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Articles 1 - 13 of 13
Full-Text Articles in Physical Sciences and Mathematics
The Application Of Category Theory And Analysis Of Receiver Operating Characteristics To Information Fusion, Steven N. Thorsen
The Application Of Category Theory And Analysis Of Receiver Operating Characteristics To Information Fusion, Steven N. Thorsen
Theses and Dissertations
Multisensor data fusion is presented in a rigorous mathematical format, with definitions consistent with the desires of the data fusion community. A model of event-state fusion is developed and described. Definitions of fusion rules and fusors are introduced, along with the functor categories of which they are objects. Defining fusors and competing fusion rules involves the use of an objective function of the researcher's choice. One such objective function, a functional on families of classification systems, and in particular, receiver operating characteristics (ROCs), is introduced. Its use as an objective function is demonstrated in that the argument that minimizes it …
Classifcation Of Conics In The Tropical Projective Plane, Amanda Ellis
Classifcation Of Conics In The Tropical Projective Plane, Amanda Ellis
Theses and Dissertations
This paper defines tropical projective space, TP^n, and the tropical general linear group TPGL(n). After discussing some simple examples of tropical polynomials and their hypersurfaces, a strategy is given for finding all conics in the tropical projective plane. The classification of conics and an analysis of the coefficient space corresponding to such conics is given.
Totally Real Galois Representations In Characteristic 2 And Arithmetic Cohomology, Heather Aurora Florence De Melo
Totally Real Galois Representations In Characteristic 2 And Arithmetic Cohomology, Heather Aurora Florence De Melo
Theses and Dissertations
The purpose of this paper is to provide new examples supporting a conjecture of Ash, Doud, and Pollack. This conjecture involves Galois representations taking Gal(Q bar/Q) to the general linear group of 3 x 3 matrices in characterisic 2, and our examples are where complex conjugation is mapped to the identity. Since this case has not yet been examined, the results of this paper are quite significant.
A Mathematical Model Of Adhesion Interactions Between Living Cells, Casey P. Johnson
A Mathematical Model Of Adhesion Interactions Between Living Cells, Casey P. Johnson
Theses and Dissertations
This thesis presents a simple force-based model of moving and interacting cells that incorporates a realistic description of cell adhesion and applies it to a system of spherical cells. In addition, several results in matrix theory are proved with the end of showing that the equations produced by the model uniquely determine the motion of the system or cells.
Maximal Surfaces In Complexes, Allen J. Dickson
Maximal Surfaces In Complexes, Allen J. Dickson
Theses and Dissertations
Cubical complexes are defined in a manner analogous to that for simplicial complexes, the chief difference being that cubical complexes are unions of cubes rather than of simplices. A very natural cubical complex to consider is the complex C(k_1,...,k_n) where k_1,...,k_n are nonnegative integers. This complex has as its underlying space [0,k_1]x...x[0,k_n] subset of R^n with vertices at all points having integer coordinates and higher dimensional cubes formed by the vertices in the natural way. The genus of a cubical complex is defined to be the maximum genus of all surfaces that are subcomplexes of the cubical complex. A formula …
An Exposition Of The Deterministic Polynomial-Time Primality Testing Algorithm Of Agrawal-Kayal-Saxena, Robert Lawrence Anderson
An Exposition Of The Deterministic Polynomial-Time Primality Testing Algorithm Of Agrawal-Kayal-Saxena, Robert Lawrence Anderson
Theses and Dissertations
I present a thorough examination of the unconditional deterministic polynomial-time algorithm for determining whether an input number is prime or composite proposed by Agrawal, Kayal and Saxena in their paper [1]. All proofs cited have been reworked with full details for the sake of completeness and readability.
