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Articles 1 - 30 of 31
Full-Text Articles in Applied Mathematics
Change-Point Tests For Precipitation Data, Michael Robbins
Change-Point Tests For Precipitation Data, Michael Robbins
All Theses
A new method is required for change-point testing of precipitation data that is capable of applying valid precipitation models. First, stochastic precipation models are researched and classified. Typically, the occurrence of rain is modeled using a two-state, first-order Markov chain, and the intensity of rain is modeled using a two-parameter gamma distribution. Using the likelihood ratio test statistic, methods are devoloped for testing for fixed and unknown change-points. These methods are developed for various models, including the MC/gamma model and simplified versions. The distribution of the LRT is unknown, however its asymptotic distribution is known for both the fixed and …
A Bayesian Approach For Bandwidth Selection In Kernel Density Estimation With Censored Data, Chinthaka Kuruwita
A Bayesian Approach For Bandwidth Selection In Kernel Density Estimation With Censored Data, Chinthaka Kuruwita
All Theses
Estimating an unknown probability density function is a common problem arising frequently in many scientific disciplines. Among many density estimation methods, the kernel density estimators are widely used. However, the classical kernel density estimators suffer from an intrinsic problem as they assign positive values outside the support of the target density. This problem is commonly known as the `Spill over` effect. A modification to the regular kernel estimator is proposed to circumvent this problem. The proposed method uses a lognormal kernel and can be used even in the presence of censoring to estimate any density with a positive support without …
A New Application Of The Channel Packet Method For Low Energy 1-D Elastic Scattering, Clint M. Zeringue
A New Application Of The Channel Packet Method For Low Energy 1-D Elastic Scattering, Clint M. Zeringue
Theses and Dissertations
An algorithm is presented which uses the channel packet method (CPM) to simulate low-energy, wave-packet propagation and compute S-matrix elements. A four-by-four matrix containing the momentum, expansion coefficients of the reactants and products is introduced to account for initial and final states having both positive and negative momentum. The approach does not consider scattering from one side or the other, rather it considers both incoming and outgoing wave packets from the left and right simultaneously. Therefore, during one simulation all four S-matrix elements, and elements, S+k,-K, S-k, +k, S+k, +k and S-k,-k are computed. …
Existence Of Large Solutions To Semilinear Elliptic Equations With Multiple Terms, David N. Smith
Existence Of Large Solutions To Semilinear Elliptic Equations With Multiple Terms, David N. Smith
Theses and Dissertations
We consider the semilinear elliptic equation Δu = p(x)uα + q(x)uβ on a domain Ω ⊆ Rn, n ≥ 3, where p and q are nonnegative continuous functions with the property that each of their zeroes is contained in a bounded domain Ωp or Ωq, respectively in Ω such that p is positive on the boundary of Ωp and q is positive on the boundary of Ωq. For Ω bounded, we show that there exists a nonnegative solution u such that u(x) → ∞ as x → ∂Ω if …
Optimizing The Replication Of Multi-Quality Web Applications Using Aco And Wolf, Judson C. Dressler
Optimizing The Replication Of Multi-Quality Web Applications Using Aco And Wolf, Judson C. Dressler
Theses and Dissertations
This thesis presents the adaptation of Ant Colony Optimization to a new NP-hard problem involving the replication of multi-quality database-driven web applications (DAs) by a large application service provider (ASP). The ASP must assign DA replicas to its network of heterogeneous servers so that user demand is satisfied and replica update loads are minimized. The algorithm proposed, AntDA, for solving this problem is novel in several respects: ants traverse a bipartite graph in both directions as they construct solutions, pheromone is used for traversing from one side of the bipartite graph to the other and back again, heuristic edge values …
Development And Validation Of Reentry Simulation Using Matlab, Robert E. Jameson Jr.
Development And Validation Of Reentry Simulation Using Matlab, Robert E. Jameson Jr.
