Preface |
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vii | |
Introduction |
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xxi | |
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Functional Integration Method |
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1 | (30) |
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Functional integrals in statistical physics |
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1 | (1) |
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Functional integrals and diagram techniques for Bose-particles |
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2 | (19) |
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Functional integrals and diagram techniques for Fermi-particles |
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21 | (6) |
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Method of successive integration over fast and slow fields |
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27 | (4) |
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Collective Excitations in Superfluid Fermi-Systems with s-Pairing |
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31 | (26) |
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Effective action functional of the superfluid Fermi-gas |
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31 | (7) |
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Bose-spectrum of superfluid Fermi-gas |
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38 | (13) |
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Fermi-gas with Coulomb interaction |
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51 | (6) |
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Sound Propagation in Superfluid 3He and Superconductors |
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57 | (8) |
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Sound propagation in superfluid 3He |
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57 | (2) |
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Sound propagation in conventional superconductors |
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59 | (6) |
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Attenuation in the normal state |
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59 | (2) |
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Attenuation in the superconducting state |
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61 | (1) |
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Attenuation in the superconducting state in a magnetic field |
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62 | (1) |
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Velocity at the superconducting transition |
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63 | (2) |
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65 | (18) |
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Introduction: Fermi-systems with nontrivial pairing |
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65 | (2) |
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Properties of superfluid phases in 3He |
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67 | (16) |
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83 | (20) |
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The path integral approach |
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83 | (14) |
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97 | (6) |
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Collective Excitations in the B-Phase of 3H |
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103 | (48) |
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The quadratic form of action functional |
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103 | (6) |
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The collective mode frequencies |
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109 | (5) |
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Dispersion corrections to the collective mode spectrum |
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114 | (9) |
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Dispersion laws for rsq- and sq-modes |
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114 | (6) |
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Dispersion induced splitting of the rsq- and sq-mode |
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120 | (3) |
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The pair-breaking mode dispersion law |
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123 | (7) |
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Collective mode spectrum calculated by the kinetic equation method |
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130 | (3) |
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133 | (1) |
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Textural effects on the squashing modes |
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134 | (7) |
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Coupling of order-parameter collective modes to ultrasound |
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141 | (10) |
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Collective Excitations in the A-Phase of 3He |
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151 | (52) |
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151 | (1) |
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The collective mode spectrum in the absence of magnetic fields |
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152 | (14) |
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The latent symmetry, additional Goldstone modes, W-bosons |
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166 | (7) |
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The linear Zeeman effect for clapping- and pair-breaking modes |
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173 | (8) |
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The equations for the collective mode spectrum in an arbitrary magnetic field and at arbitrary collective mode momenta |
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173 | (4) |
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The collective mode spectrum for small magnetic fields and zero collective mode momenta (linear Zeeman effect for clapping and pairbreaking modes) |
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177 | (4) |
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Kinetic equation results on collective modes in A-phase |
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181 | (14) |
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Sound and the order parameter collective modes |
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181 | (7) |
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188 | (7) |
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Textural effects in A-phase |
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195 | (8) |
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Identification of 3He-A by Ultrasound Experiments |
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203 | (14) |
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203 | (1) |
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Mermin-Star's phase diagram analysis |
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203 | (4) |
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207 | (9) |
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211 | (2) |
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The second variation of free energy |
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213 | (3) |
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216 | (1) |
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Stability of Goldstone Modes |
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217 | (24) |
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Stability of Goldstone-modes and their dispersion laws |
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217 | (2) |
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Stability of Goldstone-modes in the B-phase |
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219 | (9) |
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Stability of Goldstone-modes in the axial A-phase |
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228 | (7) |
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Stability of Goldstone-modes in the planar 2D-phase |
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235 | (6) |
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Influence of Dipole Interaction and Magnetic Field on Collective Excitations |
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241 | (20) |
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The influence of the dipole interaction on collective excitations |
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241 | (14) |
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The influence of the magnetic field on collective excitations |
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255 | (3) |
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258 | (3) |
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The Influence of the Electric Field on the Collective Excitations in 3He and 4He |
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261 | (24) |
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The energy spectrum and hydrodynamics of 4He in a strong electric field (macroscopic approach) |
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261 | (5) |
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Superfluid Bose-systems in the electric field (microscopic approach) |
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266 | (4) |
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The effective action functional for the superfluid 3He in the electric field |
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270 | (4) |
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The influence of the electric field on the Bose-spectrum in the B-phase |
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274 | (6) |
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The influence of the electric field on the Bose-spectrum in the A-phase |
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280 | (5) |
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The Order Parameter Distortion and Collective Modes in 3He-B |
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285 | (36) |
