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Table of Contents Page |
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CHAPTER 1 INTRODUCTION 1 |
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1.1 Background 1 |
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1.2 Historical Approach 2 |
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1.3 Neutron Density 5 |
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1.4 Reaction Rates 6 |
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1.5 Design Approximations 11 |
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1.6 Reactor Design Implications 12 |
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11 |
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CHAPTER 2 INTERACTIONS OF NEUTRONS |
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WITH MATTER 17 |
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14 |
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2.1 Compound Nucleus - Cross Sections 17 |
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2.2 Nuclear Systematics of Naturally Occurring |
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Isotopes 23 |
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2.3 Level Widths and Partial Cross Sections 25 |
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2.3 Cross Section for Formulation of the Compound |
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Nucleus 26 |
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2.5 Reaction Probabilities 28 |
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2.6 Kinematics in the Center-of-Mass System 30 |
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2.7 Relationships Between the Scattering |
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Angles in the LAB and CM Systems 36 |
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25 |
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CHAPTER 3 NUCLEAR FISSION 45 |
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27 |
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28 |
3.1 Binding Energy 45 |
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3.2 Liquid Drop Model of Fission 48 |
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3.3 Fission Product Yields 55 |
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3.4 Fission Neutron Spectrum 57 |
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3.5 Prompt Neutrons 59 |
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3.6 Delayed Neutrons 62 |
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3.7 Energy Production in Fission 64 |
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35 |
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CHAPTER 4 DERIVATION OF THE NEUTRON |
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DIFFUSION EQUATION 69 |
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38 |
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4.1 Fick's Law Derivation of the Diffusion Equation 69 |
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4.2* The One-Speed Transport Equation 74 |
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4.3* One-Dimensional, One-Speed Transport Equation 80 |
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4.4* Derivation of the P1 Equations 86 |
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4.5 The P1 Diffusion Theory Approximation 89 |
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4.6 Comments on the P1 Equations of Diffusion Theory 92 |
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4.7* Alternate Derivation of the Diffusion Equation 94 |
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46 |
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47 |
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48 |
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49 |
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50 |
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51 |
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CHAPTER 5 ANALYTIC SOLUTIONS TO THE |
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ONE-SPEED DIFFUSION EQUATION 99 |
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54 |
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5.1 Partial Currents and the Extrapolated Boundary |
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Condition 99 |
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5.2 Source Plane Boundary Conditions 107 |
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5.3 Two Region Planar Problem 111 |
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5.4 Point and Line Sources 113 |
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5.5 Solution to the Inhomogeneous Source Problem 120 |
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5.6* General Derivation of the Green's Function |
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Superposition Integral 123 |
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5.7 Diffusion Length 126 |
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5.8 Critical Reactors 128 |
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5.9 Homogeneous Bare Critical Slab Reactor 131 |
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5.10 Two Region Slab Reactor 135 |
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5.11 One-Dimensional Bare Homogeneous Cylindrical Reactor 138 |
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5.12 Bare Homogeneous Spherical Reactor 141 |
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5.13 Comments on Multi-region One-Dimensional |
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Reactors 145 |
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5.14 Multidimensional Reactors 149 |
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5.15* Diffusion Length Experiment 152 |
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73 |
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CHAPTER 6 FEW-GROUP EQUATIONS AND |
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NUMERICAL SOLUTION METHODS 165 |
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76 |
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6.1 Energy-Dependent Diffusion Equation 165 |
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6.2 Few-Group Diffusion Equations 167 |
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6.3 Finite Difference Few-Group Equations in |
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One Dimension 172 |
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6.4 Specification of Boundary Conditions 180 |
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6.5 Direct Solution of the Source Problem 182 |
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6.6* Iterative Solution of the Source Problem 187 |
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6.7 Iterative Solution of the Critical Reactor |
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Problem 193 |
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6.8* Convergence of the Outer Iteration to the |
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Fundamental Mode Solution 198 |
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6.9 Qualitative Comparison Between One-Speed |
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and Two-Group Solutions 202 |
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90 |
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CHAPTER 7 PERTURBATION THEORY 211 |
