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In this work we will consider the steady and two-dimensional potential flow of an incompressible fluid past a body without friction. Contrary to common experience, we will show that it is possible to calculate the Lie point symmetries that will leave the boundary value problem invariant. We are able to do this by solving the determining equation for the Lie point symmetries subject to a side condition. The side condition is a consequence of the boundary condition that occurs in the boundary value problem. We will show that solutions of the boundary value problem that were obtained previously using the method of conformal transformations are also group invariant solutions of the boundary value problem. We will also show that every group invariant solution of the boundary value problem can be used to generate new group invariant solutions of the same boundary value problem.

Keywords: General transformation model, Model Misspecification, Marginal likelihood, Markov chain Monte Carlo, Stochastic approximation, Mixed-effects model, Consistency, Asymptotic normality, Discretization technique. / Part II of this thesis concerns studies of mixed-effects general transformation models, i.e. general transformation models incorporating both fixed and random effects, to analyze grouped or clustered data. Rank-based marginal likelihood estimation is proposed. The estimation procedure is baseline-free, a good property enjoyed by the Cox partial likelihood. A three-stage Markov chain Monte Carlo stochastic approximation (MCMC-SA) algorithm is developed to find the maximum marginal likelihood estimation (MMLE). The asymptotic normality is obtained via a discretization procedure. Monte Carlo simulation shows that the MMLE has a good small- and moderate-sample behavior. In the end we illustrate an application of the proposed method to Hong Kong horse racing data. / Since it was first proposed by Dabrowska and Doksum in 1988, there is an explosive growth in both studies and applications of transformation model. Transformation model has many naturally endowed merits such as flexibility and conciseness in modeling lifetime or duration and ranking data involving covariates. However, like many other statistical models, transformation model may suffer the problem of misspecification due to falsely specified error term distribution or omitted covariates. The author investigates the large sample behavior of the rank-based quasi maximum marginal likelihood estimator (QMMLE) when transformation model is misspecified, and shows that owing to model misspecification, the QMMLE converges not to the true value of the parameter of interest, but to a "pseudo-true value" which minimizes the Kullback-Leibler divergence between the true model and the misspecified working model. A robust "sandwich" estimate of variance is proposed. The asymptotic normality of the QMMLE is also proved. Following the steps of White (1982), the appropriate Wald test statistic, Lagrange Multiplier test statistic and Information matrix specification test statistic are proposed. / Ni, Zhongxin. / Adviser: Ming Gao Gu. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3587. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 86-99). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

by Zheng Yu-kun. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1991. / Includes bibliographical references. / Preface --- p.1 / Chapter Chapter 1. --- Gauge Transformation and the Higher Order Korteweg-de Vries Equations --- p.6 / Chapter 1. --- Higher order KdV equations --- p.6 / Chapter 2. --- η2-dependent higher order mKdV equations --- p.9 / Chapter 3. --- η2-dependent Miura transformation and Backlund transformation --- p.13 / Chapter 4. --- Gauge transformation of the wave function --- p.15 / Chapter 5. --- Backlund transformation for the η2 -dependent higher order mKdV equation --- p.24 / Chapter 6. --- Applications --- p.25 / Chapter 7. --- References --- p.30 / Chapter Chapter 2. --- Solutions of a Nonisospectral and Variable Coefficient Korteweg-de Vries Equation --- p.31 / Chapter 1. --- Introduction --- p.31 / Chapter 2. --- Nonisospectral variable coefficient KdV-type equations --- p.32 / Chapter 3. --- Invariance of LP under the Crum transformation --- p.34 / Chapter 4. --- Backlund transformation for the h-t-KdV equation --- p.35 / Chapter 5. --- Solutions --- p.39 / Chapter 6. --- References --- p.43 / Chapter Chapter 3. --- Nonisospectral Variable Coefficient Higher Order Korteweg-de Vries Equations --- p.45 / Chapter 1. --- Introduction --- p.45 / Chapter 2. --- Nonisospectral t-ho-KdV equations --- p.47 / Chapter 3. --- Nonisospectral η2 dependent variable coefficient higher order modified KdV equation --- p.50 / Chapter 4. --- Backlund transformation and gauge transformation --- p.57 / Chapter 5. --- Example. Solutions of second order ni-t-KdV equation and its corresponding ni-t-η2-mKdV equation --- p.61 / Chapter 6. --- References --- p.66 / Chapter Chapter 4. --- Gauge and Backlund Transformations for the Variable Coefficient Higher-Order Modified Korteweg-de Vries Equation --- p.67 / Chapter 1. --- Introduction --- p.67 / Chapter 2. --- The t-ho-mKdV equation --- p.68 / Chapter 3. --- Some results about the t-ho-KdV equation --- p.74 / Chapter 4. --- A Backlund transformation for the t-ho-mKdV equation --- p.76 / Chapter 5. --- Gauge transformat ion and the Backlund transformation --- p.78 / Chapter 6. --- References --- p.85 / Chapter Chapter 5. --- Gauge and Backlund Transformat ions for the Generalized Sine-Gordon Equation and Its η Dependent Modified Equation --- p.86 / Chapter 1. --- Introduction --- p.86 / Chapter 2. --- Generalized Sine-Gordon equation --- p.87 / Chapter 3. --- Backlund transformation for the GSGE --- p.92 / Chapter 4. --- Gauge transformations for AKNS systems --- p.98 / Chapter 5. --- η dependent modified GSGE and its Backlund transformation --- p.102 / Chapter 6. --- Summary and example --- p.105 / Chapter 7. --- References --- p.110 / Chapter Chapter 6. --- Backlund Transformation for the Nonisospectral and Variable Coefficient Nonlinear Schrodinger Equation --- p.111 / Chapter 1. --- Introduction --- p.111 / Chapter 2. --- A generalized NLSE --- p.112 / Chapter 3. --- Γ Riccati equation system --- p.114 / Chapter 4. --- Invariance of the Γ-system --- p.116 / Chapter 5. --- Lax pair corresponding to the GNLSE --- p.119 / Chapter 6. --- BT´ةs for the Γ evolution equation and the GNLSE --- p.121 / Chapter 7. --- References --- p.126 / Chapter Chapter 7. --- Backlund Transformations for the Caudrey-Dodd-Gibbon-Sawada-Kotera Equation and Its λ-Modified Equation --- p.127 / Chapter 1. --- Introduction --- p.127 / Chapter 2. --- The CDGSKE and the λ-mCDGSKE --- p.128 / Chapter 3. --- The general solution for the scattering problem of the CDGSKE --- p.130 / Chapter 4. --- The BT for the λ-mCDGSKE --- p.135 / Chapter 5. --- The BT for the CDGSKE --- p.136 / Chapter 6. --- References --- p.139 / Summary --- p.140