Matrix Representations Of Automorphism Groups Of Free Groups, Ivan B. Andrus
Matrix Representations Of Automorphism Groups Of Free Groups, Ivan B. Andrus
Theses and Dissertations
In this thesis, we study the representation theory of the automorphism group Aut (Fn) of a free group by studying the representation theory of three finite subgroups: two symmetric groups, Sn and Sn+1, and a Coxeter group of type Bn, also known as a hyperoctahedral group. The representation theory of these subgroups is well understood in the language of Young Diagrams, and we apply this knowledge to better understand the representation theory of Aut (Fn). We also calculate irreducible representations of Aut (Fn) in low dimensions and for small n.
Statistical Properties Of Thompson's Group And Random Pseudo Manifolds, Benjamin M. Woodruff
Statistical Properties Of Thompson's Group And Random Pseudo Manifolds, Benjamin M. Woodruff
Theses and Dissertations
The first part of our work is a statistical and geometric study of properties of Thompson's Group F. We enumerate the number of elements of F which are represented by a reduced pair of n-caret trees, and give asymptotic estimates. We also discuss the effects on word length and number of carets of right multiplication by a standard generator x0 or x1. We enumerate the average number of carets along the left edge of an n-caret tree, and use an Euler transformation to make some conjectures relating to right multiplication by a generator. We describe a computer algorithm which produces …
Classifying Homotopy Types Of One-Dimensional Peano Continua, Mark H. Meilstrup
Classifying Homotopy Types Of One-Dimensional Peano Continua, Mark H. Meilstrup
Theses and Dissertations
Determining the homotopy type of one-dimensional Peano continua has been an open question of some interest. We give a complete invariant of the homotopy type of such continua, which consists of a pair of subspaces together with a relative homology group. Along the way, we describe reduced forms for one-dimensional Peano continua.
Three Pension Cost Methods Under Varying Assumptions, Linda S. Grizzle
Three Pension Cost Methods Under Varying Assumptions, Linda S. Grizzle
Theses and Dissertations
A pension plan administrator promises certain benefits in the future in exchange for labor today. In order to budget for this expense and create more security for the participant, the administrator uses a pension cost method. Each cost method assigns a portion of the future liability to the current year. This is called the normal cost. We calculate the normal cost under three cost methods using different annuity, interest and inflation assumptions. Then we make comparisons between cost methods as well as between assumption changes. The cost methods considered in this paper are the unit credit cost method, projected unit …
Explicit Computations Supporting A Generalization Of Serre's Conjecture, Brian Francis Hansen
Explicit Computations Supporting A Generalization Of Serre's Conjecture, Brian Francis Hansen
Theses and Dissertations
Serre's conjecture on the modularity of Galois representations makes a connection between two-dimensional Galois representations and modular forms. A conjecture by Ash, Doud, and Pollack generalizes Serre's to higher-dimensional Galois representations. In this paper we discuss an explicit computational example supporting the generalized claim. An ambiguity in a calculation within the example is resolved using a method of complex approximation.
The Lie Symmetries Of A Few Classes Of Harmonic Functions, Willis L. Petersen
The Lie Symmetries Of A Few Classes Of Harmonic Functions, Willis L. Petersen
Theses and Dissertations
In a differential geometry setting, we can analyze the solutions to systems of differential equations in such a way as to allow us to derive entire classes of solutions from any given solution. This process involves calculating the Lie symmetries of a system of equations and looking at the resulting transformations. In this paper we will give a general background of the theory necessary to develop the ideas of working in the jet space of a given system of equations, applying this theory to harmonic functions in the complex plane. We will consider harmonic functions in general, harmonic functions with …
Hopf Bifurcations And Horseshoes Especially Applied To The Brusselator, Steven R. Jones
Hopf Bifurcations And Horseshoes Especially Applied To The Brusselator, Steven R. Jones
Theses and Dissertations
In this paper we explore bifurcations, in particular the Hopf bifurcation. We study this especially in connection with the Brusselator, which is a model of certain chemical reaction-diffusion systems. After a thorough exploration of what a bifurcation is and what classifications there are, we give graphic representations of an occurring Hopf bifurcation in the Brusselator. When an additional forcing term is added, behavior changes dramatically. This includes the introduction of a horseshoe in the time map as well as a strange attractor in the system.