Analysis Commons^™

Double Barrier Backward Doubly Stochastic Differential Equations, Tadashi Hayashi

Journal of Stochastic Analysis

No abstract provided.

Symmetric Functions Algebras (Sfa) Iii: Stochastic And Constant Row Sum Matrices, Philip Feinsilver

Journal of Stochastic Analysis

No abstract provided.

Using Geographic Information To Explore Player-Specific Movement And Its Effects On Play Success In The Nfl, Hayley Horn, Eric Laigaie, Alexander Lopez, Shravan Reddy

SMU Data Science Review

American Football is a billion-dollar industry in the United States. The analytical aspect of the sport is an ever-growing domain, with open-source competitions like the NFL Big Data Bowl accelerating this growth. With the amount of player movement during each play, tracking data can prove valuable in many areas of football analytics. While concussion detection, catch recognition, and completion percentage prediction are all existing use cases for this data, player-specific movement attributes, such as speed and agility, may be helpful in predicting play success. This research calculates player-specific speed and agility attributes from tracking data and supplements them with descriptive …

On Solutions Of First Order Pde With Two-Dimensional Dirac Delta Forcing Terms, Ian Robinson

Rose-Hulman Undergraduate Mathematics Journal

We provide solutions of a first order, linear partial differential equation of two variables where the nonhomogeneous term is a two-dimensional Dirac delta function. Our results are achieved by applying the unilateral Laplace Transform, solving the subsequently transformed PDE, and reverting back to the original space-time domain. A discussion of existence and uniqueness of solutions, a derivation of solutions of the PDE coupled with a boundary and initial condition, as well as a few worked examples are provided.

Some New Techniques And Their Applications In The Theory Of Distributions, Kevin Kellinsky-Gonzalez

LSU Doctoral Dissertations

This dissertation is a compilation of three articles in the theory of distributions. Each essay focuses on a different technique or concept related to distributions.

The focus of the first essay is the concept of distributional point values. Distribu- tions are sometimes called generalized functions, as they share many similarities with ordi- nary functions, with some key differences. Distributional point values, among other things, demonstrate that distributions are even more akin to ordinary functions than one might think.

The second essay concentrates on two major topics in analysis, namely asymptotic expansions and the concept of moments. There are many variations …

The Existence Of Solutions To A System Of Nonhomogeneous Difference Equations, Stephanie Walker

Rose-Hulman Undergraduate Mathematics Journal

This article will demonstrate a process using Fixed Point Theory to determine the existence of multiple positive solutions for a type of system of nonhomogeneous even ordered boundary value problems on a discrete domain. We first reconstruct the problem by transforming the system so that it satisfies homogeneous boundary conditions. We then create a cone and an operator sufficient to apply the Guo-KrasnoselâA˘Zskii Fixed Point Theorem. The majority of the work involves developing the constraints ´ needed to utilized this fixed point theorem. The theorem is then applied three times, guaranteeing the existence of at least three distinct solutions. Thus, …

Schur Analysis And Discrete Analytic Functions: Rational Functions And Co-Isometric Realizations, Daniel Alpay, Dan Volok

Mathematics, Physics, and Computer Science Faculty Articles and Research

We define and study rational discrete analytic functions and prove the existence of a coisometric realization for discrete analytic Schur multipliers.

Solving The Cable Equation, A Second-Order Time Dependent Pde For Non-Ideal Cables With Action Potentials In The Mammalian Brain Using Kss Methods, Nirmohi Charbe

Master's Theses

In this thesis we shall perform the comparisons of a Krylov Subspace Spectral method with Forward Euler, Backward Euler and Crank-Nicolson to solve the Cable Equation. The Cable Equation measures action potentials in axons in a mammalian brain treated as an ideal cable in the first part of the study. We shall subject this problem to the further assumption of a non-ideal cable. Assume a non-uniform cross section area along the longitudinal axis. At the present time, the effects of torsion, curvature and material capacitance are ignored. There is particular interest to generalize the application of the PDEs including and …

Multiplication Operators By White Noise Delta Functions And Associated Differential Equations, Luigi Accardi, Un Cig Ji, Kimiaki Saitô

Journal of Stochastic Analysis

No abstract provided.

Random Variables With Overlapping Number And Weyl Algebras Ii, Ruma Dutta, Gabriela Popa, Aurel Stan

Journal of Stochastic Analysis

No abstract provided.

