Contributors |
|
ix | |
Preface |
|
xi | |
Future Contributions |
|
xiii | |
1 Convolution in (max, min)-Algebra and Its Role in Mathematical Morphology |
|
1 | (66) |
|
|
|
2 | (3) |
|
2 Basic Notions and Notations |
|
|
5 | (5) |
|
3 (max, min)-Convolutions: Definition and Properties |
|
|
10 | (17) |
|
|
10 | (1) |
|
3.2 Duality by Complement vs. Duality by Adjunction |
|
|
11 | (3) |
|
3.3 Commutation with Level Set Processing |
|
|
14 | (4) |
|
|
18 | (4) |
|
3.5 Openings, Closings Using (max, min)-Convolutions and Granulometries |
|
|
22 | (5) |
|
4 Hopf-Lax-Oleinik Formulas for Hamilton-Jacobi Equation ut plus or minus H(u, Du) = 0 |
|
|
27 | (6) |
|
4.1 Morphological PDE for Classical Dilation and Erosion |
|
|
27 | (1) |
|
4.2 Viscosity Solution of Hamilton-Jacobi Equation with Hamiltonians Containing u and Du |
|
|
28 | (5) |
|
5 Nonlinear Analysis Using Operators |
|
|
33 | (11) |
|
|
33 | (2) |
|
5.2 Lipschitz Approximation |
|
|
35 | (4) |
|
5.3 A Transform in (max, min)-Convolution |
|
|
39 | (5) |
|
6 Ubiquity of (max, min)-Convolutions in Mathematical Morphology |
|
|
44 | (16) |
|
|
44 | (1) |
|
6.2 Flat Morphological Operators Using Indicator Functions |
|
|
45 | (1) |
|
6.3 Links with Fuzzy Morphology |
|
|
46 | (2) |
|
6.4 Links with Viscous Morphology |
|
|
48 | (3) |
|
6.5 Links with Boolean Random Function Characterization |
|
|
51 | (7) |
|
6.6 Links with Geodesic Dilation and Erosion |
|
|
58 | (2) |
|
7 Conclusion and Perspectives |
|
|
60 | (3) |
|
|
63 | (1) |
|
|
63 | (4) |
2 Critical Magnetic Field and Its Slope, Specific Heat, and Gap for Superconductivity as Modified by Nanoscopic Disorder |
|
67 | (32) |
|
|
|
67 | (6) |
|
2 Relevant Statistical Energies to Use for Finding Critical Magnetic Field, Heat Capacity, and Other Parameters |
|
|
73 | (1) |
|
3 Energy Dispersion Relation Obtained from a Bogoliubov Transformation on a Mean Field BCS Hamiltonian |
|
|
74 | (5) |
|
4 Averaged Energy E to Be Used in the Free Energy Construction |
|
|
79 | (2) |
|
5 Microscopically Determined Entropy S |
|
|
81 | (1) |
|
6 Evaluating the Microscopic Entropy S |
|
|
82 | (2) |
|
7 Evaluating the Averaged Energy E |
|
|
84 | (2) |
|
8 Critical Magnetic Field from Microscopic Approach |
|
|
86 | (2) |
|
9 Specific Heat of Electrons for the System |
|
|
88 | (1) |
|
10 Slope of the Critical Magnetic Field at the Critical Temperature |
|
|
89 | (1) |
|
11 Relating the Disorder Potential Energy to the Gap Parameter |
|
|
90 | (4) |
|
|
94 | (1) |
|
|
94 | (1) |
|
|
94 | (5) |
3 Mirror Electron Microscopy |
|
99 | (63) |
|
|
|
|
|
|
100 | (5) |
|
1.1 Scanning Electron Microscope |
|
|
100 | (1) |
|
1.2 Emission Electron Microscope |
|
|
101 | (1) |
|
1.3 Reflection Electron Microscope |
|
|
101 | (1) |
|
1.4 Mirror Electron Microscope |
|
|
101 | (4) |
|
2 Contrast Formation in a Mirror Electron Microscope with Focused Images |
|
|
105 | (41) |
|
|
105 | (1) |
|
|
106 | (3) |
|
|
109 | (12) |
|
2.4 Model B (Solution of the Exact Equations of Motion 2.1a and b) |
|
|
121 | (6) |
|
|
127 | (11) |
|
2.6 Comparison with the Image Contrast for a Mirror Projection Microscope |
|
|
138 | (5) |
|
|
143 | (2) |
|
2.8 Concise List of Symbols Used in Section 2 |
|
|
145 | (1) |
|
3 Description and Design op a Mirror Electron Microscope with Focused Images |
|
|
146 | (9) |
|
|
146 | (9) |
|
4 Results and Applications |
|
|
155 | (7) |
|
|
155 | (5) |
|
|
160 | (2) |
Appendix A: A Scanning Mirror Electron Microscope with Magnetic Quadrupoles (Bok et al., 1964) |
|
162 | (4) |
Appendix B: Calculation of the Influence of the Specimen Perturbation on the Phase of the Reflected Electron Beam in a Mirror Electron Microscope |
|
166 | (5) |
Appendix C: Practice of Mirror Electron Microscopy |
|
171 | (11) |
Appendix D: Shadow Projection Mirror Electron Microscopy in "Straight" Systems |
|
182 | (8) |
References |
|
190 | (3) |
Index |
|
193 | |