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Noble B. — Methods based on the Wiener-Hopf technique for the solution of PDEs
Noble B. — Methods based on the Wiener-Hopf technique for the solution of PDEs

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Название: Methods based on the Wiener-Hopf technique for the solution of PDEs

Автор: Noble B.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1958

Количество страниц: 255

Добавлена в каталог: 18.11.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian theorems      36 46 57
Absorbent boundaries      (see Resistive boundaries)
Aerofoil, quarter-infinite      95
Aerofoil, two-dimensional      173
Alblas, J. B.      96 236
Ament, W. J.      47
Analytic continuation      7ff 38ff
Antenna, biconical      218
Antenna, cylindrical rod      213
Approximate factorization      160ff
Approximate methods      178ff 236 generalized)
Approximate methods for integral equations      23ff 233ff
Approximate methods for strips and slits      203ff
Approximate methods for thick plates      187ff
Approximate methods, meaning of “approximate”      180
Approximate methods, miscellaneous formulations      181ff
Asymptotic expansions for contour integrals      33ff 46
Asymptotic expansions for transforms      36
Asymptotic expansions in approximate solutions      200ff (see also Far-field)
Baiun, L. L.      122
Baker, B. B. and Copson, E. T.      70 206
Baldwin, G. L. and Heins, A. E.      125
Bazer, J. and Karp, S. N.      73 128 153 166 167
Biharmonic equation      (see also Elastic medium)
Biharmonic equation, approximate factorization for      162
Biharmonic equation, stresses in strip      138
Boundary conditions, specified by arbitrary functions      7 7ff
Boundary layer on flat plate      96 97
Bouwkamp, C. J.      75 179 218
Branch Cuts      8ff
Branch cuts, special cases      9 19 38 39
Branch points and poles      (see Poles and branch points)
Carlson, J. F. and Heins, A. E.      103 133
Carrier, G. F. and Munk, W. H.      94
Carslaw, H. S.      72
Chester, W.      20 132
Churchill, R. V.      27
Circular waveguide      (see Duct cylindrical)
Clemmow, P. C.      36 88 93 94 152
Cone, Laplace’s equation      165
Cone, wave equation      218
Contour integrals for sum and product decompositions      18ff
Contour integrals special type      31ff.
Convection of heat from flat plate      94
Conventions      x 10 28 86
Copson, E. T.      vii 5 6 70 95 231
Copson’s method      231
Cosine transform      147 212
Cylindrical pipe      (see Duct cylindrical)
Davison, B.      168
Dielectric slab      211 213
Diffraction      (see Disc Duct Halfplanes Strips
Diffraction, methods other than the Wiener-Hopf for      125 179
Dirac delta function      43
Disc, Laplace’s equation      166 231
Disc, low frequency      213ff 231
Disc, wave equation, high frequency      219
Divergent integrals      64
Doetsch, G.      27 36
Dual integral equations for boundary conditions specified arbitrarily      77ff
Dual integral equations for three-part problems      231
Dual integral equations formulation in terms of      4 58 150
Dual integral equations general comments      48 77 221 236
Dual integral equations, exact solution of general cases      77ff 222ff
Dual integral equations, half-plane problem solved by      58ff
Dual integral equations, involving Bessel functions viii      221
Dual integral equations, multiplying factor method for      58ff 77ff 222ff
Dual integral equations, reduction to complex variable equation      150 151 221
Duct, cylindrical, finite length      207
Duct, infinite length, resistive wall      134
Duct, propagated and attenuated modes      110
Duct, radiation from      11
Duct, radiation from coaxial      133 154
Duct, semi-infinite tube in      121
Duct, semi-infinite, electromagnetic waves      132
Duct, two-dimensional, finite length      207
Duct, two-dimensional, infinite length with semi-infinite obstacle, dielectric slab      211
Duct, two-dimensional, infinite length with step      196 207ff
Duct, two-dimensional, infinite length with strip across      122ff 212
Duct, two-dimensional, propagated and attenuated modes      98ff
Duct, two-dimensional, resistive wall      133
Duct, two-dimensional, semi-infinite      (see Half-planes two
Duct, two-dimensional, set of posts      174
Duct, two-dimensional, solution via simultaneous linear algebraic equations      175
Duct, two-dimensional, strip of finite thickness parallel to wall      212
Duct, two-dimensional, strip parallel to wall      118ff
Duct, wave incident on      116ff
Edge conditions      51 74ff
Edge conditions, references      75
Elastic medium      (see also Biharmonic equation)
Elastic medium, diffraction by half-plane in      96
Elastic medium, stresses in wedge with mixed boundary condition      173
