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Articles 301 - 330 of 370
Full-Text Articles in Mathematics
Finding Edge And Vertex Induced Cycles Within Circulants., Trina Marcella Wooten
Finding Edge And Vertex Induced Cycles Within Circulants., Trina Marcella Wooten
Electronic Theses and Dissertations
Let H be a graph. G is a subgraph of H if V (G) ⊆ V (H) and E(G) ⊆ E(H). The subgraphs of H can be used to determine whether H is planar, a line graph, and to give information about the chromatic number. In a recent work by Beeler and Jamison [3], it was shown that it is difficult to obtain an automorphic decomposition of a triangle-free graph. As many of their examples involve circulant graphs, it is of particular interest to find triangle-free subgraphs within circulants. As …
On The Attainability Of Upper Bounds For The Circular Chromatic Number Of K4-Minor-Free Graphs., Tracy Lance Holt
On The Attainability Of Upper Bounds For The Circular Chromatic Number Of K4-Minor-Free Graphs., Tracy Lance Holt
Electronic Theses and Dissertations
Let G be a graph. For k ≥ d ≥ 1, a k/d -coloring of G is a coloring c of vertices of G with colors 0, 1, 2, . . ., k - 1, such that d ≤ | c(x) - c(y) | ≤ k - d, whenever xy is an edge of G. We say that the circular chromatic number of G, denoted χc(G), is equal to the smallest k/d where a k/d -coloring exists. In [6], Pan and …
Solitary Wave Families In Two Non-Integrable Models Using Reversible Systems Theory, Jonathan Leto
Solitary Wave Families In Two Non-Integrable Models Using Reversible Systems Theory, Jonathan Leto
Electronic Theses and Dissertations
In this thesis, we apply a recently developed technique to comprehensively categorize all possible families of solitary wave solutions in two models of topical interest. The models considered are: a) the Generalized Pochhammer-Chree Equations, which govern the propagation of longitudinal waves in elastic rods, and b) a generalized microstructure PDE. Limited analytic results exist for the occurrence of one family of solitary wave solutions for each of these equations. Since, as mentioned above, solitary wave solutions often play a central role in the long-time evolution of an initial disturbance, we consider such solutions of both models here (via the normal …
Integrability Of A Singularly Perturbed Model Describing Gravity Water Waves On A Surface Of Finite Depth, Steven Little
Integrability Of A Singularly Perturbed Model Describing Gravity Water Waves On A Surface Of Finite Depth, Steven Little
Electronic Theses and Dissertations
Our work is closely connected with the problem of splitting of separatrices (breaking of homoclinic orbits) in a singularly perturbed model describing gravity water waves on a surface of finite depth. The singularly perturbed model is a family of singularly perturbed fourth-order nonlinear ordinary differential equations, parametrized by an external parameter (in addition to the small parameter of the perturbations). It is known that in general separatrices will not survive a singular perturbation. However, it was proven by Tovbis and Pelinovsky that there is a discrete set of exceptional values of the external parameter for which separatrices do survive the …
Lattice-Valued Convergence: Quotient Maps, Hatim Boustique
Lattice-Valued Convergence: Quotient Maps, Hatim Boustique
Electronic Theses and Dissertations
The introduction of fuzzy sets by Zadeh has created new research directions in many fields of mathematics. Fuzzy set theory was originally restricted to the lattice , but the thrust of more recent research has pertained to general lattices. The present work is primarily focused on the theory of lattice-valued convergence spaces; the category of lattice-valued convergence spaces has been shown to possess the following desirable categorical properties: topological, cartesian-closed, and extensional. Properties of quotient maps between objects in this category are investigated in this work; in particular, one of our principal results shows that quotient maps are productive under …
Modeling Transmission Dynamics Of Tuberculosis Including Various Latent Periods, Tracy Atkins
Modeling Transmission Dynamics Of Tuberculosis Including Various Latent Periods, Tracy Atkins
Electronic Theses and Dissertations
The systems of equations created by Blower et al. (1995) and Jia et al. (2007) designed to model the dynamics of Tuberculosis are solved using the computer software SIMULINK. The results are first employed to examine the intrinsic transmission dynamics of the disease through two models developed by Blower et al. (1995). The "simple transmission model" was used primarily to give insight to the behavior of the susceptible, latent, and infectious groups of individuals. Then, we consider a more detailed transmission model which includes several additional factors. This model captures the dynamics of not only the susceptible, latent and infectious …
Approximating The Spectral Width Of Irradiance Fluctuations With Quasi-Frequency, Andrew Reel
Approximating The Spectral Width Of Irradiance Fluctuations With Quasi-Frequency, Andrew Reel
Electronic Theses and Dissertations
Under weak turbulence theory, we will use the random thin phase screen model and the Kolmogorov power-law spectrum to derive approximate models for the scintillation index, covariance function of irradiance fluctuations, and temporal spectrum of irradiance fluctuations for collimated beams. In addition, we will provide an expression for the quasi-frequency of a collimated beam and investigate the relationship between the quasi-frequency and the maximum width of the normalized temporal spectrum of irradiance for a collimated beam.