by Sai-kee Wong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1994. / Includes bibliographical references (leaves 74-77). / Acknowledgments --- p.ii / List Of Figures --- p.v / List Of Tables --- p.vii / Abstract --- p.viii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation --- p.1 / Chapter 1.2 --- Objective of the Study --- p.2 / Chapter 1.3 --- Our Approach --- p.3 / Chapter 1.4 --- Original Contributions --- p.4 / Chapter 1.5 --- Organization of this Dissertation --- p.5 / Chapter 2 --- Previous Work --- p.6 / Chapter 2.1 --- Absolution orientation approach --- p.6 / Chapter 2.2 --- Relative orientation approach --- p.7 / Chapter 3 --- Calibration using OTV correspondences --- p.12 / Chapter 3.1 --- Problem Statement --- p.12 / Chapter 3.2 --- Recovering the orientation of an OTV from a single view --- p.14 / Chapter 3.3 --- Recovering the transformation parameters between two views --- p.18 / Chapter 3.3.1 --- Recovering R --- p.19 / Chapter 3.3.2 --- Recovering t --- p.20 / Chapter 3.3.3 --- Summary of all the steps --- p.20 / Chapter 3.3.4 --- Recovering R and t using more than 2 OTVs --- p.21 / Chapter 4 --- Experimental Results --- p.23 / Chapter 4.1 --- Simulated Data Experiments --- p.23 / Chapter 4.1.1 --- Error versus the smallest angle among the projected branches of an OTV --- p.23 / Chapter 4.1.2 --- Comparison with a point correspondence algorithm --- p.24 / Chapter 4.2 --- Real Image Experiment --- p.41 / Chapter 5 --- Error Analysis --- p.52 / Chapter 5.1 --- Translation in x only --- p.55 / Chapter 5.1.1 --- Jacobian Matrix on Rotation --- p.56 / Chapter 5.1.2 --- Jacobian Matrix on Translation --- p.57 / Chapter 5.2 --- "Rotation + translation in x, y, z" --- p.60 / Chapter 5.2.1 --- Jacobian Matrix on Rotation --- p.60 / Chapter 5.2.2 --- Jacobian Matrix on Translation --- p.61 / Chapter 5.3 --- "Rotation + translation in x,y" --- p.64 / Chapter 5.3.1 --- Jacobian Matrix on Rotation --- p.65 / Chapter 5.3.2 --- Jacobian Matrix on Translation --- p.65 / Chapter 6 --- Conclusion and Future work --- p.68 / Chapter Appendix A --- Least-squares Approximation of a set of Rotation Matrices --- p.70 / Chapter Appendix B --- Epipolar Lines independent of the Translation Magnitude --- p.72

