PROCEEDINGS INTERNATIONAL CONGRESS MATHEMATICIANS

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DONORS Northwestern National Life Insurance Company Northwestern Mutual Life Insurance Company Philco Corporation Provident Mutual Life Insurance Company Prudential Insurance Company Radio Corporation of America Raytheon Manufacturing Company Register and Tribune Company Shell Oil Company Standard Oil Development Company State Mutual Life Assurance Company The Travelers Insurance Company The Union Central Life Insurance Company United Fruit Company United States Steel Corporation of Delaware D. Van Nostrand Company John Wiley and Company R. W. Byerly Donald Cody J. L. Coolidge T. J. Coolidge Otto Dunkel- B. N. Everett W. B. Ford A. L. Lowell A. L. Miller Philip W. Pillsbury G. E. Roosevelt Philip Stockton
LIST OF DELEGATES (The following is a list of delegates appointed by universities, colleges, etc.) International Council of Scientific Unions EMILE BOREL International Union of Theoretical and Applied Mechanics JOHANNES MARTINUS BURGERS ANGLO-EGYPTIAN SUDAN J. C. HUNSAKER GEORGE FREDERICK JAMES TEMPLE . Foreign Gordon Memorial College, Khartoum T. H. FALLOWS ARGENTINA Academia Nacional de Ciencias Exactas, Fisicas y Naturales de Buenos Aires ALBERTO GONZALEZ DOMîNGUEZ Universidad de Cuyo, Facultad de Ciencias de la Educación GINO TURRIN Union Mathematica Argentina JULIO REY PASTOR Universidad de Buenos Aires, Facultad de Ciencias Exactas, Fisicas y Naturales ALBERTO GONZALEZ DOMîNGUEZ JUAN CARLOS VIGNAUX Universidad Nacional de Cordoba ALFREDO TECERA MARTINEZ AUSTRALIA Royal Society of Western Australia RAY DAVIS University of Melbourne T. M. CHERRY University of Sydney FREDERICK CHONG THOMAS G ROOM University of Western Australia, Perth ALBERT LAURENCE BLAKERS
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 16 and 17: AUSTRIA BELGIUM BRAZIL LIST OF DELE
Page 18 and 19: 10 LIST OF DELEGATES EGYPT ENGLAND
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
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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
Page 268 and 269:
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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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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VISUALIZAITON OF DOMAINS IN THEORY
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FUNCTIONS OP REAL VARIABLES 375 MET
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FUNCTIONS OF BEAL VARIABLES 377 THE
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FUNCTIONS OF REAL VARIABLES 379 Sec
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FUNCTIONS OF REAL VARIABLES 381 Pn
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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:
Page 405 and 406:
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 427 and 428:
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DIFFERENTIAL AND INTEGRAL EQUATIONS
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Page 449 and 450:
Page 451 and 452:
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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
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FUNCTIONAL ANALYSIS 463 inverse of
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FUNCTIONAL ANALYSIS 465 space, ther
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FUNCTIONAL ANALYSIS 467 functions a
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FUNCTIONAL ANALYSIS 469 In each of
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FUNCTIONAL ANALYSIS 471 ON VARIATIO
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FUNCTIONAL ANALYSIS 473 In this cas
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FUNCTIONAL ANALYSIS 475 wählen, we
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MEASURE THEORY ON HAUSDORFF MEASURE
Page 487:
MEASURE THEORY 479 {xn} with 5^*»i
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SECTION III. GEOMETRY AND TOPOLOGY
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INTEGRAL GEOMETRY IN GENERAL SPACES
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Page 497 and 498:
Page 499 and 500:
ARITHMETICAL PROPERTIES OF ALGEBRAI
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ARITHMETICAL PROPERTIES OF ALGEBRAI
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GEOMETRY 495 4. The sets C(r) are a
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GEOMETRY 497 Elliptic planes map in
Page 507 and 508:
(v) If S is a cube, then/r(£) = r-
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DIFFERENTIAL GEOMETRY 501 genie at
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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
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ALGEBRAIC GEOMETRY 513 {a f x) n ~
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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
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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
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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
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ON SOME ASPECTS OF STATISTICAL INFE
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Page 567 and 568:
Page 569 and 570:
Page 571 and 572:
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PROBABILITY A HISTORY OF PROBABILIT
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PROBABILITY 567 and let Q be that n
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PROBABILITY 569 ELEMENTS ALÉATOIRE
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PROBABILITY 571 being variables of
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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,
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STATISTICS 581 If £ and rj are two
Page 591 and 592:
STATISTICS 583 where Kt is the stan
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STATISTICS 585 Case Bi : 22 = 1. Ca
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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
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THE REFRACTIVE INDEX OF AN IONISED
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TUE BEFfìACTIVE INDEX OF AN IONISE
Page 609 and 610:
DEVELOPMENTS AT THE CONFLUENCE OF A
Page 611 and 612:
ANALYTIC BOUNDARY CONDITIONS 603 be
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ANALYTIC BOUNDARY CONDITIONS 605 Th
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STOPÜNGSTHEOPIE DER SPEKTPÀLZEP L
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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:
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MECHANICS : HYDRODYNAMICS ON THE ST
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MECHANICS: HYDRODYNAMICS 627 faces.
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MECHANICS: HYDRODYNAMICS 629 POHLHA
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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
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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
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RELATIVITY, GRAVITATION, AND FIELD
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RELATIVITY, GRAVITATION, AND FIELD
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NUMERICAL METHODS ALMOST-TRIANGULAR
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NUMERICAL METHODS 659 3. G. BOULANG
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NUMERICAL METHODS 661 initial v unt
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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'
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PARTIAL DIFFERENTIAL EQUATIONS 671
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MISCELLANEOUS 673
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MISCELLANEOUS 675 If in the embryon
Page 685:
SECTION VI LOGIC AND PHILOSOPHY
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680 S. C. KLEENE (freie Wahlfolge).
Page 690 and 691:
682 S. C. KLEENE dependent variable
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684 S. C. KLEENE correlated number.
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ON THE APPLICATION OF SYMBOLIC LOGI
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688 ABRAHAM ROBINSON K holds, then
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690 ABRAHAM ROBINSON sistent, it po
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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
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700 TH. SKOLEM where (x, y) G S is
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702 TH. SKOLEM by F. B. Fitch, and
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704 TH. SKOLEM sistency of formaliz
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706 ^ ALFRED TARSKI formed by a set
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708 ALFRED TARSKI A symbol of the f
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710 ALFRED TARSKI where each of the
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712 ALFRED TARSKI For instance, the
Page 722 and 723:
714 ALFRED TARSKI is a topological
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716 ALFRED TARSKI o be represented
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718 ALFRED TARSKI direction whose p
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720 ALFRED TARSKI Arithmetical clas
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722 SECTION VI. LOGIC AND PHILOSOPH
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Page 745:
SECTION VII HISTORY AND EDUCATION
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740 G. PÓLYA 27 = 1 + 2 X 13 35 =1
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742 G. PÖLYA the length of the per
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744 G. PÓLYA 2 4 6 / i \ i ^ i # _
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746 G. PÓLYA I cannot here enter i
Page 756 and 757:
HISTORY THE FOREMOST TEXTBOOK OF MO
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750 SECTION VII. HISTORY AND EDUCAT
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EDUCATION MATHEMATICS FOR THE MILLI
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Page 764 and 765:
Page 766 and 767:
Page 768 and 769:
Page 770 and 771:
762 TABLE OF CONTENTS Zariski, O.,
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ABBOTT, J. C. 303 ABELLANAS, P. 325
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KARUSII, W. 663 KASNER, E. 505 KELL
Page 777:
WALSH, J. E. 582 WALSH, J. L. 405 W
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