PROCEEDINGS INTERNATIONAL CONGRESS MATHEMATICIANS

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10 LIST OF DELEGATES EGYPT ENGLAND Institut d'Egypte, Cairo ISMAIL RATIB BEY Birkbeck College, London ALBERT CYRIL OFFORD British Association for the Advancement of Science DANIEL PEDOE JOHN TODD OLGA TAUSSKY TODD DOROTHY WRINCH Cambridge Philosophical Society WILLIAM VALLANCE DOUGLAS HODGE ROBERT ALEXANDER RANKIN Imperial College of Science and Technology, London GEORGE FREDERICK JAMES TEMPLE King's College, London RICHARD RADO London Mathematical Society EDWARD FOYLE COLLINGWOOD HANS ARNOLD HEILBRONN MAXWELL HERMAN ALEXANDER NEWMAN ALBERT CYRIL OFFORD FRANK SMITHIES Military College of Science, Shrivenham C. J. TRANTER Ministry of Supply ROBERT ARTHUR FAIRTHORNE C. K. THORNHILL Oxford University KATHLEEN SARGINSON JOHN HENRY CONSTANTINE WHITEHEAD Queen Mary College, London GEORGE CUNLIFFE MCVITTIE Royal Holloway College, Surrey MARY BRADBURN Royal Society MARY LUCY CARTWRIGHT HAROLD DAVENPORT WILLIAM VALLANCE DOUGLAS HODGE LOUIS JOEL MORDELL GEORGE FREDERICK JAMES TEMPLE HERBERT W. TURNBULL
FINLAND FRANCE University College, London HAROLD DAVENPORT University College, Southampton LIST OF DELEGATES 11 EVAN TOM DAVIES University College of the South-West of England, Exeter WALTER KURT HAYMAN University of Birmingham FREEMAN J. DYSON University of Bristol HANS ARNOLD HEILBRONN LESLIE HOWARTH Cambridge University MA^Y LUCY CARTWRIGHT WILLIAM VALLANCE DOUGLAS HODGE LOUIS JOEL MORDELL ROBERT ALEXANDER RANKIN SHAUN WYLIE FRANK SMITHIES University of Durham KURT AUGUSTUS HIRSCH FRANK F. BONSALL WERNER WOLFGANG ROGOSINSKI JEFFREY DENNIS WESTON University of Liverpool Louis ROSENHEAD University of London HAROLD DAVENPORT GEORGE FREDERICK JAMES TEMPLE Victoria University of Manchester MAXWELL HERMAN ALEXANDER NEWMAN Westfield College, London DANIEL PEDOE Abo Akademi GUSTAV ELFVING The Academy of Finland, Helsinki ROLF NEVANLINNA Académie des Sciences EMILE BOREL JEAN CHAZY ARNAUD DENJOY
Page 1 and 2: PROCEEDINGS OF THE INTERNATIONAL CO
Page 3: HOST Harvard University CO-HOSTS Am
Page 7: HONORARY PRESIDENTS G U I D O C A S
Page 10 and 11: COMMITTEES OF THE CONGRESS G. B. PR
Page 12 and 13: COMMITTEES OF THE CONGRESS COMMITTE
Page 14 and 15: DONORS Northwestern National Life I
Page 16 and 17: AUSTRIA BELGIUM BRAZIL LIST OF DELE
Page 20 and 21: 12 LIST OF DELEGATES JACQUES HADAMA
Page 22 and 23: 'Ï4 LIST OF DELEGATES University o
Page 24 and 25: 16 LIST OF DELEGATES KENKICHI IWASA
Page 26 and 27: 18 LIST OF DELEGATES PANAMA PERU Un
Page 28 and 29: 20 LIST OF DELEGATES TURKEY Univers
Page 30 and 31: 22 LIST OF DELEGATES ARIZONA Tallad
Page 32 and 33: 24 LIST OF DELEGATES University of
Page 34 and 35: 26 LIST OF DELEGATES United States
Page 36 and 37: 28 LIST OF DELEGATES FRANCIS REGAN
Page 38 and 39: 30 LIST OF DELEGATES United States
Page 40 and 41: 32 LIST OF DELEGATES Bryn Mawr Coll
Page 42 and 43: 34 LIST OF DELEGATES University of
Page 44 and 45: AABOE, Asger H., Adjunkt, Cand. Mag
Page 46 and 47: 38 LIST OF MEMBERS BACON, Harold Ma
Page 48 and 49: 40 LIST OF MEMBERS BLACK, Harold Ly
Page 50 and 51: 42 LIST OF MEMBERS BRUDNO, Charlott
Page 52 and 53: 44 LIST OF MEMBERS CHERRY, Thomas M
Page 54 and 55: 46 LIST OF MEMBERS CREMER, Hubert H
Page 56 and 57: 48 LIST OF MEMBERS DUDMAN, John Alm
Page 58 and 59: 50 LIST OF MEMBERS Mrs. Fenchel Mr.
