Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Institution
-
- Clemson University (4)
- University of Kentucky (3)
- Louisiana State University (2)
- Bucknell University (1)
- California Polytechnic State University, San Luis Obispo (1)
-
- East Tennessee State University (1)
- Harrisburg University of Science and Technology (1)
- Seattle Pacific University (1)
- The University of Southern Mississippi (1)
- University of Louisville (1)
- University of Mary Washington (1)
- University of North Florida (1)
- West Virginia University (1)
- William & Mary (1)
- Keyword
-
- Analysis (2)
- Complex Analysis (2)
- Distributions (2)
- Mathematics (2)
- Scattering (2)
-
- Adjacancy matrix (1)
- Analytic number theory (1)
- Artificial intelligence (1)
- Astronomy (1)
- Asymptotic Cone (1)
- Asymptotics (1)
- Biophysics (1)
- Black holes (1)
- Cable equation (1)
- Cauchy's equation (1)
- Classification (1)
- Common closure operators (1)
- Complex Dimensions (1)
- Complex analysis (1)
- Computational neuroscience (1)
- Content Marketing (1)
- Convex Hull (1)
- Deep neural networks (1)
- Differential equations (1)
- Dispersive (1)
- Dissertations, Academic -- UNF -- Master of Science in Mathematical Science (1)
- Dissertations, Academic -- UNF -- Mathematics (1)
- Dual Gap Polynomials (1)
- Dynamical Systems (1)
- E-Commerce (1)
Articles 1 - 20 of 20
Full-Text Articles in Physical Sciences and Mathematics
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.
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 …
Secondary Features Of Importance For A Url Ranking, Atajan Abdyyev
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 …
Concentration Theorems For Orthonormal Sequences In A Reproducing Kernel Hilbert Space, Travis Alvarez
Concentration Theorems For Orthonormal Sequences In A Reproducing Kernel Hilbert Space, Travis Alvarez
All Dissertations
Let H be a reproducing kernel Hilbert space with reproducing kernel elements {Kx} indexed by a measure space {X,mu}. If H can be embedded in L2(X,mu), then H can be viewed as a framed Hilbert space. We study concentration of orthonormal sequences in such reproducing kernel Hilbert spaces.
Defining different versions of concentration, we find quantitative upper bounds on the number of orthonormal functions that can be classified by such concentrations. Examples are shown to prove sharpness of the bounds. In the cases that we can add "concentrated" orthonormal vectors indefinitely, the growth rate of doing so is shown.
Asymptotic Cones Of Quadratically Defined Sets And Their Applications To Qcqps, Alexander Joyce
Asymptotic Cones Of Quadratically Defined Sets And Their Applications To Qcqps, Alexander Joyce
All Dissertations
Quadratically constrained quadratic programs (QCQPs) are a set of optimization problems defined by a quadratic objective function and quadratic constraints. QCQPs cover a diverse set of problems, but the nonconvexity and unboundedness of quadratic constraints lead to difficulties in globally solving a QCQP. This thesis covers properties of unbounded quadratic constraints via a description of the asymptotic cone of a set defined by a single quadratic constraint. A description of the asymptotic cone is provided, including properties such as retractiveness and horizon directions.
Using the characterization of the asymptotic cone, we generalize existing results for bounded quadratically defined regions with …
Recovering Coefficients Of Second-Order Hyperbolic And Plate Equations Via Finite Measurements On The Boundary, Scott Randall Scruggs
Recovering Coefficients Of Second-Order Hyperbolic And Plate Equations Via Finite Measurements On The Boundary, Scott Randall Scruggs
All Dissertations
Abstract In this dissertation, we consider the inverse problem for a second-order hyperbolic equation of recovering n + 3 unknown coefficients defined on an open bounded domain with a smooth enough boundary. We also consider the inverse problem of recovering an unknown coefficient on the Euler- Bernoulli plate equation on a lower-order term again defined on an open bounded domain with a smooth enough boundary. For the second-order hyperbolic equation, we show that we can uniquely and (Lipschitz) stably recover all these coefficients from only using half of the corresponding boundary measurements of their solutions, and for the plate equation, …
Stability Of Cauchy's Equation On Δ+., Holden Wells
Stability Of Cauchy's Equation On Δ+., Holden Wells
Electronic Theses and Dissertations
The most famous functional equation f(x+y)=f(x)+f(y) known as Cauchy's equation due to its appearance in the seminal analysis text Cours d'Analyse (Cauchy 1821), was used to understand fundamental aspects of the real numbers and the importance of regularity assumptions in mathematical analysis. Since then, the equation has been abstracted and examined in many contexts. One such examination, introduced by Stanislaw Ulam and furthered by Donald Hyers, was that of stability. Hyers demonstrated that Cauchy's equation exhibited stability over Banach Spaces in the following sense: functions that approximately satisfy Cauchy's equation are approximated with the same level of error by functions …
Some New Techniques And Their Applications In The Theory Of Distributions, Kevin Kellinsky-Gonzalez
Some New Techniques And Their Applications In The Theory Of Distributions, Kevin Kellinsky-Gonzalez
LSU Doctoral Dissertations
This dissertation is a compilation of three articles in the theory of distributions. Each essay focuses on a different technique or concept related to distributions.
