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Articles 1 - 14 of 14
Full-Text Articles in Physical Sciences and Mathematics
Solutions To The Kaluza-Klein Field Equations, Abel Eshete
Solutions To The Kaluza-Klein Field Equations, Abel Eshete
All Graduate Theses, Dissertations, and Other Capstone Projects
This Alternate Paper Plan explores Kaluza-Klein theory, a multidimensional framework designed to unify Einstein’s gravitational field theory and Maxwell’s electromagnetic field theory. The objectives of this research can be summarized in two key areas: The first objective is to present a comprehensive introduction to the compactified Kaluza-Klein theory. The second aim involves the application of differential geometry, specifically E ́lie Cartan’s tetrad formalism, to derive exact solutions in two distinct scenarios: a. A Levi-Civita spacetime, b. A general spherical system. Furthermore, Lagrangian and Hamiltonian formalism are utilized to define stability conditions and describe gravitational lensing and Precession of Perihelion within …
Rankings Of Mma Fighters, Michael Schaefer
Rankings Of Mma Fighters, Michael Schaefer
All Graduate Theses, Dissertations, and Other Capstone Projects
Ranking is an essential process that allows sporting authorities to determine the relative performance of athletes. While ranking is straightforward in some sports, it is more complicated in MMA (mixed martial arts), where competition is often fragmented. This paper describes the mathematics behind four existing ranking algorithms: Elo’s System, Massey’s Method, Colley’s Method, and Google’s PageRank, and shows how to adapt them to rank MMA fighters in the UFC (Ultimate Fighting Championship). We also provide a performance analysis for each ranking method.
Discrete Morse Theory By Vector Fields: A Survey And New Directions, Matthew Nemitz
Discrete Morse Theory By Vector Fields: A Survey And New Directions, Matthew Nemitz
All Graduate Theses, Dissertations, and Other Capstone Projects
We synthesize some of the main tools in discrete Morse theory from various sources. We do this in regards to abstract simplicial complexes with an emphasis on vector fields and use this as a building block to achieve our main result which is to investigate the relationship between simplicial maps and homotopy. We use the discrete vector field as a catalyst to build a chain homotopy between chain maps induced by simplicial maps.
Gröbner Bases And Systems Of Polynomial Equations, Rachel Holmes
Gröbner Bases And Systems Of Polynomial Equations, Rachel Holmes
All Graduate Theses, Dissertations, and Other Capstone Projects
This paper will explore the use and construction of Gröbner bases through Buchberger's algorithm. Specifically, applications of such bases for solving systems of polynomial equations will be discussed. Furthermore, we relate many concepts in commutative algebra to ideas in computational algebraic geometry.
Heat Kernel Voting With Geometric Invariants, Alexander Harr
Heat Kernel Voting With Geometric Invariants, Alexander Harr
All Graduate Theses, Dissertations, and Other Capstone Projects
Here we provide a method for comparing geometric objects. Two objects of interest are embedded into an infinite dimensional Hilbert space using their Laplacian eigenvalues and eigenfunctions, truncated to a finite dimensional Euclidean space, where correspondences between the objects are searched for and voted on. To simplify correspondence finding, we propose using several geometric invariants to reduce the necessary computations. This method improves on voting methods by identifying isometric regions including shapes of genus greater than 0 and dimension greater than 3, as well as almost retaining isometry.
A Measure Theoretic Approach To Problems Of Number Theory With Applications To The Proof Of The Prime Number Theorem, Russell Lee Jahn
A Measure Theoretic Approach To Problems Of Number Theory With Applications To The Proof Of The Prime Number Theorem, Russell Lee Jahn
All Graduate Theses, Dissertations, and Other Capstone Projects
In this paper we demonstrate how the principles of measure theory can be applied effectively to problems of number theory. Initially, necessary concepts from number theory will be presented. Next, we state standard concepts and results from measure theory to which we will need to refer. We then develop our repertoire of measure theoretic machinery by constructing the needed measures and defining a generalized version of the multiplicative convolution of measures. A suitable integration by parts formula, one that is general enough to handle various combinations of measures, will then be derived. At this juncture we will be ready to …
Building A Predictive Model For Baseball Games, Jordan Robertson Tait
Building A Predictive Model For Baseball Games, Jordan Robertson Tait
All Graduate Theses, Dissertations, and Other Capstone Projects
In this paper, we will discuss a method of building a predictive model for Major League Baseball Games. We detail the reasoning for pursuing the proposed predictive model in terms of social popularity and the complexity of analyzing individual variables. We apply a coarse-grain outlook inspired by Simon Dedeos' work on Human Social Systems, in particular the open source website Wikipedia [2] by attempting to quantify the influence of winning and losing streaks instead of analyzing individual performance variables. We will discuss initial findings of data collected from the LA Dodgers and Colorado Rockies and apply further statistical analysis to …
Creating A User Satisfaction Index From A Parsimonious Survey Instrument, Brian Barthel
Creating A User Satisfaction Index From A Parsimonious Survey Instrument, Brian Barthel
All Graduate Theses, Dissertations, and Other Capstone Projects
In this paper we present a comprehensive method for creating a user satisfaction index using a survey instrument. First we construct a parsimonious survey instrument, using the PageRank Centrality, to measure attributes of user satisfaction. Then confirmatory factor analysis is applied to extract ``weights'' on the questions that are used in a linear model of computing the user satisfaction index. Throughout the paper an analysis of an existing data set is implemented to illustrate the proposed method. In addition the validity of the confirmatory factor model is tested using bootstrap sampling.
