Thesis (Ph. D.)--Ohio State University, 2003. / Title from first page of PDF file. Document formatted into pages; contains x, 227 p.; also includes graphics Includes bibliographical references (p. 224-227). Available online via OhioLINK's ETD Center

Liu, Li. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 41-44). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Empirical Likelihood --- p.1 / Chapter 1.2 --- Empirical Likelihood for Dependent Data --- p.4 / Chapter 1.2.1 --- Spectral Method --- p.5 / Chapter 1.2.2 --- Blockwise Method --- p.6 / Chapter 1.3 --- Edgeworth Expansions and Bartlett Correction --- p.9 / Chapter 1.3.1 --- Coverage Errors --- p.10 / Chapter 1.3.2 --- Edgeworth Expansions --- p.11 / Chapter 1.3.3 --- Bartlett Correction --- p.13 / Chapter 2 --- Bartlett Correction for EL --- p.16 / Chapter 2.1 --- Empirical Likelihood in Time Series --- p.16 / Chapter 2.2 --- Stochastic Expansions of EL in Time Series --- p.19 / Chapter 2.3 --- Edgeworth Expansions of EL in Time Series --- p.22 / Chapter 2.3.1 --- Validity of the Formal Edgeworth Expansions --- p.22 / Chapter 2.3.2 --- Cumulant Calculations --- p.24 / Chapter 2.4 --- Main Results --- p.30 / Chapter 3 --- Simulations --- p.32 / Chapter 3.1 --- Confidence Region --- p.33 / Chapter 3.2 --- Coverage Error of Confidence Regions --- p.35 / Chapter 4 --- Conclusion and Future Work --- p.38 / Bibliography --- p.41

vii, 99 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / We investigate Cesàro summability of the Fourier orthogonal expansion of functions on B d × I m , where B d is the closed unit ball in [Special characters omitted] and I m is the m -fold Cartesian product of the interval [-1, 1], in terms of orthogonal polynomials with respect to the weight functions (1 - z ) α (1 + z ) β (1 - |x| 2 ) λ-1/2 , with z ∈ I m and x ∈ B d . In addition, we study a discretized Fourier orthogonal expansion on the cylinder B 2 × [-1, 1], which uses a finite number of Radon projections. The Lebesgue constant of this operator is obtained, and the proof utilizes generating functions for associated orthogonal series. / Committee in charge: Yuan Xu, Chairperson, Mathematics; Huaxin Lin, Member, Mathematics Jonathan Brundan, Member, Mathematics; Marcin Bownik, Member, Mathematics; Jun Li, Outside Member, Computer & Information Science

No description available.

Taylor vortex flow is one of the basic problems of nonlinear hydrodynamic stability. In contrast with the wide region of wavenumber predicted by the linear theory, experiments show that Taylor vortex flow only appears in a small region containing the critical wavenumber ß_er This phenomenon is called wave selection. In this work, several high-order perturbation methods and a numerical method are established. Both evolution and steady state of the How caused by single or several disturbances are studied. The existence of multiple steady states for disturbances with small wavenumber is discovered and proved. The stable and unstable steady state solutions and some associated phenomena such as jump phenomenon and hysteresis phenomenon are found. and explained. In the small region, the wavenumbers and initial amplitudes of disturbances determine the wavenumber of the flow. But outside this region, only the wavenumbers of the disturbances have effect on the wave selection. These results indicate that unstable solutions play a key role in wave selection. The side-band stability curve produced by the high-order perturbation methods is accurate at low Taylor numbers but incorrect at relatively high Taylor numbers. The relation of the unstable solutions and side-band stability is discussed. Besides, the overshoot and the oscillation phenomena during evolution are studied in detail. Connections between this work and experiments are discussed. / Ph. D.

Le résultat principal de cette thèse est l'étude de l'ampleur dans des expansions des structures géométriques et de SU-rang oméga par un prédicat dense/codense indépendant. De plus, nous étudions le rapport entre l'ampleur et l'équationalite, donnant une preuve directe de l'équationalite de certaines théories CM-triviales. Enfin, nous considérons la topologie indiscernable et son lien avec l'équationalite et calculons la complexité indiscernable du pseudoplan libre / The main result of this thesis is the study of how ampleness grows in geometric and SU-rank omega structures when adding a new independent dense/codense subset. In another direction, we explore relations of ampleness with equational theories; there, we give a direct proof of the equationality of certain CM-trivial theories. Finally, we study indiscernible closed sets—which are closely related with equations—and measure their complexity in the free pseudoplane