Theses and Dissertations
This research effort develops a program using MATLAB to solve the equations of motion for atmospheric reentry and analyzes the validity of the program for use as a tool to expeditiously predict reentry profiles. The reentry vehicle is modeled as a point mass with constant aerodynamic properties as defined by the user. The equations of motion for reentry are based on the two-body problem. The atmosphere is modeled as a single layer exponentially decreasing in density. The MATLAB program has the ability to derive the initial trajectory conditions from the position and velocity relative to the rotating surface of the …
Dynamics Of A Two Serotype Disease With Antibody Dependent Enhancement, Amy Fiorillo
Dynamics Of A Two Serotype Disease With Antibody Dependent Enhancement, Amy Fiorillo
Theses, Dissertations and Culminating Projects
The dengue virus is a serious infectious disease that can be found in many regions of Southeast Asia. There exist four serotypes of the virus. Recovery from one serotype produces a natural immunity from that serotype. However, it also creates complexes with a second infection and will increase viral production. This process is know as antibody dependent enhancement (ADE). As a result, it is very difficult to vaccinate against the disease. An optimal vaccination would have to cover all four serotypes at once. To understand the dynamics of the disease, we will study a mathematical model for two coexisting serotypes …
A Numerical Method For Obtaining An Optimal Temperature Distribution In A Three-Dimensional Triple-Layered Skin Structure Embedded With Multi-Level Blood Vessels, Xingui Tang
Doctoral Dissertations
The research related to hyperthermia has stimulated a lot of interest in recent years because of its application in cancer treatment. When heating the tumor tissue, the crucial problem is keeping the temperature of the surrounding normal tissue below a certain threshold in order to avoid the damage to the normal tissue. Hence, it is important to obtain the temperature field of the entire region during the treatment. The objective of this dissertation is to develop a numerical method for obtaining an optimal temperature distribution in a 3D triple-layered skin structure embedded with multi-level blood vessels where the surface of …
An Interactive Relaxation Approach For Anomaly Detection And Preventive Measures In Computer Networks, Garrick A. Bell
An Interactive Relaxation Approach For Anomaly Detection And Preventive Measures In Computer Networks, Garrick A. Bell
Theses and Dissertations
It is proposed to develop a framework of detecting and analyzing small and widespread changes in specific dynamic characteristics of several nodes. The characteristics are locally measured at each node in a large network of computers and analyzed using a computational paradigm known as the Relaxation technique. The goal is to be able to detect the onset of a worm or virus as it originates, spreads-out, attacks and disables the entire network. Currently, selective disabling of one or more features across an entire subnet, e.g. firewalls, provides limited security and keeps us from designing high performance net-centric systems. The most …
Doppler Aliasing Reduction In Wide-Angle Synthetic Aperture Radar Using Phase Modulated Random Stepped-Frequency Waveforms, Andrew W. Hyatt
Doppler Aliasing Reduction In Wide-Angle Synthetic Aperture Radar Using Phase Modulated Random Stepped-Frequency Waveforms, Andrew W. Hyatt
Theses and Dissertations
This research effort examines the theory, application and results of side-looking airborne radar operation in hot clutter. Hot clutter is an electronic counter-measure used to degrade the performance of airborne radar. Hot clutter occurs by illuminating the ground with an airborne jammer at some velocity, azimuth, elevation, and range from the airborne radar. When the received RCS scattered hot clutter waveform is perfectly coherent with the radar waveform, the radar believes the returns created by the hot clutter jammer resulted from the transmitting radar. Hot clutter degrades radar performance at locations in azimuth and Doppler. The effect of hot clutter …
Quantitative Object Reconstruction Using Abel Transform Tomography And Mixed Variable Optimization, Kevin R. O'Reilly
Quantitative Object Reconstruction Using Abel Transform Tomography And Mixed Variable Optimization, Kevin R. O'Reilly
Theses and Dissertations
