Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Mathematics." Includes bibliographical references (p. 51-52).

Thesis (Ph. D.)--University of Texas at Austin, 2000. / Vita. Includes bibliographical references (leaves 178-187). Available also in a digital version from Dissertation Abstracts.

Thesis (M. Phil.)--University of Hong Kong, 2002. / Includes bibliographical references (leaves 112-116).

The ability of asphalt binders (bitumen) in road surfaces to self-heal after cracking is important to developing a robust transportation system that can tolerate heavy traffic and varying weather conditions. In order to develop improved binders, there is a need for noninvasive, in-situ, interface-specific methods of monitoring the kinetics, physics and chemistry of self-healing bitumen interfaces. Here the feasibility of using optical second-harmonic generation (SHG) by focused femtosecond laser pulses to monitor bitumen surfaces is demonstrated. SHG signals are observed in transmission through a sample composed of bitumen spin-coated onto a borosilicate microscope coverslip. The SHG signals are absent from uncoated coverslips, demonstrating that they originate from the bitumen layer. Further tests demonstrate that the bitumen-air surface makes the dominant contribution to the SHG signal. The SHG signal is observed to decay on a time scale comparable to typical self-healing times because of sample heating by the incident laser irradiation. Methods to control this effect by translating the sample during data acquisition are developed. Although the present results were obtained with a single incident wavelength (800 nm), they demonstrate the feasibility of probing bitumen interfaces spectroscopically with tunable light sources in order to monitor bond-specific chemical kinetics. / text

published_or_final_version / Mathematics / Master / Master of Philosophy

No description available.

No description available.

We study quasi superharmonic functions in Brelot spaces and the relationship between a reduced function, and harmonic and Jensen measures. We introduce the concept of quasi multiply superharmonic functions on a product of two Brelot spaces and study their properties. A main result obtained is characterizing the quasi superharmonic functions in terms of harmonic, finely harmonic and Jensen measures. Then we prove that a quasi multiply superharmonic function on a product of Brelot spaces equals its lower semicontinuous regularization out side of a 2-negligible set. Further we give a sufficient condition on a Brelot space O under which O becomes an extension space for superharmonic functions. As a result we characterize the extreme Jensen measures in such spaces. Finally we study extreme Jensen measures relative to several classes of multiply superharmonic functions.

No description available.

No description available.