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Baker G.A., Gammel J.L. — The Padé Approximant in Theoretical Physics
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Название: The Padé Approximant in Theoretical PhysicsАвторы: Baker G.A., Gammel J.L. Аннотация: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 1Год издания: 1970Количество страниц: 378Добавлена в каталог: 18.04.2010Операции: Положить на полку |
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Предметный указатель
Muckerman, J. 41 78 75 79 79 57 52 95 Mueller, C. R. 78 Muir 11 59 Mukherji, A. 66 66 96 Multipole expansions 194 Multipole-multipole contribution to atomic interactions 49 Multivariate normal ensembles 139 Munn, R. J. 75 Munroe, M. E. 253 256 Muskhelishvili, N. I. 752 Musulin, B. 54 96 Muto, Y. 50 96 N/D method 197 231 241 Nelson, E. 205 275 Nelson’s theorem 205 Neumann series 171 174 Nevanlinna, R. 19 59 Newton, M. A. 552 Newton, R. G. 271 257 Neynaber, R. H. 75 Nieland, H. 197 275 Noyes, H. P. 178 752 289 302 Nucleon-nucleon scattering 333 Nuttall, J. 5 6 34 59 178 179 180 752 197 275 219 220 226 227 230 280 257 334 341 567 Ohnuma, S. 334 567 Operators in Hilbert space, definitions pertaining to 172 202 204 Operators in Hilbert space, Pad 206 Optical polarizability 41 Orszag, S. A. 149 170 Orthogonal expansions of Stieltjes transforms see Continuous orthogonal expansions of Stieltjes transforms Oscillator strengths see Moments Oscillator strengths for atomic helium 66 Oscillator strengths operator for atomic hydrogen 56 64 Pad see also Bounds Convergence Stieltjes Pad 1 45 Pad 3 5 Pad 20 106 186 189 193 Pad 177—178 201 227— 228 Pad 4 Pad 16 258 263 Pad 3 Pad 2 59 Pad 2 13 Pagels, H. 241 242 256 Palciauskas, V. V. 33 59 Parsons, A. S. L. 70 74 74 96 Partition function 100 Pauling, L. 76 Pauly, H. 41 75 78 79 79 96 Peck, E. R. 69 70 74 96 Pekeris, C. L. 66 66 96 Pengelly, R. 75 79 50 85 55 86 56 90 95 Peres model of quantum field theory 35 334—1 Peres, A. 35 59 Perturbation expansions 1 Perturbation expansions for diffusion problem 144 Perturbation theory of dipole-dipole contribution to atomic interactions 43 Pfluger, A. 12 59 Piof atomic hydrogen 76 Piof atomic hydrogen of atomic helium 77 Piof atomic hydrogen, series of Stieltjes 44 Pion-nucleon scattering 290 303 Pitzer, K. S. 90 91 96 Podolsky, B. 54 96 Pogorzelski, W. 171 752 Polder, D. 41 43 51 95 Poles and zeros of Pad see Poead Pollack, E. 63 80 96 Potential scattering see scattering problems Pransnitz, J. 51 96 Present, R. D. 51 95 Primitive diagram expansion 129 150 probability density 139 Product difference algorithm 124 Pusterla M. 197 217 219 229 305 3311 332 Pyatt, K. D., Jr 333 567 Quantum field theory 129 140 198 220 313 Quantum field theory, mass operator 147 Quantum field theory, self energy parts 148 Quotient-difference algorithm 124 Random velocity field 139 Rational fraction fitting 263 282 Rayleigh — Ritz variational principle 262 Razl 33 59 Recursive schemes for generating Pad 6 Recursive schemes for generating Pad, approximants 4 Refractive index 45 67 71 Refractive index, argon, compared with experiment 74 Refractive index, atomic helium 68 Refractive index, atomic hydrogen 68 Refractive index, compared with experiment 73 Refractive index, molecular hydrogen 69 Refractive index, molecular nitrogen 69 Regge daughters 289 Reinfelds, J. 239 240 Reisz, F. 18 59 171—174 752 202 215 275 234 240 Relativistic corrections to two-body atomic interactions 42 Relativistic corrections to two-body atomic interactions, bounds 84 Remiddi, E. 305 552 Renormalized quantum field theory 197 (see also Quantum field theory) Renormalized quantum field theory of symmetric operator 202 Renormarized diagram expansion 129 148 Resolvent 255 Robinson, P. D. 94 96 Rothe, E. W. 78 81 Rushbrooke, G. S. 32 55 Rutishauer’s quotient-difference algorithm 124 Rutishauser, H. 124 128 Saffman, P. 152 770 Salem, L. 88 90 96 Salop, A. 63 80 96 Salpeter, E. E. 56 95 Salsburg, Z. 121 128 Samson, J. A. R. 62 96 Sawyer, R. E. 178 182 Scaling laws 33 Scattering problems see also Bethe- Salpeter equation Lippman variational N/D Quantum Peres Scattering problems, 303 Scattering problems, 333 Scattering problems, 290 303 Scattering problems, atomic 285 Scattering problems, Coupled channels 269 303 350 Scattering problems, potential scattering 33—35 178 197 257 Scattering problems, separable potentials 307 Scattering problems, three body problem 280 Schiff, B. 66 66 96 Schlessinger, L. 