Electromagnetic waves, boundary conditions      134
Electromagnetic waves, diffraction by half-plane      95
Electromagnetic waves, diffraction by semi-infinite cylinder      132
Electromagnetic waves, edge conditions      76
Electromagnetic waves, terminology      85 92
End correction, cylindrical tube      115
End correction, thick semi-infinite strip      196
Erdelyi, A.      36 46
Erdelyi, A. et al.      148 176 213
Factorization      (see Product factorization)
Far-field, examples of calculation of      105 110 115 192 206
Fel’d, A. N.      174
Fock, V.      168
Fourier transforms      2
Fourier transforms, basic example      53ff
Fox, E. N.      232
Fox’s integral identity      232
Fredholm integral equations, first kind      (see Wiener-Hopf integral equations)
Fredholm integral equations, second kind      221
Fresnel functions      33 45 73 213
Function-theoretic methods      153
Gamma functions      40
Gamma functions, factorization by means of      41 167 171 215
Greene, T. R. and Heins, A. E.      94
Green’s function      6
Half-planes with flange      183
Half-planes, algebraic equations      175
Half-planes, dielectric material      213
Half-planes, infinite set of staggered      133
Half-planes, single infinitely thin, basic (Sommerfeld) diffraction problem      48ff
Half-planes, single infinitely thin, diffraction of electromagnetic waves by      95
Half-planes, single infinitely thin, finite resistivity      83
Half-planes, single infinitely thin, generalizations of basic problem      5
Half-planes, single of finite thickness      181 187ff
Half-planes, three parallel      154
Half-planes, two parallel, radiation from      105ff
Half-planes, two parallel, staggered      154
Half-planes, wave falling on      100ff 125 126
Hankel functions, asymptotic behaviour      45
Hankel functions, integral representation      32
Harrington, R. F.      88
Heins, A. E.      94 103 127 131 133 134 157 171
Heins, A. E. and Carlson, J. F.      133
Heins, A. E. and Feshbach, H.      92 93 134
Hilbert problem      49 14
Hilbert problem, equation application      169
Hopf, E.      168
Imperfect conductivity      (see Resistive boundaries)
Indentation of contour      30 44 86
Indentation of contour for transform in time      44
Infinite product      15 40 103 129 130
Infinite product or gamma functions      41
Infinite product, asymptotic behaviour of      104 128 129
Infinite product, computation of      127 128
Institute of Mathematical Sciences, New York, reports      237
Integral equation method, general remarks      49 71 76 236
Integral equations      (see Fredholm Volterra Wiener-Hopf)
Integral functions      6 178 197
Jets      139
Jones, D. S. vii, viii      48 52 75 95 97 127 130 131 167 173 187 190 195 196 199 200 207 231
Jones’s method for approximate solutions      17 8ff 236
Jones’s method for boundary conditions specified arbitrarily      79ff
Jones’s method, detailed application to a special example      52ff
Jones’s method, general remarks      48 71 76 98
Jones’s method, routine applications      100ff
Jost, Res      219
Karp, S. N. and Russek, A.      206
Karp, S. N. and Williams, W. E.      125
Klunker, E. B. and Harder, K. C.      139
Koiter, W. T.      75 139 161 162 173
Kourganoff, V.      133 168
Laplace transform      10 21 52 86
Laplace transform, complete equivalence with Fourier transform      22 26
Laplace-type equations      135 (see also Biharmonic equation)
Laplace’s equation as limit of wave equation      135ff
Laplace’s equation in jet problem      140
Laplace’s equation in polar coordinates      164ff 177
Latter, R.      236
Lebedev — Kontorovich transform      148 213ff
Lebesgue integration, reason for not using      23
Leitner, A. and WELLS,C.P.      213 216
Lennox, S. C.      139
Levine, H.      236 242
Levine, H. and Sch winger, J.      20 42 115 130 132
Levine, H. and Wu, T. T.      236
Lewin, L.      131 179 242
Lewis, J. A. and Carrier, G. F.      97
Linfoot, E. H. and Shepherd, W. M.      175
Liouville’s theorem      6 38 57 69 103 114
Magnus, W.      175
Magnus, W. and Oberhettinger, F.      175
Marcuvitz, N.      122 133 179
Mark, C.      168
Marshak, R. E.      168
Maue, A. W.      75 96
Meier, J. A. and Leitner, A.      218
Meixner, J.      75
Meromorphic functions      39
Miles, J. W.      95
Milne’s integral equation      167
Milne’s integral, equation      167
Milne’s integral, reduction of more general types to Fredholm equations of second kind      232 233ff
Milne’s integral, reduction to repeated Volterra equations      230
Milne’s integral, solution by the Wiener — Hopf technique      67ff 167ff 227
Mixed boundary value problem      1
Mixed boundary value problem, solution of a specific example      77ff
