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- Accelerate life model (1)
- Alternating direction implicit (1)
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- Buchberger's algorithm; Higman's lemma; Well quasi orderings (1)
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Articles 1 - 15 of 15
Full-Text Articles in Physical Sciences and Mathematics
On Well-Quasi-Orderings, Forrest Thurman
On Well-Quasi-Orderings, Forrest Thurman
HIM 1990-2015
A quasi-order is a relation on a set which is both reflexive and transitive, while a well-quasi-order has the additional property that there exist no infinite strictly descending chains nor infinite antichains. Well-quasi-orderings have many interesting applications to a variety of areas which includes the strength of certain logical systems, the termination of algorithms, and the classification of sets of graphs in terms of excluded minors. My thesis explores how well-quasi-orderings are related to these topics through examples of four known well-quasi-orderings which are given by Dickson's Lemma, Higmans's Lemma, Kruskal's Tree Theorem, and the Robertson-Seymour Theorem. The well-quasi-ordering conjecture …
Partially Integrable Pt-Symmetric Hierarchies Of Some Canonical Nonlinear Partial Differential Equations, Keri Pecora
Partially Integrable Pt-Symmetric Hierarchies Of Some Canonical Nonlinear Partial Differential Equations, Keri Pecora
Electronic Theses and Dissertations
In this dissertation, we generalize the work of Bender and co-workers to derive new partially-integrable hierarchies of various PT -symmetric, nonlinear partial differential equations. The possible integrable members are identified employing the Painlev´e Test, a necessary but not sufficient integrability condition, and are indexed by the integer n, corresponding to the negative of the order of the dominant pole in the singular part of the Painlev´e expansion for the solution. For the PT -symmetric Korteweg-de Vries (KdV) equation, as with some other hierarchies, the first or n = 1 equation fails the test, the n = 2 member corresponds to …
Numerical Simulations For The Flow Of Rocket Exhaust Through A Granular Medium, Kristina Kraakmo
Numerical Simulations For The Flow Of Rocket Exhaust Through A Granular Medium, Kristina Kraakmo
Electronic Theses and Dissertations
Physical lab experiments have shown that the pressure caused by an impinging jet on a granular bed has the potential to form craters. This poses a danger to landing success and nearby spacecraft for future rocket missions. Current numerical simulations for this process do not accurately reproduce experimental results. Our goal is to produce improved simulations to more accurately and effi- ciently model the changes in pressure as gas flows through a porous medium. A two-dimensional model in space known as the nonlinear Porous Medium Equation as it is derived from Darcy’s law is used. An Alternating-Direction Implicit (ADI) temporal …
Smooth And Non-Smooth Traveling Wave Solutions Of Some Generalized Camassa-Holm Equations, Taslima Rehman
Smooth And Non-Smooth Traveling Wave Solutions Of Some Generalized Camassa-Holm Equations, Taslima Rehman
Electronic Theses and Dissertations
In this thesis we employ two recent analytical approaches to investigate the possible classes of traveling wave solutions of some members of recently derived integrable family of generalized Camassa-Holm (GCH) equations. In the first part, a novel application of phase-plane analysis is employed to analyze the singular traveling wave equations of four GCH equations, i.e. the possible non-smooth peakon, cuspon and compacton solutions. Two of the GCH equations do no support singular traveling waves. We generalize an existing theorem to establish the existence of peakon solutions of the third GCH equation. This equation is found to also support four segmented, …
Spectrally Uniform Frames And Spectrally Optimal Dual Frames, Saliha Pehlivan
Spectrally Uniform Frames And Spectrally Optimal Dual Frames, Saliha Pehlivan
Electronic Theses and Dissertations
Frames have been useful in signal transmission due to the built in redundancy. In recent years, the erasure problem in data transmission has been the focus of considerable research in the case the error estimate is measured by operator (or matrix) norm. Sample results include the characterization of one-erasure optimal Parseval frames, the connection between two-erasure optimal Parseval frames and equiangular frames, and some characterization of optimal dual frames. If iterations are allowed in the reconstruction process of the signal vector, then spectral radius measurement for the error operators is more appropriate then the operator norm measurement. We obtain a …
Modified Pal Interpolation And Sampling Bilevel Signals With Finite Rate Of Innovation, Gayatri Ramesh
Modified Pal Interpolation And Sampling Bilevel Signals With Finite Rate Of Innovation, Gayatri Ramesh
Electronic Theses and Dissertations
Sampling and interpolation are two important topics in signal processing. Signal processing is a vast field of study that deals with analysis and operations of signals such as sounds, images, sensor data, telecommunications and so on. It also utilizes many mathematical theories such as approximation theory, analysis and wavelets. This dissertation is divided into two chapters: Modified Pal´ Interpolation and Sampling Bilevel Signals with Finite Rate of Innovation. In the first chapter, we introduce a new interpolation process, the modified Pal interpolation, based on papers by P ´ al, J ´ oo´ and Szabo, and we establish the existence and …
Can One Hear...? An Exploration Into Inverse Eigenvalue Problems Related To Musical Instruments, Christine Adams
Can One Hear...? An Exploration Into Inverse Eigenvalue Problems Related To Musical Instruments, Christine Adams
Electronic Theses and Dissertations
The central theme of this thesis deals with problems related to the question, “Can one hear the shape of a drum?” first posed formally by Mark Kac in 1966. More precisely, can one determine the shape of a membrane with fixed boundary from the spectrum of the associated differential operator? For this paper, Kac received both the Lester Ford Award and the Chauvant Prize of the Mathematical Association of America. This problem has received a great deal of attention in the past forty years and has led to similar questions in completely different contexts such as “Can one hear the …