Page 60 and 61: 52 LIST OF MEMBERS GEPHART, F. L.,
Page 62 and 63: 54 LIST OF MEMBERS GRIFFIN, Frank L
Page 64 and 65: 56 Miss S. Jean Herriot Mr. James W
Page 66 and 67: 58 LIST OF MEMBERS INZINGER, Rudolf
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60 LIST OF MEMBERS KINCAID, Wilfred
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62 LIST OF MEMBERS LARGUIER, Rev. E
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64 LIST OF MEMBERS LUCE, Robert Dun
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66 LIST OF MEMBERS MAY, Lida B., Pr
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68 LIST OF MEMBERS MOUSINHO, Maria
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70 LIST OF MEMBERS OXTOBY, John C,
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72 LIST OF MEMBERS PRESTON, Glenn W
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74 LIST OF MEMBERS RIES, Henry Fran
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76 LIST OF MEMBERS SANCHEZ-DIAZ, Ra
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78 LIST OF MEMBERS SHAPIRO, George
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80 LIST OF MEMBERS STARKE, Emory Po
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82 LIST OF MEMBERS TOMBER, Marvin L
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84 LIST OF MEMBERS WALLACE, Andrew
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86 LIST OF MEMBERS WILLIAMSON, Char
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PROGRAM WEDNESDAY, AUGUST 30 ADDRES
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90 PROGRAM THURSDAY, AUGUST 31 10:1
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92 PROGRAM THURSDAY, AUGUST 31 2:15
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94 PROGRAM D. ELLIS, University of
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96 PROGRAM J. B. ROSSER, Institute
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98 PROGRAM FRIDAY, SEPTEMBER 1 2:15
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100 PROGRAM M. GUT, University of Z
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102 PROGRAM W. R. WASOW, Institute
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104 PROGRAM SATURDAY, SEPTEMBER 2 -
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106 PROGRAM S. CHOWLA and A. L. WHI
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108 PROGRAM MONDAY, SEPTEMBER 4 9:0
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110 PROGRAM J. C. OXTOBY, Bryn Mawr
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112 PROGRAM TUESDAY, SEPTEMBER 5 AD
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114 PROGRAM TUESDAY, SEPTEMBER 5 2
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116 PROGRAM A. GLEASON, Harvard Uni
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118 PROGRAM WEDNESDAY, SEPTEMBER 6
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120 PROGRAM V. L. KLEE, JR., Univer
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122 SECRETARY'S REPORT Kline, Unive
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OPENING ADDRESS OF PROFESSOR OSWALD
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126 SECRETARY'S REPORT Immediately
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128 HARALD BOHR some of the most im
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130 HARALD BOHR To the proof in its
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132 HARALD BOHR integration i.e., t
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134 HARALD BOHR congratulate you mo
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136 SECRETARY'S REPORT Stated Addre
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138 SECRETARY'S REPORT Hurewicz, S.
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140 SECRETARY'S REPORT Hull, J. R.