Because of the measuring instrument or the biological variability, many studies with survival data involve covariates which are subject to measurement error. In such cases, the naive estimates are usually biased. In this thesis, we propose a bias corrected estimate of the regression parameter for the multinomial probit regression model with covariate measurement error. Our method handles the case when the response variable is subject to interval censoring, a frequent occurrence in many medical and health studies where patients are followed periodically. A sandwich estimator for the variance is also proposed. Our procedure can be generalized to general measurement error distribution as long as the first four moments of the measurement error are known. The results of extensive simulations show that our approach is very effective in eliminating the bias when the measurement error is not too large relative to the error term of the regression model. / Censoring is an intrinsic part in survival analysis. In this thesis, we establish the asymptotic properties of MMLE to general transformation models when data is subject to right or left censoring. We show that MMLE is not only consistent and asymptotically normal, but also asymptotically efficient. Thus our asymptotic results give a definite answer to a long-term argument on the efficiency of the maximum marginal likelihood estimator. The difficulty in establishing these results comes from the fact that the score function derived from the marginal likelihood does not have ordinary independence or martingale structure. We will develop a discretization method in establishing our results. As a special case, our results imply the consistency, asymptotic normality and efficiency for the multinomial probit regression, a popular alternative to the Cox regression model. / General transformation model is an important family of semiparametric models in survival analysis which generalizes the linear transformation model. It not only includes typical Cox regression model, proportional odds model and multinomial probit regression model, but also includes heteroscedastic hazard regression model, general heteroscedastic rank regression model and frailty model. By maximizing the marginal likelihood, a parameter estimation (MMLE) can be obtained with the property that it avoids estimating the baseline survival function and censoring distribution, and such property is enjoyed by the Cox regression model. In this thesis, we study three areas of generalization of general transformation models: main response variable is subject to censoring, covariates are time-varying and covariates are subject to measurement error. / In medical studies, the covariates are not always the same during the whole period of study. Covariates may change at certain time points. For example, at the beginning, n patients accept drug A as treatment. After certain percentage of patients have died, the investigator might add new drug B to the rest of the patients. This corresponds to the case of time-varying covariates. In this thesis, we propose an estimation procedure for the parameters in general transformation model with this type of time-varying covariates. The results of extensive simulations show that our approach works well. / Wu, Yueqin. / Adviser: Ming Gao Gu. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3589. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 74-78). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

General transformation models are a class of semiparametric survival models. The models generalize simple transformation models with more flexibility in modeling data coming from statistical practice. The models include many popular survival models as their special cases, e.g., proportional hazard Cox regression models, proportional odds models, generalized probit models, frailty survival models and heteroscedastic hazard regression models etc. Although the maximum marginal likelihood estimate of parameters in general transformation models with interval censored data is very satisfactory, its large sample properties are open. In this thesis, we will consider the problem and use discretization technique to establish the large sample properties of maximum marginal likelihood estimates with interval censored data. / In general, to reduce possible model bias, many covariates will be collected into a model. Hence a high-dimensional regression model is built. But at the same time, some non-significant variables may be also included in. So one of tasks to build an efficient survival model is to select significant variables. In this thesis, we will focus on the variable selection for general transformation models with ranking data, right censored data and interval censored data. Ranking data are widely seen in epidemiological studies, population pharmacokinetics and economics. Right censored data are the most common data in clinical trials. Interval censored data are another type common data in medical studies, financial, epidemiological, demographical and sociological studies. For example, a patient visits a doctor with a prespecified schedule. In his last visit, the doctor did not find occurrence of an interested event but at the current visit, the doctor found the event has occurred. Then the exact occurrence time of this event was censored in an interval bracketed by the two consecutive visiting dates. Based on rank-based penalized log-marginal likelihood approach, we will propose an uniform variable selection procedure for all three types of data mentioned above. In the penalized marginal likelihood function, we will consider non-concave and Adaptive-LASSO (ALASSO) penalties. For the non-concave penalties, we will adopt HARD thresholding, SCAD and LASSO penalties. ALASSO is an extended version of LASSO. The key of ALASSO is that it can assign weights to effects adaptively according to the importance of corresponding covariates. Therefore it has received more attention recently. By incorporating Monte Carlo Markov Chain stochastic approximation (MCMC-SA) algorithm, we also propose an uniform algorithm to find the rank-based penalized maximum marginal likelihood estimates. Based on the numeric approximation for marginal likelihood function, we propose two evaluation criteria---approximated GCV and BIC---to select proper tuning parameters. Using the procedure, we not only can select important variables but also be able to estimate corresponding effects simultaneously. An advantage of the proposed procedure is that it is baseline-free and censoring-distribution-free. With some regular conditions and proper penalties, we can establish the n -consistency and oracle properties of penalized maximum marginal likelihood estimates. We illustrate our proposed procedure by some simulations studies and some real data examples. At last, we will extend the procedures to analyze stratified survival data. / Keywords: General transformation models; Marginal likelihood; Ranking data; Right censored data; Interval censored data; Variable selection; HARD; SCAD; LASSO; ALASSO; Consistency; Oracle. / Li, Jianbo. / Adviser: Minggao Gu. / Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 104-111). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

