Reference List for “Famous Trails to Paul Erdös”

This is a list of the primary references to the abbreviated version of the paper “Famous Trails to Paul Erdös” by Rodrigo De Castro and Jerrold W. Grossman, The Mathematical Intelligencer, vol. 21, no. 3 (Summer 1999), 51–63. Please report any errors to Jerry Grossman.

  1. K. Alder, A. Bohr, T. Huus, B. Mottelson & A. Winther, Study of nuclear structure by electromagnetic excitation with accelerated ions, Rev. Modern Physics 28 (1956), 432-542; MR 18,976g.

  2. R. A. Alpher, H. Bethe & G. Gamow, The origin of chemical elements, Phys. Rev. (2) 73 (1948), 803-804.

  3. Luis W. Alvarez, Walter Alvarez, Frank Asaro & Helen V. Michel, Extraterrestrial cause for the Cretaceous-Tertiary extinction: experimental results and theoretical interpretation, Science 208 (1980), no. 4448, 1095-1108.

  4. Luis Alvarez-Gaume & Edward Witten, Gravitational anomalies, Nuclear Phys. B 234 (1984), no. 2, 269-330; MR 85j:81062.

  5. K. J. Arrow, E. W. Barankin & D. Blackwell, Admissible points of convex sets, in Contributions to the Theory of Games, vol. 2, Princeton University Press, 1953, pp. 87-91; MR 14,998h.

  6. Kenneth J. Arrow, Samuel Karlin, Herbert Scarf, et al., Studies in the Mathematical Theory of Inventory and Production, Stanford University Press, 1958; MR 20#767.

  7. Yehoshua Bar-Hillel & Rudolf Carnap, Semantic information, British J. Philos. Sci. 4 (1953), 147-157; MR 15,386g.

  8. Y. Bar-Hillel, M. Perles & E. Shamir, On formal properties of simple phrase structure grammars, Z. Phonetik Sprachwiss. Kommunikat. 14 (1961), 143-172; MR 27#1361.

  9. M. Baranger, H. A. Bethe & R. P. Feynman, Relativistic correction to the Lamb shift, Phys Rev. (2) 92 (1953), 482-501; MR 15,589h.

  10. E. W. Barankin & R. Dorfman, On quadratic programming, Univ. California Publ. Statist. 2 (1958), 285-318; MR 20#775.

  11. J. Bardeen & W. H. Brattain, Physical principles involved in transistor action, Phys. Rev. (2) 75 (1949), 1208-1225.

  12. J. Bardeen, L. N. Cooper & J. R. Schrieffer, Microscopic theory of superconductivity, Phys. Rev. (2) 106 (1957) 162-164; MR 21#5470.

  13. J. Bardeen, L. N. Cooper & J. R. Schrieffer, Theory of superconductivity, Phys. Rev. (2) 108 (1957) 1175-1204; MR 20#2196.

  14. John Bardeen & David Pines, Electron-phonon interactions in metals, Phys. Rev. (2) 99 (1955), 1140-1150.

  15. J. Bardeen & W. Shockley, Scattering of electrons in crystals in the presence of large electric fields, Phys. Rev. (2) 80 (1950), 69-71; MR 12,786h.

  16. M. Beckmann & T. Marschak, An activity analysis approach to location theory, in Proc. Second Symposium in Linear Programming (Washington, DC, 1955), National Bureau of Standards, Washington, D.C., pp. 331-379; MR 17,382f.

  17. Evert W. Beth & Jean Piaget, Mathematical Epistemology and Psychology, D. Reidel Publishing Co., 1966; MR 41#5183.

  18. David Bohm & David A. Pines, A collective description of electron interactions. I, II, III, Phys. Rev. (2) 82 (1951), 625-634; 85 (1952), 338-353; 92 (1953), 609-625; MR 12,886e, 21#1124, 21#1125.

