Ng, Ka Shing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 45-47). / Abstracts in English and Chinese. / Introduction --- p.v / Chapter 1 --- Preliminaries --- p.1 / Chapter 1.1 --- Noncommutative probability spaces and Free in- dependence --- p.1 / Chapter 1.2 --- C*-probability spaces --- p.4 / Chapter 1.3 --- Fock spaces --- p.5 / Chapter 1.4 --- Cauchy transform and R-transform of probability measures with bounded support --- p.7 / Chapter 1.5 --- Helton-Howe formula --- p.8 / Chapter 1.6 --- Stieltjes inversion formula --- p.9 / Chapter 1.7 --- Pick functions --- p.11 / Chapter 2 --- Free convolution and R-transform --- p.13 / Chapter 2.1 --- Additive free convolution and R-transform --- p.13 / Chapter 2.2 --- R-transform and algebraic Cauchy transform --- p.18 / Chapter 2.3 --- Properties of R-transform --- p.26 / Chapter 2.4 --- Properties of --- p.29 / Chapter 3 --- Examples of free convolution --- p.32 / Chapter 3.1 --- Measures with compact support --- p.32 / Chapter 3.2 --- Examples of free convolution --- p.33 / Chapter 4 --- Free Central Limit Theorem --- p.42 / Bibliography --- p.45

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Free trade agreements (FTAs) now play an increasingly significant role in international trade. The removal of tariff and non-tariff barriers through a bilateral FTA could promote and facilitate trade in both directions by increasing the opportunities available to exporters from both countries. Beyond opening up important new market access opportunities, these agreements may also deepen economic integration with trading partners and thus strengthen trade and economic relationships. Drawing on conventional and new trade theoretical approaches, this thesis attempts to suggest that new trade theory might be more superior to shed light on policies to secure greater benefits from FTAs.There is now an extensive body of literature analyzing the economic impacts of FTAs. In common with a broader division in trade theory (Rangasamy 2003), this literature may be classified into two categories; namely, that informed by conventional trade theory (which has a neo-classical foundation) and new trade theory. The conventional approach is one grounded on the theories of trade creation and trade diversion pioneered by Viner, and based on the assumptions of perfect competition and constant returns in production, this strongly emphasizes a neutral policy environment to ensure the gains from trade and FTAs are reaped. The new trade theory is based on an opposing set of assumptions emphasizing the existence of imperfect competition and economies of scale (see e.g. Dixit and Norman 1980, Krugman 1980, 1981, Helpman, 1981). In this view, neutral incentives and laissez faire policies are not always beneficial to industrial development as advocated by conventional trade theory. On the contrary, government policies play an increasingly important role to ensure the gains from trade and FTAs are realized.Drawing on the perspective of new trade theory, a number of important policy suggestions have been put forward to improve the gains from FTAs, including profit-shifting, innovation and R&D, and industry clustering arguments. In addition to these theoretical insights, the practical experience of FTAs in Singapore may present further lessons. The available evidence suggests that FTAs have brought tremendous gains in terms of trade and GDP growth, welfare improvement, as well as structural changes. The Singaporean government has put in place an extensive policy framework to ensure that these benefits are maximized. A close examination of the policy mix that they have pursued should therefore have important implications for policy makers in New Zealand.In light of the theoretical framework and empirical findings, the present thesis makes a number of policy suggestions with regard to the maximization of the long term benefit of FTAs in New Zealand economic settings. These suggestions aim to deal with the impact of FTAs and enable New Zealand to compete more effectively for profit in an FTA environment.

With an estimated 400 million domestic cats worldwide, free-roaming cats issues are of global importance due to animal welfare and public health concerns, as well as impacts on native wildlife through predation, competition and disease transmission. Though these impacts have been well documented, no research has evaluated the ecology and population dynamics of unmanaged, free-roaming cat populations using radio-telemetry. My objectives were to (1) compare population demographics (survival, fecundity and annual ranges/movements) among sex and ownership classifications (feral, semi-feral, and owned), (2) evaluate mark-resight and distance sampling for estimating cat abundances in urban areas, and (3) evaluate the effectiveness and costs associated with euthanasia and trap/treat/neuter/release (TTNR) programs for controlling urban cat populations. I radio-collared free-roaming cats (feral, n = 30; semi-feral, n = 14; owned, n = 10) in Caldwell, Texas (October 2004-2005). I found (1) increased levels of ownership or feeding reduce free-roaming cats’ ranges and movements while increasing survival and fecundity, (2) distance sampling resulted in precise abundance estimates providing an alternative to estimating urban cat densities, and (3) both euthanasia and TTNR may effectively reduce free-roaming cat numbers if implemented at high rates (>50% of population treated) the first year. I recommend euthanasia be implemented in ecologically sensitive areas and TTNR in areas lacking public support for lethal control. Population control solutions should include public education to increase awareness of cat issues and impacts, and pre- and post-implementation monitoring plans.