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The external perturbations and the order parameter distortions |
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285 | (7) |
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The collective mode spectrum under the order parameter distortion |
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292 | (20) |
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295 | (3) |
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298 | (1) |
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299 | (10) |
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309 | (2) |
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Rotational effects (vortices and gyromagnetism) |
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311 | (1) |
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Sound experiments at the absorption edge |
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312 | (1) |
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Subdominant f-wave pairing interactions in superfluid 3He |
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313 | (8) |
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Splitting of the Squashing Mode and the Method of Superfluid Velocity Measurement in 3He-B |
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321 | (10) |
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A doublet splitting of the squashing mode in superfluid 3He-B |
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321 | (7) |
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The method of superfluid velocity measurement in 3He-B |
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328 | (3) |
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Superfluid Phase of 3He-B Near the Boundary |
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331 | (14) |
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331 | (1) |
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Transverse sound experiments |
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332 | (1) |
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Possible new phases near the boundary |
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333 | (7) |
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Different branches of squashing mode |
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340 | (1) |
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341 | (2) |
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343 | (2) |
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Collective Excitations in the Planar 2D-Phase of Superfluid 3He |
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345 | (10) |
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The planar 2D-phase of superfluid 3He |
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345 | (3) |
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Collective modes in 3He-2D at zero momenta of excitations |
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348 | (7) |
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Dispersion Induced Splitting of the Collective mode Spectrum in Axial- and Planar-Phases of Superfluid 3He |
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355 | (30) |
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356 | (1) |
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357 | (9) |
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The model of superfluid 3He |
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359 | (2) |
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The equations for the collective mode spectrum in an arbitrary magnetic field and at arbitrary collective mode momenta |
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361 | (3) |
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The dispersion corrections to collective mode spectrum in 3He-A |
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364 | (2) |
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366 | (16) |
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367 | (3) |
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The equations for collective mode spectrum in 3He-2D |
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370 | (4) |
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The equations for collective mode spectrum in 3He-2D with dispersion corrections |
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374 | (4) |
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The collective mode spectrum in 3He-2D with dispersion corrections |
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378 | (4) |
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382 | (3) |
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Collective Excitations in the Polar-Phase |
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385 | (6) |
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Calculation of the collective mode spectrum |
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386 | (4) |
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390 | (1) |
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Collective Mode Spectrum in Ai-Phase of Superfluid 3He |
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391 | (8) |
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Calculation of the collective mode spectrum |
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391 | (7) |
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398 | (1) |
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Superfluidity of Two-Dimensional and One-Dimensional Systems |
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399 | (90) |
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Phase transitions in two-dimensional systems |
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399 | (2) |
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Two-dimensional superfluidity |
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401 | (27) |
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428 | (12) |
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440 | (2) |
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Superfluidity in Fermi films. Singlet pairing |
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442 | (4) |
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Triplet pairing. Thick films |
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446 | (9) |
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455 | (3) |
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Superfluid phases of a two-dimensional superfluid 3He |
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458 | (10) |
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Bose-spectrum of the a-phase |
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468 | (8) |
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Bose-spectrum of the b-phase |
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476 | (5) |
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The two-dimensional superfluidity must exist! |
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481 | (5) |
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New possibility for the search of 2D-superfluidity in 3He-films |
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486 | (3) |
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Bose-Spectrum of Superfluid Solutions 3He-4He |
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489 | (40) |
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Superfluidity of 3He, dissolved in 4He |
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489 | (1) |
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The case of s-pairing in 3He. Effective action functional of the 3He-4He solutions |
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490 | (8) |
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Bose-spectrum of the 3He-4He solution |
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498 | (5) |
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The case of p-pairing. The effective action functional of the 3He-4He solution |
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503 | (6) |
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Bose-spectrum of a solution of the type 3He-B-4He |
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509 | (9) |
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Bose-spectrum of a system of the type 3He-A-4He |
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518 | (6) |
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Bose-spectrum of films of the types 3He-a-4He and 3He-b-4He |
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524 | (3) |
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527 | (2) |
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Novel Sound Phenomena in Impure Superfluids |
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529 | (42) |
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530 | (2) |
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Decoupling of first and second sound in pure superfluids |
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532 | (2) |
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Sounds coupling in impure superfluids |
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534 | (8) |
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Superfluids with different impurities, 3He-4He mixtures |
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534 | (3) |
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Sounds coupling in superfluid He in aerogel |
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537 | (5) |
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Slow pressure (density) oscillations, fast temperature (entropy) oscillations |
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542 | (1) |
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Fast mode frequency shift at Tc(Tλ) |
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542 | (3) |
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Difference in nature of first and second sound In impure superfluids |
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545 | (2) |
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Sound conversion phenomena |
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547 | (7) |
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Conservation laws in sound conversion |
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547 | (3) |