  19. A. Bohr, B. R. Mottelson & D. Pines, Possible analogy between the excitation spectra of nuclei and those of the superconducting metallic state, Phys. Rev. (2) 110 (1958), 936-938.

  20. Harald Bohr & Borge Jessen, Mean motions and almost periodic functions, in Analyse Harmonique, Colloques Internationaux du Centre National de la Recherche Scientifique, no. 15, pp. 75-84, Centre National de la Recherche Scientifique, Paris, 1949; MR 11,349f.

  21. Niels Bohr & Dirk Coster, Zeit. Physik 32 (1923), 342.

  22. Niels Bohr, H. A. Kramers & J. C. Slater, Phil. Mag. 42 (1924), 785.

  23. Niels Bohr & John Archibald Wheeler, The mechanism of nuclear fission, Phys. Rev. (2) 56 (1939), 426-450.

  24. Max Born, W. Heisenberg & P. Jordan, Zur Quantenmechanik. II, Zeit. Physik 35 (1926), 557-615.

  25. Max Born & T. von Kármán, Zur Theorie der spezifischen Wärme, Phys. Zeitschr. 14 (1913), 15-19.

  26. Max Born & Max von Laue, Phys. Zeitschr. 24 (1923), 49-53.

  27. Max Born & Norbert Wiener, A new formulation of the laws of quantization for periodic and aperiodic phenomena, J. Math. Phys. 5 (1926), 84-98.

  28. W. M. Brobeck, E. O. Lawrence, K. R. MacKenzie, E. M. McMillan, R. Serber, D. C. Sewell, K. M. Simpson & R. L. Thornton, Initial performance of the 184-inch cyclotron of the University of California, Phys. Rev. (2) 71 (1947), 449-450.

  29. Louis de Broglie, David Bohm, Pierre Hillion, Francis Halbwachs, Takehiko Takabayasi & Jean-Pierre Vigier, Rotator model of elementary particles considered as relativistic extended structures in Minkowski space, Phys. Rev. (2) 129 (1963), 438-450; MR 27#1202.

  30. P. Candelas, Gary T. Horowitz, Andrew Strominger & Edward Witten, Vacuum configurations for superstrings, Nuclear Phys. B 258 (1985), no. 1, 46-74; MR 87k:83091a.

  31. O. Chamberlain, E. Segrè & C. Wiegand, Experiments on proton-proton scattering from 120 to 345 Mev, Phys. Rev. (2) 83 (1951), 923-932.

  32. A. Charnes, W. W. Cooper & Merton Miller, Dyadic programs and subdual methods, Naval Res. Logist. Quart. 8 (1961), 1-23; MR 24#B841.

  33. A. Charnes, Fred Glover & D. Klingman, The lower bounded and partial upper bounded distribution model, Naval Res. Logist. Quart. 18 (1971), 277-281; MR 47#1283.

  34. J. G. Charney, R. Fjörtoft & J. von Neumann, Numerical integration of the barotropic vorticity equation, Tellus 2 (1950), 237-254; MR 13,164f.

  35. N. Chomsky & M. P. Schutzenberger, The algebraic theory of context-free languages, in Computer programming and formal systems, North-Holland, 1963, 118-161; MR 27#2371.

  36. J. D. Cole, H. B. Keller & P. G. Saffman, The flow of a viscous compressible fluid through a very narrow gap, SIAM J. Appl. Math. 15 (1967) 605-617; MR 36#2352.

  37. Dirk Coster & George De Hevesy, Nature 111 (1923), 79.

  38. F. H. C. Crick, J. S. Griffith & L. E. Orgel, Codes without commas, Proc. Nat. Acad. Sci. U. S. A. 43 (1957), 416-421; MR 19,234e.

  39. M. Curie, H. A. Lorentz & A. Einstein, The establishment of an international bureau of meteorology, Science 65 (1927), 415-417.

