Mathematics Commons^™

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

Journal of Stochastic Analysis

No abstract provided.

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

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

Journal of Stochastic Analysis

No abstract provided.

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

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

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

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

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 …

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.

Dirichlet Problems In Perforated Domains, Robert Righi

Theses and Dissertations--Mathematics

We establish W^1,p estimates for solutions u_ε to the Laplace equation with Dirichlet boundary conditions in a bounded C¹ domain Ω_{ε, η} perforated by small holes in ℝ^d. 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 L^p estimate for ∇u_ε, whose proof is divided into two main parts. First, we show that solutions of an intermediate problem for a …

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

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.

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 …

Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost

All Dissertations

In confocal single-molecule FRET experiments, the joint distribution of FRET efficiency and donor lifetime distribution can reveal underlying molecular conformational dynamics via deviation from their theoretical Forster relationship. This shift is referred to as a dynamic shift. In this study, we investigate the influence of the free energy landscape in protein conformational dynamics on the dynamic shift by simulation of the associated continuum reaction coordinate Langevin dynamics, yielding a deeper understanding of the dynamic and structural information in the joint FRET efficiency and donor lifetime distribution. We develop novel Langevin models for the dye linker dynamics, including rotational dynamics, based …

(R2054) Convergence Of Lagrange-Hermite Interpolation Using Non-Uniform Nodes On The Unit Circle, Swarnima Bahadur, Sameera Iqram, Varun .

Applications and Applied Mathematics: An International Journal (AAM)

In this research article, we brought into consideration the set of non-uniformly distributed nodes on the unit circle to investigate a Lagrange-Hermite interpolation problem. These nodes are obtained by projecting vertically the zeros of Jacobi polynomial onto the unit circle along with the boundary points of the unit circle on the real line. Explicitly representing the interpolatory polynomial as well as establishment of convergence theorem are the key highlights of this manuscript. The result proved are of interest to approximation theory.

(R2061) Differential Equations Involving A New Definition Of Complex Number Derivatives, Mehmet Pakdemirli

Applications and Applied Mathematics: An International Journal (AAM)

The recently proposed complex number differential operator is used in formulating ordinary differential equations for the first time. The differential operator definition is totally different than the real number differentiation of complex valued functions. The basic definitions and properties of the differential operator are given first. Various linear differential equations are treated containing the new differential operator. Associated theorems with the differential equations are given. Then the nonlinear differential equations of complex valued functions are treated. In separated form, the complex differential operator equations lead to nonlinear coupled real valued equations. Various nonlinear differential equations with complex number derivatives are …

Complex Dimensions Of 100 Different Sierpinski Carpet Modifications, Gregory Parker Leathrum

Master's Theses

We used Dr. M. L. Lapidus's Fractal Zeta Functions to analyze the complex fractal dimensions of 100 different modifications of the Sierpinski Carpet fractal construction. We will showcase the theorems that made calculations easier, as well as Desmos tools that helped in classifying the different fractals and computing their complex dimensions. We will also showcase all 100 of the Sierpinski Carpet modifications and their complex dimensions.

Understanding Impact Of Educational Awareness And Vaccines As Optimal Control Mechanisms For Changing Human Behavior In Disease Epidemics, Manal Badgaish, Dr. Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Effects Of Persistent Post-Concussion Syndrome, Jackson Flemming, Olivia Schleifer, Megan Powell

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

On A Stationary Random Knot, Andrey A. Dorogovtsev

Journal of Stochastic Analysis

No abstract provided.

The General Theory Of Superoscillations And Supershifts In Several Variables, Fabrizio Colombo, Stefano Pinton, Irene Sabadini, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we describe a general method to generate superoscillatory functions of several variables starting from a superoscillating sequence of one variable. Our results are based on the study of suitable infinite order differential operators acting on holomorphic functions with growth conditions of exponential type. Additional constraints are required when dealing with infinite order differential operators whose symbol is a function that is holomorphic in some open set, but not necessarily entire. The results proved for superoscillating sequences in several variables are extended to sequences of supershifts in several variables.

Backward Stochastic Differential Equations In A Semi-Markov Chain Model, Robert J. Elliott, Zhe Yang

Journal of Stochastic Analysis

No abstract provided.

Are The Cans In The Store “Volume Optimized”? [Mathematics], Bukurie Gjoci

Open Educational Resources

This is one of LaGuardia’s Project Connexion STEM Team’s experiential learning activities. Project Connexion's purpose is to promote creative thinking on how to engage students in the classroom. As part of this, the STEM team developed Experiential/co-curricular activities that demonstrated to students how their work in class connects to the world around them. These activities were embedded into the syllabus to ensure the participation of all students. Each professor designed a Co-curricular activity for their courses, ensuring that the Co-curricular activity directly linked course material to the outside world.

This Calculus I Experiential Learning Project aligns with one of the …

An Analysis Of The Sequence Xn+2 = I M Xn+1 + Xn, David Duncan, Prashant Sansgiry, Ogul Arslan, Jensen Meade

Journal of the South Carolina Academy of Science

We analyze the sequence Xn+2 = imXn+1 + Xn, with X1 = X2 = 1 + i, where i is the imaginary number and m is a real number. Plotting the sequence in the complex plane for different values of m, we see interesting figures from the conic sections. For values of m in the interval (−2, 2) we show that the figures generated are ellipses. We also provide analysis which prove that for certain values of m, the sequence generated is periodic with even period.

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 …

Secondary Features Of Importance For A Url Ranking, Atajan Abdyyev

Dissertations and Theses

This paper investigates the impact of secondary ranking factors on webpage relevance and rankings in the context of Search Engine Optimization (SEO), focusing on the jewelry domain within the United States e-commerce market. By generating a keyword list related to jewelry and retrieving top URLs from Google's search results, the study employs machine learning models including XGBoost, CatBoost, and Linear Regression to identify key features influencing webpage relevance and rankings.The findings highlight specific optimal ranges for features like Outlinks, Unique Inlinks, Flesch Reading Ease Score, and others, indicating their significant impact on better rankings. Notably, Random Forest model performed best …