| 摘要 | 第3-4页 |
| Abstract | 第4-5页 |
| 1 Introduction | 第8-13页 |
| 2 Inverse Black-body Radiation Problem | 第13-26页 |
| 2.1 Introduction | 第13-17页 |
| 2.1.1 The Exact Solution and The Improved Unique Existence Theorem | 第15-16页 |
| 2.1.2 M(o|¨)bius Inversion and Chen's Solution | 第16-17页 |
| 2.2 Unifying Two Solutions and Proving Convergence | 第17-18页 |
| 2.2.1 Ming's Theorem | 第17页 |
| 2.2.2 Unification of Two Solutions and Proving Convergence | 第17-18页 |
| 2.3 Some serieses of Exact Solutions | 第18-22页 |
| 2.3.1 First Class of Exact Solutions | 第18-19页 |
| 2.3.2 Second Class of Exact Solutions | 第19-21页 |
| 2.3.3 The UFS Method in BRI | 第21-22页 |
| 2.4 Discussion and Concluding Remarks | 第22-26页 |
| 3 Inverse Transmissivity Problem | 第26-36页 |
| 3.1 Introduction | 第26-27页 |
| 3.2 Exact Solution Formula and Technique for Eliminating Divergences | 第27-29页 |
| 3.3 Derivation of a Solution Formula | 第29-31页 |
| 3.4 Some Exact Solutions for Transmissivity Inverse Problem | 第31-32页 |
| 3.5 A Possible Application of the Model | 第32页 |
| 3.6 A Method for Practical Use | 第32-33页 |
| 3.7 Discussion and Concluding Remarks | 第33-36页 |
| 4 Inversion on the Flux Relaxation Problem | 第36-51页 |
| 4.1 Introduction | 第36-37页 |
| 4.2 The exact solution and its analytic expression | 第37-38页 |
| 4.3 Numerical Calculation | 第38-46页 |
| 4.3.1 Two Lemmas | 第38-40页 |
| 4.3.2 The Expansion Solution and Numerical Calculations | 第40-46页 |
| 4.4 Discussion and Remarks | 第46-51页 |
| 5 Bose-Einstein Condensation in Confined Geometry: Thermodynamic Mapping Study | 第51-65页 |
| 5.1 Introduction | 第51-52页 |
| 5.2 Confinement Effects | 第52页 |
| 5.3 Thermodynamic Mapping | 第52-55页 |
| 5.3.1 Proof of the TM Relation Eq. (5.8) | 第54-55页 |
| 5.4 Mapping Relation for Confined BEC | 第55-59页 |
| 5.5 Determination of the Critical Temperature | 第59-63页 |
| 5.6 Discussion | 第63-65页 |
| 6 The Spatial and Momentum Distribution of Bose-Einstein Condensation in Harmonic Traps | 第65-78页 |
| 6.1 Introduction | 第65-66页 |
| 6.2 The generalized expression for particles density | 第66-68页 |
| 6.3 The Distribution for Ideal System | 第68-69页 |
| 6.4 New Expression with Clear Physics Picture | 第69-71页 |
| 6.5 The Momentum Distribution | 第71页 |
| 6.6 Results from numerical calculation | 第71-72页 |
| 6.7 Discussion and Concluding Remarks | 第72-78页 |
| 7 Summary | 第78-81页 |
| 7.1 Conclusions and Discussion | 第78-81页 |
| Bibliography | 第81-95页 |
| A Publication List | 第95-97页 |
| B 致谢 | 第97-98页 |
