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Articles 181 - 210 of 232
Full-Text Articles in Applied Mathematics
Representation Properties Of Definite Lattices In Function Fields, Jean Edouard Bureau
Representation Properties Of Definite Lattices In Function Fields, Jean Edouard Bureau
LSU Doctoral Dissertations
This work is made of two different parts. The first contains results concerning isospectral quadratic forms, and the second is about regular quadratic forms. Two quadratic forms are said to be isospectral if they have the same representation numbers. In this work, we consider binary and ternary definite integral quadratic form defined over the polynomial ring F[t], where F is a finite field of odd characteristic. We prove that the class of such a form is determined by its representation numbers. Equivalently, we prove that there is no nonequivalent definite F[t]-lattices of rank 2 or 3 having the same theta …
Limit Theorems For Weighted Stochastic Systems Of Interacting Particles, Jie Wu
Limit Theorems For Weighted Stochastic Systems Of Interacting Particles, Jie Wu
LSU Doctoral Dissertations
The goal of this dissertation is to (a) establish the weak convergence of empirical measures formed by a system of stochastic differential equations, and (b) prove a comparison result and compactness of support property for the limit measure. The stochastic system of size n has coefficients that depend on the empirical measure determined by the system. The weights for the empirical measure are determined by a further n-system of stochastic equations. There is a random choice among N types of weights. The existence and uniqueness of solutions of the interacting system, weak convergence of the empirical measures, and the identification …
Index Future Pricing Under Imperfect Market And Stochastic Volatility, Wei-Hsien Li
Index Future Pricing Under Imperfect Market And Stochastic Volatility, Wei-Hsien Li
LSU Master's Theses
Financial markets in emerging countries are volatile and imperfect, so pricing model under traditional perfect-market frameset may not give reliable price of financial derivatives. The most famous pricing model for stock index future is the cost of carry model. The mis-pricing of cost of carry model inspires lots of following researches. Even transaction costs, dividends, stochastic interest rate, stochastic volatility, market imperfection, and other factors are considered, we still do not obtain a model price consistently better than cost of carry model. But these researches offer important insights, for example, the market needs time to mature and the more complex …
Filippov's Operator And Discontinuous Differential Equations, Khalid Abdulaziz Alshammari
Filippov's Operator And Discontinuous Differential Equations, Khalid Abdulaziz Alshammari
LSU Doctoral Dissertations
The thesis is mainly concerned about properties of the so-called Filippov operator that is associated with a differential inclusion x'(t) ε F(x(t)) a.e. t ε [0,T], where F : Rn → Rn is given set-valued map. The operator F produces a new set-valued map F[F], which in effect regularizes F so that F[F] has nicer properties. After presenting its definition, we show that F[F] is always upper-semicontinuous as a map from Rn to the metric space of compact subsets of Rn endowed with the Hausdorff metric. Our main approach is to study the …
Circuits And Structure In Matroids And Graphs, Brian Daniel Beavers
Circuits And Structure In Matroids And Graphs, Brian Daniel Beavers
LSU Doctoral Dissertations
This dissertation consists of several results on matroid and graph structure and is organized into three main parts. The main goal of the first part, Chapters 1-3, is to produce a unique decomposition of 3-connected matroids into more highly connected pieces. In Chapter 1, we review the definitions and main results from the previous work of Hall, Oxley, Semple, and Whittle. In Chapter 2, we introduce operations that allow us to decompose a 3-connected matroid M into a pair of 3-connected pieces by breaking the matroid apart at a 3-separation. We also generalize a result of Akkari and Oxley. In …
On Moment Conditions For The Girsanov Theorem, See Keong Lee
On Moment Conditions For The Girsanov Theorem, See Keong Lee
LSU Doctoral Dissertations
