The Mathematical Aspects Of Theoretical Physics,
2018
The University of Texas Rio Grande Valley
The Mathematical Aspects Of Theoretical Physics, Hassan Kesserwani
Theses and Dissertations
The aim of this thesis is to outline the mathematical machinery of general relativity, quantum gravity, cosmology and an introduction to string theory under one body of work. We will flesh out tensor algebra and the formalism of differential geometry. After deriving the Einstein field equation, we will outline its traditional applications. We then linearize the field equation by a perturbation method and describe the mathematics of gravitational waves and their spherical harmonic analysis. We then transition into the derivation of the Schwarzschild metric and the Kruskal coordinate transformation, in order to set the stage for quantum gravity. This sets …
Scheduling Problems,
2018
University of Mississippi
Scheduling Problems, Aamir Kudai
Honors Theses
Manufacturing industry is growing exponentially. The need of using algorithms and computational techniques to enhance processes is increasing every day. Algorithms help us solve almost all kind of computational problems. Not only choosing the right algorithm for a problem is important but also optimizing its time and space efficiency is crucial. BorgWarner Transmission Systems located in Water Valley, Mississippi is one among the leading manufacturing companies. This paper will demonstrate a real-world audit scheduling problem happened at BorgWarner and the techniques used to solve it. A gentle introduction to some of the heuristic algorithms such as Genetic algorithm, Randomized algorithm, …
A Plausible Resolution To Hilbert’S Failed Attempt To Unify Gravitation & Electromagnetism,
2018
University of New Mexico
A Plausible Resolution To Hilbert’S Failed Attempt To Unify Gravitation & Electromagnetism, Florentin Smarandache, Victor Christianto, Robert Neil Boyd
Branch Mathematics and Statistics Faculty and Staff Publications
In this paper, we explore the reasons why Hilbert’s axiomatic program to unify gravitation theory and electromagnetism failed and outline a plausible resolution of this problem. The latter is based on Gödel’s incompleteness theorem and Newton’s aether stream model.
Multi-Resolution Analysis Using Wavelet Basis Conditioned On Homogenization,
2018
Utah State University
Multi-Resolution Analysis Using Wavelet Basis Conditioned On Homogenization, Abibat Adebisi Lasisi
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
This dissertation considers an approximation strategy using a wavelet reconstruction scheme for solving elliptic problems. The foci of the work are on (1) the approximate solution of differential equations using multiresolution analysis based on wavelet transforms and (2) the homogenization process for solving one and two-dimensional problems, to understand the solutions of second order elliptic problems. We employed homogenization to compute the average formula for permeability in a porous medium. The structure of the associated multiresolution analysis allows for the reconstruction of the approximate solution of the primary variable in the elliptic equation. Using a one-dimensional wavelet reconstruction algorithm proposed …
Identities For Partitions Of N With Parts From A Finite Set,
2018
The University of Texas Rio Grande Valley
Identities For Partitions Of N With Parts From A Finite Set, Acadia Larsen
Theses and Dissertations
We show for a prime power number of parts m that the first differences of partitions into at most m parts can be expressed as a non-negative linear combination of partitions into at most m – 1 parts. To show this relationship, we combine a quasipolynomial construction of p(n,m) with a new partition identity for a finite number of parts. We prove these results by providing combinatorial interpretations of the quasipolynomial of p(n,m) and the new partition identity. We extend these results by establishing conditions for when partitions of n with parts coming from …
Blow-Up Solutions Of Wave Map Equations With Periodic In Time Speed Of Propagation,
2018
The University of Texas Rio Grande Valley
Blow-Up Solutions Of Wave Map Equations With Periodic In Time Speed Of Propagation, Nathalie M. Luna-Rivera
Theses and Dissertations
We study the initial value problem for the wave map equation with time-dependent speed of propagation. In particular, for arbitrary, small, and smooth initial data we construct blow-up solutions of the wave map with coefficients that are periodic in time. For the proof we use Lyapunov-Floquet theory and Borg’s theorem.
