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Articles 1 - 12 of 12
Full-Text Articles in Physical Sciences and Mathematics
Consistency Properties For Growth Model Parameters Under An Infill Asymptotics Domain, David T. Mills
Consistency Properties For Growth Model Parameters Under An Infill Asymptotics Domain, David T. Mills
Theses and Dissertations
Growth curves are used to model various processes, and are often seen in biological and agricultural studies. Underlying assumptions of many studies are that the process may be sampled forever, and that samples are statistically independent. We instead consider the case where sampling occurs in a finite domain, so that increased sampling forces samples closer together, and also assume a distance-based covariance function. We first prove that, under certain conditions, the mean parameter of a fixed-mean model cannot be estimated within a finite domain. We then numerically consider more complex growth curves, examining sample sizes, sample spacing, and quality of …
A Toolkit For The Construction And Understanding Of 3-Manifolds, Lee R. Lambert
A Toolkit For The Construction And Understanding Of 3-Manifolds, Lee R. Lambert
Theses and Dissertations
Since our world is experienced locally in three-dimensional space, students of mathematics struggle to visualize and understand objects which do not fit into three-dimensional space. 3-manifolds are locally three-dimensional, but do not fit into 3-dimensional space and can be very complicated. Twist and bitwist are simple constructions that provide an easy path to both creating and understanding closed, orientable 3-manifolds. By starting with simple face pairings on a 3-ball, a myriad of 3-manifolds can be easily constructed. In fact, all closed, connected, orientable 3-manifolds can be developed in this manner. We call this work a tool kit to emphasize the …
The Minimum Rank, Inverse Inertia, And Inverse Eigenvalue Problems For Graphs, Mark Condie Kempton
The Minimum Rank, Inverse Inertia, And Inverse Eigenvalue Problems For Graphs, Mark Condie Kempton
Theses and Dissertations
For a graph G we define S(G) to be the set of all real symmetric n by n matrices whose off-diagonal zero/nonzero pattern is described by G. We show how to compute the minimum rank of all matrices in S(G) for a class of graphs called outerplanar graphs. In addition, we obtain results on the possible eigenvalues and possible inertias of matrices in S(G) for certain classes of graph G. We also obtain results concerning the relationship between two graph parameters, the zero forcing number and the path cover number, related to the minimum rank problem.
Wild Low-Dimensional Topology And Dynamics, Mark H. Meilstrup
Wild Low-Dimensional Topology And Dynamics, Mark H. Meilstrup
Theses and Dissertations
In this dissertation we discuss various results for spaces that are wild, i.e. not locally simply connected. We first discuss periodic properties of maps from a given space to itself, similar to Sharkovskii's Theorem for interval maps. We study many non-locally connected spaces and show that some have periodic structure either identical or related to Sharkovskii's result, while others have essentially no restrictions on the periodic structure. We next consider embeddings of solenoids together with their complements in three space. We differentiate solenoid complements via both algebraic and geometric means, and show that every solenoid has an unknotted embedding …
A Lift Of Cohomology Eigenclasses Of Hecke Operators, Brian Francis Hansen
A Lift Of Cohomology Eigenclasses Of Hecke Operators, Brian Francis Hansen
Theses and Dissertations
A considerable amount of evidence has shown that for every prime p &neq; N observed, a simultaneous eigenvector v_0 of Hecke operators T(l,i), i=1,2, in H^3(Γ_0(N),F(0,0,0)) has a “lift” v in H^3(Γ_0(N),F(p−1,0,0)) — i.e., a simultaneous eigenvector v of Hecke operators having the same system of eigenvalues that v_0 has. For each prime p>3 and N=11 and 17, we construct a vector v that is in the cohomology group H^3(Γ_0(N),F(p−1,0,0)). This is the first construction of an element of infinitely many different cohomology groups, other than modulo p reductions of characteristic zero objects. We proceed to show that v …
Applications Of Descriptive Set Theory In Homotopy Theory, Samuel M. Corson
Applications Of Descriptive Set Theory In Homotopy Theory, Samuel M. Corson
Theses and Dissertations
This thesis presents new theorems in homotopy theory, in particular it generalizes a theorem of Saharon Shelah. We employ a technique used by Janusz Pawlikowski to show that certain Peano continua have a least nontrivial homotopy group that is finitely presented or of cardinality continuum. We also use this technique to give some relative consistency results.
