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Articles 1 - 30 of 1688
Full-Text Articles in Physical Sciences and Mathematics
On Axially Rational Regular Functions And Schur Analysis In The Clifford-Appell Setting, Daniel Alpay, Fabrizio Colombo, Antonino De Martino, Kamal Diki, Irene Sabadini
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, Jorge Villalobos Alvarado
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, Iswarya Sitiraju
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′ = O1,n(R) be the Lorentz group, and let H′ = O1,n−1(R) ⊂ G′ be its subset. The de Sitter space dSn is a one-sheeted hyperboloid in R1,n isomorphic to G′/H′. A spherical distribution is an H′-invariant eigendistribution of the Laplace-Beltrami operator on dSn. The space of spherical distributions with eigenvalue λ, denoted by DλH'(dSn), has dimension 2. We construct a basis for the space of …
A Cohomological Perspective To Nonlocal Operators, Nicholas White
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, Clayton Allard, Iddo Ben-Ari, Shrikant Chand, Van Hovenga, Edith Lee, Julia Shapiro
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
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
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
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
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
Nonlinear Filtering Of Classical And Quantum Spin Systems, Sivaguru S. Sritharan, Saba Mudaliar
Journal of Stochastic Analysis
No abstract provided.
Machine Learning Approaches For Cyberbullying Detection, Roland Fiagbe
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 …
Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen
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
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 …
Dirichlet Problems In Perforated Domains, Robert Righi
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 …
Holomorphic Motion Of Julia Sets Of Polynomial-Like Maps, And Continuity Of Compact Sets And Their Green Functions, Bazarbaev Sardor, Sobir Boymurodov
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.
Translation-Invariant Gibbs Measures For Potts Model With Competing Interactions With A Countable Set Of Spin Values On Cayley Tree, Zarinabonu Mustafoyeva
Translation-Invariant Gibbs Measures For Potts Model With Competing Interactions With A Countable Set Of Spin Values On Cayley Tree, Zarinabonu Mustafoyeva
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
In the present paper we consider of an infinite system of functional equations for the Potts model with competing interactions and countable spin values Φ = {0, 1, ..., } on a Cayley tree of order k. We study translation-invariant Gibbs measures that gives the description of the solutions of some infinite system of equations. For any k ≥ 1 and any fixed probability measure ν we show that the set of translation-invariant splitting Gibbs measures contains one and two points for odd k and even k, respectively, independently on parameters of the Potts model with a countable …
An Analogue Of Hartogs Lemma For Separately Harmonic Functions With Variable Radius Of Harmonicity, Sevdiyor Imomkulov, Sultanbay Abdikadirov
An Analogue Of Hartogs Lemma For Separately Harmonic Functions With Variable Radius Of Harmonicity, Sevdiyor Imomkulov, Sultanbay Abdikadirov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
In this note we prove that if a function u(x,y) is separately harmonic in a domain D × Vr = D × {y∈ℝ2:|y|<r, r>1} ⊂ ℝn × ℝ2 and for each fixed point x0 ∈ D the function u(x0,y) of variable y continues harmonically into the great circle {y∈ℝ2:|y|<R(x0), R(x0)>r}, then it continues harmonically into a domain {(x …
Investigating Bremsstrahlung Radiation In Tungsten Targets: A Geant4 Simulation Study, Sindor Ashurov, Satimboy Palvanov, Abror Tuymuradov, Dilmurod Tuymurodov
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.
Cyclically Compact Operators In Banach Modules Over L0(B), Jasurbek Karimov
Cyclically Compact Operators In Banach Modules Over L0(B), Jasurbek Karimov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
In this paper the properties of linear cyclically compact operators in Banach modules over space L0(B) are given.
Laterally Complete Regular Modules, Jasurbek Karimov
Laterally Complete Regular Modules, Jasurbek Karimov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
In this paper we introduce the notion laterally complete regular modules and study some properties of theese modules.
Complex Dimensions Of 100 Different Sierpinski Carpet Modifications, Gregory Parker Leathrum
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.
(R2054) Convergence Of Lagrange-Hermite Interpolation Using Non-Uniform Nodes On The Unit Circle, Swarnima Bahadur, Sameera Iqram, Varun .
(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.
Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost
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 …
Understanding Impact Of Educational Awareness And Vaccines As Optimal Control Mechanisms For Changing Human Behavior In Disease Epidemics, Manal Badgaish, Dr. Padmanabhan Seshaiyer
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
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
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
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
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
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 …
Gibbs Measures Of Models With Uncountable Set Of Spin Values On Lattice Systems, Farhod Haydarov
Gibbs Measures Of Models With Uncountable Set Of Spin Values On Lattice Systems, Farhod Haydarov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
In this paper, we shall discuss the construction of Gibbs measures for models with uncountable set of spin values on Cayley trees. It is known that "translation-invariant Gibbs measures" of the model with an uncountable set of spin values can be described by positive fixed points of a nonlinear integral operator of Hammerstein type. The problem of constructing a kernel with non-uniqueness of the integral operator is sufficient in Gibbs measure theory. In this paper, we construct a degenerate kernel in which the number of solutions does not exceed 3, and in turn, it only gives us a chance to …