| Foreword |
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| Introduction |
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1 | (8) |
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9 | (16) |
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1.1 What is a Clifford algebra? |
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10 | (1) |
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1.2 Clifford algebra Cl2 of a Euclidean plane |
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11 | (1) |
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1.3 Clifford algebra Cl3 of the physical space |
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12 | (7) |
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1.3.1 Cross-product, orientation |
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13 | (1) |
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13 | (1) |
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1.3.3 Three conjugations are used |
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14 | (1) |
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1.3.4 Gradient, divergence and curl |
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15 | (1) |
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1.3.5 Space-time in space algebra |
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16 | (1) |
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1.3.6 Relativistic invariance |
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16 | (3) |
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1.3.7 Restricted Lorentz group |
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19 | (1) |
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1.4 Clifford algebra Cl1,3 of the space-time |
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19 | (3) |
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21 | (1) |
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1.5 Clifford Algebra Cl1,5 |
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22 | (3) |
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25 | (14) |
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2.1 With the Dirac matrices |
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25 | (3) |
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2.1.1 Relativistic invariance |
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27 | (1) |
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2.2 The wave with the space algebra |
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28 | (6) |
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2.2.1 Relativistic invariance |
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30 | (1) |
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31 | (2) |
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33 | (1) |
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2.3 The Dirac equation in space-time algebra |
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34 | (1) |
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2.4 Invariant Dirac equation |
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35 | (2) |
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37 | (2) |
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3 The homogeneous nonlinear wave equation |
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39 | (10) |
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41 | (1) |
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42 | (1) |
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3.3 Relativistic invariance |
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43 | (3) |
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46 | (2) |
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48 | (1) |
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4 Invariance of electromagnetic laws |
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49 | (26) |
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4.1 Maxwell--de Broglie electromagnetism |
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49 | (6) |
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4.1.1 Invariance under Cl*3 and numeric dimension |
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51 | (3) |
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54 | (1) |
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4.2 Electromagnetism with magnetic monopoles |
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55 | (1) |
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56 | (3) |
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57 | (1) |
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58 | (1) |
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59 | (6) |
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4.4.1 The electromagnetism of the photon |
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62 | (3) |
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65 | (10) |
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65 | (3) |
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68 | (2) |
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5.3 Equation without Lagrangian formalism |
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70 | (1) |
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71 | (1) |
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5.4 Three other photons of Lochak |
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72 | (1) |
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5.5 Uniqueness of the electromagnetic field |
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73 | (2) |
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6 Electro-weak interactions: The lepton case |
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75 | (18) |
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6.1 The Weinberg--Salam model for the electron |
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75 | (10) |
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85 | (2) |
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6.3 Geometry linked to the wave in space-time algebra |
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87 | (2) |
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6.4 Existence of the inverse |
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89 | (1) |
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90 | (3) |
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7 Electro-weak and strong interactions |
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93 | (18) |
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7.1 Electro-weak interactions: the quark sector |
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93 | (4) |
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97 | (2) |
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7.3 Three generations, four neutrinos |
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99 | (2) |
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7.4 Geometric transformation linked to the complete wave |
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101 | (3) |
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103 | (1) |
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7.5 Existence of the inverse |
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104 | (2) |
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7.6 Wave equation with mass term |
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106 | (4) |
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7.6.1 Form invariance of the wave equation |
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109 | (1) |
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110 | (1) |
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111 | (22) |
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8.1 Russian experimental works |
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111 | (2) |
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113 | (12) |
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8.2.1 Results about powder and gas |
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114 | (3) |
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117 | (1) |
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118 | (7) |
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8.3 Electrons and monopoles |
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125 | (8) |
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126 | (1) |
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8.3.2 The interaction electron-monopole |
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127 | (1) |
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8.3.3 Electro-weak interactions with monopoles |
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128 | (2) |
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8.3.4 Gauge invariant wave equation |
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130 | (3) |
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9 Inertia and gravitation |
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133 | (10) |
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9.1 Differential geometry |
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133 | (6) |
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9.1.1 Uniform movement of rotation |
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137 | (1) |
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9.1.2 Uniformly accelerated movement of translation |
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138 | (1) |
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139 | (1) |
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140 | (2) |
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142 | (1) |
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143 | (18) |
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143 | (1) |
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144 | (4) |
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10.3 Principle of minimum |
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148 | (2) |
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10.4 Theory versus experiment |
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150 | (1) |
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151 | (1) |
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10.6 Improved standard model |
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152 | (2) |
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10.7 Algorithmic and data structures |
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154 | (3) |
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10.8 Beyond the standard model, back to physical reality |
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157 | (4) |
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Appendix A Calculations in Clifford algebras |
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161 | (10) |
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A.1 Invariant equation and Lagrangian |
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161 | (6) |
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A.2 Calculation of the reverse in Cl1,5 |
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167 | (4) |
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Appendix B Electron+neutrino+quarks |
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171 | (32) |
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171 | (2) |
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B.2 Tensorial densities for electron+neutrino |
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173 | (2) |
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B.3 Getting the wave equation |
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175 | (7) |
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182 | (6) |
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183 | (1) |
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B.4.2 Gauge invariance --- group generated by P0 |
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184 | (1) |
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B.4.3 Gauge invariance --- group generated by P3 |
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185 | (2) |
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B.4.4 Gauge invariance --- group generated by P1 |
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187 | (1) |
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188 | (15) |
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188 | (1) |
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189 | (1) |
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B.5.3 Group generated by P0 |
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189 | (1) |
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B.5.4 Group generated by P1 |
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190 | (2) |
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B.5.5 Group generated by P2 |
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192 | (2) |
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B.5.6 Group generated by P3 |
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194 | (1) |
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B.5.7 Group generated by Γ1 |
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195 | (2) |
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B.5.8 Group generated by Γk, k > 1 |
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197 | (1) |
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B.5.9 Group generated by Γ3 |
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198 | (1) |
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B.5.10 Group generated by Γ8 |
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199 | (4) |
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Appendix C The hydrogen atom |
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203 | (18) |
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203 | (5) |
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C.2 Angular momentum operators |
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208 | (2) |
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C.3 Resolution of the linear radial system |
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210 | (5) |
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C.4 Calculation of the Yvon--Takabayasi angle |
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215 | (3) |
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C.5 Radial polynomials with degree 0 |
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218 | (3) |
| Bibliography |
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221 | (4) |
| Index |
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225 | |
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