Mathematics Commons^™

Epidemiological Models For Mutating Pathogens With Temporary Immunity, Neeta Singh

Electronic Theses and Dissertations

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Significant progress has been made in understanding different scenarios for disease transmissions and behavior of epidemics in recent years. A considerable amount of work has been done in modeling the dynamics of diseases by systems of ordinary differential equations. But there are very few mathematical models that deal with the genetic mutations of a pathogen. In-fact, not much has been done to model the dynamics of mutations of pathogen explaining its effort to escape the host's immune defense system after it has infected the host. In this dissertation we develop an SIR model with variable infection age for the transmission …

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The Integral Cohomology Of The Group Of Loops, Craig Jensen, Jon Mccammond, John Meier

Mathematics Faculty Publications

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No abstract provided.

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Application Of The Empirical Likelihood Method In Proportional Hazards Model, Bin He

Electronic Theses and Dissertations

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In survival analysis, proportional hazards model is the most commonly used and the Cox model is the most popular. These models are developed to facilitate statistical analysis frequently encountered in medical research or reliability studies. In analyzing real data sets, checking the validity of the model assumptions is a key component. However, the presence of complicated types of censoring such as double censoring and partly interval-censoring in survival data makes model assessment difficult, and the existing tests for goodness-of-fit do not have direct extension to these complicated types of censored data. In this work, we use empirical likelihood (Owen, 1988) …

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Effects Of Atmospheric Turbulence On The Propagation Of Flattened Gaussian Optical Beams, Doris Cowan

Electronic Theses and Dissertations

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In an attempt to mitigate the effects of the atmosphere on the coherence of an optical (laser) beam, interest has recently been shown in changing the beam shape to determine if a different power distribution at the transmitter will reduce the effects of the random fluctuations in the refractive index. Here, a model is developed for the field of a flattened Gaussian beam as it propagates through atmospheric turbulence, and the resulting effects upon the scintillation of the beam and upon beam wander are determined. A comparison of these results is made with the like effects on a standard TEM00 …

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Intrinsic Linking And Knotting Of Graphs In Arbitrary 3–Manifolds, Erica Flapan, Hugh Howards, Don Lawrence, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

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We prove that a graph is intrinsically linked in an arbitrary 3–manifold MM if and only if it is intrinsically linked in S³. Also, assuming the Poincaré Conjecture, we prove that a graph is intrinsically knotted in M if and only if it is intrinsically knotted in S³.

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Intersection Graphs For String Links, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

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We extend the notion of intersection graphs for knots in the theory of finite type invariants to string links. We use our definition to develop weight systems for string links via the adjacency matrix of the intersection graph, and show that these weight systems are related to the weight systems induced by the Conway and Homfly polynomials.

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Chord Diagrams And Gauss Codes For Graphs, Thomas Fleming, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

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Chord diagrams on circles and their intersection graphs (also known as circle graphs) have been intensively studied, and have many applications to the study of knots and knot invariants, among others. However, chord diagrams on more general graphs have not been studied, and are potentially equally valuable in the study of spatial graphs. We will define chord diagrams for planar embeddings of planar graphs and their intersection graphs, and prove some basic results. Then, as an application, we will introduce Gauss codes for immersions of graphs in the plane and give algorithms to determine whether a particular crossing sequence is …

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Tree Diagrams For String Links, Blake Mellor

Mathematics, Statistics and Data Science Faculty Works

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In previous work, the author defined the intersection graph of a chord diagram associated with string links (as in the theory of finite type invariants). In this paper, we classify the trees which can be obtained as intersection graphs of string link diagrams.

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Linked Exact Triples Of Triangulated Categories And A Calculus Of T-Structures, Michael Berg

Mathematics, Statistics and Data Science Faculty Works

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We introduce a new formalism of exact triples of triangulated categories arranged in certain types of diagrams. We prove that these arrangements are well-behaved relative to the process of gluing and ungluing t-structures defined on the indicated categories and we connect our con. structs to· a problem (from number theory) involving derived categories. We also briefly address a possible connection with a result of R. Thomason.