In this dissertation, the well-known Girsanov Theorem will be proved under a set of moment conditions on exponential processes. Our conditions are motivated by the desire to avoid using the local martingale theory in the proof of the Girsanov Theorem. Namely, we will only use the martingale theory to prove the Girsanov Theorem. Many sufficient conditions for the validity of the Girsanov Theorem have been found since the publication of the result by Girsanov in 1960. We will compare our conditions with some of these conditions. As an application of the Girsanov Theorem, we will show the nonexistence of an …
Impulsive Systems, Stanislav Zabic
Impulsive Systems, Stanislav Zabic
LSU Doctoral Dissertations
Impulsive systems arise when dynamics produce discontinuous trajectories. Discontinuties occur when movements of states happen over a small interval that resembles a point-mass measure. We adopt the formalism in which the controlled dynamic inclusion is the sum of a slow and a fast time velocities belonging to two distinct vector fields. Fast time velocities are controlled by a vector valued Borel measure. The trajectory of impulsive systems is a function of bounded variation. To give a definition of solutions, a notion of graph completion of the control measure is needed. In the nonimpulsive case, a solution can be defined as …
Zeta Functions Of Finite Graphs, Debra Czarneski
Zeta Functions Of Finite Graphs, Debra Czarneski
LSU Doctoral Dissertations
Ihara introduced the zeta function of a finite graph in 1966 in the context of p-adic matrix groups. The idea was generalized to all finite graphs in 1989 by Hashimoto. We will introduce the zeta function from both perspectives and show the equivalence of both forms. We will discuss several properties of finite graphs that are determined by the zeta function and show by counterexample several properties of finite graphs that are not determined by the zeta function. We will also discuss the relationship between the zeta function of a finite graph and the spectrum of a finite graph.
The Asymptotic Z-Transform, Scott Jude Champagne
The Asymptotic Z-Transform, Scott Jude Champagne
LSU Master's Theses
Sequences of numbers and transformations from sequences to functions have been studied extensively, including the multiplication of two sequences through convolution and the equivalent multiplication of functions. The focal points of this thesis are the convolution field of causal sequences and their Z-transforms. Classically, the treatment of the Z-transform has been limited to those causal sequences for which the power series has a nontrivial radius of convergence. In this thesis it is shown that the Z-transform can be extended to all causal sequences without compromising any of the operational properties of the classical Z-transform.
Stability Of Stochastic Pricing Models Under Volatility Fluctuations, Krassimir Zhivkov Nikolov
Stability Of Stochastic Pricing Models Under Volatility Fluctuations, Krassimir Zhivkov Nikolov
LSU Master's Theses
The standard theory of the stochastic models used to value financial derivatives contracts involves models whose input parameters are deterministic functions and often constants. Because of the random nature of the changes in the market prices of the financial instruments, the coefficients of these models are inevitably susceptible to random perturbation from their initial estimates. In this paper we will investigate the behavior of some of the most widely used models when small changes are applied to their volatility component. Starting with the Black-Scholes model for the price of a European call option, we will continue our analysis of the …
Modern Interpretation Of Euclid's Theory Of Ratio And Proportion, Mark Robert Stecher
Modern Interpretation Of Euclid's Theory Of Ratio And Proportion, Mark Robert Stecher
LSU Master's Theses
Euclid’s Elements is the foundation for geometry. Book V of Euclid’s Elements, which is independent from the earlier books, focuses on multiples, ratios, and proportions. This paper presents a model of the conceptual content of Book V, but using carefully selected modern notation to represent Euclid’s ideas without changing them drastically. All of the propositions and proofs from Euclid have been restated using just enough modern language to make clear for a modern reader. We also present a modern theory that bears analogy, proposition by proposition, to Euclid’s theory, but uses rigorous modern methods of proof.
