Bounded Linear Operators That Preserve The Weak Supermajorization On $\Ell^1(I)^+$, 2018 Faculty of Mechanical Engineering, Department of Mathematics,University of Niš, Serbia

#### Bounded Linear Operators That Preserve The Weak Supermajorization On $\Ell^1(I)^+$, Martin Z. Ljubenović, Dragan S. Djordjevic

*Electronic Journal of Linear Algebra*

Linear preservers of weak supermajorization which is defined on positive functions contained in the discrete Lebesgue space $\ell^1(I)$ are characterized. Two different classes of operators that preserve the weak supermajorization are formed. It is shown that every linear preserver may be decomposed as sum of two operators from the above classes, and conversely, the sum of two operators which satisfy an additional condition is a linear preserver. Necessary and sufficient conditions under which a bounded linear operator is a linear preserver of the weak supermajorization are given. It is concluded that positive linear preservers of the weak supermajorization ...

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.

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.

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.

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.

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.

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.

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 ...

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.

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.

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 ...

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.

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.

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.