The focus of the first essay is the concept of distributional point values. Distribu- tions are sometimes called generalized functions, as they share many similarities with ordi- nary functions, with some key differences. Distributional point values, among other things, demonstrate that distributions are even more akin to ordinary functions than one might think.
The second essay concentrates on two major topics in analysis, namely asymptotic expansions and the concept of moments. There are many variations …
Solving The Cable Equation, A Second-Order Time Dependent Pde For Non-Ideal Cables With Action Potentials In The Mammalian Brain Using Kss Methods, Nirmohi Charbe
Master's Theses
In this thesis we shall perform the comparisons of a Krylov Subspace Spectral method with Forward Euler, Backward Euler and Crank-Nicolson to solve the Cable Equation. The Cable Equation measures action potentials in axons in a mammalian brain treated as an ideal cable in the first part of the study. We shall subject this problem to the further assumption of a non-ideal cable. Assume a non-uniform cross section area along the longitudinal axis. At the present time, the effects of torsion, curvature and material capacitance are ignored. There is particular interest to generalize the application of the PDEs including and …
Using Deep Neural Networks To Classify Astronomical Images, Andrew D. Macpherson
Using Deep Neural Networks To Classify Astronomical Images, Andrew D. Macpherson
Honors Projects
As the quantity of astronomical data available continues to exceed the resources available for analysis, recent advances in artificial intelligence encourage the development of automated classification tools. This paper lays out a framework for constructing a deep neural network capable of classifying individual astronomical images by describing techniques to extract and label these objects from large images.
Examining Factors Using Standard Subspaces And Antiunitary Representations, Paul Anderson
Examining Factors Using Standard Subspaces And Antiunitary Representations, Paul Anderson
Undergraduate Honors Theses
In an effort to provide an axiomization of quantum mechanics, John von Neumann and Francis Joseph Murray developed many tools in the theory of operator algebras. One of the many objects developed during the course of their work was the von Neumann algebra, originally called a ring of operators. The purpose of this thesis is to give an overview of the classification of elementary objects, called factors, and explore connections with other mathematical objects, namely standard subspaces in Hilbert spaces and antiunitary representations. The main results presented here illustrate instances of these interconnections that are relevant in Algebraic Quantum Field …
Enestr¨Om-Kakeya Type Results For Complex And Quaternionic Polynomials, Matthew Gladin
Enestr¨Om-Kakeya Type Results For Complex And Quaternionic Polynomials, Matthew Gladin
Electronic Theses and Dissertations
The well known Eneström-Kakeya Theorem states that: for P(z)=∑i=0n ai zi, a polynomial of degree n with real coefficients satisfying 0 ≤ a0 ≤ a1 ≤ ⋯≤ an, all zeros of P(z) lie in |z|≤1 in the complex plane. In this thesis, we will find inner and outer bounds in which the zeros of complex and quaternionic polynomials lie. We will do this by imposing restrictions on the real and imaginary parts, and on the moduli, of the complex and quaternionic coefficients. We also apply similar restrictions on complex polynomials with …
Using A Distributive Approach To Model Insurance Loss, Kayla Kippes
Using A Distributive Approach To Model Insurance Loss, Kayla Kippes
Student Research Submissions
Insurance loss is an unpredicted event that stands at the forefront of the insurance industry. Loss in insurance represents the costs or expenses incurred due to a claim. An insurance claim is a request for the insurance company to pay for damage caused to an individual’s property. Loss can be measured by how much money (the dollar amount) has been paid out by the insurance company to repair the damage or it can be measured by the number of claims (claim count) made to the insurance company. Insured events include property damage due to fire, theft, flood, a car accident, …
Analytic Continuation Of Toeplitz Operators And Commuting Families Of C*-Algebras, Khalid Bdarneh
Analytic Continuation Of Toeplitz Operators And Commuting Families Of C*-Algebras, Khalid Bdarneh
LSU Doctoral Dissertations
In this thesis we consider the Toeplitz operators on the weighted Bergman spaces and their analytic continuation. We proved the commutativity of the $C^*-$algebras generated by the analytic continuation of Toeplitz operators with special class of symbols that are invariant under suitable subgroups of $SU(n,1)$, and we showed that commutative $C^*-$algebras with symbols invariant under compact subgroups of $SU(n,1)$ are completely characterized in terms of restriction to multiplicity free representations. Moreover, we extended the restriction principal to the analytic continuation case for suitable maximal abelian subgroups of the universal covering group $\widetilde{SU(n,1)}$, and we obtained the generalized Segal-Bargmann transform, where …