A Comparison Of Smale Spaces And Laminations Via Inverse Limits, Rebecca Elizabeth Targove
A Comparison Of Smale Spaces And Laminations Via Inverse Limits, Rebecca Elizabeth Targove
All Graduate Theses, Dissertations, and Other Capstone Projects
Inverse limits began as a purely topological concept, but have since been applied to areas such as dynamical systems and manifold theory. R.F. Williams related inverse limits to dynamical systems by presenting a construction and realization result relating expanding attractors to inverse limits of branched manifolds. Wieler then adapted these results for Smale Spaces with totally disconnected local stable sets. Rojo used tiling space results to relate inverse limits of branched manifolds to codimension zero laminations. This paper examines the results of Wieler and Rojo and shows that they are analogous.
Spring-Block Models Of Earthquake Dynamics, Ashley E. Mccall
Spring-Block Models Of Earthquake Dynamics, Ashley E. Mccall
All Graduate Theses, Dissertations, and Other Capstone Projects
In this paper, the dynamics of spring-block models are studied. A brief overview of the history of spring-block models relating to earthquakes is presented, along with the development of friction laws. Several mathematical topics relating to dynamical systems are also discussed. We consider two spring-block models; one with Dieterich-Ruina rate and state dependent friction and another with a modified Dieterich-Ruina style friction. For each system, the qualitative behavior and numerical solutions are presented. In the first case, we find that the system undergoes a Hopf bifurcation from a stationary solution to a periodic orbit, and eventually transitions to chaos. In …
A Duality Theory For The Algebraic Invariants Of Substitution Tiling Spaces, Jeffrey Myers Ford
A Duality Theory For The Algebraic Invariants Of Substitution Tiling Spaces, Jeffrey Myers Ford
All Graduate Theses, Dissertations, and Other Capstone Projects
We present here a method for computing the homology of a substitution tiling space. There is a well established cohomology theory that uses simple matrix computations to determine if two tiling spaces are dierent. We will show how to compute Putnam's homology groups for these spaces using simple linear algebra. We construct a Markov Partition based on the substitution rules, and exploit the properties of this partition as a shift of finite type to construct algebraic invariants for the tiling space. These invariants form a chain complex, of which we can compute the homology. In our examples we will demonstrate …
Class Discovery And Prediction Of Tumor With Microarray Data, Bo Liu
Class Discovery And Prediction Of Tumor With Microarray Data, Bo Liu
All Graduate Theses, Dissertations, and Other Capstone Projects
Current microarray technology is able take a single tissue sample to construct an Affymetrix oglionucleotide array containing (estimated) expression levels of thousands of different genes for that tissue. The objective is to develop a more systematic approach to cancer classification based on Affymetrix oglionucleotide microarrays. For this purpose, I studied published colon cancer microarray data. Colon cancer, with 655,000 deaths worldwide per year, has become the fourth most common form of cancer in the United States and the third leading cause of cancer - related death in the Western world. This research has been focuses in two areas: class discovery, …
Determining A Patient Recovery From A Total Knee Replacement Using Fuzzy Logic And Active Databases, Robert Azarbod
Determining A Patient Recovery From A Total Knee Replacement Using Fuzzy Logic And Active Databases, Robert Azarbod
All Graduate Theses, Dissertations, and Other Capstone Projects
The purpose of the knowledge-based system is to predict the rehabilitation timeline of a patient in physical therapy for a total knee replacement. All patients have various attributes that contribute to their rehabilitation rate such as: weight, gender, smoking habit, medications, physical ability, or other medical problems. A combination of any one or several of these attributes will affect the recovery process. The proposed FRTP (Fuzzy Rehabilitation Timeline Predictor) is a fuzzy data mining model that can predict the recovery length of a patient in physical therapy for a total knee replacement and provide feedback to experts for revision of …
Employing The Spectral Collocation Method In The Modeling Of Laminar Tube Flow Dynamics, Corey Michael Thibeault
Employing The Spectral Collocation Method In The Modeling Of Laminar Tube Flow Dynamics, Corey Michael Thibeault
All Graduate Theses, Dissertations, and Other Capstone Projects
The spectral collocation method is a numerical approximation technique that seeks the solution of a differential equation using a finite series of infinitely differentiable basis functions. This inherently global technique enjoys an exponential rate of convergence and has proven to be extremely effective in computational fluid dynamics. This paper presents a basic review of the spectral collocation method. The derivation is driven with an example of the approximation to the solution of a 1D Helmholtz equation. A Matlab code modeling two fluid dynamics problems is then given. First, the classic two-dimensional Graetz problem is simulated and compared to an analytical …