Pseudoquotients: Construction, Applications, And Their Fourier Transform, Mehrdad Khosravi
Pseudoquotients: Construction, Applications, And Their Fourier Transform, Mehrdad Khosravi
Electronic Theses and Dissertations
A space of pseudoquotients can be described as a space of either single term quotients (the injective case) or the quotient of sequences (the non-injective case) where the parent sets for the numerator and the denominator satisfy particular conditions. The first part of this project is concerned with the minimal of conditions required to have a well-defined set of pseudoquotients. We continue by adding more structure to our sets and discuss the effect on the resultant pseudoquotient. Pseudoquotients can be thought of as extensions of the parent set for the numerator since they include a natural embedding of that set. …
Degree Of Aproximation Of Hölder Continuous Functions, Benjamin Landon
Degree Of Aproximation Of Hölder Continuous Functions, Benjamin Landon
Electronic Theses and Dissertations
Pratima Sadangi in a Ph.D. thesis submitted to Utkal University proved results on degree of approximation of functions by operators associated with their Fourier series. In this dissertation, we consider degree of approximation of functions in Hα,ρ by different operators. In Chapter 1 we mention basic definitions needed for our work. In Chapter 2 we discuss different methods of summation. In Chapter 3 we define the Hα,ρ metric and present the degree of approximation problem relating to Fourier series and conjugate series of functions in the Hα,ρ metric using Karamata (Κλ) means. In Chapter 4 we present the degree of …
A Numerical Analysis Approach For Estimating The Minimum Traveling Wave Speed For An Autocatalytic Reaction, Erika Blanken
A Numerical Analysis Approach For Estimating The Minimum Traveling Wave Speed For An Autocatalytic Reaction, Erika Blanken
Electronic Theses and Dissertations
This thesis studies the traveling wavefront created by the autocatalytic cubic chemical reaction A + 2B → 3B involving two chemical species A and B, where A is the reactant and B is the auto-catalyst. The diffusion coefficients for A and B are given by DA and DB. These coefficients differ as a result of the chemical species having different size and/or weight. Theoretical results show there exist bounds, v* and v*, depending on DB/DA, where for speeds v ≥ v*, a traveling wave solution exists, while for speeds v < v*, a solution does not exist. Moreover, if DB ≤ DA, and v* and v* are similar to one another and in the order of DB/DA when it is small. On the other hand, when DA ≤ DB there exists a minimum speed vmin, such that there is a traveling wave solution if the speed v > vmin. The determination of vmin is very important in determining …
Fractal Interpolation, Gayatri Ramesh
Fractal Interpolation, Gayatri Ramesh
Electronic Theses and Dissertations
This thesis is devoted to a study about Fractals and Fractal Polynomial Interpolation. Fractal Interpolation is a great topic with many interesting applications, some of which are used in everyday lives such as television, camera, and radio. The thesis is comprised of eight chapters. Chapter one contains a brief introduction and a historical account of fractals. Chapter two is about polynomial interpolation processes such as Newton s, Hermite, and Lagrange. Chapter three focuses on iterated function systems. In this chapter I report results contained in Barnsley s paper, Fractal Functions and Interpolation. I also mention results on iterated function system …
Analysis Of Kolmogorov's Superposition Theorem And Its Implementation In Applications With Low And High Dimensional Data., Donald Bryant
Analysis Of Kolmogorov's Superposition Theorem And Its Implementation In Applications With Low And High Dimensional Data., Donald Bryant
Electronic Theses and Dissertations
In this dissertation, we analyze Kolmogorov's superposition theorem for high dimensions. Our main goal is to explore and demonstrate the feasibility of an accurate implementation of Kolmogorov's theorem. First, based on Lorentz's ideas, we provide a thorough discussion on the proof and its numerical implementation of the theorem in dimension two. We present computational experiments which prove the feasibility of the theorem in applications of low dimensions (namely, dimensions two and three). Next, we present high dimensional extensions with complete and detailed proofs and provide the implementation that aims at applications with high dimensionality. The amalgamation of these ideas is …