Quasicontinuous Derivatives And Viscosity Functions, Rodica Cazacu
Quasicontinuous Derivatives And Viscosity Functions, Rodica Cazacu
LSU Doctoral Dissertations
In this work we demonstrate how the continuous domain theory can be applied to the theory of nonlinear optimization, particularly to the theory of viscosity solutions. We consider finding the viscosity solution for the Hamilton-Jacobi equation H(x, y) = g(x), with continuous hamiltonian, but with possibly discontinuous right-hand side. We begin by finding a new function space Q(X,L), the space of equivalence classes of quasicontinuous functions from a locally compact set X to a bicontinuous lattice L and we will define on Q(X,L) the qo-topology, which is a variant of classical order topology defined on complete lattices. On this …
Multiscale Strain Analysis, Timothy Donald Breitzman
Multiscale Strain Analysis, Timothy Donald Breitzman
LSU Doctoral Dissertations
The mathematical homogenization and corrector theory relevant to prestressed heterogeneous materials in the linear-elastic regime is discussed. A suitable corrector theory is derived to reconstruct the local strain field inside the composite. Based on this theory, we develop an inexpensive numerical method for multi scale strain analysis within a prestressed heterogeneous material. The theory also provides a characterization of the macroscopic strength domain. The strength domain places constraints on the homogenized strain field which guarantee that the actual strain in the heterogeneous material lies inside the strength domain of each material participating in the structure.
Laguerre Functions Associated To Euclidean Jordan Algebras, Michael Aristidou
Laguerre Functions Associated To Euclidean Jordan Algebras, Michael Aristidou
LSU Doctoral Dissertations
Certain differential recursion relations for the Laguerre functions, defined on a symmetric cone Ω, can be derived from the representations of a specific Lie algebra on L2(Ω,dμv). This Lie algebra is the corresponding Lie algebra of the Lie group G that acts on the tube domain T(Ω)=Ω+iV, where V is the associated Euclidean Jordan algebra of Ω. The representations involved are the highest weight representations of G on L2(Ω,dμv). To obtain these representations, we start from the highest weight representations of G on Hv(T(Ω)), the Hilbert space of holomorphic functions …
Virtual Strings For Closed Curves With Multiple Components And Filamentations For Virtual Links, William Schellhorn
Virtual Strings For Closed Curves With Multiple Components And Filamentations For Virtual Links, William Schellhorn
LSU Doctoral Dissertations
The theory of filaments on oriented chord diagrams can be used to detect some non-classical virtual knots. We extend existing filament techniques to virtual links with more than one component and give examples of virtual links that these techniques can detect as non-classical. Given a signed Gauss word underlying an oriented chord diagram, we describe how to construct a finite sequence of integers that encodes all of the filament information for the diagram. We also introduce a square array of integers called a MIN-square that summarizes the filament information about all of the signed Gauss words having a given Gauss …
Dynamical Systems With Time Delay, Norma Ortiz
Dynamical Systems With Time Delay, Norma Ortiz
LSU Doctoral Dissertations
In this dissertation, we study necessary conditions and weak invariance properties of dynamical systems with time delay. A number of results have been obtained recently that refine necessary conditions of optimal solutions for nonsmooth dynamical systems without time delay. In this dissertation, we examine the extension of some of these results to problems with time delay. In particular, we study the generalized problem of Bolza with the addition of delay in the state and velocity variables and refer to this problem as the Neutral Problem of Bolza. We consider the relationship between the generalized problem of Bolza with time delay …
Stability In Dynamical Polysystems, George Cazacu
Stability In Dynamical Polysystems, George Cazacu
LSU Doctoral Dissertations
A dynamical polysystem consists of a family of continuous dynamical systems, all acting on a given metric space. The first chapter of the present thesis shows a generalization of control systems via dynamical polysystems and establishes the equivalence of the two notions under certain lipschitz condition on the function defining the dynamics. The remaining chapters are focused on a basic theory of dynamical polysystems. Some topological properties of limit sets are described in Chapter 2. Chapters 3 and 4 provide characterizations for various notions of strong stability. Chapter 5 makes use of the theory of closed relations to study Lyapunov …
Dissipative Lipschitz Dynamics, Vinicio Rafael Rios
Dissipative Lipschitz Dynamics, Vinicio Rafael Rios
LSU Doctoral Dissertations