Asymptotic Behaviour Of Hyperbolic Partial Differential Equations, Shi-Zhuo Looi
Asymptotic Behaviour Of Hyperbolic Partial Differential Equations, Shi-Zhuo Looi
Theses and Dissertations--Mathematics
We investigate the asymptotic behaviour of solutions to a range of linear and nonlinear hyperbolic equations on asymptotically flat spacetimes. We develop a comprehensive framework for the analysis of pointwise decay of linear and nonlinear wave equations on asymptotically flat manifolds of three space dimensions that are allowed to be time-varying or nonstationary, including quasilinear wave equations. The Minkowski space and time-varying perturbations thereof are included among these spacetimes. A result on scattering for a nonlinear wave equation with finite-energy solutions on nonstationary spacetimes is presented. This work was motivated in part by the investigation of more precise asymptotic behaviour …
Peer-To-Peer Energy Trading In Smart Residential Environment With User Behavioral Modeling, Ashutosh Timilsina
Peer-To-Peer Energy Trading In Smart Residential Environment With User Behavioral Modeling, Ashutosh Timilsina
Theses and Dissertations--Computer Science
Electric power systems are transforming from a centralized unidirectional market to a decentralized open market. With this shift, the end-users have the possibility to actively participate in local energy exchanges, with or without the involvement of the main grid. Rapidly reducing prices for Renewable Energy Technologies (RETs), supported by their ease of installation and operation, with the facilitation of Electric Vehicles (EV) and Smart Grid (SG) technologies to make bidirectional flow of energy possible, has contributed to this changing landscape in the distribution side of the traditional power grid.
Trading energy among users in a decentralized fashion has been referred …
A Scattering Result For The Fifth-Order Kp-Ii Equation, Camille Schuetz
A Scattering Result For The Fifth-Order Kp-Ii Equation, Camille Schuetz
Theses and Dissertations--Mathematics
We will prove scattering for the fifth-order Kadomtsev-Petviashvilli II (fifth-order KP-II) equation. The fifth-order KP-II equation is an example of a nonlinear dispersive equation which takes the form $u_t=Lu + NL(u)$ where $L$ is a linear differential operator and $NL$ is a nonlinear operator. One looks for solutions $u(t)$ in a space $C(\R,X)$ where $X$ is a Banach space. For a nonlinear dispersive differential equation, the associated linear problem is $v_t=Lv$. A solution $u(t)$ of the nonlinear equation is said to scatter if as $t \to \infty$, the solution $u(t)$ approaches a solution $v(t)$ to the linear problem in the …
Elliptic Functions And Iterative Algorithms For Π, Eduardo Jose Evans
Elliptic Functions And Iterative Algorithms For Π, Eduardo Jose Evans
UNF Graduate Theses and Dissertations
Preliminary identities in the theory of basic hypergeometric series, or `q-series', are proven. These include q-analogues of the exponential function, which lead to a fairly simple proof of Jacobi's celebrated triple product identity due to Andrews. The Dedekind eta function is introduced and a few identities of it derived. Euler's pentagonal number theorem is shown as a special case of Ramanujan's theta function and Watson's quintuple product identity is proved in a manner given by Carlitz and Subbarao. The Jacobian theta functions are introduced as special kinds of basic hypergeometric series and various relations between them derived using the triple …
Graphs, Adjacency Matrices, And Corresponding Functions, Yang Hong
Graphs, Adjacency Matrices, And Corresponding Functions, Yang Hong
Honors Theses
Stable polynomials, in the context of this research, are two-variable polynomials like $p(z_1,z_2) = 2 - z_1 - z_2$ that are guaranteed to be non-zero if both input variables have an absolute value less than one in the complex plane. Stable polynomials are used in a variety of mathematical fields, thus finding ways to construct stable polynomials is valuable. An important property of these polynomials is whether they have boundary zeros, which are points in the complex plane where the polynomial equals zero and both variables have an absolute value of 1. Overall, it is challenging to find stable polynomials …
Finite Matroidal Spaces And Matrological Spaces, Ziyad M. Hamad
Finite Matroidal Spaces And Matrological Spaces, Ziyad M. Hamad
Graduate Theses, Dissertations, and Problem Reports
The purpose of this thesis is to present new different spaces as attempts to generalize the concept of topological vector spaces. A topological vector space, a well-known concept in mathematics, is a vector space over a field \mathbb{F} with a topology that makes the addition and scalar multiplication operations of the vector space continuous functions. The field \mathbb{F} is usually \mathbb{R} or \mathbb{C} with their standard topologies. Since every vector space is a finitary matroid, we define two spaces called finite matroidal spaces and matrological spaces by replacing the linear structure of the topological vector space with a finitary matroidal …