Mathematics Commons^™

Mathematics In Amusement Parks, Kacey Laumann

Honors Projects

This project focuses specifically on the Walt Disney World Park, Magic Kingdom. I started by collecting data through the MyDisneyExperience app. By recording the data, I was then able to create polynomial functions to the fifth the degree. Each attraction received a function which allowed me to predict the wait times for that attraction. Then, by graphing the functions and analyzing the graph using calculus the “best time” and “worst time” to go to the attraction were found. After the analysis the information is used to build a unique schedule for a guest. Then the guest receives this schedule after …

(R2100) Optimality Conditions Of A Topsis Optimization Model And Its Application On Interval-Valued Data, Sudipta Roy, Sandip Chatterjee

Applications and Applied Mathematics: An International Journal (AAM)

The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is widely used in the field of multi-criteria decision analysis. Despite its popularity and widespread application, little attention has been given to the mathematical foundation that underlies the TOPSIS algorithm. The existing literature on this subject is far from comprehensive, leaving many aspects of the algorithm unexplored. This paper aims to address this gap in the literature by delving into the optimization problem associated with TOPSIS. Unlike traditional interval analysis theory, which only covers a limited scope, our approach extends to a broader range of scenarios and offers …

(R2109) Characterizations Of Tzitzeica Curves Using Conformable Frenet Frame, Aykut Has, Beyhan Yılmaz, Kebire Hilal Ayvacı

Applications and Applied Mathematics: An International Journal (AAM)

The aim of this study, the conditions for a conformable curve and its spherical indicator curves to be a Tzitzeica curve, will be examined. Thus, by understanding the behavior of the Tzitzeica curve, researchers can gain insight into complex systems and make more accurate predictions about their behavior.

Computational Representation, Analysis And Verification Of Requirements In Engineering Design And Systems Engineering, Chandan Kumar Sahu

All Dissertations

Systems are developed to satisfy a set of requirements derived from stakeholders’ needs, defining the problem space for which the system is created as a feasible solution. The system design process begins with eliciting these requirements and concludes with validating whether the created system meets them. Requirements engineering (RE) encompasses elicitation, representation, analysis, documentation, verification, and validation. However, challenges in RE, such as imprecision in natural language (NL), proprietary restrictions, and a lack of standardized quality metrics, hinder the creation of well-formed and comprehensive requirements. These challenges complicate formalization and analysis of requirements.

This dissertation addresses these challenges by proposing …

(R2093) Fixed Point Of Hybrid Jaggi-Meir-Keeler Type Multivalued Contraction, Sirajo Yahaya, Mohammed Shehu Shagari

Applications and Applied Mathematics: An International Journal (AAM)

One of the most applicable results in metric fixed point theory is based on the contractive inequalities, including both rational and non-rational types. In this manuscript, a general idea under the name Jaggi-Meir-Keeler hybrid type multivalued contraction is introduced. We investigate the existence of fixed points for such operators in the setting of a complete metric space. The presented concept herein unifies the above-mentioned contractions and the corresponding invariant point results. A comparative nontrivial example is constructed to show the connection between the main idea in this paper and the related literature.

New Fueter-Type Variables Associated To The Global Operator In The Quaternionic Case, Daniel Alpay, Kamal Diki, Mihaela Vajiac

Mathematics, Physics, and Computer Science Faculty Articles and Research

The purpose of this paper is to develop a new theory of three non-commuting quaternionic variables and its related Schur analysis theory for a modified version of the quaternionic global operator.

Pricing Variance Swaps For The Discrete Bn-S Model, Semere Gebresilasie

Journal of Stochastic Analysis

No abstract provided.

(Si13-06) Analysis Of Some Unified Integral Equations Of Fredholm Type Associated With Multivariable Incomplete H And I-Functions, Rahul Sharma, Vinod Gill, Naresh Kumar, Kanak Modi, Yudhveer Singh

Applications and Applied Mathematics: An International Journal (AAM)

In this research paper, we examine various effective methods for addressing the problem of solving Fredholm-type integral equations. Our investigation commences by applying the principles of fractional calculus theory. We employ series representations and products of multivariable incomplete H-functions and multivariable incomplete I-functions to solve these integrals. The outcomes derived from our analysis possess a general nature and hold the potential to yield numerous results.