This research develops a procedure to determine the applied stresses in rails using the acoustoelastic effect of ultrasonic waves. Acoustoelasticity is defined as the stress dependency of ultrasonic wave speed or wave polarization. Analytical models are developed that predict the acoustoelastic effect for longitudinal waves, shear waves, Lamb waves, and Rayleigh waves. Using a programming tool, a numerical simulation of the models is generated to obtain the stress dependent curves of wave velocity and polarization of the various ultrasonic waves propagating in rail steel. A comparison of the sensitivity of the acoustoelastic effect is made to determine the feasibility of ultrasonic waves for further study. Rayleigh waves are found to be most sensitive to stress change. Rayleigh waves are generated using ultrasonic transducer and detected using a laser Doppler vibrometer (LDV). The LDV measures the in-plane and out-of-plane velocities. Polarization is defined as the ratio of in-plane and out-of-plane displacements. Initially, polarization is determined for the specimen in unstressed condition. Thereafter, the rail specimen is stressed in a compression testing machine, the experiment repeated, and the polarization determined. Thus, Rayleigh wave polarization is obtained as a function of applied stress. Finally, the change in polarization obtained experimentally is compared with the analytical model.

This research develops a procedure to determine the applied stresses in rails using the acoustoelastic effect of ultrasonic waves. Acoustoelasticity is defined as the stress dependency of ultrasonic wave speed or wave polarization. Analytical models are developed that predict the acoustoelastic effect for longitudinal waves, shear waves, Lamb waves, and Rayleigh waves. Using a programming tool, a numerical simulation of the models is generated to obtain the stress dependent curves of wave velocity and polarization of the various ultrasonic waves propagating in rail steel. A comparison of the sensitivity of the acoustoelastic effect is made to determine the feasibility of ultrasonic waves for further study. Rayleigh waves are found to be most sensitive to stress change. Rayleigh waves are generated using ultrasonic transducer and detected using a laser Doppler vibrometer (LDV). The LDV measures the in-plane and out-of-plane velocities. Polarization is defined as the ratio of in-plane and out-of-plane displacements. Initially, polarization is determined for the specimen in unstressed condition. Thereafter, the rail specimen is stressed in a compression testing machine, the experiment repeated, and the polarization determined. Thus, Rayleigh wave polarization is obtained as a function of applied stress. Finally, the change in polarization obtained experimentally is compared with the analytical model.

Pipelines from offshore petroleum fields must frequently pass overareas with uneven seafloor.  In such cases the pipeline may havefree spans when crossing depressions. Hence, if dynamic loads canoccur, the free span may oscillate and time varying stresses maygive unacceptable fatigue damage. A major source for dynamicstresses in free span pipelines is vortex induced vibrations (VIV)caused by steady current. This effect is in fact dominating ondeep water pipelines since wave induced velocities andaccelerations will decay with increasing water depth. Thechallenge for the industry is then to verify that such spans cansustain the influence from the environment throughout the lifetimeof the pipeline.\\\\The aim of the present project is to improve the understanding ofvortex induced vibrations (VIV) of free span pipelines, andthereby improve methods, existing computer programs and guidelinesneeded for design verification.  This will result in more costeffective and reliable offshore pipelines when laid on a veryrugged seafloor.\\\\VIV for multiple span pipeline is investigated and the dynamicalinteraction between adjacent spans has been shown. The interactionmay lead to increased or decreased response of each spansdepending on the current speed and the properties for the twospans. The extension of the contact zone between the spans andseafloor parameters will of course also be important for theinteraction effect.\\\\The influence from temperature variation on vortex inducedvibrations has been demonstrated. The response frequency isinfluenced through changes in pipe tension and sag. Both increaseand decrease of the response frequency may be experienced.Moreover, it is shown that the influence from snaking of the pipeon the temperature effect is small, at least for large diameterpipes.\\\\A free span pipeline will necessarily oscillate close to the seabed.The presence of the seabed will therefore have some influences onthe ambient flow profile and also on the flow pattern around thecylinder during oscillation. Hydrodynamic parameters may thereforevary when the pipe is close to the seabed. In the present work, theinfluence from spatial varying current profiles is investigated forboth single and multiple span pipeline. It is shown that thedifference between using uniform and spatial varying currentprofiles is significant for some current speeds. It is also shownthat use of spatial varying current profiles can be even moreimportant for multiple span pipeline.\\\\The comparison of VIVANA analysis results with MARINTEK testresults has been given. It shows VIVANA predicts the cross-flow responsegenerally much higher than the test measurements, especially for thehigher mode responses. To improve understanding of this phenomena, the VIVANA model was tuned tothe test model and results are compared in different cases. Attempts were made to obtain a better agreement by adjusting some of the input parameters to VIAVANA. The reference point is tuned by changing various hydrodynamic properties, i.e. $C_{L}$, $St$ and added mass. The response frequenciesare also tuned in order to have a better agreement on the results. It is been concluded that the method used here by VIVANA is not able to describe VIV for free spanning pipelines adequately. It is not possible to find a set of parameter in a rational way that will give reasonably correct results. The discrepancy between the analysis and test results are highlighted which confirms the interaction between the in-line and cross-flow vibrations.Discussions are given and addressed on different reasons which may cause this phenomena.\\\\An improved strategy for non-linear analysis of free span pipelineis outlined. Time domain analysis for free span pipeline hasbeen performed. The difference between time and frequency domainanalysis has also been investigated by varying boundary conditions,pipe properties and axial tension. A significant difference is shownbetween results from time and frequency domain analysis at each endof the span where the pipe is started to interact with the seafloor.Due to high fatigue at this point, the importance of usingnon-linear time domain analysis is therefor obvious and highlyrecommended.