Curvelets And The Radon Transform, Jill Dickerson
Curvelets And The Radon Transform, Jill Dickerson
Electronic Theses and Dissertations
Computed Tomography (CT) is the standard in medical imaging field. In this study, we look at the curvelet transform in an attempt to use it as a basis for representing a function. In doing so, we seek a way to reconstruct a function from the Radon data that may produce clearer results. Using curvelet decomposition, any known function can be represented as a sum of curvelets with corresponding coefficients. It can be shown that these corresponding coefficients can be found using the Radon data, even if the function is unknown. The use of curvelets has the potential to solve partial …
Optimization Problem In Single Period Markets, Tian Jiang
Optimization Problem In Single Period Markets, Tian Jiang
Electronic Theses and Dissertations
There had been a number of researches that investigated on the security market without transaction costs. The focus of this research is in the area that when the security market with transaction costs is fair and in such fair market how one chooses a suitable portfolio to optimize the financial goal. The research approach adopted in this thesis includes linear algebra and elementary probability. The thesis provides evidence that we can maximize expected utility function to achieve our goal (maximize expected return under certain risk tolerance). The main conclusions drawn from this study are under certain conditions the security market …
Nonparametric And Empirical Bayes Estimation Methods, Rida Benhaddou
Nonparametric And Empirical Bayes Estimation Methods, Rida Benhaddou
Electronic Theses and Dissertations
In the present dissertation, we investigate two different nonparametric models; empirical Bayes model and functional deconvolution model. In the case of the nonparametric empirical Bayes estimation, we carried out a complete minimax study. In particular, we derive minimax lower bounds for the risk of the nonparametric empirical Bayes estimator for a general conditional distribution. This result has never been obtained previously. In order to attain optimal convergence rates, we use a wavelet series based empirical Bayes estimator constructed in Pensky and Alotaibi (2005). We propose an adaptive version of this estimator using Lepski’s method and show that the estimator attains …
Valuation Of Over-The-Counter (Otc) Derivatives With Collateralization, Leon Guerrero
Valuation Of Over-The-Counter (Otc) Derivatives With Collateralization, Leon Guerrero
Electronic Theses and Dissertations
Collateralization in over-the-counter (OTC) derivatives markets has grown rapidly over the past decade, and even faster in the past few years, due to the impact of the recent financial crisis and the particularly important attention to the counterparty credit risk in derivatives contracts. The addition of collateralization to such contracts significantly reduces the counterparty credit risk and allows to offset liabilities in case of default. We study the problem of valuation of OTC derivatives with payoff in a single currency and with single underlying asset for the cases of zero, partial, and perfect collateralization. We assume the derivative is traded …
Dynamical Invariants And The Fluid Impulse In Plasma Models, Martin Michalak
Dynamical Invariants And The Fluid Impulse In Plasma Models, Martin Michalak
Electronic Theses and Dissertations
Much progress has been made in understanding of plasmas through the use of the MHD equations and newer models such as Hall MHD and electron MHD. As with most equations of fluid behavior, these equations are nonlinear, and no general solutions can be found. The use of invariant structures allows limited predictions of fluid behavior without requiring a full solution of the underlying equations. The use of gauge transformation can allow the creation of new invariants, while differential geometry offers useful tools for constructing additional invariants from those that are already known. Using these techniques, new geometric, integral and topological …
Extensions Of S-Spaces, Bernd Losert
Extensions Of S-Spaces, Bernd Losert
Electronic Theses and Dissertations
Given a convergence space X, a continuous action of a convergence semigroup S on X and a compactification Y of X, under what conditions on X and the action on X is it possible to extend the action to a continuous action on Y . Similarly, given a Cauchy space X, a Cauchy continuous action of a Cauchy semigroup S on X and a completion Y of X, under what conditions on X and the action on X is it possible to extend the action to a Cauchy continuous action on Y . We answer the first question for some …
Hjb Equation And Statistical Arbitrage Applied To High Frequency Trading, Yonggi Park
Hjb Equation And Statistical Arbitrage Applied To High Frequency Trading, Yonggi Park
Electronic Theses and Dissertations
In this thesis we investigate some properties of market making and statistical arbitrage applied to High Frequency Trading (HFT). Using the Hamilton-Jacobi-Bellman(HJB) model developed by Guilbaud, Fabien and Pham, Huyen in 2012, we studied how market making works to obtain optimal strategy during limit order and market order. Also we develop the best investment strategy through Moving Average, Exponential Moving Average, Relative Strength Index, Sharpe Ratio.
Accelerated Life Model With Various Types Of Censored Data, Kathryn Pridemore
Accelerated Life Model With Various Types Of Censored Data, Kathryn Pridemore
Electronic Theses and Dissertations
The Accelerated Life Model is one of the most commonly used tools in the analysis of survival data which are frequently encountered in medical research and reliability studies. In these types of studies we often deal with complicated data sets for which we cannot observe the complete data set in practical situations due to censoring. Such difficulties are particularly apparent by the fact that there is little work in statistical literature on the Accelerated Life Model for complicated types of censored data sets, such as doubly censored data, interval censored data, and partly interval censored data. In this work, we …