Open Access. Powered by Scholars. Published by Universities.®

Analysis Commons

Open Access. Powered by Scholars. Published by Universities.®

2024

Discipline
Institution
Keyword
Publication
Publication Type

Articles 31 - 45 of 45

Full-Text Articles in Analysis

A Cohomological Perspective To Nonlocal Operators, Nicholas White Mar 2024

A Cohomological Perspective To Nonlocal Operators, Nicholas White

Honors Program: Senior Projects (Public)

Nonlocal models have experienced a large period of growth in recent years. In particular, nonlocal models centered around a finite horizon have been the subject of many novel results. In this work we consider three nonlocal operators defined via a finite horizon: a weighted averaging operator in one dimension, an averaging differential operator, and the truncated Riesz fractional gradient. We primarily explore the kernel of each of these operators when we restrict to open sets. We discuss how the topological structure of the domain can give insight into the behavior of these operators, and more specifically the structure of their …


Quasistationary Distribution For The Invasion Model On A Complete Bipartite Graph, Clayton Allard, Iddo Ben-Ari, Shrikant Chand, Van Hovenga, Edith Lee, Julia Shapiro Mar 2024

Quasistationary Distribution For The Invasion Model On A Complete Bipartite Graph, Clayton Allard, Iddo Ben-Ari, Shrikant Chand, Van Hovenga, Edith Lee, Julia Shapiro

Journal of Stochastic Analysis

No abstract provided.


The Basel Problem And Summing Rational Functions Over Integers, Pranjal Jain Mar 2024

The Basel Problem And Summing Rational Functions Over Integers, Pranjal Jain

Rose-Hulman Undergraduate Mathematics Journal

We provide a general method to evaluate convergent sums of the form ∑_{k∈Z} R(k) where R is a rational function with complex coefficients. The method is entirely elementary and does not require any calculus beyond some standard limits and convergence criteria. It is inspired by a geometric solution to the famous Basel Problem given by Wästlund (2010), so we begin by demonstrating the method on the Basel Problem to serve as a pilot application. We conclude by applying our ideas to prove Euler’s factorisation for sin x which he originally used to solve the Basel Problem.


A Characterization Of The Operator Entropy In Terms Of An Isometry Property Related To Trace Norms, Ryo Inayoshi Mar 2024

A Characterization Of The Operator Entropy In Terms Of An Isometry Property Related To Trace Norms, Ryo Inayoshi

Journal of Stochastic Analysis

No abstract provided.


Two Non–*–Isomorphic *–Lie Algebra Structures On Sl(2,R) And Their Physical Origins, Luigi Accardi, Irina Ya. ArefʹEva, Yungang Lu, Igorʹ VasilʹEvich Volovich Feb 2024

Two Non–*–Isomorphic *–Lie Algebra Structures On Sl(2,R) And Their Physical Origins, Luigi Accardi, Irina Ya. ArefʹEva, Yungang Lu, Igorʹ VasilʹEvich Volovich

Journal of Stochastic Analysis

No abstract provided.


Covariant Anyons Via Mackey Machinery, Radhakrishnan Balu Jan 2024

Covariant Anyons Via Mackey Machinery, Radhakrishnan Balu

Journal of Stochastic Analysis

No abstract provided.


Nonlinear Filtering Of Classical And Quantum Spin Systems, Sivaguru S. Sritharan, Saba Mudaliar Jan 2024

Nonlinear Filtering Of Classical And Quantum Spin Systems, Sivaguru S. Sritharan, Saba Mudaliar

Journal of Stochastic Analysis

No abstract provided.