In this dissertation we study two related important issues in control theory: invariance of dynamical systems and Hamilton-Jacobi theory associated with optimal control theory. Given a control system modelled as a differential inclusion, we provide necessary and sufficient conditions for the strong invariance property of the system when the dynamic satisfies a dissipative Lipschitz condition. We show that when the dynamic is almost upper semicontinuous and satisfies the dissipative Lipschitz property, these conditions can be expressed in terms of approximate Hamilton-Jacobi inequalities, which subsumes the classic infinitesimal characterization of strongly invariant systems given under the Lipschitz assumtion. In the important …
Error Estimates For Stabilized Approximation Methods For Semigroups, Sarah Campbell Mcallister
Error Estimates For Stabilized Approximation Methods For Semigroups, Sarah Campbell Mcallister
LSU Doctoral Dissertations
In this work we analyze error estimates for rational approximation methods, and their stabilizations, for strongly continuous semigroups. Chapter 1 consists of a brief survey of time discretization methods for semigroups. In Chapter 2, we demonstrate a new method for obtaining convergent approximations in the absence of stability for strongly continuous semigroups with arbitrary initial data. In Section 2.2, we state the stabilization result in more general form and show that this method can be used to improve known error estimates by a magnitude of up to one half for smooth initial data. In Section 2.3, we give concrete examples …
Wavelet Sets With And Without Groups And Multiresolution Analysis, Mihaela Dobrescu
Wavelet Sets With And Without Groups And Multiresolution Analysis, Mihaela Dobrescu
LSU Doctoral Dissertations
In this dissertation we study a special kind of wavelets, the so-called minimally supported frequency wavelets and the associated wavelet sets. Most of the examples of wavelet sets are for dilation sets which are groups. In this work we construct wavelet sets for which the dilation set, D, is of the form D=MN, where the product is direct, and so D is not necessarily group. In the second part of this dissertation we construct multiwavelets associated with MRA's and we generalize the rotations in the dilation sets to Coxeter groups.
Asymptotic Laplace Transforms, Claudiu Mihai
Asymptotic Laplace Transforms, Claudiu Mihai
LSU Doctoral Dissertations
In this work we discuss certain aspects of the classical Laplace theory that are relevant for an entirely analytic approach to justify Heaviside's operational calculus methods. The approach explored here suggests an interpretation of the Heaviside operator ${cdot}$ based on the "Asymptotic Laplace Transform." The asymptotic approach presented here is based on recent work by G. Lumer and F. Neubrander on the subject. In particular, we investigate the two competing definitions of the asymptotic Laplace transform used in their works, and add a third one which we suggest is more natural and convenient than the earlier ones given. We compute …
Query Of Image Content Using Wavelets And Gibbs-Markov Random Fields, Imtiaz Hossain
Query Of Image Content Using Wavelets And Gibbs-Markov Random Fields, Imtiaz Hossain
LSU Master's Theses
The central theme of this thesis is the application of Wavelets and Random Processes to content-based image query (on texture patterns, in particular). Given a query image, a content-based search extracts a certain representative measure (or signature) from the query image and likewise for all the target images in the search archive. A good representative measure is one that provides us with the ability to differentiate easily between different patterns. A distance measure is computed between the query properties and the properties of each of the target images. The lowest distance measure gives us the best target match for the …
A Meta-Analysis Of Randomness In Human Behavioral Research, Summer Ann Armstrong
A Meta-Analysis Of Randomness In Human Behavioral Research, Summer Ann Armstrong
LSU Master's Theses
This work analyzes the concept of randomness in binary sequences from three different perspectives: mathematically, statistically, and psychologically and examines the research on human perception of randomness and the question of whether or not humans can simulate random behavior. Generally, research shows that human subjects have great difficulty producing random sequences, even when they are instructed and motivated. We survey some of the literature and present some leading theoretical proposals. Finally, we present some basic statistical tests that can be used to evaluate randomness in a given binary sequence.
Cox Regression Model, Lindsay Sarah Smith
Cox Regression Model, Lindsay Sarah Smith
LSU Master's Theses
Cox, in 1972, came up with the Cox Regression Model to deal handle failure time data. This work presents background information leading up to the Cox's regression model for censored survival data. The marginal and partial likelihood approaches to estimate the parameters in this model are presented in detail. The estimation techniques of the hazard and survivor functions are explained. All of these ideas are illustrated using data from the Veteran’s Administration lung cancer study.