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142 DETLEV BRONK in rare goods, the
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144 DETLEV BRONX of this, we know t
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STATED ADDRESSES
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ON NULL-SETS IN HARMONIC ANALYSIS A
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PROBLÈMES GLOBAUX DANS LA THÉORIE
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154 HENRI CARTAN 2. Domaines d'holo
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156 HENRI CARTAN 3. Etude globale d
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158 HENRI CARTAN une ancienne conje
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160 v HENRI CARTAN réelles donnée
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162 HENRICARTAN En fait, dès 1941,
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164 . HENRI CARTAN f(zi, z2), unifo
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RECENT PROGRESS IN THE GEOMETRY OF
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168' H. DAVENPORT depending only on
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170 H. DAVENPORT stated by Minkowsk
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172 H. DAVENPORT integer for all va
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174 H. DAVENPORT and had given this
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176 KURT GÖDEL In such a coordinat
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178 KURT GÖDEL (where hih is posit
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180 • KURT GÖDEL lines of matter
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THE TOPOLOGICAL INVARIANTS OF ALGEB
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184 ' * , • W, V. D, HODGE that t
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186 W. V. D. HODGE of K2m . Its bou
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188 W. V. D. HODGE The effective p-
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190 W. V. D. HODGE the Jacobian mat
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192 W. V. D. HODGE 15. , Proc. Lond
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194 HEINZ HOPF Man kann diesen Unte
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196 HEINZ HOPP als Basisvektoren in
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198 HEINZ HOPF zu beweisen, versagt
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200 HEINZ HOPF A'(3) > 1 und A'(7)
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202 HEINZ HOPF der Frage nach der E
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ERGODIC THEORY S. KAKUTANI This add
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SHOCK INTERACTION AND ITS MATHEMATI
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208 J. F. RITT their derivatives, w
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210 A. ROME Theon says that he has
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212 A. ROME can we use a modern tab
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214 A. ROME the sought days and hou
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216 A. ROME distance; and finally,
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218 A. ROME of corrections, one val
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THÉORIE DES NOYAUX 1 LAURENT SCHWA
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222 LAURENT SCHWARTZ Y n X X m asso
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224 LAURENT SCHWARTZ 1°. (3D)
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226 LAURENT SCHWARTZ Les noyaux des
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228 LAURENT SCHWARTZ (et $(X) doit
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230 LAURENT SCHWARTZ donne lieu à
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232 ABRAHAM WALD experimentation wi
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234 ABRAHAM WALD that the decision
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236 ABRAHAM WALD decision rules dis
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238 ABRAHAM WALD obtained by Krylof
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240 ABRAHAM WALD (8.1) z. = l o g ^
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242 ' ABRAHAM WALD As a last exampl
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NUMBER-THEORY AND ALGEBRAIC GEOMETR
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246 HASSLER WHITNEY 2. The general
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248 HASSLER WHITNEY (3.3) | * r |*
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250 HASSLER WHITNEY Moreover, using
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252 HASSLER WHITNEY A "simple" cont
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254 v HASSLER WHITNEY schitz r-chai
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256 HASSLER WHITNEY the differentia
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THE CULTURAL BASIS OF MATHEMATICS 1
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260 R. L. WILDER punch to the nose?
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262 R. L. WILDER Chinese practiced
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264 R. L. WILDER Some evidence perh
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266 R. L. WILDER relationships betw