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The Formal Laplace-Borel Transform Of Fliess Operators And The Composition Product, Yaqin Li, W. Steven Gray

Electrical & Computer Engineering Faculty Publications

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The formal Laplace-Borel transform of an analytic integral operator, known as a Fliess operator, is defined and developed. Then, in conjunction with the composition product over formal power series, the formal Laplace-Borel transform is shown to provide an isomorphism between the semigroup of all Fliess operators under operator composition and the semigroup of all locally convergent formal power series under the composition product. Finally, the formal Laplace-Borel transform is applied in a systems theory setting to explicitly derive the relationship between the formal Laplace transform of the input and output functions of a Fliess operator. This gives a compact interpretation …

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Eigenvalue Comparisons For Boundary Value Problems Of The Discrete Beam Equation, Jun Ji, Bo Yang

Faculty Articles

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We study the behavior of all eigenvalues for boundary value problems of fourth-order difference equations Delta(4)yi = lambda a(i+2)y(i+2), - 1= b(j), 1

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The Ground Axiom, Jonas Reitz

Dissertations, Theses, and Capstone Projects

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A new axiom is proposed, the Ground Axiom, asserting that the universe is not a nontrivial set-forcing extension of any inner model. The Ground Axiom is first-order expressible, and any model of ZFC has a class-forcing extension which satisfies it. The Ground Axiom is independent of many well-known set-theoretic assertions including the Generalized Continuum Hypothesis, the assertion V=HOD that every set is ordinal definable, and the existence of measurable and supercompact cardinals. The related Bedrock Axiom, asserting that the universe is a set-forcing extension of a model satisfying the Ground Axiom, is also first-order expressible, and its negation is consistent. …

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The Kronecker Product, Bobbi Jo Broxson

UNF Graduate Theses and Dissertations

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This paper presents a detailed discussion of the Kronecker product of matrices. It begins with the definition and some basic properties of the Kronecker product. Statements will be proven that reveal information concerning the eigenvalues, singular values, rank, trace, and determinant of the Kronecker product of two matrices. The Kronecker product will then be employed to solve linear matrix equations. An investigation of the commutativity of the Kronecker product will be carried out using permutation matrices. The Jordan - Canonical form of a Kronecker product will be examined. Variations such as the Kronecker sum and generalized Kronecker product will be …

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[Introduction To] The Cauchy Transform, William T. Ross, Joseph A. Cima, Alec L. Matheson

Bookshelf

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The Cauchy transform of a measure on the circle is a subject of both classical and current interest with a sizable literature. This book is a thorough, well-documented, and readable survey of this literature and includes full proofs of the main results of the subject. This book also covers more recent perturbation theory as covered by Clark, Poltoratski, and Aleksandrov and contains an in-depth treatment of Clark measures.

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A Mathematical Study Of Malaria Models Of Ross And Ngwa, William Plemmons

Electronic Theses and Dissertations

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Malaria is a vector borne disease that has been plaguing mankind since before recorded history. The disease is carried by three subspecies of mosquitoes Anopheles gambiae, Anopheles arabiensis and Anopheles funestu. These mosquitoes carry one of four type of Plasmodium specifically: P. falciparum, P. vivax, P. malariae or P. ovale. The disease is a killer; the World Health Organization (WHO) estimates that about 40% of the world's total populations live in areas where malaria is an endemic disease and as global warming occurs, endemic malaria will spread to more areas. The malaria parasite kills a child every 30 seconds. In …

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Monodomain Dynamics For Rigid Rod And Platelet Suspensions In Strongly Coupled Coplanar Linear Flow And Magnetic Fields. Ii. Kinetic Theory, M. Gregory Forest, Sarthok Sircar, Qi Wang, Ruhai Zhou

Mathematics & Statistics Faculty Publications

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We establish reciprocity relations of the Doi-Hess kinetic theory for rigid rod macromolecular suspensions governed by the strong coupling among an excluded volume potential, linear flow, and a magnetic field. The relation provides a reduction of the flow and field driven Smoluchowski equation: from five parameters for coplanar linear flows and magnetic field, to two field parameters. The reduced model distinguishes flows with a rotational component, which map to simple shear (with rate parameter) subject to a transverse magnetic field (with strength parameter), and irrotational flows, for which the reduced model consists of a triaxial extensional flow (with two extensional …

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Prediction In The Panel Data Model With Spatial Correlation: The Case Of Liquor, Badi H. Baltagi, Dong Li

Center for Policy Research

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This paper considers the problem of prediction in a panel data regression model with spatial autocorrelation in the context of a simple demand equation for liquor. This is based on a panel of 43 states over the period 1965-1994. The spatial autocorrelation due to neighboring states and the individual heterogeneity across states is taken explicitly into account. We compare the performance of several predictors of the states demand for liquor for one year and five years ahead. The estimators whose predictions are compared include OLS, fixed effects ignoring spatial correlation, fixed effects with spatial correlation, random effects GLS estimator ignoring …

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Testing For Cointegrating Rank Via Model Selection: Evidence From 165 Data Sets, Badi H. Baltagi, Zijun Wang

Center for Policy Research

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The model selection approach has been proposed as an alternative to the popular tests for cointegration such as the residual-based ADF test and the system-based trace test. Using information criteria, we conduct cointegration tests on 165 data sets used in published studies. The empirical results demonstrate the usefulness of the model selection approach for applied researchers.

