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# Analysis Commons™

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Articles 1 - 30 of 943

## Full-Text Articles in Analysis

An Anatomical And Functional Analysis Of Digital Arteries, Katie Highsmith Apr 2019

#### An Anatomical And Functional Analysis Of Digital Arteries, Katie Highsmith

##### Student Scholar Showcase

Blood flow to the tissue of the hands and digits is efficiently regulated by vasoconstriction and vasodilation. Through a series of cadaveric dissection, we examined arteries in the hands and digits, including ulnar artery, radial artery, palmar arteries, and digital arteries, for their distribution (branching) patterns and morphological parameters (e.g., thickness, length between branches, external and internal diameters). Using data directly collected from three female cadavers as input variables to our mathematical model, we simulated vasoconstriction (-20% and -10% diameter) and vasodilation (+10% and +20 diameter) to evaluate the extent of changes in blood volume and flow within the ...

#### Fourier Series Expansion Methods For The Heat And Wave Equations In Two And Three Dimensions On Spherical Domains, Matthew Eller

##### Student Research and Creative Activity Fair

Description: The Fourier series expansion method is an invaluable approach to solving partial differential equations, including the heat and wave equations. For homogeneous heat and wave equations, the solution can readily be found through separation of variables and then expansion of the solution in terms of the eigenfunctions. Solutions to inhomogeneous heat and wave equations through Fourier series expansion methods were not readily available in the literature for two- and three-dimensional cases. In my previous paper, I developed an approach for solving inhomogeneous heat and wave equations on cubic domains using Fourier series expansion methods. I shall extend my general ...

In-Sphere Property And Reverse Inequalities For Matrix Means, Trung Hoa Dinh, Tin-Yau Tam, Bich Khue T Vo Feb 2019

#### In-Sphere Property And Reverse Inequalities For Matrix Means, Trung Hoa Dinh, Tin-Yau Tam, Bich Khue T Vo

##### Electronic Journal of Linear Algebra

The in-sphere property for matrix means is studied. It is proved that the matrix power mean satisfies in-sphere property with respect to the Hilbert-Schmidt norm. A new characterization of the matrix arithmetic mean is provided. Some reverse AGM inequalities involving unitarily invariant norms and operator monotone functions are also obtained.

Improving Vix Futures Forecasts Using Machine Learning Methods, James Hosker, Slobodan Djurdjevic, Hieu Nguyen, Robert Slater Jan 2019

#### Improving Vix Futures Forecasts Using Machine Learning Methods, James Hosker, Slobodan Djurdjevic, Hieu Nguyen, Robert Slater

##### SMU Data Science Review

The problem of forecasting market volatility is a difficult task for most fund managers. Volatility forecasts are used for risk management, alpha (risk) trading, and the reduction of trading friction. Improving the forecasts of future market volatility assists fund managers in adding or reducing risk in their portfolios as well as in increasing hedges to protect their portfolios in anticipation of a market sell-off event. Our analysis compares three existing financial models that forecast future market volatility using the Chicago Board Options Exchange Volatility Index (VIX) to six machine/deep learning supervised regression methods. This analysis determines which models provide ...

Composition Of Gaussian Noises From Successive Convex Integrations, Amites Dasgupta Jan 2019

#### Composition Of Gaussian Noises From Successive Convex Integrations, Amites Dasgupta

##### Communications on Stochastic Analysis

No abstract provided.

Random Matrices, Continuous Circular Systems And The Triangular Operator, Romuald Lenczewski Jan 2019

#### Random Matrices, Continuous Circular Systems And The Triangular Operator, Romuald Lenczewski

##### Communications on Stochastic Analysis

No abstract provided.

Generalized Stochastic Burgers' Equation With Non-Lipschitz Diffusion Coefficient, Vivek Kumar, Ankik Kumar Giri Jan 2019

#### Generalized Stochastic Burgers' Equation With Non-Lipschitz Diffusion Coefficient, Vivek Kumar, Ankik Kumar Giri

##### Communications on Stochastic Analysis

No abstract provided.

#### Global Strong Solutions Of The Stochastic Three Dimensional Inviscid Simplified Bardina Turbulence Model, Manil T. Mohan

##### Communications on Stochastic Analysis

No abstract provided.

Limiting Means For Spherical Slices, Amy Peterson, Ambar Sengupta Jan 2019

#### Limiting Means For Spherical Slices, Amy Peterson, Ambar Sengupta

##### Communications on Stochastic Analysis

No abstract provided.

Normally Ordered Disentanglement Of Multi-Dimensional Schrödinger Algebra Exponentials, Luigi Accardi, Andreas Boukas Jan 2019

#### Normally Ordered Disentanglement Of Multi-Dimensional Schrödinger Algebra Exponentials, Luigi Accardi, Andreas Boukas

##### Communications on Stochastic Analysis

No abstract provided.

Exponential Inequalities For Exit Times For Stochastic Navier-Stokes Equations And A Class Of Evolutions, Po-Han Hsu, Padamanbhan Sundar Jan 2019

#### Exponential Inequalities For Exit Times For Stochastic Navier-Stokes Equations And A Class Of Evolutions, Po-Han Hsu, Padamanbhan Sundar

##### Communications on Stochastic Analysis

No abstract provided.

Nov 2018

#### 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 ...

Bounded Linear Operators That Preserve The Weak Supermajorization On $\Ell^1(I)^+$, Martin Z. Ljubenović, Dragan S. Djordjevic Oct 2018

#### 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 ...

#### 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, Hyun-Jung Kim, Sergey Vladimir Lototsky Oct 2018

#### 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, Shinya Hibino, Hui-Hsiung Kuo, Kimiaki Saitô Oct 2018

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

##### Communications on Stochastic Analysis

No abstract provided.

Reversibility Checking For Markov Chains, P. H. Brill, Chi Ho Cheung, Myron Hlynka, Q. Jiang Oct 2018

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

##### Communications on Stochastic Analysis

No abstract provided.

Parametric Family Of Sdes Driven By Lévy Noise, Suprio Bhar, Barun Sarkar Oct 2018

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

##### Communications on Stochastic Analysis

No abstract provided.

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

##### Communications on Stochastic Analysis

No abstract provided.

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

##### Communications on Stochastic Analysis

No abstract provided.

Topological Vector Spaces, Chunqing Li Sep 2018

#### 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, Phung Thanh Tran Sep 2018

#### 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, Yao Yao, Ivelin Angelov, Jack Rasmus-Vorrath, Mooyoung Lee, Daniel W. Engels Aug 2018

#### 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, Rasoul Eskandari, Xiaochun Fang, Mohammad Sal Moslehian, Qingxiang Xu Aug 2018

#### 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, Alice A. Wise Aug 2018

#### 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, 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 ...

Aug 2018

#### 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, Stephen Drury, Huiqiu Lin Aug 2018

#### 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, Aissa Sghir, Driss Seghir, Soukaina Hadiri Aug 2018

#### 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, David Nualart, Raghid Zeineddine Aug 2018

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

##### Communications on Stochastic Analysis

No abstract provided.