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26S R. L. WILDER point for mathemat
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270 R. L. WILDER matical. In the ea
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THE FUNDAMENTAL IDEAS OF ABSTRACT A
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SECTION I. ALGEBRA AND THEORY OF NU
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BINARY MODULARY CONGRUENCE GROUPS 2
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BINARY MODULARY CONGRUENCE GROUPS 2
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FAREY SECTIONS IN THE FIELDS OF GAU
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FAREY SECTIONS 283 a combination of
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FAREY SECTIONS 285 Theorem C is unc
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SIEVE-METHOD IN PRIME NUMBER THEORY
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THEORY OF NUMBERS AND FORMS ON THE
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THEORY OF NUMBERS AND FORMS 295 An
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THEORY OF NUMBERS AND FORMS 297 PRO
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THEORY OF NUMBERS AND FORMS 299 EXP
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THEORY OF NUMBERS AND FORMS 301 THE
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GROUPS AND UNIVERSAL ALGEBRA SIMILA
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GROUPS AND UNIVERSAL ALGEBRA 305 sa
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GROUPS AND UNIVERSAL ALGEBRA 307 va
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GROUPS AND UNIVERSAL ALGEBRA 309 an
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GROUPS AND UNIVERSAL ALGEBRA 311 re
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GROUPS AND UNIVERSAL ALGEBRA 313 TH
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GROUPS AND UNIVERSAL ALGEBRA 315 ON
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RINGS AND ALGEBRAS 317 (A, A, R) =
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RINGS AND ALGEBRAS 319 ON THE THEOR
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RINGS AND ALGEBRAS 321 simple Jorda
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ARITHMETIC ALGEBRA 323 &i2/i + •
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VECTOR SPACES AND MATRICES VARIÉT
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VECTOR SPACES AND MATRICES 327 CYCL
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VECTOR SPACES AND MATRICES 329 {s +
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THEORY OF FIELDS AND EQUATIONS 331
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THEORY OF FIELDS AND EQUATIONS 333
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max mm, um Z. / / Z) ai3ri(x)sj(y)
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SECTION IL ANALYSIS A SURVEY OF THE
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THEORY OF ALMOST PERIODIC FUNCTIONS
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QUELQUES THÉORÈMES D'UNICITÉ 1 S
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QUELQUES THÉORÈMES D'UNICITÉ 351
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ADDITIVE ALGEBRAIC NUMBER THEORY 35
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Page 369 and 370:
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ON VISUALIZATION OF DOMAINS IN THE
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(2.1a) * = Zi, (2.1b) Zi = Z2, VISU
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VISUALIZATION OF DOMAINS IN THEORY
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Page 379 and 380:
VISUALIZAITON OF DOMAINS IN THEORY
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Page 383 and 384:
FUNCTIONS OP REAL VARIABLES 375 MET
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FUNCTIONS OF BEAL VARIABLES 377 THE
Page 387 and 388:
FUNCTIONS OF REAL VARIABLES 379 Sec
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FUNCTIONS OF REAL VARIABLES 381 Pn
Page 391 and 392:
FUNCTIONS OF REAL VARIABLES 383 DIF
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FUNCTIONS OF REAL VARIABLES 385 and
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FUNCTIONS OF REAL VARIABLES 387 THE
Page 397 and 398:
FUNCTIONS OF COMPLEX VARIABLES ON A
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FUNCTIONS OF COMPLEX VARIABLES 391
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Page 403 and 404:
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Page 407 and 408:
Page 409 and 410:
Page 411 and 412:
FUNCTIONS OP COMPLEX VARIABLES 403
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Page 415 and 416:
Page 417 and 418:
THEORY OF SERIES AND SUMMABILITY 40
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THEORY OF SERIES AND SUMM ABILITY 4
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Page 423 and 424:
Page 425 and 426:
Page 427 and 428:
Page 429 and 430:
Page 431 and 432:
Page 433 and 434:
Page 435 and 436:
DIFFERENTIAL AND INTEGRAL EQUATIONS
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Page 439 and 440:
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Page 447 and 448:
Page 449 and 450:
Page 451 and 452:
Page 453 and 454:
Page 455 and 456:
Page 457 and 458:
FUNCTIONAL ANALYSIS 449 APPROXIMATE
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FUNCTIONAL ANALYSIS 451 (i) iterati