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92 |
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7.1 Adjoint Equations 211 |
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7.2 Matrix Form of the Adjoint Equations 217 |
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7.3 First-Order Perturbation Theory 220 |
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7.4* Perturbation Effects on Higher Harmonic |
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Modes 224 |
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7.5 Control Rod Worth 226 |
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7.6* Inhomogeneous Case 230 |
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100 |
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101 |
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102 |
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103 |
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104 |
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CHAPTER 8 REACTOR KINETICS 239 |
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106 |
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8.1 Multigroup Reactor Kinetics Equation 240 |
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8.2 Interpretation of Spatial Kinetics Results 246 |
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8.3 Point Kinetics Equations 249 |
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8.4 Results for One Group of Delayed Neutrons 255 |
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8.5 Experimental Measurement of Control Rod Worth 261 |
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8.6* "Point" Kinetics Equations Derivation 263 |
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8.7 Method of Obtaining and 267 |
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114 |
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CHAPTER 9 POISONING, TEMPERATURE EFFECTS, |
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AND DEPLETION IN REACTORS 275 |
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117 |
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118 |
9.1 The Fission Product Xenon-135 276 |
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9.2 Xenon Poisoning 277 |
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9.3 General Transient Solution for Buildup |
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of Xenon and Iodine 279 |
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9.4 Spatial Xenon Transients 283 |
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9.5 Xenon-Induced Spatial Power Oscillations 284 |
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9.6 Samarium Poisoning 289 |
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9.7 Temperature Effects on Reactivity 293 |
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9.8 Effect of Thermal Feedback on Reactor Kinetics 297 |
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127 |
9.9 Depletion 308 |
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128 |
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129 |
CHAPTER 10 NEUTRON MODERATION 321 |
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130 |
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10.1 Scattering Collisions 322 |
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10.2 Slowing Down Problem 329 |
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10.3 Slowing Down in Hydrogen With No Absorption 330 |
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10.4 The Slowing Down Density in Hydrogen, |
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No Absorption 333 |
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10.5 Moderation for A > 1, No Absorption 335 |
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10.6 Asymptotic Slowing Down Theory, A > 1, |
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No Absorption 339 |
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10.7* Slowing Down in Hydrogen With Absorption 343 |
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10.8* Special Cases of Slowing Down With |
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Absorption, A > 1 347 |
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10.9 Final Comments 353 |
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143 |
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CHAPTER 11 SLOWING DOWN IN THE PRESENCE |
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OF RESONANCES 357 |
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146 |
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11.1 Resonance Cross Sections 358 |
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148 |
11.2 Doppler Effect 365 |
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11.3 Slowing Down in the Presence of Resonances 373 |
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11.4 Homogeneous-Medium Resonance Absorption 376 |
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11.5 Homogeneous Resonance Integrals 385 |
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11.6* Heterogeneous System Resonance Absorption 391 |
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11.7 Reactor Design Implications of |
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Heterogeneous Lumping 407 |
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11.8 The GAM Multigroup Slowing Down Equations 412 |
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156 |
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157 |
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158 |
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159 |
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CHAPTER 12 THERMALIZATION 429 |
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161 |
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162 |
12.1 Neutron Balance Equation 430 |
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12.2* Monatomic Gas Moderator Cross Sections 432 |
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12.3 Solution to the Monatomic Gas |
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Thermalization Problem 443 |
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12.4 General Case Solution 446 |
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12.5 Spatial Effects in the Thermalization |
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Problem 451 |
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169 |
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170 |
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APPENDIX A. THE SINGULARITY FUNCTIONS 461 |
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172 |
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173 |
APPENDIX B. THE LAPLACE TRANSFORM 465 |
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174 |
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APPENDIX C. MATRIX RELATIONSHIPS 473 |
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176 |
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APPENDIX D. SPHERICAL HARMONICS 479 |
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178 |
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APPENDIX E. DIFFERENTIATION OF AN |
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INTEGRAL 483 |
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181 |
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INDEX 485 |
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