Free volume and free volume distribution have long been used to explain differences in the gas transport properties of polymeric materials. However, only a few experimental techniques allow a comprehensive evaluation of polymeric void space. Through the use of computer simulations, the free volume was characterized of two polyester systems used for beverage packaging and polynorbornene, a unique polymer with possible applications in both microelectronic fabrication and membrane separations. Delaunay Tessellation was used to calculate the fractional free volume (FFV) of both polyethylene terephthalate (PET) and polyethylene naphthalate (PEN) molecular models. It was hypothesized that differences in the FFV distributions could be used to explain the higher experimental O2 solubility in PEN relative to PET. The analysis showed that there was no statistical difference between the FFV distributions for O2 sized penetrants. Clustering analysis was performed based upon the tetrahedra formed by Delaunay Tessellation to examine the connectivity of free volume pockets. These results show that there is a statistically larger number of small (containing less than 10 tetrahedra/cluster and between 20-30 and #506;3 in volume) clusters in PEN. It is this difference in small clusters which provides for the 30% higher O2 solubility in PEN. The free volume of a representative high molecular weight amorphous model of Hexafluroalcohol Subsituted Polynorbornene (HFA-PNB) was also characterized in to examine the shape of the free volume cavities and to draw correlations with the mean lifetime of ortho-positronium (o-Ps) from Positron Annihilation Lifetime Spectroscopy (PALS). Delaunay Tessellation and clustering analysis indicated that the free volume clusters in high molecular weight HFA-PNB are slightly non-spherical. Correcting lifetimes for the somewhat non-spherical shape of these free volume clusters was insufficient to reproduce experimentally measured positron annihilation lifetimes because the clusters contained many tortuous connections within the clusters. Inclusion of this connectivity information does produce a more accurate estimate of the measured life times. This indicates that the o-Ps does sample many tetrahedra in these static clusters, but does not freely sample every section of these clusters.

This research develops a procedure to determine the applied stresses in rails using the acoustoelastic effect of ultrasonic waves. Acoustoelasticity is defined as the stress dependency of ultrasonic wave speed or wave polarization. Analytical models are developed that predict the acoustoelastic effect for longitudinal waves, shear waves, Lamb waves, and Rayleigh waves. Using a programming tool, a numerical simulation of the models is generated to obtain the stress dependent curves of wave velocity and polarization of the various ultrasonic waves propagating in rail steel. A comparison of the sensitivity of the acoustoelastic effect is made to determine the feasibility of ultrasonic waves for further study. Rayleigh waves are found to be most sensitive to stress change. Rayleigh waves are generated using ultrasonic transducer and detected using a laser Doppler vibrometer (LDV). The LDV measures the in-plane and out-of-plane velocities. Polarization is defined as the ratio of in-plane and out-of-plane displacements. Initially, polarization is determined for the specimen in unstressed condition. Thereafter, the rail specimen is stressed in a compression testing machine, the experiment repeated, and the polarization determined. Thus, Rayleigh wave polarization is obtained as a function of applied stress. Finally, the change in polarization obtained experimentally is compared with the analytical model.