Errata: 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 Saito

Journal of Stochastic Analysis

No abstract provided.

Bernoulli Convolution Of The Depth Of Nodes In Recursive Trees With General Affinities, Toshio Nakata, Hosam Mahmoud

Journal of Stochastic Analysis

No abstract provided.

Probabilistic Frames And Concepts From Optimal Transport, Dongwei Chen

All Dissertations

As the generalization of frames in the Euclidean space $\mathbb{R}^n$, a probabilistic frame is a probability measure on $\mathbb{R}^n$ that has a finite second moment and whose support spans $\mathbb{R}^n$. The p-Wasserstein distance with $p \geq 1$ from optimal transport is often used to compare probabilistic frames. It is particularly useful to compare frames of various cardinalities in the context of probabilistic frames. We show that the 2-Wasserstein distance appears naturally in the fundamental objects of frame theory and draws consequences leading to a geometric viewpoint of probabilistic frames.

We convert the classic lower bound estimates of 2-Wasserstein distance \cite{Gelbrich90, …

Short-Time Fourier Transform And Superoscillations, Daniel Alpay, Antonino De Martino, Kamal Diki, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we investigate new results on the theory of superoscillations using time-frequency analysis tools and techniques such as the short-time Fourier transform (STFT) and the Zak transform. We start by studying how the short-time Fourier transform acts on superoscillation sequences. We then apply the supershift property to prove that the short-time Fourier transform preserves the superoscillatory behavior by taking the limit. It turns out that these computations lead to interesting connections with various features of time-frequency analysis such as Gabor spaces, Gabor kernels, Gabor frames, 2D-complex Hermite polynomials, and polyanalytic functions. We treat different cases depending on the …

Stochastic Solutions For Hyperbolic Pde, Abdol-Reza Mansouri, Zachary Selk

Journal of Stochastic Analysis

No abstract provided.

Uniformly Distributing Points On A Sphere, Flavio Arrigoni

Rose-Hulman Undergraduate Mathematics Journal

In this paper, we are going to present and discuss different procedures for distributing points on a sphere's surface. Furthermore, we will assess their quality with three different distribution tests. The MATHEMATICA package that we created for testing and plotting the points is publicly available.

Limit Theorems For Increments Of Branching Particle Systems With Linear Rates And Poisson Initial Condition, Alexander Kreinin, Vladimir V. Vinogradov

Journal of Stochastic Analysis

No abstract provided.

Asymptotic Formula For Scattering Problems Related To Thin Metasurfaces, Zachary Jermain

LSU Doctoral Dissertations

The goal of this work is to develop an asymptotic formula for the behavior of a scattered electromagnetic field in the presence of a thin metamaterial known as a metasurface. By using a carefully chosen Green’s function and the single and double layer potentials we analyze the perturbed scattering problem in the presence of the metamaterial and a background scattering problem. By using Lippman-Schwinger type representation formulas for the two fields we develop the asymptotic formula for the perturbed field. From here we prove the asymptotic formula holds up to a specific error term based on the size of the …

Holomorphic Functional Calculus Approach To The Characteristic Function Of Quantum Observables, Andreas Boukas

Journal of Stochastic Analysis

No abstract provided.

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.

Bi-Harmonic Maps' Existence And P-Balanced Energy And Connections To Harmonic Maps, Lina Wu

Publications and Research

We discover a bi-harmonic map’ existence, its energy growth, and its connections to a harmonic map. First, we prove the existence of a nontrivial bi-harmonic map in a unit sphere. Second, we investigate the p-balanced energy growth of biharmonic maps. As the most important energy technical breakthroughs, we propose an innovative energy algorithm called p-balanced energy technique to break the constraints of the existing L^q-energy technique in detecting L^q-energy growth towards boundlessness. The disadvantage of the finite L^q -energy technique in the L ^q spaces is not effective in dealing with infinite L^q- energy in Non-L^q spaces. Third, we study …

