| Preface |
|
v | |
|
Basic Problems of Mathematics and Physics |
|
|
1 | (12) |
|
|
|
1 | (1) |
|
Retrospection of Fundamentals |
|
|
1 | (4) |
|
|
|
5 | (3) |
|
|
|
8 | (5) |
|
|
|
8 | (1) |
|
|
|
9 | (1) |
|
The Sine and Related Curves |
|
|
10 | (1) |
|
|
|
10 | (3) |
|
Mathematics of Grand Unified Theory |
|
|
13 | (32) |
|
|
|
13 | (1) |
|
Hybrid Real Number System |
|
|
13 | (12) |
|
The Construction of Hybrid Real Number System |
|
|
14 | (2) |
|
The Nonterminating Decimals |
|
|
16 | (5) |
|
|
|
21 | (2) |
|
More Properties of Nonstandard Numbers |
|
|
23 | (1) |
|
|
|
24 | (1) |
|
Special Functions and the Generalized Curves |
|
|
25 | (7) |
|
Some Mischievous Functions |
|
|
25 | (1) |
|
|
|
25 | (1) |
|
Significance of the Infinitesimal Zigzag |
|
|
26 | (1) |
|
The Wild Oscillation sin1/x |
|
|
27 | (1) |
|
Rapid Spiral and Oscillation |
|
|
28 | (1) |
|
|
|
28 | (1) |
|
Application of the Infinitesimal Zigzag |
|
|
29 | (2) |
|
|
|
31 | (1) |
|
Generalized Fractal and Chaos |
|
|
32 | (6) |
|
|
|
32 | (1) |
|
The Peano Space-Filling Curve |
|
|
33 | (2) |
|
|
|
35 | (1) |
|
The Infinitesimal Zigzag as Limit Set of Fractal |
|
|
35 | (1) |
|
|
|
36 | (2) |
|
The Integrated Pontrajagin Maximum Principle |
|
|
38 | (7) |
|
|
|
38 | (1) |
|
Formulation of the Problem |
|
|
38 | (1) |
|
|
|
39 | (2) |
|
The Pontrajagin Maximum Principle |
|
|
41 | (2) |
|
The Integrated Form of the Pontrjagin Maximum Principle |
|
|
43 | (2) |
|
Grand Unified Theory (GUT) |
|
|
45 | (38) |
|
|
|
45 | (1) |
|
The Search for the Basic Constituent of Matter |
|
|
45 | (6) |
|
|
|
48 | (1) |
|
|
|
49 | (1) |
|
Primum, Photon and Wave-Particle Duality |
|
|
50 | (1) |
|
Matter-Anti-Matter Interaction |
|
|
51 | (1) |
|
Qualitative and Computational Models of the Primum and Photon |
|
|
51 | (1) |
|
|
|
51 | (8) |
|
Primal Coupling and Interaction |
|
|
52 | (1) |
|
Do Coupled Prima have Anti-Matter? |
|
|
53 | (1) |
|
Genesis of the Atom and Formation of Heavy Isotope |
|
|
53 | (1) |
|
Superconductivity and the Bose-Einstein Condensate |
|
|
54 | (2) |
|
Electric Current, Generation and Conduction |
|
|
56 | (1) |
|
|
|
57 | (1) |
|
Further Verification of Quantum Gravity |
|
|
58 | (1) |
|
|
|
59 | (1) |
|
|
|
59 | (8) |
|
The Cosmology of our Universe |
|
|
61 | (2) |
|
Early Cosmological History of the Earth |
|
|
63 | (1) |
|
Cosmological Vortex Interaction and the Trek Back Home to Dark Matter |
|
|
64 | (3) |
|
|
|
67 | (1) |
|
|
|
67 | (7) |
|
Issues, Facts and Internal Dynamics of our Universe |
|
|
68 | (2) |
|
The Milky Way and Andromeda and their ``Cannibalistic'' Activity |
|
|
70 | (1) |
|
|
|
70 | (1) |
|
|
|
71 | (1) |
|
|
|
71 | (1) |
|
The Transitory Natural Laws |
|
|
72 | (1) |
|
Ultra-Energetic Cosmic Waves |
|
|
72 | (1) |
|
|
|
72 | (1) |
|
More Verification in the Cosmos |
|
|
73 | (1) |
|
Verification in the Solar System |
|
|
73 | (1) |
|
|
|
74 | (9) |
|
|
|
75 | (2) |
|
|
|
77 | (2) |
|
|
|
79 | (4) |
|
|
|
83 | (24) |
|
|
|
83 | (1) |
|
The Solution of the Gravitational n-Body Problem |
|
|
83 | (8) |
|
|
|
83 | (2) |
|
The Solution of the Gravitational n-Body Problem |
|
|
85 | (2) |
|
General Case of the Problem |
|
|
87 | (1) |
|
Solution for the Other Categories of Bodies in the Cosmos |
|
|
87 | (1) |
|
|
|
88 | (2) |
|
|
|
90 | (1) |
|
|
|
91 | (7) |
|
|
|
91 | (1) |
|
|
|
92 | (1) |
|
|
|
92 | (1) |
|
|
|
93 | (1) |
|
|
|
94 | (2) |
|
|
|
96 | (2) |
|
|
|
98 | (1) |
|
|
|
98 | (9) |
|
|
|
98 | (1) |
|
|
|
99 | (1) |
|
|
|
100 | (1) |
|
|
|
100 | (1) |
|
|
|
101 | (3) |
|
Value, Perception and Cognition |
|
|
104 | (3) |
|
|
|
107 | (18) |
|
|
|
107 | (2) |
|
|
|
109 | (2) |
|
Inanimate and Animate Matter |
|
|
111 | (2) |
|
|
|
113 | (2) |
|
|
|
115 | (1) |
|
Sristi and Laya (Creation and Dissolution) |
|
|
116 | (1) |
|
Infinite Void and Infinite Light |
|
|
117 | (3) |
|
|
|
120 | (2) |
|
|
|
122 | (3) |
| Bibliography |
|
125 | (6) |
| Index |
|
131 | |
