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Thesis (Ph.D.)--Boston University / PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you. / This investigation is concerned with the evaluation and interpretation of the propagator, or conditional probability distribution function P(y,t| y0), of the Linear Boltzmann or Master equation from the "central limit viewpoint". We have obtained what is to our knowledge the first evaluation in series of the propagator for the typical kinetic-theoretical processes studied here, which are those underlying the problems usually studied in the approximation of the Fokker-Planck equation. We have been able to put the successive terms of this series in closed form; and have shown that the series can be interpreted as a generalized solution of the central limit problem of mathematical probability theory, the generalization consisting in the extension to a process in continuous time with non-independent increments. [TRUNCATED] / 2031-01-01

by Chan Chi-kin. / Includes bibliographical references / Thesis (M.Ph.)--Chinese University of Hong Kong, 1985

by Kang Xiaosong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 44-47). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.4 / Chapter 2 --- Preliminary Analysis --- p.11 / Chapter 3 --- Liapunov-Schmidt Reduction --- p.16 / Chapter 4 --- A Maximizing Procedure --- p.27 / Chapter 5 --- Proof of Theorem 1.1 --- p.30 / Chapter 6 --- Proof of Theorem 1.2 --- p.33 / Chapter 7 --- Concluding Remarks --- p.42

by Tso Man Kit. / Thesis submitted in: December 2001. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 58-61). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Preliminary analysis --- p.14 / Chapter 3 --- Liapunov-Schmidt reduction --- p.23 / Chapter 4 --- A minimizing procedure --- p.36 / Chapter 5 --- Proof of theorem 11 --- p.40 / Chapter 6 --- Proof of theorem 12 --- p.43 / Chapter 7 --- Proof of theorem 13 --- p.55 / Bibliography --- p.58

Ho Chiu Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 100-103). / Text in English; abstracts in English and Chinese. / Ho Chiu Man. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Historical Background --- p.1 / Chapter 1.2 --- Motivations of the Project --- p.3 / Chapter 1.3 --- Outline of Thesis --- p.4 / Chapter 2 --- Review on a One-dimensional Vibrating Cavity --- p.5 / Chapter 2.1 --- The R Function --- p.5 / Chapter 2.2 --- Photon Generation --- p.7 / Chapter 2.3 --- Instantaneous Mode Expansion --- p.10 / Chapter 2.4 --- Vacuum Energy Density --- p.15 / Chapter 3 --- Graphical Method --- p.17 / Chapter 3.1 --- Construction of R-function --- p.17 / Chapter 3.2 --- Fixed-point Analysis --- p.19 / Chapter 3.3 --- A Special Class of Mirror Trajectories --- p.23 / Chapter 3.4 --- Further Analysis --- p.27 / Chapter 4 --- Wave Evolution in a One-dimensional Vibrating Cavity --- p.32 / Chapter 4.1 --- Instantaneous Mode Expansion Method --- p.32 / Chapter 4.2 --- Transformation Method --- p.34 / Chapter 4.3 --- R-Method --- p.34 / Chapter 4.4 --- Consistency between Different Methods --- p.35 / Chapter 5 --- Floquet's Theory --- p.40 / Chapter 5.1 --- System of Linear Differential Equations with Time-dependent Coefficients --- p.40 / Chapter 5.2 --- Fundamental Set of Solutions and Matrizant --- p.41 / Chapter 5.3 --- System of Linear Differential Equations with Periodic Coefficients --- p.42 / Chapter 5.4 --- Possible Properties of the Solution --- p.43 / Chapter 5.5 --- Eigenvalues for the One-dimensional Vibrating Cavity --- p.44 / Chapter 6 --- Photon Creation in an Oscillating Spherical Cavity --- p.46 / Chapter 6.1 --- Mode Decomposition --- p.46 / Chapter 6.2 --- Bogoliubov Transformation --- p.48 / Chapter 6.3 --- Photon Creation --- p.51 / Chapter 6.4 --- Mean Electric Field Operator --- p.53 / Chapter 6.5 --- Illustrations and Observations --- p.54 / Chapter 7 --- Multiple Scale Analysis --- p.61 / Chapter 7.1 --- Photon Creation by First-order Multiple Scale Analysis --- p.61 / Chapter 7.2 --- Parametric Resonance --- p.64 / Chapter 7.3 --- Nonstationary Medium --- p.71 / Chapter 7.4 --- Photon Statistics --- p.74 / Chapter 7.5 --- Finite Temperature Correction --- p.75 / Chapter 8 --- Squeezing Effect of the Classical Waves --- p.76 / Chapter 8.1 --- Squeezing Effect in the One-dimensional Vibrating Cavity --- p.76 / Chapter 8.2 --- Squeezing Effect in the Oscillating Spherical Cavity --- p.81 / Chapter 9 --- Supersymmetric Approach to Photon Generation --- p.88 / Chapter 9.1 --- Field Quantization --- p.88 / Chapter 9.2 --- Adiabatic Approximation --- p.90 / Chapter 9.3 --- Scattering Interpretation --- p.91 / Chapter 9.4 --- Supersymmetric Approach --- p.93 / Chapter 9.5 --- Examples --- p.94 / Chapter 10 --- Conclusion --- p.98 / Bibliography --- p.100

Sun Siu-wing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 50-51). / Abstracts in English and Chinese. / Acknowledgments --- p.i / Abstract --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Equation without viscosity --- p.5 / Chapter 3 --- Equation with standard viscosity --- p.8 / Chapter 3.1 --- "Particular convective flux, f(x) =u2" --- p.8 / Chapter 3.2 --- Convex convective flux --- p.10 / Chapter 4 --- Equation with monotonic dissipative flux --- p.11 / Chapter 4.1 --- Large initial data --- p.12 / Chapter 4.2 --- Small initial data --- p.19 / Chapter 4.3 --- Unbounded dissipative flux --- p.28 / Chapter 5 --- Equation with non-monotonic dissipative flux --- p.31 / Chapter 5.1 --- Large initial data --- p.32 / Chapter 5.2 --- Small initial data --- p.37 / Chapter 6 --- Comparison and conclusions --- p.39 / Appendices --- p.42 / Chapter A --- Hopf-Cole transformation --- p.42 / Chapter B --- Dirichlet problem --- p.45 / Bibliography --- p.50

Cho, Chi Lam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 63-65). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.