Asymptotic Quantization For A Condensation System Associated With A Discrete Distribution,
2018
The University of Texas Rio Grande Valley
Asymptotic Quantization For A Condensation System Associated With A Discrete Distribution, Shankar Parajulee
Theses and Dissertations
Let P := (1/3)P ○ S1–1 + (1/3)P ○ S2–1 + (1/3)v be a condensation measure on R, where S1(x) = (1/5)x, S2(x) = (1/5)x + 4/5 for all x ∈ R , and v is a discrete distribution on R with the support of v equals C := {(2/5), (3/5)}. For such a measure P we determine the optimal sets of n–means and the nth quantization errors for all n ≥ 2. In addition, we show that the quantization dimension of the condensation measure P exists and equals …
Exploring Flag Matroids And Duality,
2018
California State University, San Bernardino
Exploring Flag Matroids And Duality, Zachary Garcia
Electronic Theses, Projects, and Dissertations
Matroids capture an abstraction of independence in mathematics, and in doing so, connect discrete mathematical structures that arise in a variety of contexts. A matroid can be defined in several cryptomorphic ways depending on which perspective of a matroid is most applicable to the given context. Among the many important concepts in matroid theory, the concept of matroid duality provides a powerful tool when addressing difficult problems. The usefulness of matroid duality stems from the fact that the dual of a matroid is itself a matroid. In this thesis, we explore a matroid-like object called a flag matroid. In particular, …
Italian Domination On Ladders And Related Products,
2018
East Tennessee State University
Italian Domination On Ladders And Related Products, Bradley Gardner
Electronic Theses and Dissertations
An Italian dominating function on a graph $G = (V,E)$ is a function such that $f : V \to \{0,1,2\}$, and for each vertex $v \in V$ for which $f(v) = 0$, we have $\sum_{u\in N(v)}f(u) \geq 2$. The weight of an Italian dominating function is $f(V) = \sum_{v\in V(G)}f(v)$. The minimum weight of all such functions on a graph $G$ is called the Italian domination number of $G$. In this thesis, we will consider Italian domination in various types of products of a graph $G$ with the complete graph $K_2$. We will find the value of the Italian domination …
Symmetric Presentations And Double Coset Enumeration,
2018
California State University, San Bernardino
Symmetric Presentations And Double Coset Enumeration, Charles Seager
Electronic Theses, Projects, and Dissertations
In this project, we demonstrate our discovery of original symmetric presentations and constructions of important groups, including nonabelian simple groups, and groups that have these as factor groups. The target nonabelian simple groups include alternating, linear, and sporadic groups. We give isomorphism types for each finite homomorphic image that has been found. We present original symmetric presentations of $M_{12}$, $M_{21}:(2 \times 2)$, $L_{3}(4):2^2$, $2:^{\cdot}L_{3}(4):2$, $S(4,3)$, and $S_{7}$ as homomorphism images of the progenitors $2^{*20}$ $:$ $A_{5}$, $2^{*10}$ $:$ $PGL(2,9)$, $2^{*10}$ $:$ $Aut(A_{6})$, $2^{*10}$ $:$ $A_{6}$, $2^{*10}$ $:$ $A_{5}$, and $2^{*24}$ $:$ $S_{5}$, respectively. We also construct $M_{12}$, $M_{21}:(2 \times 2)$, …
Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence,
2018
Utah State University
Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Lie algebra cohomology is an important tool in many branches of mathematics. It is used in the Topology of homogeneous spaces, Deformation theory, and Extension theory. There exists extensive theory for calculating the cohomology of semi simple Lie algebras, but more tools are needed for calculating the cohomology of general Lie algebras. To calculate the cohomology of general Lie algebras, I used the symbolic software program called Maple. I wrote software to calculate the cohomology in several different ways. I wrote several programs to calculate the cohomology directly. This proved to be computationally expensive as the number of differential forms …
Hartogs Domains And The Diederich-Fornæss Index,
2018
University of Arkansas, Fayetteville
Hartogs Domains And The Diederich-Fornæss Index, Muhenned Abdulameer Abdulsahib
Graduate Theses and Dissertations
The Diederich-Fornss Index has played a crucial role in studying regularity of the Bergman projection on pseudoconvex domains in Sobolov spaces as is shown by Kohn, Harrington, Pinton and Zampieri and others. In this work, we discuss the Diederich-Fornss Index on Hartogs domains, and its relation to other properties connected to regularity of the Bergman projection. An upper and lower bound for the Diederich-Fornss Index is calculated for Hartogs domains and computed sharply for worm domains. Related conditions for the existence of a strong Stein neighborhood basis for Hartogs domains are introduced.