Exploring The Role Of Undergraduate And Graduate Real Analysis Experiences In The Mathematical Trajectories Of Women Mathematicians From Historically Disenfranchised Groups, Te'a Riley Jan 2024

Exploring The Role Of Undergraduate And Graduate Real Analysis Experiences In The Mathematical Trajectories Of Women Mathematicians From Historically Disenfranchised Groups, Te'a Riley

Mathematics Dissertations - Archive

This phenomenological study examines the role of undergraduate and graduate Real Analysis courses in shaping the mathematical trajectories of seven women Ph.D. mathematicians from groups historically disenfranchised in mathematics.Qualitative analysis of interviews explores various aspects of their development as mathematicians with a focus on their experiences in Real Analysis. This study applies Ryan & Deci’s (1985) Self-Determination Theory's Basic Psychological Need Theory and Critical Race Theory to analyze the trajectories of the participants. The research explores how the fulfillment of basic psychological needs in their Real Analysis courses may have influenced their academic and professional journeys. The basic psychological need …


Quantifying Non-Primary Dna Formations Through Mechanical And Geometric Models, Sonia E. Teodorescu Jan 2024

Quantifying Non-Primary Dna Formations Through Mechanical And Geometric Models, Sonia E. Teodorescu

Undergraduate Journal of Mathematical Modeling: One + Two

In this article, mechanical and geometric models for DNA strains (regarded as a helical structure in 3 dimensions, embedded into surfaces of various shapes (straight or curved cylinders, spheres, or projected into planes), are analyzed in order to obtain parameter estimates for DNA characteristics which can be used to detect the formation of secondary and tertiary formations in the presence of disorder. The models allow for the explicit representation of the DNA shape on constrained geometries and can therefore be implemented directly into {\it{ab initio}} or synthetic simulation studies.


Machine Learning Approaches For Cyberbullying Detection, Roland Fiagbe Jan 2024

Machine Learning Approaches For Cyberbullying Detection, Roland Fiagbe

Data Science and Data Mining

Cyberbullying refers to the act of bullying using electronic means and the internet. In recent years, this act has been identifed to be a major problem among young people and even adults. It can negatively impact one’s emotions and lead to adverse outcomes like depression, anxiety, harassment, and suicide, among others. This has led to the need to employ machine learning techniques to automatically detect cyberbullying and prevent them on various social media platforms. In this study, we want to analyze the combination of some Natural Language Processing (NLP) algorithms (such as Bag-of-Words and TFIDF) with some popular machine learning …


Dirichlet Problems In Perforated Domains, Robert Righi Jan 2024

Dirichlet Problems In Perforated Domains, Robert Righi

Theses and Dissertations--Mathematics

We establish W1,p estimates for solutions uε to the Laplace equation with Dirichlet boundary conditions in a bounded C1 domain Ωε, η perforated by small holes in ℝd. The bounding constants will depend explicitly on epsilon and eta, where epsilon is the order of the minimal distance between holes, and eta denotes the ratio between the size of the holes and epsilon. The proof relies on a large-scale Lp estimate for ∇uε, whose proof is divided into two main parts. First, we show that solutions of an intermediate problem for a …


Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen Jan 2024

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen

Theses and Dissertations (Comprehensive)

The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …


Centers Of N-Degree Poncelet Circles, Georgia Corbett Jan 2024

Centers Of N-Degree Poncelet Circles, Georgia Corbett

Honors Theses

Given a circle inscribed in a polygon inscribed in the unit circle, if one connects all the vertices with line segments we get a family of circles called a package of Poncelet circles, due to its connection to a theorem of Poncelet. We are interested in where the centers of the Poncelet circles can be. Specifically, we have shown that if one of the circles in the Poncelet package is centered at 0, then all of the circles must be centered at 0 as well. This was proven by Spitkovsky and Wegert in 2021 using elliptic integrals but we …


A Corona Theorem For Multipliers On The Dirichlet Space, Alea Wittig Jan 2024

A Corona Theorem For Multipliers On The Dirichlet Space, Alea Wittig

Electronic Theses & Dissertations (2024 - present)

An analogue to Wolff's ideal problem for the multiplier algebra of the Dirichlet space, the main theorem provides sufficient conditions to classify membership of an arbitrary function in an infinitely generated ideal of the multiplier algebra.


Linear Topological Space, Vi Nguyen Jan 2024

Linear Topological Space, Vi Nguyen

UNF Graduate Theses and Dissertations

This thesis begins with an introduction to linear and topological spaces and then defines linear topological spaces. It studies key properties such as neighborhoods, convexity, reflexivity, and weak and weak* topologies. Finally, it concludes with solving non-linear partial differential equations.