On Qualitative Properties And Convergence Of Time-Discretization Methods For Semigroups, Mihaly Kovacs
On Qualitative Properties And Convergence Of Time-Discretization Methods For Semigroups, Mihaly Kovacs
LSU Doctoral Dissertations
In this dissertation we use functional calculus methods to investigate convergence and qualitative properties of time-discretization methods for strongly continuous semigroups. Stability, convergence, and preservation of contractivity (or norm-bound) of the semigroup under time-discretization is investigated in a Banach space setting. Preservation of positivity, concavity and other qualitative shape properties which can be described via positivity are treated in a Banach lattice framework. The use of the Hille-Phillips (H-P) functional calculus instead of the Dunford-Taylor functional calculus allows us to extend fundamental qualitative results concerning time-discretization methods and simplify their proofs, including results on multi-step schemes and variable step-sizes. We …
The Radon-Gauss Transform, Vochita Mihai
The Radon-Gauss Transform, Vochita Mihai
LSU Doctoral Dissertations
Gaussian measure is constructed for any given hyperplane in an infinite dimensional Hilbert space, and this is used to define a generalization of the Radon transform to the infinite dimensional setting, using Gauss measure instead of Lebesgue measure. An inversion formula is obtained and a support theorem proved.
Class Groups And Norms Of Units, Costel Ionita
Class Groups And Norms Of Units, Costel Ionita
LSU Doctoral Dissertations
Our object of study is relative quadratic extensions of algebraic number fields. In 'Class Number Parity', the authors P.E. Conner and J. Hurrelbrink study in detail the cases of real and CM-extensions. In this paper we generalize some of the results without any assumption on the type of the relative quadratic extension.
Orbit Structure On The Silov Boundary Of A Tube Domain And The Plancherel Decomposition Of A Causally Compact Symmetric Space, With Emphasis On The Rank One Case, Troels Roussau Johansen
Orbit Structure On The Silov Boundary Of A Tube Domain And The Plancherel Decomposition Of A Causally Compact Symmetric Space, With Emphasis On The Rank One Case, Troels Roussau Johansen
LSU Doctoral Dissertations
We construct a G-equivariant causal embedding of a compactly causal symmetric space G/H as an open dense subset of the Silov boundary S of the unbounded realization of a certain Hermitian symmetric space G1/K1 of tube type. Then S is an Euclidean space that is open and dense in the flag manifold G1/P', where P' denotes a certain parabolic subgroup of G1. The regular representation of G on L2(G/H) is thus realized on L2(S), and we use abelian harmonic analysis in the study thereof. In particular, …
Which Mean Do You Mean?: An Exposition On Means, Mabrouck K. Faradj
Which Mean Do You Mean?: An Exposition On Means, Mabrouck K. Faradj
LSU Master's Theses
The objective of this thesis is to give a brief exposition on the theory of means. In Greek mathematics, means are intermediate values between two extremes, while in modern mathematics, a mean is a measure of the central tendency for a set of numbers. We begin by exploring the origin of the antique means and list the classical means. Next, we present an overview of the theories of binary means and n-ary means. We include a general discussion on axiomatic systems for means and present theorems on properties that characterize the most common types of means.
Stock Price Modeling And Insider Trading Theory, Jessica J. Guillory
Stock Price Modeling And Insider Trading Theory, Jessica J. Guillory
LSU Master's Theses
The mathematical study of stock price modeling using Brownian motion and stochastic calculus is a relatively new field. The randomness of financial markets, geometric brownian motions, martingale theory, Ito's lemma, enlarged filtrations, and Girsanov's theorem provided the motivation for a simple characterization of the concepts of stock price modeling. This work presents the theory of stochastic calculus and its use in the financial market. The problems on which we focus are the models of an investor's portfolio of stocks with and without the possibility of insider trading, opportunities for fair pricing of an option, enlarged filtrations, consumptions, and admissibility. This …