Predicted Deepwater Bathymetry From Satellite Altimetry: Non-Fourier Transform Alternatives,
2018
University of Southern Mississippi
Predicted Deepwater Bathymetry From Satellite Altimetry: Non-Fourier Transform Alternatives, Maxsimo Salazar
Dissertations
Robert Parker (1972) demonstrated the effectiveness of Fourier Transforms (FT) to compute gravitational potential anomalies caused by uneven, non-uniform layers of material. This important calculation relates the gravitational potential anomaly to sea-floor topography. As outlined by Sandwell and Smith (1997), a six-step procedure, utilizing the FT, then demonstrated how satellite altimetry measurements of marine geoid height are inverted into seafloor topography. However, FTs are not local in space and produce Gibb’s phenomenon around discontinuities. Seafloor features exhibit spatial locality and features such as seamounts and ridges often have sharp inclines. Initial tests compared the windowed-FT to wavelets in reconstruction of …
Topological Properties Of A 3-Rung Möbius Ladder,
2018
Stephen F. Austin State University
Topological Properties Of A 3-Rung Möbius Ladder, Rebecca Woods
Electronic Theses and Dissertations
In this work, we discuss the properties of the 3-rung Möbius ladder on the torus. We also prove ℤ2 is an orientation preserving topological symmetry group of the 3-rung Möbius ladder with sides and rungs distinct, embedded in the torus.
Dispersion Analysis Of Hdg Methods,
2018
Portland State University
Dispersion Analysis Of Hdg Methods, Jay Gopalakrishnan, Manuel Solano, Felipe Vargas
Mathematics and Statistics Faculty Publications and Presentations
This work presents a dispersion analysis of the Hybrid Discontinuous Galerkin (HDG) method. Considering the Helmholtz system, we quantify the discrepancies between the exact and discrete wavenumbers. In particular, we obtain an analytic expansion for the wavenumber error for the lowest order Single Face HDG (SFH) method. The expansion shows that the SFH method exhibits convergence rates of the wavenumber errors comparable to that of the mixed hybrid Raviart–Thomas method. In addition, we observe the same behavior for the higher order cases in numerical experiments.
Finite Simple Graphs And Their Associated Graph Lattices,
2018
Middle Tennessee State University
Finite Simple Graphs And Their Associated Graph Lattices, James B. Hart, Brian Frazier
Theory & Applications of Graphs
In his 2005 dissertation, Antoine Vella explored combinatorical aspects of finite graphs utilizing a topological space whose open sets are intimately tied to the structure of the graph. In this paper, we go a step further and examine some aspects of the open set lattices induced by these topological spaces. In particular, we will characterize all lattices that constitute the opens for finite simple graphs endowed with this topology, explore the structure of these lattices, and show that these lattices contain information necessary to reconstruct the graph and its complement in several ways.
Markov Chains And Generalized Wavelet Multiresolutions,
2018
Southern Illinois University Edwardsville
Markov Chains And Generalized Wavelet Multiresolutions, Myung-Sin Song, Palle Jorgensen
SIUE Faculty Research, Scholarship, and Creative Activity
We develop some new results for a general class of transfer operators, as they are used in a construction of multi-resolutions. We then proceed to give explicit and concrete applications. We further discuss the need for such a constructive harmonic analysis/dynamical systems approach to fractals.
Group Theory And Particles,
2018
Georgia Southern University
Group Theory And Particles, Elizabeth V. Hawkins
Honors College Theses
We begin by a brief overview of the notion of groups and Lie groups. We then explain what group representations are and give their main properties. Finally, we show how group representation form a natural framework to understand the Standard Model of physics.
Distance And Intersection Number In The Curve Complex Of A Closed Surface,
2018
Northeastern Illinois University
Distance And Intersection Number In The Curve Complex Of A Closed Surface, Nancy C. Wrinkle
Faculty Research and Creative Activities Symposium
No abstract provided.
Linear Analysis Of Tumor Morphology During Growth Using Bending Energy,
2018
Northeastern Illinois University
Linear Analysis Of Tumor Morphology During Growth Using Bending Energy, Emma A. Turian
Faculty Research and Creative Activities Symposium
No abstract provided.