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FUNCTIONAL ANALYSIS 453 in a bounde
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FUNCTIONAL ANALYSIS 455 a single po
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FUNCTIONAL ANALYSIS 457 linear isom
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FUNCTIONAL ANALYSIS 459 A multiplic
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FUNCTIONAL ANALYSIS 461 et par O (S
Page 471 and 472:
FUNCTIONAL ANALYSIS 463 inverse of
Page 473 and 474:
FUNCTIONAL ANALYSIS 465 space, ther
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FUNCTIONAL ANALYSIS 467 functions a
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FUNCTIONAL ANALYSIS 469 In each of
Page 479 and 480:
FUNCTIONAL ANALYSIS 471 ON VARIATIO
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FUNCTIONAL ANALYSIS 473 In this cas
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FUNCTIONAL ANALYSIS 475 wählen, we
Page 485 and 486:
MEASURE THEORY ON HAUSDORFF MEASURE
Page 487:
MEASURE THEORY 479 {xn} with 5^*»i
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SECTION III. GEOMETRY AND TOPOLOGY
Page 493 and 494:
INTEGRAL GEOMETRY IN GENERAL SPACES
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Page 497 and 498:
Page 499 and 500:
ARITHMETICAL PROPERTIES OF ALGEBRAI
Page 501 and 502:
ARITHMETICAL PROPERTIES OF ALGEBRAI
Page 503 and 504:
GEOMETRY 495 4. The sets C(r) are a
Page 505 and 506:
GEOMETRY 497 Elliptic planes map in
Page 507 and 508:
(v) If S is a cube, then/r(£) = r-
Page 509 and 510:
DIFFERENTIAL GEOMETRY 501 genie at
Page 511 and 512:
DIFFERENTIAL GEOMETRY 503 vertex v
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DIFFERENTIAL GEOMETRY 505 THE CONVE
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DIFFERENTIAL GEOMETRY 507 dätische
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DIFFERENTIAL GEOMETRY 509 SUR CERTA
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ALGEBRAIC GEOMETRY SOPRA ALCUNE SUP
Page 521 and 522:
ALGEBRAIC GEOMETRY 513 {a f x) n ~
Page 523 and 524:
ALGEBRAIC GEOMETRY 515 SYSTEMS OF S
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ALGEBRAIC GEOMETRY 517 folds, then
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ALGEBRAIC GEOMETRY 519 The matrix C
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ALGEBRAIC TOPOLOGY IRREDUCIBLE RING
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ALGEBRAIC TOPOLOGY 523 R which are
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ALGEBRAIC TOPOLOGY 525 In order tha
Page 535 and 536:
ALGEBRAIC TOPOLOGY 527 This result
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ALGEBRAIC TOPOLOGY 529 near b,+i. S
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ALGEBRAIC TOPOLOGY 531 Moreover, co
Page 541 and 542:
FUNCTION SPACES AND POINT SET TOPOL
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Page 545 and 546:
Page 547:
Page 551 and 552:
SECTION IV. PROBABILITY AND STATIST
Page 553 and 554:
MATHEMATICS OP FACTORIAL DESIGNS 54
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MATHEMATICS OF FACTORIAL DESIGNS 54
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PROCESSUS À LA FOIS STATIONNAIRES
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PROCESSUS STATIONNAIRES ET MARKOVIE
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PROCESSUS STATIONNAIRES ET MARKOVIE
Page 563 and 564:
ON SOME ASPECTS OF STATISTICAL INFE
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Page 567 and 568:
Page 569 and 570:
Page 571 and 572:
Page 573 and 574:
PROBABILITY A HISTORY OF PROBABILIT
Page 575 and 576:
PROBABILITY 567 and let Q be that n
Page 577 and 578:
PROBABILITY 569 ELEMENTS ALÉATOIRE
Page 579 and 580:
PROBABILITY 571 being variables of
Page 581 and 582:
PROBABILITY 573 difficulties, and t
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PROBABILITY 575 information passes
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INTERPOLATION NEW DEVELOPMENTS IN I
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INTERPOLATION 579 polation. If ei,
Page 589 and 590:
STATISTICS 581 If £ and rj are two
Page 591 and 592:
STATISTICS 583 where Kt is the stan
Page 593 and 594:
STATISTICS 585 Case Bi : 22 = 1. Ca
Page 595 and 596:
STATISTICS 587 chosen by means of a
Page 597:
ECONOMICS 589 quantità dei due ben
Page 601 and 602:
SECTION V. MATHEMATICAL PHYSICS AND
Page 603 and 604:
THE REFRACTIVE INDEX OF AN IONISED
Page 605 and 606:
THE REFRACTIVE INDEX OF AN IONISED
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TUE BEFfìACTIVE INDEX OF AN IONISE
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DEVELOPMENTS AT THE CONFLUENCE OF A
Page 611 and 612:
ANALYTIC BOUNDARY CONDITIONS 603 be
Page 613 and 614:
ANALYTIC BOUNDARY CONDITIONS 605 Th
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STOPÜNGSTHEOPIE DER SPEKTPÀLZEP L
Page 617 and 618:
STORÜNGSTHEORIE DER SPEKTRALZERLEG
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ST0EÜNGSTI1E0R1E DER SPEKTRALZERLE
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STÖRUNG STHEORIE DER SPEKTRALZERLE
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MECHANICS 615 ROTORS IN SPHERICAL P
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MECHANICS: ELASTICITY AND PLASTICIT
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Page 629 and 630:
Page 631 and 632:
Page 633 and 634:
MECHANICS : HYDRODYNAMICS ON THE ST
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MECHANICS: HYDRODYNAMICS 627 faces.
