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Some of the material in is restricted to members of the community. By logging in, you may be able to gain additional access to certain collections or items. If you have questions about access or logging in, please use the form on the Contact Page.
A new numerical method is developed for the solution of the diffusion problem in a system of several materials. In such a system, the diffusion coefficients are piecewise continuous and jumps in their values can occur across the complex...
An exploratory study of the effectiveness of computer graphic and simulations in a computer-student interactive environment in illustrating random sampling and the central limit theorem
"The purposes of this study were: (1) to investigate the effectiveness of the computer-student interactive method in presenting statistical concepts and in instructing students in the applications of these concepts, and (2) to develop...
CANONICAL SYSTEMS OF TORI AND KLEIN BOTTLES IN NON-ORIENTABLE 3-MANIFOLDS OF GENUS TWO
Description:
Let M be a closed non-orientable 3-manifold with a Heegaard splitting of genus two. We show that, if M has a non-separating essential Klein bottle, then there is a non-separating essential Klein bottle (or torus) K such that the...
The purpose of this study was to explore domain-general cognitive skills, domain-specific academic skills, and demographic characteristics that are associated with calculation development from first grade to third grade among young...
"The purpose of this paper is to record the results of a study of an abstract set upon which a distance function, having certain properties, has been defined. It is assumed that the reader is familiar with the fundamental concepts of set...
In financial markets under uncertainty, the classical Black-Scholes model cannot explain the empirical facts such as fat tails observed in the probability density. To overcome this drawback, during the last decade, Lévy process and...
The connections between algebra, geometry, and analysis have led the way for numerous results in many areas of mathematics, especially complex analysis. Considerable effort has been made to develop higher dimensional analogues of the...
Aquaponics is an integrated biological system that essentially combines a soil-less garden with an aquarium. It is important because it uses less water than commercial farming, is ecofriendly, and provides a local source of food for its...
The purpose of this dissertation is to, first outline a theory of Zeta regularized products which will work for sequences of complex numbers, and second to use this theory to compute Zeta regularized products and modular constants for... The gamma function $\Gamma(z)$ is represented as the ratio of two Zeta regularized products. This relation is then extended to define multiple gamma functions as the ratio of two corresponding Zeta regularized products. A full account of... Some other special functions are also discussed. Namely Jacobi's theta function $\theta\sb1$, the Weierstrass sigma function $\sigma(z), $ and $P(z\vert\tau)$ defined by The determinant of the Laplacian on an n-dimensional flat Torus is computed for $n \geq$ 2, by computing
This dissertation presents studies of effective methods in two main areas of algebraic geometry: intersection theory and characteristic classes, and combinatorial algebraic geometry. We begin in chapter 2 by giving an effective algorithm...
In this dissertation, we evaluate existing Monte Carlo estimators and develop new Monte Carlo estimators for pricing financial options with the goal of improving precision. In Chapter 2, we discuss the conditional expectation Monte Carlo...
We develop partial differential equation methods with well-posed boundary conditions to price average strike options and swing options in the energy market. We use the energy method to develop boundary conditions that make a two space...
Quantifying uncertainty in modeling and simulation is crucial since the parameters of the physical system are inherently non-deterministic and knowledge of the system embodied in the model is incomplete or inadequate. The most well...
There have been recent pushes for more active learning in mathematics classrooms, especially at the undergraduate level. To incorporate more active learning, there is a need for tasks that explicitly support this type of instruction, ...
Crew costs are the second largest direct operating cost of airlines next to fuel costs. Therefore much research has been devoted to the planning and scheduling of crews over the last thirty years. The planning and scheduling of crews is...
The objective of this work is to quantify uncertainty and perform global sensitivity analysis for nonlinear models with a moderate or large number of stochastic parameters. We implement non-intrusive methods that do not require...