  40. R. H. Dalitz & F. J. Dyson, Renormalization in the new Tamm-Dancoff theory of meson-nucleon scattering, Phys. Rev. (2) 99 (1955), 301-314; MR 17,112h.

  41. R. H. Dalitz & D. G. Ravenhall, On the Tomonaga method for intermediate coupling in meson field theory, Philos. Mag. (7) 42 (1951), 1378-1383; MR 13,712g.

  42. R. H. Dalitz, M. K. Sundaresen & H. A. Bethe, A singular integral equation in the theory of meson-nucleon scattering, Proc. Cambridge Philos. Soc. 52 (1956), 251-272; MR 18,173g.

  43. Gerard Debreu & Tjalling C. Koopmans, Additively decomposed quasiconvex functions, Math. Programming 24 (1982), no. 1, 1-38; MR 83m:26012.

  44. Gerard Debreu & Herbert Scarf, The limit of the core of an economy, in Decision and Organization, North Holland, 1972, pp. 283-295; MR 54#6905.

  45. P. Debije [Peter Debye] & A. Sommerfeld, Theorie des lichtelektrischen Effektes vom Standpunkte des Wirkungsquantums, Ann. Physik 41 (1913), 873-930.

  46. P. Debye & Linus Pauling, The inter-ionic attraction theory of ionized solutes. IV. The influence of variation of dielectric constant on the limiting law for small concentrations, J. Am. Chem. Soc. 47 (1925), 2129-2134.

  47. Otto Diels & Kurt Alder, Synthesen in der hydroaromatischen Reihe, Justus Liebigs Annalen der Chemie 460 (1928), 98-122.

  48. P. A. M. Dirac, V. A. Fock & Boris Podolsky, On quantum electrodynamics, Physik. Zeits. Sowjetunion 2, no. 6 (1932), 468-479.

  49. Robert Dorfman, Paul A. Samuelson & Robert M. Solow, Linear Programming and Economic Analysis, McGraw-Hill, 1958; MR 23#B1582.

  50. P. Ehrenfest & R. Oppenheimer, Note on the statistics of nuclei, Phys. Rev. (2) 37 (1931), 333-338.

  51. Samuel Eilenberg & M. P. Schutzenberger, On pseudovarieties, Advances in Math. 19 (1976), no. 3, 413-418; MR 53#5431.

  52. A. Einstein & P. Ehrenfest, Quantentheoretische Bemerkungen zum Experiment von Stern und Gerlach, Z. Phys. 11 (1922), 31-34.

  53. Albert Einstein & Sigmund Freud, Warum Krieg? Ein Briefwechsel, Institut International de Coopération Intellectuele, 1933.

  54. Albert Einstein & Hans Mühsam, Experimentelle Bestimmung der Kanalweite von Filtern, Deutsch. med. Wochenschr. 49 (1923), 1012-1013.

  55. A. Einstein & W. Pauli, On the non-existence of regular stationary solutions of relativistic field equations, Ann. Math. (2) 44 (1943), 131-137; MR 4,226d.

  56. A. Einstein, B. Podolsky & N. Rosen, Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev. (2) 47 (1935), 777-780.

  57. A. Einstein & O. Stern, Einige Argumente für die Annahme einer molekularen Agitation beim absoluten Nullpunkt, Ann. Phys. Lpz. (4) 40 (1913), 551-560.

  58. M. Ferentz, M. Gell-Mann & D. Pines, The giant nuclear dipole resonance, Phys. Rev. (2) 92 (1953), 836-837.

  59. E. Fermi & E. Segrè, Zur Theorie der Hyperfeinstruktur, Zeit. Physik 82 (1933), 729-749.

  60. E. Fermi, E. Teller & V. Weisskopf, The decay of negative mesotrons in matter, Phys. Rev. (2) 71 (1947), 314-315.

  61. Enrico Fermi & George E. Uhlenbeck, On the recombination of electrons and positrons, Phys. Rev. (2) 44 (1933), 510-511.