Planar Cat(K) Subspaces, Russell M. Ricks
Planar Cat(K) Subspaces, Russell M. Ricks
Theses and Dissertations
Let M_k^2 be the complete, simply connected, Riemannian 2-manifold of constant curvature k ± 0. Let E be a closed, simply connected subspace of M_k^2 with the property that every two points in E are connected by a rectifi able path in E. We show that E is CAT(k) under the induced path metric.
Verification Of Kam Theory On Earth Orbiting Satellites, Christian L. Bisher
Verification Of Kam Theory On Earth Orbiting Satellites, Christian L. Bisher
Theses and Dissertations
This paper uses KAM torus theory and Simplified General Perturbations 4 (SGP4) orbit prediction techniques compiled by Dr. William Wiesel and compares it to Analytical Graphics ® Incorporated (AGI) Satellite Toolkit ® (STK) orbit data. The goal of this paper is to verify KAM torus theory can be used to describe and propagate an Earth satellite orbit with similar accuracy to existing general perturbation techniques. Using SGP4 code including only truncated geopotential effects, KAM torus generating code, and other utilities were used to describe a particular satellite orbit as a torus and then propagate the satellite using traditional and KAM …
Numerical Investigation Of Pre-Detonator Geometries For Pde Applications, Robert T. Fievisohn
Numerical Investigation Of Pre-Detonator Geometries For Pde Applications, Robert T. Fievisohn
Theses and Dissertations
A parametric study was performed to determine optimal geometries to allow the successful transition of a detonation from a pre-detonator into the thrust tube of a pulse detonation engine. The study was performed using a two-dimensional Euler solver with progress variables to model the chemistry. The geometrical configurations for the simulations look at the effect of shock reflections, flow obstructions, and detonation diffraction to determine successful geometries. It was observed that there are success and failure rates associated with pre-detonators. These success rates appear to be determined by the transverse wave structure of a stably propagating detonation wave and must …
Validation Of A Novel Approach To Solving Multibody Systems Using Hamilton's Weak Principle, Ashton D. Hainge
Validation Of A Novel Approach To Solving Multibody Systems Using Hamilton's Weak Principle, Ashton D. Hainge
Theses and Dissertations
A novel approach for formulating and solving for the dynamic response of multibody systems has been developed using Hamilton’s Law of Varying Action as its unifying principle. In order to assure that the associated computer program is sufficiently robust when applied across a wide range of dynamic systems, the program must be verified and validated. The purpose of the research was to perform the verification and validation of the program. Results from the program were compared with closed-form and numerical solutions of simple systems, such as a simple pendulum and a rotating pendulum. The accuracy of the program for complex …
Simulation Of A Diode Pumped Alkali Laser, A Three Level Numerical Approach, Shawn W. Hackett
Simulation Of A Diode Pumped Alkali Laser, A Three Level Numerical Approach, Shawn W. Hackett
Theses and Dissertations
This paper develops a three level model for a continuous wave diode pumped alkali laser by creating rate equations based on a three level system. The three level system consists of an alkali metal vapor, typically Rb or Cs, pumped by a diode from the 2S1/2 state to the 2P3/2 , a collisional relaxation from 2P3/2 to 2P1/ 2 , and then lasing from 2P1/2 to 2S1/2 . The hyperfine absorption and emission cross sections for these transitions are developed in detail. Differential equations for intra-gain pump attenuation …
Asian Spread Option Pricing Models And Computation, Sijin Chen
Asian Spread Option Pricing Models And Computation, Sijin Chen
Theses and Dissertations
In the commodity and energy markets, there are two kinds of risk that traders and analysts are concerned a lot about: multiple underlying risk and average price risk. Spread options, swaps and swaptions are widely used to hedge multiple underlying risks and Asian (average price) options can deal with average price risk. But when those two risks are combined together, then we need to consider Asian spread options and Asian-European spread options for hedging purposes. For an Asian or Asian-European spread call option, its payoff depends on the difference of two underlyings' average price or of one average price and …