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On The Existence Of Infinitely Many Closed Geodesics On Orbifolds Of Revolution, Joseph Borzellino, Christopher R. Jordan-Squire, Gregory C. Petrics, D. Mark Sullivan

Mathematics

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Using the theory of geodesics on surfaces of revolution, we introduce the period function. We use this as our main tool in showing that any two-dimensional orbifold of revolution homeomorphic to S2 must contain an infinite number of geometrically distinct closed geodesics. Since any such orbifold of revolution can be regarded as a topological two-sphere with metric singularities, we will have extended Bangert’s theorem on the existence of infinitely many closed geodesics on any smooth Riemannian two-sphere. In addition, we give an example of a two-sphere cone-manifold of revolution which possesses a single closed geodesic, thus showing that Bangert’s result …

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A Brief Study Of Real-Valued Continuous Functions On Various Spaces, Dusty Ross

Honors Program Theses

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The intent of this study is to find sufficient criteria on a space X in order to bound the cardinality of the real-valued continuous functions on X by 2w. The desired result is known for X separable and for X first-countable, Hausdorff, and either Lindelof or ccc, but these are all very strong properties on a space. It is the goal of this study to find properties that are weaker, yet sufficient in bounding .the number of real-valued continuous functions on a space by the size of the continuum.

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Mathematically Modeling The Effects Of Counting Factor (Cf) In Dictyostelium Discoideum, J. C. Dallon, W. Jang, R. H. Gomer

Faculty Publications

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Size regulation is a crucial feature in many biological systems, with misregulation leading to dysplasia or hyperplasia. The recent discovery of counting factor (CF) in Dictyostelium discoideum will lead to a greater understanding of how the system regulates the size of a group of cells. In this paper we mathematically model the known effects of CF using two different models: a cellular automata model and a discrete continuum hybrid model. With the use of these models we are able to understand how modulation of adhesion and motile forces by CF can facilitate stream breakup. In addition, the modelling suggests a …

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On The Use Of Gaussian Filter Functions For Adaptive Optics, Merfit Assad

Electronic Theses and Dissertations

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For adaptive optic systems, the use of aperture filter functions calculated using various Zernike modes can be useful in removing lower-order aberrations caused by atmospheric turbulence. Traditionally, these filter functions are calculated using the step function depicting a hard aperture that introduces integrals that are sometimes difficult to integrate and must be done numerically. The Gaussian method can be used in place of the conventional method for calculating the aperture filter functions. Evaluation of the Gaussian approximation for modeling a finite receiver aperture can be made by comparison of reduction in phase variance with results achieved using the conventional method. …

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Matrix-J-Unitary Non-Commutative Rational Formal Power Series, Daniel Alpay, D. S. Kalyuzhnyi-Verbovetzkii

Mathematics, Physics, and Computer Science Faculty Articles and Research

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Formal power series in N non-commuting indeterminates can be considered as a counterpart of functions of one variable holomorphic at 0, and some of their properties are described in terms of coefficients. However, really fruitful analysis begins when one considers for them evaluations on N-tuples of n × n matrices (with n = 1, 2, . . .) or operators on an infinite-dimensional separable Hilbert space. Moreover, such evaluations appear in control, optimization and stabilization problems of modern system engineering.

In this paper, a theory of realization and minimal factorization of rational matrix-valued functions which are J-unitary on the imaginary …

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Melting And Solidification Study Of As-Deposited And Recrystallized Bi Thin Films, M. K. Zayed, H. E. Elsayed-Ali

Electrical & Computer Engineering Faculty Publications

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Melting and solidification of as-deposited and recrystallized Bi crystallites, deposited on highly oriented 002-graphite at 423 K, were studied using reflection high-energy electron diffraction (RHEED). Films with mean thickness between 1.5 and 33 ML (monolayers) were studied. Ex situ atomic force microscopy was used to study the morphology and the size distribution of the formed nanocrystals. The as-deposited films grew in the form of three-dimensional crystallites with different shapes and sizes, while those recrystallized from the melt were formed in nearly similar shapes but different sizes. The change in the RHEED pattern with temperature was used to probe the melting …

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