Library: Mathematics

Attrition and time-to-degree issues remain poorly understood in academia, and almost completely unexplored in criminology and criminal justice. Loss rates of fifty percent or more are common in the social sciences, while the success rates for criminal justice are unknown for most schools. This study attempts to investigate completion levels at the Florida State University (FSU) College of Criminology and Criminal Justice, using descriptive and inferential techniques, survival analysis, and questionnaires. Problems with data collection impeded analysis of even basic statistical operations, resu...

The purpose of this qualitative study was to measure the effectiveness of a new reusable learning object design model for elementary mathematics. This study was motivated by the lack of general reusable learning object design models and, specifically, elementary mathematics design models that include both technical and learning specifications. The research design method was a qualitative Delphi technique and included participants across the United States and other countries. Ten participants were provided the design model and a questionnaire to analyze the effectiveness of the model on the onl...

Quasi-Monte Carlo methods, which are often described as deterministic versions of Monte Carlo methods, were introduced in the 1950s by number theoreticians. They improve several deficiencies of Monte Carlo methods; such as providing estimates with deterministic bounds and avoiding the paradoxical difficulty of generating random numbers in a computer. However, they have their own drawbacks. First, although they provide faster convergence than Monte Carlo methods asymptotically, the advantage may not be practical to obtain in "high" dimensional problems. Second, there is not a practical way to m...

The thesis starts with a short description of the credit derivatives' place in the credit risk management. Then it proceeds by outlining the basic forms of credit derivatives, their applications, and their contract elements. A short description of the two common pricing frameworks for credit derivatives, the Firm's Value Models and the Credit Rating Transition Models is given. The major approach reviewed in this thesis is the one of Duffie-Singleton for valuing credit derivatives with term structure models. This framework is also applied in a simulation and examines the importance of the di...

The study of Multivariate Time Series has always been more difficult at the modeling stage than the univariate case. Identification of a suitable model, questions of stability, and the difficulties of prediction are well recognised. A variety of methods appear to be worth examining. This thesis is concerned with the proposal of an useful tool which is to apply canonical analysis to a realisation of a Multivariate Time Series and concentrates it's attention on k-variate ARMA(p,q) models. The multivariate series is partitioned into two overlapping or non-overlapping sets of different sizes. The ...

In this work we explore the relation between some local Dirichlet spaces and some operator ranges. As an application we give numerical bounds for an equivalence of norms on a particular subspace of the Hardy space. Based on these results we introduce an operator on H^2 which we study in some detail. We also introduce a Hilbert space of analytic functions on the unit disc, prove the polynomials are dense in it, and give a characterization of its elements. On these spaces we study the action of composition operators induced by holomorphic self maps of the disc. We give characterizations o...

Combinatorial Games are a generalization of real numbers. Each game has a recursively defined complexity (birthday). In this paper we establish some game bounds. We find some limit cases for how big and how small a game can be, based on its complexity. For each finite birthday, N, we find the smallest positive number and the greatest game born by day N, as well as the smallest and the largest positive infinitesimals. As for each particular birthday we provide the extreme values for those types of games, these results extend those in [1, page 214]. The main references in the theory of combinat...

This thesis focuses on iterative methods for the treatment of the steady state neutron transport equation in slab geometry, bounded convex domain of Rn (n = 2,3) and in 1-D spherical geometry. We introduce a generic Alternate Direction Implicit (ADI)-like iterative method based on positive definite and m-accretive splitting (PAS) for linear operator equations with operators admitting such splitting. This method converges unconditionally and its SOR acceleration yields convergence results similar to those obtained in presence of finite dimensional systems with matrices possessing the Young pr...

When in 1900 David Hilbert produced a list of 23 mathematical problems and expressed optimism in the power of the human mind to proffer positive solutions to them, little did he know that it would take much of the century for solutions to be found for some of the problems. The problems numbered 1, 2, and 10 which concern mathematical logic and which gave birth to what is called the entscheidungsproblem or the decision problem were eventually solved though in the negative by Alonzo Church and Alan Turing in their famous Church-Turing thesis. Given any fixed machine M and input n, there are gamm...

Radiative transfer of photons though a random distribution of scatterers is considered. The Boltzmann transport eq is used to develop a program to obtain real values of intensity based on a set of discrete time intervals. A Newton-Raphson method is used to determine a set of eigenvalues based on the boundary conditions and system geometry. A numerical method due to Lanczos is used to approximately invert a Laplace transform. The algorithm is designed for easy modification to more general problems. PART II: Eigenvalues for the intensity distribution from the one speed Boltzmann tra...