Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2006. / Includes bibliographical references (leaves 70-74). Also available in electronic version.

University of Macau / Faculty of Science and Technology / Department of Mathematics

The Besov class $B_{pq}^s$ is defined by ${ f : { 2^{|n|s}||W_n*f||_p } _{ninmathbb{Z}}in ell^q(mathbb{Z}) }$. When $s=1$, $p=q $, we know if $f in B_p$ if and only if $int_mathbb{D} |f^{(n)}(z)|^p(1-|z|^2)^{2pn-2}dv(z) <+infty$. It is shown in [5] that $int_{mathbb{D}}|f^{'}(z)|^q K(z,z)^{1-q}dv(z)= O(L(b(e^{-(q-p)^{-1}})))$ if $f in B_{L,p}$. In this paper we will show that $f in B_{L,p}$ if and only if $sum_{n=0}^{infty}2^{nq}||W_n*f||_p^q = O(L(b(e^{-(q-p)^{-1}})))$.

In this thesis, a systematic study is carried out for effectively approximating Gerber-Shiu functions under L´evy subordinator models. It is a hardly touched topic in the recent literature and our approach is via the popular Fourier-cosine method. In theory, classical Gerber-Shiu functions can be expressed in terms of an infinite sum of convolutions, but its inherent complexity makes efficient computation almost impossible. In contrast, Fourier transforms of convolutions could be evaluated in a far simpler manner. Therefore, an efficient numerical method based on Fourier transform is pursued in this thesis for evaluating Gerber-Shiu functions. Fourier-cosine method is a numerical method based on Fourier transform and has been very popular in option pricing since its introduction. It then evolves into a number of extensions, and we here adopt its spirit to insurance risk theory. In this thesis, the proposed approximant of Gerber-Shiu functions under an L´evy subordinator model has O(n) computational complexity in comparison with that of O(n log n) via the usual numerical Fourier inversion. Also, for Gerber-Shiu functions within the proposed refined Sobolev space, an explicit error bound is given and error bound of this type is seemingly absent in the literature. Furthermore, the error bound for our estimation can be further enhanced under extra assumptions, which are not immediate from Fang and Oosterlee’s works. We also suggest a robust method on the estimation of ruin probabilities (one special class of Gerber-Shiu functions) based on the moments of both claim size and claim arrival distributions. Rearrangement inequality will also be adopted to amplify the use of our Fourier-cosine method in ruin probability, resulting in an effective global estimation. Finally, the effectiveness of our result will be further illustrated in a number of numerical studies and our enhanced error bound is apparently optimal in our demonstration; more precisely, empirical evidence exhibiting the biggest possible error convergence rate agrees with our theoretical conclusion. / published_or_final_version / Mathematics / Master / Master of Philosophy

published_or_final_version / Statistics / Master / Master of Philosophy

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

No description available.

As a contribution to increasing the areal density of digital data stored on a magnetic recording medium, this thesis provides mathematical analyses of various magnetic recording heads. Each of the heads considered here is for use in a perpendicular recording system, writing to or reading from a multi-layer medium which includes a high magnetic permeability layer between the data storage layer and the substrate. The exact two-dimensional analysis is performed in each case by one of two methods: either Fourier analysis or conformal mapping. The types of heads analysed include conventional styles but particular emphasis is placed on the effects of the novel idea of potential grading across the pole pieces. Exact head fields are derived for thin film heads with both constant and linearly varying pole potentials, single pole heads with linearly and arbitrarily varying pole potentials and shielded magnetoresistive heads, all in the presence of a magnetic underlayer. These and other published solutions are used to derive output characteristics for perpendicular replay heads, which are compared with published theoretical and experimental results where possible. The Fourier solutions obtained are in the form of infinite series dependent on at least one set of coefficients which are determined by infinite systems of linear equations. Approximations to the potentials in the head face planes, independent of these coefficients, are derived from the exact Fourier solutions. The accuracy of these approximations is demonstrated when they are used to estimate the vertical field components and the spectral response functions. Heads with graded pole potentials are found to have more localised vertical field components than the corresponding constant potential heads. They are also better suited for use with thin media for 'in contact' recording.

Liposomes are used as biocompatible carriers of drugs, peptides, proteins, plasmic DNA, antisense oligonucleotides or ribozymes, for pharmaceutical, cosmetic, and biochemical purposes. They are considered as effective drug delivery systems due to their colloidal size, easily controllable surface and membrane properties, large carrying capacity of drugs and biocompatibility. / This study was concerned with the stability of liposomes, their interaction at solid-liquid interfaces and their release of hydrophilic drug compounds. Either conventional liposomes containing lecithin and cholesterol, and Stealth® liposomes containing polyethylene glycol (PEG) 5000-lipids or PEG2000-lipids were investigated. Steric hindrance introduced by PEG chains proved to be influential in controlling liposome stability, interaction and drug release processes. Electrostatic forces were shown to be essential to the mechanisms and kinetics of liposome adsorption and colloidal stability, but not influential for the release of guanosine, used as a model hydrophilic drug. / Findings from this research improve the understanding of liposome interaction during drug delivery, give insight into the actions of liposomes in the body and may form the basis for improved liposome formulation. In addition, this research has developed a more comprehensive understanding of the role of PEG in controlling the colloidal stability, interfacial interactions of liposomes and drug transport kinetics across the lipid bilayers of liposomes. / Thesis (PhDAppliedScience)--University of South Australia, 2005.

Thesis (M.S.)--West Virginia University, 2008. / Title from document title page. Document formatted into pages; contains x, 81, 9 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 73-75).