A unified, asymptotically-preserving method for simulating multiphase flows using an exactly mass, momentum, and energy conserving Cell-Integrated Semi-Lagrangian advection algorithm is presented. The new algorithm uses a semi-implicit...
Every year we join in on the celebration of high school students all over the country graduating and preparing for the next phase of their adult life, whether starting their careers or entering college. Some students who choose to...
The tame symbol serves many purposes in mathematics, and is of particular value when we use it to evaluate curves over certain number _elds. A well-known example is that of the Hilbert symbol, which gives us insight into the existence of...
Belief function theory, also known as Dempster-Shafer theory or evidence theory, gives a general framework for quantifying, representing, and managing uncertainty, and it is widely used in several applications from artificial...
Global sensitivity analysis studies how uncertainty in a model's output can be attributed to uncertainties in the model's inputs. This analysis has applications in various fields such as natural sciences, engineering, social sciences, ...
High order finite difference schemes are generally less dispersive, less dissipative and more isotropic than low order schemes. They are, therefore, better suited for the solution of wave propagation problems. High order schemes, however...
This dissertation develops and evaluates a computationally efficient and high-order numerical method to compute wave reflection and transmission from moving material boundaries. We use a discontinuous Galerkin spectral element...
This folder contains rough calculations with action-angle variables. These are used to solve for rotation or oscillation without calculating the equations of motion.
The objective of this dissertation is to study the queuing and point process models that try to capture as many features as possible of the high-frequency data of a limit order book. First, we use a generalized birth-death stochastic...
"The present investigation was designed to study the effect of two instructional treatments on the achievement of students of different abilities--Verbal and Spatial. This was achieved by studying the interaction between the two...
THE EIGENVALUES OF THE SPHEROIDAL WAVE EQUATION AND THEIR BRANCH POINTS
Description:
A comprehensive account is given of the behavior of the eigenvalues of the spheroidal wave equation as functions of the complex variable c('2). The convergence of their small-c('2) expansions is limited by an infinite sequence of rings...
In this dissertation, we introduce a genetic algorithm approach to estimate the star discrepancy of a point set. This algorithm allows for the estimation of the star discrepancy in dimensions larger than seven, something that could not...
A three layer, wind driven, general circulation model involving both subtropical and subpolar gyres has been developed to study intergyre exchange. Following Schopp and Arhan (1986), the present work allows flow to cross the intergyre... A class of thermocline structures at the zero Ekman pumping line has been constructed which permit intergyre exchange, or communication. These so-called 'windows', which are where the communication occurs at the intergyre boundary, have... In addition to the model results, observed tracer distributions have been reexamined within the context of this model. Possible explanations for the potential vorticity contours in the North Atlantic Ocean, which connect the northern and...
Most of the data encountered is bounded nonlinear data. The Universe is bounded, planets are sphere like shaped objects, and life growing on Earth comes in various shapes and colors that can hardly be represented as points on a linear...
We develop an adaptive spectral element method to price American options, whose solutions contain a moving singularity, automatically and to within prescribed errors. The adaptive algorithm uses an error estimator to determine where...
Our work builds on that of Barbot and Fenley to generalize Bonatti and Langevin's famous construction of a graph manifold with pseudo-Anosov flow in which all Seiftert fibered pieces of the torus decomposition are periodic. We provide...
Shape represents a complex and rich source of biological information that is fundamentally linked to underlying mechanisms and functions. Many fields of biology employ mathematical tools for the statistical analysis of shape variation....
In this thesis we present an algorithm that finds closed form solutions for homogeneous linear recurrence equations. The key idea is transforming an input operator Linp to an operator Lg with known solutions. The main problem of this...
The results reported here are the product of the research titled: Using history in the teaching of mathematics. The subjects are students in two classes of algebra II course at Florida State University High School-- 36 students-- makes...
Some of the material in is restricted to members of the community. By logging in, you may be able to gain additional access to certain collections or items. If you have questions about access or logging in, please use the form on the Contact Page.