Matrix Approximation And Image Compression, Isabella R. Padavana

Master's Theses

This thesis concerns the mathematics and application of various methods for approximating matrices, with a particular eye towards the role that such methods play in image compression. An image is stored as a matrix of values with each entry containing a value recording the intensity of a corresponding pixel, so image compression is essentially equivalent to matrix approximation. First, we look at the singular value decomposition, one of the central tools for analyzing a matrix. We show that, in a sense, the singular value decomposition is the best low-rank approximation of any matrix. However, the singular value decomposition has some …

(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, 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. …

Pt-Symmetry And Eigenmodes, Tamara Gratcheva

University Honors Theses

Spectra of systems with balanced gain and loss, described by Hamiltonians with parity and time-reversal (PT) symmetry is a rich area of research. This work studies by means of numerical techniques, how eigenvalues and eigenfunctions of a Schrodinger operator change as a gain-loss parameter changes. Two cases on a disk with zero boundary conditions are considered. In the first case, within the enclosing disk, we place a parity (P) symmetric configuration of three smaller disks containing gain and loss media, which does not have PT-symmetry. In the second case, we study a PT-symmetric configuration …

Exploring The Mandelbrot Set, James Shirley

Electronic Theses and Dissertations

The Mandelbrot set is a mathematical mystery. Finding its home somewhere be-
tween holomorphic dynamics and complex analysis, the Mandelbrot set showcases
its usefulness in fields across the many realms of math—ranging from physics to nu-
merical methods and even biology. While typically defined in terms of its bounded
sequences, this thesis intends to illuminate the Mandelbrot set as a type of param-
eterization of connectivity itself, specifically that of complex-valued rational maps
of the form z → z² + c. This fully illustrated guide to the Mandelbrot set merges
the worlds of intuition and theory with a series of …

Spatiotemporal Negative Inventory Outlier Decomposition For Supply Chain Applications In Consumer-Packaged Goods (Cpg), Hayden Mcdonald

Data Science Undergraduate Honors Theses

Coca-Cola is a popular soft drink brand with sales occurring in every Walmart store across the world, which generates large quantities of data and requires a robust supply chain system. However, the company does not currently have a sophisticated, automated, and/or prescriptive system for detecting where, when, and why inventory outages occur and applying preventative measures to avoid loss of revenue from the absence of inventory on store shelves. This thesis proposes and applies a novel, prescriptive system for this purpose. An inventory outage can be seen as a ‘negative’ statistical outlier in a time series of inventory for an …

How To Explain Allen-Manandhar’S Method To Beginner Mathematicians : A Convergence Analysis Of A Hybrid Method For Variable-Coefficient Boundary Value Problems, Rebecca Scariano

Honors Theses

In this project, analogies are employed to make complex math concepts approachable to beginners who may only have a basic understanding of calculus and linear algebra. Serving as the focal point of this project, Allen-Manandhar’s method solves an equation, known as an ordinary differential equation (ODE). The mentioned equation with its coefficients is comparable to a pie recipe with ingredients. With the outcome to a recipe seen as its solution, the solution to our pie recipe is a perfectly baked pie, as in without error. The chosen method for baking a pie then classifies as its baking approach that when …

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

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

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 dSⁿ 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 dSⁿ. The space of spherical distributions with eigenvalue λ, denoted by D_λ^H'(dSⁿ), has dimension 2. We construct a basis for the space of …

Abstract Measures On Totally Ordered Sets, Gregory Whitehurst

Mathematics Senior Capstone Papers

Two specific notions of integration were the motivation of this paper: Riemann-Stieltjes and Lebesgue-Stieltjes integration. The question that arose from these notions was the idea of generalization. How can Stieltjes integration be generalized to an arbitrary measure? The buildup to this question requires a beautiful combination of measure theory and order theory to deliver a measure on totally ordered sets that provide structure for a potential generalization. This paper shows that the set of chains in a totally ordered set is a σ-algebra and defines cumulative cardinality measure on (X, Σ) in an attempt to give insight on the structure …