Comparing Assessment Methods As Predictors Of Student Learning In Undergraduate Mathematics, Nichole Shorter
Comparing Assessment Methods As Predictors Of Student Learning In Undergraduate Mathematics, Nichole Shorter
Electronic Theses and Dissertations
This experiment was designed to determine which assessment method: continuous assessment (in the form of daily in-class quizzes), cumulative assessment (in the form of online homework), or project-based learning, best predicts student learning (dependent upon posttest grades) in an undergraduate mathematics course. Participants included 117 university-level undergraduate freshmen enrolled in a course titled "Mathematics for Calculus". Initially, a multiple regression model was formulated to model the relationship between the predictor variables (the continuous assessment, cumulative assessment, and project scores) versus the outcome variable (the posttest scores). However, due to the possibility of multicollinearity present between the cumulative assessment predictor variable …
Decomposition, Packings And Coverings Of Complete Digraphs With A Transitive-Triple And A Pendant Arc., Janice Gail Lewenczuk
Decomposition, Packings And Coverings Of Complete Digraphs With A Transitive-Triple And A Pendant Arc., Janice Gail Lewenczuk
Electronic Theses and Dissertations
In the study of design theory, there are eight orientations of the complete graph on three vertices with a pendant edge, K3∪{e}. Two of these are the 3-circuit with a pendant arc and the other six are transitive triples with a pendant arc. Necessary and sufficient conditions are given for decompositions, packings and coverings of the complete digraph with each of the six transitive triples with a pendant arc.
Packings And Coverings Of Various Complete Digraphs With The Orientations Of A 4-Cycle., Melody Elaine Cooper
Packings And Coverings Of Various Complete Digraphs With The Orientations Of A 4-Cycle., Melody Elaine Cooper
Electronic Theses and Dissertations
There are four orientations of cycles on four vertices. Necessary and sufficient conditions are given for covering complete directed digraphs Dv, packing and covering complete bipartite digraphs, Dm,n, and packing and covering the complete digraph on v vertices with hole of size w, D(v,w), with three of the orientations of a 4-cycle, including C4, X, and Y.
Chromatic Number Of The Alphabet Overlap Graph, G(2, K , K-2)., Jerry Brent Farley
Chromatic Number Of The Alphabet Overlap Graph, G(2, K , K-2)., Jerry Brent Farley
Electronic Theses and Dissertations
A graph G(a, k, t) is called an alphabet overlap graph where a, k, and t are positive integers such that 0 ≤ t < k and the vertex set V of G is defined as, V = {v : v = (v1v2...vk); vi ∊ {1, 2, ..., a}, (1 ≤ i ≤ k)}. That is, each vertex, v, is a word of length k over an alphabet of size a. There exists an edge between two vertices u, …
Decompositions, Packings, And Coverings Of Complete Directed Gaphs With A 3-Circuit And A Pendent Arc., Chrys Gwellem
Decompositions, Packings, And Coverings Of Complete Directed Gaphs With A 3-Circuit And A Pendent Arc., Chrys Gwellem
Electronic Theses and Dissertations
In the study of Graph theory, there are eight orientations of the complete graph on three vertices with a pendant edge, K3 ∪ {e}. Two of these are the 3-circuit with a pendant arc and the other six are transitive triples with a pendant arc. Necessary and sufficient conditions are given for decompositions, packings, and coverings of the complete digraph with the two 3-circuit with a pendant arc orientations.
Tricyclic Steiner Triple Systems With 1-Rotational Subsystems., Quan Duc Tran
Tricyclic Steiner Triple Systems With 1-Rotational Subsystems., Quan Duc Tran
Electronic Theses and Dissertations
A Steiner triple system of order v, denoted STS(v), is said to be tricyclic if it admits an automorphism whose disjoint cyclic decomposition consists of three cycles. In this thesis we give necessary and sufficient conditions for the existence of a tricyclic STS(v) when one of the cycles is of length one. In this case, the STS(v) will contain a subsystem which admits an automorphism consisting of a fixed point and a single cycle. The subsystem is said to be 1-rotational.
