The Product Of Distributions And Stochastic Differential Equations Arising From Powers Of Infinite Dimensional Brownian Motions, 2024 Institute for Industrial and Applied Mathematics, Chungbuk National University, Cheongju 28644, Korea

#### The Product Of Distributions And Stochastic Differential Equations Arising From Powers Of Infinite Dimensional Brownian Motions, Un Cig Ji, Hui-Hsiung Kuo, Hara-Yuko Mimachi, Kimiaki Saitô

*Journal of Stochastic Analysis*

No abstract provided.

(R2067) Solutions Of Hyperbolic System Of Time Fractional Partial Differential Equations For Heat Propagation, 2024 NMIMS Deemed to be University

#### (R2067) Solutions Of Hyperbolic System Of Time Fractional Partial Differential Equations For Heat Propagation, Sagar Sankeshwari, Vinayak Kulkarni

*Applications and Applied Mathematics: An International Journal (AAM)*

Hyperbolic linear theory of heat propagation has been established in the framework of a Caputo time fractional order derivative. The solution of a system of integer and fractional order initial value problems is achieved by employing the Adomian decomposition approach. The obtained solution is in convergent infinite series form, demonstrating the method’s strengths in solving fractional differential equations. Moreover, the double Laplace transform method is employed to acquire the solution of a system of integer and fractional order boundary conditions in the Laplace domain. An inversion of double Laplace transforms has been achieved numerically by employing the Xiao algorithm in …

(R2074) A Comparative Study Of Two Novel Analytical Methods For Solving Time-Fractional Coupled Boussinesq-Burger Equation, 2024 Sardar Vallabhbhai National Institute of Technology

#### (R2074) A Comparative Study Of Two Novel Analytical Methods For Solving Time-Fractional Coupled Boussinesq-Burger Equation, Jyoti U. Yadav, Twinkle R. Singh

*Applications and Applied Mathematics: An International Journal (AAM)*

In this paper, a comparative study between two different methods for solving nonlinear timefractional coupled Boussinesq-Burger equation is conducted. The techniques are denoted as the Natural Transform Decomposition Method (NTDM) and the Variational Iteration Transform Method (VITM). To showcase the efficacy and precision of the proposed approaches, a pair of different numerical examples are presented. The outcomes garnered indicate that both methods exhibit robustness and efficiency, yielding approximations of heightened accuracy and the solutions in a closed form. Nevertheless, the VITM boasts a distinct advantage over the NTDM by addressing nonlinear predicaments without recourse to the application of Adomian polynomials. …

On Axially Rational Regular Functions And Schur Analysis In The Clifford-Appell Setting, 2024 Chapman University

#### On Axially Rational Regular Functions And Schur Analysis In The Clifford-Appell Setting, Daniel Alpay, Fabrizio Colombo, Antonino De Martino, Kamal Diki, Irene Sabadini

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

In this paper we start the study of Schur analysis for Cauchy–Fueter regular quaternionic-valued functions, i.e. null solutions of the Cauchy–Fueter operator in . The novelty of the approach developed in this paper is that we consider axially regular functions, i.e. functions spanned by the so-called Clifford-Appell polynomials. This type of functions arises naturally from two well-known extension results in hypercomplex analysis: the Fueter mapping theorem and the generalized Cauchy–Kovalevskaya (GCK) extension. These results allow one to obtain axially regular functions starting from analytic functions of one real or complex variable. Precisely, in the Fueter theorem two operators play a …

Reducibility Of Schrödinger Operators On Multilayer Graphs, 2024 Louisiana State University

#### Reducibility Of Schrödinger Operators On Multilayer Graphs, Jorge Villalobos Alvarado

*LSU Doctoral Dissertations*

A local defect in an atomic structure can engender embedded eigenvalues when the associated Schrödinger operator is either block reducible or Fermi reducible, and having multilayer structures appears to be typically necessary for obtaining such types of reducibility. Discrete and quantum graph models are commonly used in this context as they often capture the relevant features of the physical system in consideration.