Researchers at the Los Alamos National Laboratory (LANL) are interested in quantitatively reconstructing an object using Abel transform x-ray tomography. Specifically, they obtain a radiograph by x-raying an object and attempt to quantitatively determine the number and types of materials and the thicknesses of each material layer. Their current methodologies either fail to provide a quantitative description of the object or are generally too slow to be useful in practice. As an alternative, the problem is modeled here as a mixed variable programming (MVP) problem, in which some variables are nonnumeric and for which no derivative information is available. The …
Doppler-Only Multistatic Radar, Dustin G. Mixon
Doppler-Only Multistatic Radar, Dustin G. Mixon
Theses and Dissertations
In order to estimate the position and velocity of a target, most multistatic radar systems require multiple independent target measurements, such as angle-of-arrival, time-of-arrival, and Doppler information. Though inexpensive and reliable, Doppler-only systems have not been widely implemented due to the inherent nonlinear problem of determining a target’s position and velocity from their measurements. We solve this problem. In particular, we first establish the lack of observability in the Doppler-only bistatic system, thereby demonstrating the need for multiple transmitters and/or receivers. Next, for a multistatic system with a sufficient number of transmitter-receiver pairs, we invoke classical optimization techniques, such as …
Existence Of Explosive Solutions To Non-Monotone Semilinear Elliptic Equations, Zachary H. Proano
Existence Of Explosive Solutions To Non-Monotone Semilinear Elliptic Equations, Zachary H. Proano
Theses and Dissertations
We consider the semilinear elliptic equation Δu = p(x)f(u) on a domain Ω ⊆ Rn, n ≥ 3, where f is a nonnegative function which vanishes at the origin and satisfies g1 ≤ f ≤ g2 where g1; g2 are nonnegative, nondecreasing functions which also vanish at the origin, and p is a nonnegative continuous function with the property that any zero of p is contained in a bounded domain in such that p is positive on its boundary. For Ω bounded, we show that a nonnegative solution u satisfying u(x) …
The Dynamics Of Newton's Method On Cubic Polynomials, Shannon N. Miller
The Dynamics Of Newton's Method On Cubic Polynomials, Shannon N. Miller
Theses, Dissertations and Capstones
The field of dynamics is itself a huge part of many branches of science, including the motion of the planets and galaxies, changing weather patterns, and the growth and decline of populations. Consider a function f and pick x0 in the domain of f . If we iterate this function around the point x0, then we will have the sequence x0, f (x0), f (f (x0)), f (f (f (x0))), ..., which becomes our dynamical system. We are essentially interested in the end behavior of this system. Do …
Extension Of Shor's Period-Finding Algorithm To Infinite Dimensional Hilbert Spaces, Jeremy James Becnel
Extension Of Shor's Period-Finding Algorithm To Infinite Dimensional Hilbert Spaces, Jeremy James Becnel
LSU Doctoral Dissertations
Over the last decade quantum computing has become a very popular field in various disciplines, such as physics, engineering, and mathematics. Most of the attraction stemmed from the famous Shor period--finding algorithm, which leads to an efficient algorithm for factoring positive integers. Many adaptations and generalizations of this algorithm have been developed through the years, some of which have not been ripened with full mathematical rigor. In this dissertation we use concepts from white noise analysis to rigorously develop a Shor algorithm adapted to find a hidden subspace of a function with domain a real Hilbert space. After reviewing the …
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 …
Classifying Quadratic Number Fields Up To Arf Equivalence, Jeonghun Kim
Classifying Quadratic Number Fields Up To Arf Equivalence, Jeonghun Kim
LSU Doctoral Dissertations
Two number fields K and L are said to be Arf equivalent if there exists a bijection T : ΩK → ΩL of places of K and of L such that KP and LTP are locally Arf equivalent for every place P ε ΩK. That is, |K*p/K*2p| = |L*TP/L*2TP|, type[( , )P] = type[( , )TP], and Arf(rP ) = Arf(rTP ) for every place P ε ΩK, where rP is the local …
Integral Cohomology Of The Siegel Modular Variety Of Degree Two And Level Three, Mustafa Arslan
Integral Cohomology Of The Siegel Modular Variety Of Degree Two And Level Three, Mustafa Arslan
LSU Doctoral Dissertations
In this thesis work Deligne's spectral sequence Ep,qr with integer coefficients for the embedding of the Siegel modular variety of degree two and level three, A2(3) into its Igusa compactification, A2(3)*, is investigated. It is shown that E3 = E∞ and this information is applied to compute the cohomology groups of A2(3) over the integers.