(R2028) A Brief Note On Space Time Fractional Order Thermoelastic Response In A Layer, Navneet Lamba, Jyoti Verma, Kishor Deshmukh

Applications and Applied Mathematics: An International Journal (AAM)

In this study, a one-dimensional layer of a solid is used to investigate the exact analytical solution of the heat conduction equation with space-time fractional order derivatives and to analyze its associated thermoelastic response using a quasi-static approach. The assumed thermoelastic problem was subjected to certain initial and boundary conditions at the initial and final ends of the layer. The memory effects and long-range interaction were discussed with the help of the Caputo-type fractional-order derivative and finite Riesz fractional derivative. Laplace transform and Fourier transform techniques for spatial coordinates were used to investigate the solution of the temperature distribution and …

A Strong-Type Furstenberg–Sárközy Theorem For Sets Of Positive Measure, Polona Durcik, Vjekoslav Kovač, Mario Stipčić

Mathematics, Physics, and Computer Science Faculty Articles and Research

For every β ∈ (0,∞), β ≠ 1, we prove that a positive measure subset A of the unit square contains a point (x₀, y₀) such that A nontrivially intersects curves y − y0 = a(x −x0)^β for a whole interval I ⊆ (0,∞) of parameters a ∈ I . A classical Nikodym set counterexample prevents one to take β = 1, which is the case of straight lines. Moreover, for a planar set A of positive density, we show that the interval I can be arbitrarily large on the logarithmic scale. These results can …

Using Deep Neural Networks To Classify Astronomical Images, Andrew D. Macpherson

Honors Projects

As the quantity of astronomical data available continues to exceed the resources available for analysis, recent advances in artificial intelligence encourage the development of automated classification tools. This paper lays out a framework for constructing a deep neural network capable of classifying individual astronomical images by describing techniques to extract and label these objects from large images.

Modelling Illiquid Stocks Using Quantum Stochastic Calculus: Asymptotic Methods, Will Hicks

Journal of Stochastic Analysis

No abstract provided.

Movie Recommender System Using Matrix Factorization, Roland Fiagbe

Data Science and Data Mining

Recommendation systems are a popular and beneficial field that can help people make informed decisions automatically. This technique assists users in selecting relevant information from an overwhelming amount of available data. When it comes to movie recommendations, two common methods are collaborative filtering, which compares similarities between users, and content-based filtering, which takes a user’s specific preferences into account. However, our study focuses on the collaborative filtering approach, specifically matrix factorization. Various similarity metrics are used to identify user similarities for recommendation purposes. Our project aims to predict movie ratings for unwatched movies using the MovieLens rating dataset. We developed …

Formula 101 Using 2022 Formula One Season Data To Understand The Race Results, Christopher Garcia, Oliver Lopez

Student Scholar Symposium Abstracts and Posters

The reason why I am interested in Formula One is that my friend showed me what Formula One was all about. It became interesting to see the action of the sport, including the battles the drivers have during the race and how fast they go through a corner. Also, when qualifying comes around, they push their car to the absolute limit to gain a few seconds off their opponents. The drivers only in the top 10 receive points from the winner getting 25 points, the last driver in the top 10 getting 1 point, and those below the top ten …

Enestr¨Om-Kakeya Type Results For Complex And Quaternionic Polynomials, Matthew Gladin

Electronic Theses and Dissertations

The well known Eneström-Kakeya Theorem states that: for P(z)=∑_i=0ⁿ a_i zⁱ, a polynomial of degree n with real coefficients satisfying 0 ≤ a₀ ≤ a₁ ≤ ⋯≤ a_n, all zeros of P(z) lie in |z|≤1 in the complex plane. In this thesis, we will find inner and outer bounds in which the zeros of complex and quaternionic polynomials lie. We will do this by imposing restrictions on the real and imaginary parts, and on the moduli, of the complex and quaternionic coefficients. We also apply similar restrictions on complex polynomials with …

Examining Factors Using Standard Subspaces And Antiunitary Representations, Paul Anderson

Undergraduate Honors Theses

In an effort to provide an axiomization of quantum mechanics, John von Neumann and Francis Joseph Murray developed many tools in the theory of operator algebras. One of the many objects developed during the course of their work was the von Neumann algebra, originally called a ring of operators. The purpose of this thesis is to give an overview of the classification of elementary objects, called factors, and explore connections with other mathematical objects, namely standard subspaces in Hilbert spaces and antiunitary representations. The main results presented here illustrate instances of these interconnections that are relevant in Algebraic Quantum Field …

Employee Attrition: Analyzing Factors Influencing Job Satisfaction Of Ibm Data Scientists, Graham Nash

Symposium of Student Scholars

Employee attrition is a relevant issue that every business employer must consider when gauging the effectiveness of their employees. Whether or not an employee chooses to leave their job can come from a multitude of factors. As a result, employers need to develop methods in which they can measure attrition by calculating the several qualities of their employees. Factors like their age, years with the company, which department they work in, their level of education, their job role, and even their marital status are all considered by employers to assist in predicting employee attrition. This project will be analyzing a …

Analysis Of The Discrete Cosine Transform Coefficients, Dillon C. Mckinley

ATU Research Symposium

No abstract provided.