Alliance Partitions In Graphs., Jason Lachniet
Alliance Partitions In Graphs., Jason Lachniet
Electronic Theses and Dissertations
For a graph G=(V,E), a nonempty subset S contained in V is called a defensive alliance if for each v in S, there are at least as many vertices from the closed neighborhood of v in S as in V-S. If there are strictly more vertices from the closed neighborhood of v in S as in V-S, then S is a strong defensive alliance. A (strong) defensive alliance is called global if it is also a dominating set of G. The alliance partition number (respectively, strong …
Efficient Inversion Of The Cone Beam Transform For A General Class Of Curves, Mikhail Kapralov
Efficient Inversion Of The Cone Beam Transform For A General Class Of Curves, Mikhail Kapralov
Electronic Theses and Dissertations
We extend an efficient cone beam transform inversion formula, proposed earlier for helices, to a general class of curves. The conditions that describe the class are very natural. Curves C are smooth, without self-intersections, have positive curvature and torsion, do not bend too much in a certain sense, and do not admit lines which are tangent to C at one point and intersect C at another point. A domain U is found where reconstruction is possible with a filtered backprojection type algorithm. Results of numerical experiments demonstrate very good image quality. The algorithm developed is useful for image reconstruction in …
Dissipative Solitons In The Cubic-Quintic Complex Ginzburg-Landau Equation:Bifurcations And Spatiotemporal Structure, Ciprian Mancas
Dissipative Solitons In The Cubic-Quintic Complex Ginzburg-Landau Equation:Bifurcations And Spatiotemporal Structure, Ciprian Mancas
Electronic Theses and Dissertations
Comprehensive numerical simulations (reviewed in Dissipative Solitons, Akhmediev and Ankiewicz (Eds.), Springer, Berlin, 2005) of pulse solutions of the cubic--quintic Ginzburg--Landau equation (CGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal various intriguing and entirely novel classes of solutions. In particular, there are five new classes of pulse or solitary waves solutions, viz. pulsating, creeping, snake, erupting, and chaotic solitons. In contrast to the regular solitary waves investigated in numerous integrable and non--integrable systems over the last three decades, these dissipative solitons are not stationary in time. Rather, they are …
An Examination Of The Effectiveness Of The Adomian Decomposition Method In Fluid Dynamic Applications, Sonia Holmquist
An Examination Of The Effectiveness Of The Adomian Decomposition Method In Fluid Dynamic Applications, Sonia Holmquist
Electronic Theses and Dissertations
Since its introduction in the 1980's, the Adomian Decomposition Method (ADM) has proven to be an efficient and reliable method for solving many types of problems. Originally developed to solve nonlinear functional equations, the ADM has since been used for a wide range of equation types (like boundary value problems, integral equations, equations arising in flow of incompressible and compressible fluids etc...). This work is devoted to an evaluation of the effectiveness of this method when used for fluid dynamic applications. In particular, the ADM has been applied to the Blasius equation, the Falkner-Skan equation, and the Orr-Sommerfeld equation. This …
Categorical Properties Of Lattice-Valued Convergence Spaces, Paul Flores
Categorical Properties Of Lattice-Valued Convergence Spaces, Paul Flores
Electronic Theses and Dissertations
This work can be roughly divided into two parts. Initially, it may be considered a continuation of the very interesting research on the topic of Lattice-Valued Convergence Spaces given by Jager [2001, 2005]. The alternate axioms presented here seem to lead to theorems having proofs more closely related to standard arguments used in Convergence Space theory when the Lattice is L = f0; 1g:Various Subcategories are investigated. One such subconstruct is shown to be isomorphic to the category of Lattice Valued Fuzzy Convergence Spaces defined and studied by Jager [2001]. Our principal category is shown to be a topological universe …
Impulse Formulations Of The Euler Equations For Incompressible And Compressible Fluids, Victor David Pareja
Impulse Formulations Of The Euler Equations For Incompressible And Compressible Fluids, Victor David Pareja
Electronic Theses and Dissertations
The purpose of this paper is to consider the impulse formulations of the Euler equations for incompressible and compressible fluids. Different gauges are considered. In particular, the Kuz'min gauge provides an interesting case as it allows the fluid impulse velocity to describe the evolution of material surface elements. This result affords interesting physical interpretations of the Kuz'min invariant. Some exact solutions in the impulse formulation are studied. Finally, generalizations to compressible fluids are considered as an extension of these results. The arrangement of the paper is as follows: in the first chapter we will give a brief explanation on the …