In this thesis, we also investigated various conversion techniques concerning how to improve the performance of multiplierless fast 1-D DCT, and row column 2-D DCT fast algorithms. We have explored a number of choices of conversion techniques having an impact on the performance of multiplierless fast DCT algorithms. Based on our analytical analysis, and experiment results, we have the following findings: (1) a transform based on a reversible inverse generally performs better than a version based on a traditional inverse; (2) a transform with a delayed uniform normalization step can achieve a much better performance; (3) a lifting structure transform can usually achieve better performance than its non-lifting structure version; (4) using an optimized configuration of non-zero digits to approximate the coefficients can help to achieve a much better performance than using a non-optimized configuration. / This thesis proposes effective methods to convert fast DCT algorithms, including 1-D DCT, row column 2-D DCT, and direct 2-D DCT, into their multiplierless versions. The basic conversion techniques used include: (1) to convert any butterfly structures in a DCT algorithm into lifting steps; (2) to use an optimized configuration of non-zero digits to approximate the coefficients so that multiplications can be converted into shift and add operations. We devised an effective algorithm based on the remainder theorem for finding an MSD representation, with minimum wordlength, of any float constant. As the approximation errors of different coefficients often affect the MSE of an approximated fast DCT algorithm differently, we developed an efficient search algorithm for finding an optimized configuration of non-zero digits for approximating each of the coefficients with an appropriate number of non-zero signed digits so that the approximated algorithm could achieve a minimum MSE. / When compared to those multiplierless fast 1-D DCT algorithms developed by others, the multiplierless 1-D DCT fast algorithms developed via our proposed conversion method can achieve similar or better performance in terms of MSE and PSNR. While the published methods were use to approximate only the kernels of the 1-D DCT fast algorithms with butterfly structures, our proposed methods can approximate both the kernels and the normalization steps of any 1-D DCT, row column 2-D DCT, and direct 2-D DCT fast algorithms. / Chan, Kwong Wing Raymond. / "February 2007." / Adviser: Lee Moon Chuen. / Source: Dissertation Abstracts International, Volume: 68-09, Section: B, page: 6172. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 110-117). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

On-line induction machine condition monitoring techniques have been used widely in the detection of motor broken rotor bars for decades. Research has found that when broken bars occur in the machine rotor, the anomaly of electromagnetic field in the air gap will cause two sideband frequency components presenting in the stator current spectrum. Therefore, identification of these sideband frequencies can be used as a convenient and reliable approach to broken rotor bar fault diagnosis. Discrete Fourier Transform (DFT) is a conventional spectral analysis method used in this application. However, the use of DFT has several limitations. The most important one among them is the restriction of frequency resolution by window length. Due to this limitation, the accuracy of broken rotor bar detection can be highly affected in cases such as light machine load and limited data records. However, Prony's method for spectral analysis has the ability of overcoming the restriction of data window length on the frequency resolution, from which the DFT suffers. Such feature makes Prony's method a promising choice for broken rotor bar diagnosis when the machine is operating under light or varying load, or when only restricted data is available. In this thesis, I have demonstrated the implementation of this technique in the induction motor broken rotor bar detection, revealed its better performance than DFT in terms of maintaining high resolution in frequency domain whilst using a much shorter window, and analyzed the influential factors to the method of Prony Analysis (PA). In this thesis, an induction machine model that includes broken rotor bars is developed using Matlab/Simulink and verified by comparing the experimental and the simulated results. The Prony Analysis method for broken bar diagnosis is implemented and tested using both simulated and measured stator current data. Comparisons between PA and DFT results are presented, clearly indicating improvements of broken bar diagnostics using PA. / Thesis (M.Eng.Sc.) -- University of Adelaide, School of Electrical and Electronic Engineering, 2008

The paper presents a simple model for recovering affine shape and correspondence from two orthographic views of a 3D object. It is shown that four corresponding points along two orthographic views, taken under similar illumination conditions, determine affine shape and correspondence for all other points. The scheme is useful for purposes of visual recognition by generating novel views of an object given two model views. It is also shown that the scheme can handle objects with smooth boundaries, to a good approximation, without introducing any modifications or additional model views.