  62. E. Fermi & C. N. Yang, Are messons elementary particles?, Phys. Rev. (2) 76 (1949), 1739-1743.

  63. R. P. Feynman, M. Gell-Mann & G. Zweig, Group U(6) x U(6) generated by current components, Phys. Rev. Lett. 13 (1964), 678-680; MR 30#4511.

  64. M. Flato, C. Piron, J. Grea, D. Sternheimer & J.-P. Vigier, Are Bell's inequalities concerning hidden variables really conclusive?, Helv. Phys. Acta 48 (1975), no. 2, 219-225; MR 54#1906.

  65. G. W. Ford, J. T. Lewis & R. F. O'Connell, Quantum oscillator in a blackbody radiation field, Phys. Rev. Lett. 55 (1985), no. 21, 2273-2276; MR 87a:82017.

  66. K. O. Friedrichs & H. B. Keller, A finite difference scheme for generalized Neumann problems, in Numerical Solution of Partial Differential Equations (Proc. Sympos. Univ. Maryland, 1965), Academic Press, 1966, pp. 1-19; MR 34#3803.

  67. G. Frobenius & I. Schur, Über die Äquivalenz der Gruppen linearer Substitutionen, Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin (1906), 209-217.

  68. W. H. Furry & N. F. Ramsey, Significance of potentials in quantum theory, Phys. Rev. (2) 118 (1960), 623-626; MR 22#5380.

  69. G. W. Gibbons, S. W. Hawking, Gary T. Horowitz & M. J. Perry, Positive mass theorems for black holes, Comm. Math. Phys. 88 (1983), no. 3, 295-308; MR 84k:83015.

  70. Sheldon L. Glashow & Murray Gell-Mann, Gauge theories of vector particles, Ann. Physics 15 (1961), 437-460; MR 24#B277.

  71. S. L. Glashow & D. J. Kleitman, Baryon resonances in W-sub-3 symmetry, Phys. Lett. 11 (1964), 84-86; MR 32#5182.

  72. Kurt Gödel, K. Menger & A. Wald, Diskussion über koordinatenlose Differentialgeometrie, Ergebnisse eines mathematischen Kolloquiums 5 (1933), 25-26.

  73. Jeffrey Goldstone, Abdus Salam & Steven Weinberg, Broken symmetries, Phys. Rev. (2) 127 (1962), 965-970; MR 28#3712.

  74. Nelson Goodman & W. V. Quine, Steps toward a constructive nominalism, J. Symbolic Logic 12 (1947), 105-122; MR 9,262a.

  75. Fred Gross & Herbert Hauptman, On a functional equation related to the Weierstrass sigma function, Indian J. Pure Appl. Math. 5 (1974), no. 11, 1022-1032; MR 57#6385.

  76. S. Gudder & C. Piron, Observables and the field in quantum mechanics, J. Mathematical Phys. 12 (1971), 1583-1588; MR 46#8552.

  77. Beat Hahn, D. G. Ravenhall & Robert Hofstadter, High-energy electron scattering and the charge distributions of selected nuclei, Phys. Rev. (2) 101 (1956), 1131-1142.

  78. John C. Harsanyi & Reinhard Selten, A generalized Nash solution for two-person bargaining games with incomplete information, Management Sci. 18 (1971/72), P80-P106; MR 45#4838.

  79. H. Hauptman & J. Karle, Rational dependence and the renormalization of structure factors for phase determination, Acta Cryst. 12 (1959), 846-850; MR 21#6151.

  80. S. W. Hawking & R. Penrose, The singularities of gravitational collapse and cosmology, Proc. Roy. Soc. London Ser. A 314 (1970), 529-548; MR 41#9548.