258 263 280 285 287 Schmidt kernels 173 231 Schwartz, C. 61 65 96 220 226 230 258 261 262 273 274 275 276 279 286 287 299 302 335 367 Schweber, S. S. 342 367 Schwinger variational principle 6 219 221 276 Scotti, A. 341 342 557 Self-energy parts in quantum field theory 148 Sengupta, S. 66 66 96 Separable potentials 307 Series of derivatives of delta functions 183 Series of Stieltjes see Stieltjes series Shanks algorithm for accelerating convergence of sequence 139 Sharma, R. D. 342 367 Shaw, G. L. 239 240 Sherwood, A. E. 51 96 Shohat, J. A. 103 106 128 Shreider, Y. A. 337 367 Simple harmonic solid, equilibrium thermal properties of 115 Slater — Kirkwood formula 75 Slater, J. C. 42 44 75 90 96 Smirnov, V. I. 234 236 240 Smith, F. J. 78 96 Smith, M. W. 66 66 97 Smithies, F. 246 249 256 Solids see simple harmonic solid Spectral theorem for operators in Hilbert space 202 Spectral theorem for operators in Hilbert space, spectrum of self-adjoint bounded operator 313 Spectral theorem for operators in Hilbert space, use of Pad 205 Stapp, H. P. 333 341 567 Stengun, I. 259 273 277 287 Stephen, M. J. 88 90 96 Stewart, A. L. 66 66 95 Stieltjes integral 129 Stieltjes inversion formula for moment problem 199—200 Stieltjes, series of 10 184—5 199 245 Stieltjes, series of, connection with spectral theorem for symmetric operator 203 206 Stieltjes, series of, difference of two 36 Stieltjes, series of, extended series of 198 204 238 Stieltjes, series of, polarizability of atoms 42 Stieltjes, series of, reduction of arbitrary, bounded analytic function to 18 Stieltjes, T. J. 100 128 Stochastic field theory 131 Stone 206 210 275 Strange particles 304 Studden, W. J. 100 111 725 Sweig, M. J. 246 256 Swift, J. 33 59 Symmetric operators see operators in Hilbert space Sz. — Nagy, B. 171 172 173 174 752 202 215 275 234 240 Taketani 334 367 Tamarkin, J. D. 103 106 725 Tang 55 88 90 93 94 96 97 Tani, S. 34 59 197 275 Taylor series 2 Tchebychev, P. 100 725 Teller, E. 50 95 Temkin, A. 286 257 Test function space 188 Thermodynamic properties of Ising model 31 Thermodynamic properties of Ising model of Ising model, error bounds 31 Thermodynamic properties of Ising model of simple harmonic solid 115 Third virial coefficients 51 Thomas — Reiche — Kuhn sum rule 48 Three-body dipole interactions 49—51 Three-body dipole interactions, bounds 84 Three-body dipole interactions, estimated from third virial coefficient 51 Three-body scattering 280 Tiktopoulos, G. 254 256 Time-dependent perturbation theory 53 Tjon, J. A. 197 275 220 230 289 302 Toennies, J. P. 41 78 79 96 Transition probabilities for atomic helium 66 Transition probabilities for atomic helium for atomic hydrogen 56 64 Trapping of particles in velocity field 141 144 Tricomi, F. G. 171 174 752 Turbulent diffusion 129 Turchetti, G. 349 364 365 367 Two channel potential problems see Coupled channel Unbounded operators 198 Uniformization 271 Unitarity 233 242 261 272 289 294 334 Unitarity for three particles 297 Van der Waals forces 41 Van Hove, L. 117 725 Variational principles 6 219 257 262 275 Vasavada, K. V. 239 240 Velocity field 139 Vibrational spectrum of simple harmonic solid 142 Vibrational spectrum of simple harmonic solid, used to establish connection of intensity of magnetization with series of Stieltjes 30 Vibrational spectrum of simple harmonic solid, Yang — Lee theorem on poles of grand partition function 29 Vibrational spectrum of simple harmonic solid, Yukawa potential 180; see Scattering problems potential Victor, G. A. 57 59 60 60 66 68 76 85 95 Vitale, B. 341 342 567 Vorobyev, Yu. V. 205 206 209 212 213 275 Wall, H. S. 13 36 59 198 199 200 202 214 215 275 238 240 263 265 257 308 552 Walsh, J. L. 7 59 Watson 178 179 180 752 280 257 334 367 Watson, G. N. 87 97 Weinhold, F. 92 93 97 Wheeler, R. G. 100 115 117 120 725 Whittaker, E. 87 97 Widder, D. V. 187 795 Wiese, W. L. 66 66 97 Wigner, O. 304 552 Wilkinson, P. G. 69 70 75 74 97 Williams, D. A. 75 Wills, J. G. 19 55 Wilson, J.N. 90 91 97 Wong, D. Y. 341 342 346 365 367 Woolcock, W. S. 299 302 Wortman, W. R. 342 349 350 367 Wright, J. 220 230 2 9 302 Wright, R. 350 567 Wynn, P. 4 5 59 Yang, C. N. 29 30 31 59 Ypsilantis, J. J. 341 367 Yukawa, H. 333 367 Zemach, C. 220 230 261 262 273 274 275 276 279 287 299 302 335 367 Zeros and poles of Pad see Pad Zorn, J. C. 63 63 80 95
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approximants to resolvent symmetric operator 
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