Effect Of Inner Scale Atmospheric Spectrum Models On Scintillation In All Optical Turbulence Regimes, Kenneth Mayer
Effect Of Inner Scale Atmospheric Spectrum Models On Scintillation In All Optical Turbulence Regimes, Kenneth Mayer
Electronic Theses and Dissertations
Experimental studies have shown that a "bump" occurs in the atmospheric spectrum just prior to turbulence cell dissipation.1,3,4 In weak optical turbulence, this bump affects calculated scintillation. The purpose of this thesis was to determine if a "non-bump" atmospheric power spectrum can be used to model scintillation for plane waves and spherical waves in moderate to strong optical turbulence regimes. Scintillation expressions were developed from an "effective" von Karman spectrum using an approach similar to that used by Andrews et al.8,14,15 in developing expressions from an "effective" modified (bump) spectrum. The effective spectrum extends the Rytov approximation into all optical …
Soliton Solutions Of Nonlinear Partial Differential Equations Using Variational Approximations And Inverse Scattering Techniques, Thomas Vogel
Electronic Theses and Dissertations
Throughout the last several decades many techniques have been developed in establishing solutions to nonlinear partial differential equations (NPDE). These techniques are characterized by their limited reach in solving large classes of NPDE. This body of work will study the analysis of NPDE using two of the most ubiquitous techniques developed in the last century. In this body of work, the analysis and techniques herein are applied to unsolved physical problems in both the fields of variational approximations and inverse scattering transform. Additionally, a new technique for estimating the error of a variational approximation is established. Note that the material …
Stability And Preservation Properties Of Multisymplectic Integrators, Tomasz Wlodarczyk
Stability And Preservation Properties Of Multisymplectic Integrators, Tomasz Wlodarczyk
Electronic Theses and Dissertations
This dissertation presents results of the study on symplectic and multisymplectic numerical methods for solving linear and nonlinear Hamiltonian wave equations. The emphasis is put on the second order space and time discretizations of the linear wave, the Klein-Gordon and the sine-Gordon equations. For those equations we develop two multisymplectic (MS) integrators and compare their performance to other popular symplectic and non-symplectic numerical methods. Tools used in the linear analysis are related to the Fourier transform and consist of the dispersion relationship and the power spectrum of the numerical solution. Nonlinear analysis, in turn, is closely connected to the temporal …
Pade Approximants And One Of Its Applications, Tame-Kouontcho Fowe
Pade Approximants And One Of Its Applications, Tame-Kouontcho Fowe
Electronic Theses and Dissertations
This thesis is concerned with a brief summary of the theory of Pade approximants and one of its applications to Finance. Proofs of most of the theorems are omitted and many developments could not be mentioned due to the vastness of the field of Pade approximations. We provide reference to research papers and books that contain exhaustive treatment of the subject. This thesis is mainly divided into two parts. In the first part we derive a general expression of the Pade approximants and some of the results that will be related to the work on the second part of the …
A Mathematical Study Of Two Retroviruses, Hiv And Htlv-I, Dana Ali Baxley
A Mathematical Study Of Two Retroviruses, Hiv And Htlv-I, Dana Ali Baxley
Electronic Theses and Dissertations
In this thesis, we examine epidemiological models of two different retroviruses, which infect the human body. The two viruses under study are HIV or the human immunodefiency virus and HTLV-I, which is the human T lymphotropic virus type I. A retrovirus is a virus, which injects its RNA into the host, rather than it's DNA. We will study each of the different mathematical models for each of the viruses separately. Then we use MATLAB-SIMULINK to analyze the models by studying the reproductive numbers in each case and the disease progression by examining the graphs. In Chapter 1, we mention basic …
A Complete Characterization Of Maximal Symmetric Difference-Free Families On {1,…N}., Travis Gerarde Buck
A Complete Characterization Of Maximal Symmetric Difference-Free Families On {1,…N}., Travis Gerarde Buck
Electronic Theses and Dissertations
Prior work in the field of set theory has looked at the properties of union-free families. This thesis investigates families based on a different set operation, the symmetricc difference. It provides a complete characterization of maximal symmetric differencefree families of subsets of {1, . . . n}