We develop expansion methods as a new computational approach towards high-dimensional partial differential equations (PDEs), particularly of such type as arising in the valuation of financial derivatives. The proposed methods are extended from [41] and use principal component analysis (PCA) of the underlying process in combination with a Taylor expansion of the value function into solutions to low-dimensional PDEs. They enable calculation of highly accurate approximate solutions with computational complexity polynomial in the number of dimensions for PDEs with a low number of dominant principal components. For the case of PDEs with constant coefficients, we show existence of expansion solutions and prove theoretical error bounds. We give a precise characterisation of when our methods can be applied and construct specific examples of a first and second order version. We provide numerical results showing that the empirically observed convergence speeds are in agreement with the theoretical predictions. For the case of PDEs with varying coefficients, we give a heuristic motivation using the Parametrix approach and empirically test the methods' accuracy for a range of variable parameter stock models. We demonstrate the applicability of our expansion methods to real-world securities pricing problems by considering path-dependent and early-exercise options in the LIBOR market model. Using the example of Bermudan swaptions and Ratchet floors, which are considered difficult benchmark problems, we give a careful analysis of the numerical accuracy and computational complexity. We are able to demonstrate that for problems with medium to high dimensionality, around 60-100, and moderate time horizons, the presented PDE methods deliver results comparable in accuracy to benchmark state-of-the-art Monte Carlo methods in similar or (significantly) faster run time.

No description available.

This thesis consists of two parts. In the first part, we study a class of special functions Aik (y), k = 2, 4, 6, ··· generalising the classical Airy function Ai(y) to higher orders and in the second part, we apply expressions and properties of Ai4(y) to spectral problem of a specific operator. The first part is however motivated by latter part. We establish regularity properties of Aik (y) and particularly show that Aik (y) is smooth, bounded, and extends to the complex plane as an entire function, and obtain pointwise bounds on Aik (y) for all k. Some analytic properties of Aik (y) are also derived allowing one to express Aik (y) as a finite sum of certain generalised hypergeometric functions. We further obtain full asymptotic expansions of Aik (y) and their first derivative Ai'(y) both for y > 0 and for y < 0. Using these expansions, we derive expressions for the negative real zeroes of Aik (y) and Ai'(y). Using expressions and properties of Ai4(y), we extensively study spectral properties of a non-local operator H whose physical interpretation is the massless relativistic quartic anharmonic oscillator in one dimension. Various spectral results for H are derived including estimates of eigenvalues, spectral gaps and trace formula, and a Weyl-type asymptotic relation. We study asymptotic behaviour, analyticity, and uniform boundedness properties of the eigenfunctions Ψn(x) of H. The Fourier transforms of these eigenfunctions are expressed in two terms, one involving Ai4(y) and another term derived from Ai4(y) denoted by Āi4(y). By investigating the small effect generated by Āi4(y) this work shows that eigenvalues λn of H are exponentially close, with increasing n Ε N, to the negative real zeroes of Ai4(y) and those of its first derivative Ai'4(y) arranged in alternating and increasing order of magnitude. The eigenfunctions Ψ(x) are also shown to be exponentially well-approximated by the inverse Fourier transform of Ai4(|y| - λn) in its normalised form.

Thesis (MSc (Physics))--University of Stellenbosch, 2009. / Hanbury Brown-Twiss interferometry is a correlation technique by which the size and shape of the emission function of identical particles created during collisions of high-energy leptons, hadrons or nuclei can be determined. Accurate experimental datasets of three-dimensional correlation functions in momentum space now exist; these are sometimes almost Gaussian in form, but may also show strong deviations from Gaussian shapes. We investigate the suitability of expressing these correlation functions in terms of statistical quantities beyond the normal Gaussian description. Beyond means and the covariance matrix, higher-order moments and cumulants describe the form and di erence between the measured correlation function and a Gaussian distribution. The corresponding series expansion is the Gram- Charlier series and in particular the Gram-Charlier Type A expansion found in the literature, which is based on a Gaussian reference distribution. We investigate both the Gram-Charlier Type A series as well as generalised forms based on non-Gaussian reference distributions, as well as the related Edgeworth expansion. For testing purposes, experimental data is initially represented by a suite of one-dimensional analytic non-Gaussian distributions. We conclude that the accuracy of these expansions can be improved dramatically through a better choice of reference distribution, suggested by the sign and size of the kurtosis of the experimental distribution. We further extend our investigation to simulated samples of such test distributions and simplify the theoretical expressions for unbiased estimators (k-statistics) for the case of symmetric distributions.