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 …
Methods For The Estimation Of Missing Values In Time Series, David S. Fung
Methods For The Estimation Of Missing Values In Time Series, David S. Fung
Theses: Doctorates and Masters
Time Series is a sequential set of data measured over time. Examples of time series arise in a variety of areas, ranging from engineering to economics. The analysis of time series data constitutes an important area of statistics. Since, the data are records taken through time, missing observations in time series data are very common. This occurs because an observation may not be made at a particular time owing to faulty equipment, lost records, or a mistake, which cannot be rectified until later. When one or more observations are missing it may be necessary to estimate the model and also …
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 …
Traveling Waves In A Suspension Bridge System, Robert A. Ain
Traveling Waves In A Suspension Bridge System, Robert A. Ain
UNLV Theses, Dissertations, Professional Papers, and Capstones
In this thesis, we study the traveling waves in a Lazer-McKenna suspension bridge system which is governed by two coupled nonlinear beam and wave equations. The Lazer-McKenna suspension bridge system describes the vertical deflections in the roadbed and supporting cable of a suspension bridge. Based on some basic analysis on the system, we are able to compute traveling waves numerically by using MAPLE. Multiple large-amplitude traveling waves are obtained. The graphs of various traveling waves are displayed and discussed.
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 …
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 …
Topics In Quantum Topology, Khaled Moham Qazaqzeh
Topics In Quantum Topology, Khaled Moham Qazaqzeh
LSU Doctoral Dissertations
In chapter 1, which represents joint work with Gilmer, we define an index two subcategory of a 3-dimensional cobordism category. The objects of the category are surfaces equipped with Lagrangian subspaces of their real first homology. This generalizes the result of [9] where surfaces are equipped with Lagrangian subspaces of their rational first homology. To define such subcategory, we give a formula for the parity of the Maslov index of a triple of Lagrangian subspaces of a skew symmetric bilinear form over R. In chapter 2, we find two bases for the lattices of the SU(2)-TQFT-theory modules of the torus …
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 …
Using Elimination To Describe Maxwell Curves, Lucas P. Beverlin
Using Elimination To Describe Maxwell Curves, Lucas P. Beverlin
LSU Master's Theses
Cartesian ovals are curves in the plane that have been studied for hundreds of years. A Cartesian oval is the set of points whose distances from two fixed points called foci satisfy the property that a linear combination of these distances is a fixed constant. These ovals are a special case of what we call Maxwell curves. A Maxwell curve is the set of points with the property that a specific weighted sum of the distances to n foci is constant. We shall describe these curves geometrically. We will then examine Maxwell curves with two foci and a special case …
Markov Switching And Jump Diffusion Models With Applications In Mathematical Finance, Shengkun Xie
Markov Switching And Jump Diffusion Models With Applications In Mathematical Finance, Shengkun Xie
Theses and Dissertations (Comprehensive)
In this thesis, we study some jump diffusion models with Markov switching and transition densities for Markov switching diffusion processes with and without an absorbing barrier. We work out some analytical results, which have useful applications in mathematical finance and other related fields. The first-passage time problem for a Markov switching model is also studied and European type options and lookback options are computed in closed-form as examples to show that these models can be applied in practice. We apply optimization methods and kernel smoothing techniques to produce some important numerical results that show that jump diffusion with Markov switching …
Optimal Binary Trees With Height Restrictions On Left And Right Branches, Song Ding
Optimal Binary Trees With Height Restrictions On Left And Right Branches, Song Ding
LSU Master's Theses
We begin with background definitions on binary trees. Then we review known algorithms for finding optimal binary search trees. Knuth's famous algorithm, presented in the second chapter, is the cornerstone for our work. It depends on two important results: the Quadrangle Lemma and the Monoticity Theorem. These enabled Knuth to achieve a time complexity of O(n2), while previous algorithms had been O(n3) (n = size of input). We present the known generalization of Knuth's algorithm to trees with a height restriction. Finally, we consider the previously unexamined case of trees with different restrictions on left and …
Characterization Of The Dependency Across Foreign Exchange Markets Using Copulas, Ryan Coelho
Characterization Of The Dependency Across Foreign Exchange Markets Using Copulas, Ryan Coelho
LSU Master's Theses
Though Pearson's correlation coefficient provides a convenient approach to measuring the dependency between two variables, in the last few years, there has been a significant amount of literature cautioning against the use of Pearson's correlation coefficient, as it does not remain invariant under monotone transformations of the underlying distribution functions. Since we are interested in examining the dependency pattern observed by the return on the Sterling Pound with that of the Japanese Yen, we will use the notion of a copula to approximate the joint density function between the daily returns on the Sterling Pound and the Japanese Yen. In …