronauts on board. The purpose of this work is twofold: the first is to address the issue of air pressure loss from leaks in spacecraft. Air leaks present a danger to spacecraft crew, and so a method of finding air leaks when they occur is needed. Most leak detection systems localize the leak in some way. Instead, we address the identification of air leaks in a pressurized space module, we aim to determine the ...

Applications Of Game Theory, Tableau, Analytics, And R To Fashion Design, 2018 Atlanta University Center

#### Applications Of Game Theory, Tableau, Analytics, And R To Fashion Design, Aisha Asiri

*Electronic Theses & Dissertations Collection for Atlanta University & Clark Atlanta University*

This thesis presents various models to the fashion industry to predict the profits for some products. To determine the expected performance of each product in 2016, we used tools of game theory to help us identify the expected value. We went further and performed a simple linear regression and used scatter plots to help us predict further the performance of the products of Prada. We used tools of game theory, analytics, and statistics to help us predict the performance of some of Prada's products. We also used the Tableau platform to visualize an overview of the products' performances. All ...

Some Graphs Determined By Their Distance Spectrum, 2018 Department of mathematics & statistics, McGill University, Montreal

#### Some Graphs Determined By Their Distance Spectrum, Stephen Drury, Huiqiu Lin

*Electronic Journal of Linear Algebra*

Let $G$ be a connected graph with order $n$. Let $\lambda_1(D(G))\geq \cdots\geq \lambda_n(D(G))$ be the distance spectrum of $G$. In this paper, it is shown that the complements of $P_n$ and $C_n$ are determined by their $D$-spectrum. Moreover, it is shown that the cycle $C_n$ ($n$ odd) is also determined by its $D$-spectrum.

A Discrete Time Approximations For Certain Class Of One-Dimensional Backward Stochastic Differential Equations Via Girsanov's Theorem, 2018 Université Mohammed Premier

#### A Discrete Time Approximations For Certain Class Of One-Dimensional Backward Stochastic Differential Equations Via Girsanov's Theorem, Aissa Sghir, Driss Seghir, Soukaina Hadiri

*Communications on Stochastic Analysis*

No abstract provided.

Symmetric Weighted Odd-Power Variations Of Fractional Brownian Motion And Applications, 2018 University of Kansas

#### Symmetric Weighted Odd-Power Variations Of Fractional Brownian Motion And Applications, David Nualart, Raghid Zeineddine

*Communications on Stochastic Analysis*

No abstract provided.

A Triple Comparison Between Anticipating Stochastic Integrals In Financial Modeling, 2018 Universidad Autónoma de Madrid, Spain

#### A Triple Comparison Between Anticipating Stochastic Integrals In Financial Modeling, Joan Bastons, Carlos Escudero

*Communications on Stochastic Analysis*

No abstract provided.

Stochastic Representation Of Tau Functions With An Application To The Korteweg-De Vries Equation, 2018 Sorbonne Université, Paris, France

#### Stochastic Representation Of Tau Functions With An Application To The Korteweg-De Vries Equation, Michèle Thieullen, Alexis Vigot

*Communications on Stochastic Analysis*

No abstract provided.

Exit-Time Of Granular Media Equation Starting In A Local Minimum, 2018 Université Jean Monnet, Saint-Étienne, France

#### Exit-Time Of Granular Media Equation Starting In A Local Minimum, Julian Tugaut

*Communications on Stochastic Analysis*

No abstract provided.

Bsdes On Finite And Infinite Horizon With Time-Delayed Generators, 2018 ETH Zürich, Switzerland

#### Bsdes On Finite And Infinite Horizon With Time-Delayed Generators, Peng Luo, Ludovic Tangpi

*Communications on Stochastic Analysis*

No abstract provided.

Arratia Flow With Drift And Trotter Formula For Brownian Web, 2018 Institute of Mathematics, National Academy of Sciences of Ukraine

#### Arratia Flow With Drift And Trotter Formula For Brownian Web, Andrey A. Dorogovtsev, M. B. Vovchanskii

*Communications on Stochastic Analysis*

No abstract provided.

Fractional Difference Operators And Related Boundary Value Problems, 2018 University of Nebraska-Lincoln

#### Fractional Difference Operators And Related Boundary Value Problems, Scott C. Gensler

*Dissertations, Theses, and Student Research Papers in Mathematics*

In this dissertation we develop a fractional difference calculus for functions on a discrete domain. We start by showing that the Taylor monomials, which play a role analagous to that of the power functions in ordinary differential calculus, can be expressed in terms of a family of polynomials which I will refer to as the Pochhammer polynomials. These important functions, the Taylor monomials, were previously described by other scholars primarily in terms of the gamma function. With only this description it is challenging to understand their properties. Describing the Taylor monomials in terms of the Pochhammer polynomials has made it ...

Excess Versions Of The Minkowski And Hölder Inequalities, 2018 Michigan Technological University

#### Excess Versions Of The Minkowski And Hölder Inequalities, Iosif Pinelis

*Iosif Pinelis*

No abstract provided.

On The Maximal Numerical Range Of Some Matrices, 2018 New York University Abu Dhabi

#### On The Maximal Numerical Range Of Some Matrices, Ali N. Hamed, Ilya M. Spitkovsky

*Electronic Journal of Linear Algebra*

The maximal numerical range $W_0(A)$ of a matrix $A$ is the (regular) numerical range $W(B)$ of its compression $B$ onto the eigenspace $\mathcal L$ of $A^*A$ corresponding to its maximal eigenvalue. So, always $W_0(A)\subseteq W(A)$. Conditions under which $W_0(A)$ has a non-empty intersection with the boundary of $W(A)$ are established, in particular, when $W_0(A)=W(A)$. The set $W_0(A)$ is also described explicitly for matrices unitarily similar to direct sums of $2$-by-$2$ blocks, and some insight into the behavior of $W_0(A)$ is provided when $\mathcal L$ has ...

New Perturbation Bounds In Unitarily Invariant Norms For Subunitary Polar Factors, 2018 Nanjing

#### New Perturbation Bounds In Unitarily Invariant Norms For Subunitary Polar Factors, Lei Zhu, Wei-Wei Xu, Hao Liu, Li-Juan Ma

*Electronic Journal of Linear Algebra*

Let $A\in\mathbb{C}^{m \times n}$ have generalized polar decomposition $A = QH$ with $Q$ subunitary and $H$ positive semidefinite. Absolute and relative perturbation bounds are derived for the subunitary polar factor $Q$ in unitarily invariant norms and in $Q$-norms, that extend and improve existing bounds.

Iteration With Stepsize Parameter And Condition Numbers For A Nonlinear Matrix Equation, 2018 Pusan National University

#### Iteration With Stepsize Parameter And Condition Numbers For A Nonlinear Matrix Equation, Syed M. Raza Shah Naqvi, Jie Meng, Hyun-Min Kim

*Electronic Journal of Linear Algebra*

In this paper, the nonlinear matrix equation $X^p+A^TXA=Q$, where $p$ is a positive integer, $A$ is an arbitrary $n\times n$ matrix, and $Q$ is a symmetric positive definite matrix, is considered. A fixed-point iteration with stepsize parameter for obtaining the symmetric positive definite solution of the matrix equation is proposed. The explicit expressions of the normwise, mixed and componentwise condition numbers are derived. Several numerical examples are presented to show the efficiency of the proposed iterative method with proper stepsize parameter and the sharpness of the three kinds of condition numbers.