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Sound conversion in pure superfluids |
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550 | (2) |
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Sound conversion in 3He-4He mixtures |
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552 | (2) |
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Sound conversion experimens in pure superfluids |
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554 | (1) |
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Some possible new sound experiments in impure superfluids |
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555 | (1) |
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Coupling of two slow modes in superfluid 3He-4He mixture in aerogel |
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556 | (6) |
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Nonlinear hydrodynamic equations for superfluid helium in aerogel |
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562 | (3) |
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Putterman's type equations |
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565 | (3) |
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568 | (3) |
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Path Integral Approach to the Theory of Crystals |
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571 | (18) |
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Effective Interaction of Electrons Near the Fermi-Surface |
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589 | (10) |
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The Path Integral Models of p- and d-Pairing for Bulk Superconductors |
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599 | (8) |
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Models of p- and d-pairing |
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599 | (2) |
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601 | (2) |
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603 | (4) |
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High Temperature Superconductors (HTSC) and Their Physical Properties |
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607 | (16) |
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607 | (6) |
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Physical properties of HTSC |
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613 | (10) |
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613 | (10) |
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Symmetry of Order Parameter in HTSC |
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623 | (88) |
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623 | (9) |
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Superconductivity and broken symmetry |
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624 | (6) |
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630 | (2) |
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Symmetry classification of HTSC states |
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632 | (9) |
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632 | (2) |
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634 | (2) |
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636 | (3) |
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639 | (2) |
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641 | (12) |
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641 | (2) |
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Mixing of states of different irreducible representations |
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643 | (7) |
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Orthorhombicity and twins |
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650 | (1) |
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651 | (2) |
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Pairing symmetry and pairing interactions |
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653 | (15) |
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Two scenarios for d-wave pairing |
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654 | (3) |
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Tests of the pairing interaction |
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657 | (4) |
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Influence of electron-phonon interaction on dx2-y2-pairing |
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661 | (7) |
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Experimental symmetry probes |
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668 | (28) |
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669 | (8) |
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Magnetic induction of dx2-y2 + idxy order in HTSC |
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677 | (2) |
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Transition splitting, spontaneous strain and magnetism |
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679 | (3) |
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Critical phenomena and Gaussian fluctuations |
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682 | (4) |
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686 | (4) |
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690 | (3) |
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Probes of the gap function |
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693 | (2) |
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Distinction of a scalar from a tensor Order parameter |
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695 | (1) |
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Experimental evidence for dx2-x2 pairing |
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696 | (8) |
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696 | (5) |
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701 | (3) |
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704 | (4) |
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List of abridgements for chapters XXV and XXVI |
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708 | (3) |
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711 | (10) |
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711 | (2) |
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Bulk HTSC under d-pairing |
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713 | (8) |
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How to Distinguish the Mixture of Two d-Wave States from Pure d-Wave State of HTSC |
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721 | (20) |
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The mixture of two d-wave states |
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721 | (2) |
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Equations for collective modes spectrum in a mixed d-wave state of unconventional superconductors |
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723 | (15) |
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723 | (4) |
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Equations for collective modes spectrum in a mixed d-wave state at arbitrary admixture of dxy state |
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727 | (5) |
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Equations for collective modes spectrum in a mixed d-wave state at an equal admixtures of dx2-y2 and dxy states |
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732 | (3) |
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dx2-y2-state of high temperature superconductors with a small admixture of dxy-state |
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735 | (3) |
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738 | (3) |
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741 | (14) |
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741 | (1) |
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Bulk p-wave superconductivity |
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741 | (14) |
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Two Dimensional p- and d-Wave Superconductivity |
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755 | (10) |
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Two-dimensional models of p- and d-pairing in USC |
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755 | (1) |
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755 | (5) |
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Two-dimensional p-wave superconducting states |
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756 | (2) |
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The collective mode spectrum |
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758 | (2) |
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Two-dimensional d-wave superconductivity |
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760 | (5) |
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2D-model of d-pairing in CuO2 planes of HTSC |
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760 | (3) |
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The collective mode spectrum |
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763 | (1) |
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Lattice symmetry and collective mode spectrum |
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764 | (1) |
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Collective Modes in the Heavy-Fermion Superconductors |
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765 | (10) |
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Physical properties of heavy-fermion superconductors |
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765 | (2) |
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Bulk heavy-fermion superconductors under d-pairing |
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767 | (5) |
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772 | (3) |
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Other Application of the Theory of Collective Excitations |
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775 | (6) |
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Relativistic analogs of 3He |
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775 | (6) |
References |
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781 | (30) |
About the Authors |
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811 | |