This dissertation lays out the framework for studying different types of multilayer discrete and quantum graphs that enjoy block or Fermi reducibility. Schrödinger operators with both electric and magnetic potentials are considered. We go on to construct a …

Analytic Wavefront Sets Of Spherical Distributions On The De Sitter Space, 2024 Louisiana State University and Agricultural and Mechanical College

#### Analytic Wavefront Sets Of Spherical Distributions On The De Sitter Space, Iswarya Sitiraju

*LSU Doctoral Dissertations*

In this work, we determine the wavefront set of certain eigendistributions of the Laplace-Beltrami operator on the de Sitter space. Let G′ = O_{1,n}(R) be the Lorentz group, and let H′ = O_{1,n−1}(R) ⊂ G′ be its subset. The de Sitter space dS^{n} is a one-sheeted hyperboloid in R^{1,n} isomorphic to G′/H′. A spherical distribution is an H′-invariant eigendistribution of the Laplace-Beltrami operator on dS^{n}. The space of spherical distributions with eigenvalue λ, denoted by D_{λ}^{H'}(dS^{n}), has dimension 2. We construct a basis for the space of …

A Cohomological Perspective To Nonlocal Operators, 2024 University of Nebraska - Lincoln

#### A Cohomological Perspective To Nonlocal Operators, Nicholas White

*Honors Theses*

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, 2024 University of British Columbia, Vancouver, BC V6T 1Z4, Canada

#### 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, 2024 Indian Institute of Science Education and Research, Pune

#### 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, 2024 Meijo University, Tenpaku, Nagoya 468- 8502, Japan

#### 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, 2024 Università di Roma Tor Vergata, Roma I-00133, Italy

#### 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, 2024 Army Research Laboratory Adelphi, MD, 21005-5069, USA

#### Covariant Anyons Via Mackey Machinery, Radhakrishnan Balu

*Journal of Stochastic Analysis*

No abstract provided.

Nonlinear Filtering Of Classical And Quantum Spin Systems, 2024 National Academies/Air Force Research Laboratory, Wright Patterson Air Force Base, Ohio 45433 USA

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

*Journal of Stochastic Analysis*

No abstract provided.

Centers Of N-Degree Poncelet Circles, 2024 Bucknell University

#### 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 …

Machine Learning Approaches For Cyberbullying Detection, 2024 University of Central Florida

#### 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 …

Exploring The Role Of Undergraduate And Graduate Real Analysis Experiences In The Mathematical Trajectories Of Women Mathematicians From Historically Disenfranchised Groups, 2024 University of Texas at Arlington

#### 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*

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 …

Dirichlet Problems In Perforated Domains, 2024 University of Kentucky

#### 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 C^{1} 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 …

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, 2024 Wilfrid Laurier University

#### 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 …

Investigating Bremsstrahlung Radiation In Tungsten Targets: A Geant4 Simulation Study, 2023 National University of Uzbekistan, Tashkent, Uzbekistan

#### Investigating Bremsstrahlung Radiation In Tungsten Targets: A Geant4 Simulation Study, Sindor Ashurov, Satimboy Palvanov, Abror Tuymuradov, Dilmurod Tuymurodov

*Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences*

Bremsstrahlung radiation, a pivotal phenomenon in high-energy physics, presents numerous applications and implications in both theoretical studies and practical scenarios. This article explores the Bremsstrahlung radiation of electrons in tungsten (W) targets of varying widths subjected to different energy beams using GEANT4 simulations. By systematically altering the target widths and electron beam energies, we assess the corresponding effects on radiation yield and spectrum. The findings contribute to a deeper understanding of Bremsstrahlung processes in high-$Z$ materials and offer valuable insights for applications ranging from radiation therapy to materials analysis.

Holomorphic Motion Of Julia Sets Of Polynomial-Like Maps, And Continuity Of Compact Sets And Their Green Functions, 2023 National University of Uzbekistan, Tashkent, Uzbekistan

#### Holomorphic Motion Of Julia Sets Of Polynomial-Like Maps, And Continuity Of Compact Sets And Their Green Functions, Bazarbaev Sardor, Sobir Boymurodov

*Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences*

In this paper, we study holomorphic motion of Julia sets of polynomial-like maps. In particular, we prove that in the stable family of polynomial-like maps if all the continuos functions move continuously by parameter then the Julia sets move holomorphically. Moreover, we also study the relation between continuity of regular compact sets and their Green functions.