Mixed boundary value problem, three-part      183 203ff 231ff
Mixed boundary value problem, two-part, general theory      147
Morse, P. M. and Fesiibaoh, H.      02 115 131 134 179
Multiplying factor method      58ff 78ff 22
Muskhelishvili, N. I.      142 144 146 158
Notation      54
Notation in certain approximate methods      182 197
Numerical evaluation of infinite, products      127 128
Numerical tables      viii 122 131
Oberhettinger, F.      36
Oseen’s equations      97
Pack, D. C.      viii 139
Pai, S. I.      139
Papadopoulos, V. M.      134 196
Pearson, J. D.      132
Perpendicular boundaries      178 181 187ff 207ff
Placzek, G.      168
Placzek, G. and Seidel, W.      168
Plemelj formulae      47 145
Pol, B. van dee and Bremmer, H.      27 36
Polar coordinates, Laplace’s equation      164ff 177
Polar coordinates, steady-state wave equation      148 214ff
Polar coordinates, wedge of elastic material      173
Poles and branch points      47 133 207
Product factorization      14ff
Product factorization, approximate      160ff
Product factorization, general theorems      15 41
Product factorization, involving gamma functions      41 167 171 215
Quantum mechanics, reference to problem in      219
Quarter-plane aerofoil      95
Radiation condition at infinity      2 31
Radiation-type boundary conditions      (see Resistive boundaries)
Radio-wave propagation over landsea interface      93 94
Reflection coefficient in duct      110 114 120 124
Regularity, of functions defined by integrals      1
Resistive boundaries, half-plane      83ff
Resistive boundaries, notation      134
Resistive boundaries, strip across duct      212
Resistive boundaries, strip parallel to walls of duct      120
Rod, solid cylindrical, finite length      213
Rod, solid cylindrical, semi-infinite      196
Scattering cross-section of disc      218
Schwinger, J.      vii
Semi-infinite plane      (see Half-planes)
Senior, T. B. A.      83 85 92 93 134
Separation of variables      1 147 149
Simultaneous linear algebraic equations from simultaneous Wiener-Hopf equations      155
Simultaneous linear algebraic equations in approximate solutions      185 190ff 208 217
Simultaneous linear algebraic equations in duct problem      175
Simultaneous linear algebraic equations in half-plane problem      176
Simultaneous linear algebraic equations, solution of special sets      173 174ff
Simultaneous Wiener-Hopf equations in electromagnetic cylindrical duct problem      132
Simultaneous Wiener-Hopf equations in electromagnetic half-plane problem      95
Simultaneous Wiener-Hopf equations in two-dimensional duct problems      121 154
Simultaneous Wiener-Hopf equations, general theory      153ff
Slits      (see Strips and slits)
Sneddon, I. N. viii      2 96 168 231 236
Sommerfeld, half-plane problem      48ff
Sommerfeld, radiation condition      31
Sound waves      (see Duct Half-planes etc.)
Source distribution      44 52 87
Sparenberg, J. A.      169 171
Steady-state wave equation      28
Steepest descent      34
Strips and slits of finite thickness and finite length      213
Strips and slits of finite thickness, induct      212
Strips and slits of finite thickness, semi-infinite length      181 187ff
Strips and slits of finite width, Laplace’s equation      177
Strips and slits of finite width, low frequency      218
Strips and slits of finite width, wave equation, high frequency      183 203ff 219
Sum decomposition in approximate solutions      179 186
Sum decomposition, applications of      80 179 186 198 228
Sum decomposition, function with poles      39
Sum decomposition, general formulae for concrete cases      18
Sum decomposition, general theorem      13
Superposition, method of      81 87
Tables      (see Numerical tables)
Tides in permeable rock      94
Titchmarsh, E. C.      2 5 8 11 39 40 41 42 168 171
Titchmarsh’s method      171
Titchmarsh’s method in wedge problems      219
Titchmarsh’s method or evaluation of integrals      33
Titchmarsh’s method or sum decompositions      47
Titchmarsh’s method, applied to diffraction by half-plane      176
Transient problems      28 97
Tranter, C. J.      2
Uniqueness      72
Uniqueness and edge conditions      51 74
Uniqueness, equations      69 168
Vajnshtejn, L. A.      20 115 125 130 131 132 153
Vajnshtejn-Karp-Clemmow method      49 153 213
Verification of solution      72
via the Hilbert, problem      169
via the Hilbert, special equations      171 177
via the Hilbert, uniqueness of solution      69 168
Viscous medium      96 97 139
Volterra integral equations      229 230 233
Water waves      94 134
Watson, G. N.      36 46
Wave equation      27ff
waveguide      (see Duct two-dimensional Duct cylindrical Half-planes two
Wedges of elastic material      173
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