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MECHANICS: HYDRODYNAMICS 629 POHLHA
Page 639 and 640:
MECHANICS: HYDRODYNAMICS 631 the di
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MECHANICS: HYDRODYNAMICS 633 is, th
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MECHANICS: HYDRODYNAMICS 635 Physic
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MECHANICS: HYDRODYNAMICS 637 unifor
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MECHANICS: HYDRODYNAMICS 639 stages
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MECHANICS: HYDRODYNAMICS 641 partic
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MECHANICS: HYDRODYNAMICS 643 a) The
Page 653 and 654:
MATHEMATICAL PHYSICS 645 grals of m
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OPTICS AND ELECTROMAGNETIC THEORY 6
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OPTICS AND ELECTROMAGNETIC THEORY 6
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MATHEMATICAL PHYSICS: RELATIVITY, G
Page 661 and 662:
RELATIVITY, GRAVITATION, AND FIELD
Page 663 and 664:
RELATIVITY, GRAVITATION, AND FIELD
Page 665 and 666:
NUMERICAL METHODS ALMOST-TRIANGULAR
Page 667 and 668:
NUMERICAL METHODS 659 3. G. BOULANG
Page 669 and 670:
NUMERICAL METHODS 661 initial v unt
Page 671 and 672:
NUMERICAL METHODS 663 easily comput
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NUMERICAL METHODS 665 tion of certa
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PARTIAL DIFFERENTIAL EQUATIONS LE P
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PARTIAL DIFFERENTIAL EQUATIONS 669'
Page 679 and 680:
PARTIAL DIFFERENTIAL EQUATIONS 671
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MISCELLANEOUS 673
Page 683 and 684:
MISCELLANEOUS 675 If in the embryon
Page 685:
SECTION VI LOGIC AND PHILOSOPHY
Page 688 and 689:
680 S. C. KLEENE (freie Wahlfolge).
Page 690 and 691:
682 S. C. KLEENE dependent variable
Page 692 and 693:
684 S. C. KLEENE correlated number.
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ON THE APPLICATION OF SYMBOLIC LOGI
Page 696 and 697:
688 ABRAHAM ROBINSON K holds, then
Page 698 and 699:
690 ABRAHAM ROBINSON sistent, it po
Page 700 and 701:
692 ABRAHAM ROBINSON certain type o
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694. ABRAHAM • ROBINSON the more
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696 TH. SKOLEM and we have the axio
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698 TH. SKOLEM form xA(x) G D for a
Page 708 and 709:
700 TH. SKOLEM where (x, y) G S is
Page 710 and 711:
702 TH. SKOLEM by F. B. Fitch, and
Page 712 and 713:
704 TH. SKOLEM sistency of formaliz
Page 714 and 715:
706 ^ ALFRED TARSKI formed by a set
Page 716 and 717:
708 ALFRED TARSKI A symbol of the f
Page 718 and 719:
710 ALFRED TARSKI where each of the
Page 720 and 721:
712 ALFRED TARSKI For instance, the
Page 722 and 723:
714 ALFRED TARSKI is a topological
Page 724 and 725:
716 ALFRED TARSKI o be represented
Page 726 and 727:
718 ALFRED TARSKI direction whose p
Page 728 and 729:
720 ALFRED TARSKI Arithmetical clas
Page 730 and 731:
722 SECTION VI. LOGIC AND PHILOSOPH
Page 732 and 733:
Page 734 and 735:
Page 736 and 737:
Page 738 and 739:
Page 740 and 741:
Page 742 and 743:
Page 745:
SECTION VII HISTORY AND EDUCATION
Page 748 and 749:
740 G. PÓLYA 27 = 1 + 2 X 13 35 =1
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742 G. PÖLYA the length of the per
Page 752 and 753:
744 G. PÓLYA 2 4 6 / i \ i ^ i # _
Page 754 and 755:
746 G. PÓLYA I cannot here enter i
Page 756 and 757:
HISTORY THE FOREMOST TEXTBOOK OF MO
Page 758 and 759:
750 SECTION VII. HISTORY AND EDUCAT
Page 760 and 761:
EDUCATION MATHEMATICS FOR THE MILLI
Page 762 and 763:
Page 764 and 765:
Page 766 and 767:
Page 768 and 769:
Page 770 and 771:
762 TABLE OF CONTENTS Zariski, O.,
Page 773 and 774:
ABBOTT, J. C. 303 ABELLANAS, P. 325
Page 775 and 776:
KARUSII, W. 663 KASNER, E. 505 KELL
Page 777:
WALSH, J. E. 582 WALSH, J. L. 405 W
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