  81. Werner Heisenberg & A. Sommerfeld, Zeit. Physik 31 (1922), 131.

  82. D. Hilbert, J. v. Neumann & L. Nordheim, Über die Grundlagen der Quantenmechanik, Math. Ann. 98 (1927), 1-30.

  83. M. Hillery, R. F. O'Connell, M. O. Scully & E. P. Wigner, Distribution functions in physics: fundamentals, Phys. Rep. 106 (1984), no. 3, 121-167; MR 86b:81033.

  84. J. Hofbauer, J. Mallet-Paret & H. L. Smith, Stable periodic solutions for the hypercycle systems, J. Dynamics Differential Equations 3 (1991), no. 3, 423-436; MR 92m:34103.

  85. A. J. Hoffman & H. M. Markowitz, A note on shortest path, assignment, and transportation problems, Naval Res. Logist. Quart. 10 (1963), 375-379; MR 29#2094.

  86. John G. Kemeny, Oskar Morgenstern & Gerald L. Thompson, A generalization of the von Neumann model of an expanding economy, Econometrica 24 (1956), 115-135; MR 18,266c.

  87. Tjalling C. Koopmans & Martin Beckmann, Assignment problems and the location of economic activities, Econometrica 25 (1957), 53-76; MR 19,619i.

  88. H. A. Kramers & W. Pauli, Zur theorie der banden spektren, Zeit. Physik 13 (1923), 351-367.

  89. W. D. Krentel, J. C. C. McKinsey & W. V. Quine, A simplification of games in extensive form, Duke Math. J. 18 (1951), 885-900; MR 13,855e.

  90. Tsung-dao Lee & David Pines, Interaction of a nonrelativistic particle with a scalar field with application to slow electrons in polar crystals, Phys. Rev. (2) 92 (1953) 883-889; MR 21#1857.

  91. T. D. Lee & C. N. Yang, Parity nonconservation and a two-component theory of the neutrino, Phys. Rev. (2) 105 (1957), 1671-1675; MR 21#1174.

  92. T. D. Lee & C. N. Yang, Question of parity conservation in weak interactions, Phys. Rev. (2) 104 (1956), 254-258.

  93. T. D. Lee & C. S. Wu, Weak interactions, Annual Rev. Nuclear Sci., 15 (1965), 381-476; MR 32#5157.

  94. J. T. Lewis, James McConnell & B. K. P. Scaife, Relaxation effects in rotational Brownian motion, Proc. Roy. Irish Acad. Sect. A 76 (1976), no. 7, 43-69; MR 56#10691.

  95. Zvonko Maric, Karl Popper & Jean-Pierre Vigier, Violation of Heisenberg's uncertainty relations on individual particles within subset of gamma photons in e+ e- to 2 gamma pair creation, Found. Phys. Lett. 1 (1988), no. 4, 321-332; MR 89k:81011.

  96. Thomas Marschak & Reinhard Selten, General Equilibrium with Price-making Firms, Springer-Verlag, 1974; MR 50#12167.

  97. John Maynard Smith, Evolution and the Theory of Games, Cambridge University Press, 1982.

  98. J. Maynard Smith, The theory of games and the evolution of animal conflict, J. Theor. Biol. 47 (1974), no. 1, 209-221; MR 56#2475.

  99. J. Maynard Smith & Josef Hofbauer, The ``battle of the sexes'': a genetic model with limit cycle behavior, Theoret. Population Biol. 32 (1987), no. 1, 1-14; MR 88j:92062.

  100. James McConnell & Erwin Schrödinger, The shielding effect of planetary magnetic fields, Proc. Roy. Irish Acad. Sect. A 49 (1944), 259-273; MR 6,73c.

  101. Robert C. Merton & P. A. Samuelson, A complete model of warrant pricing that maximizes utility, Industrial Management Review 10 (1969), 17-46.

  102. Franco Modigliani & Merton Miller, The cost of capital, corporation finance and the theory of investment, Amer. Economic Review 48 (1958).

  103. Franco Modigliani & Merton Miller, Dividend policy, growth and the valuation of shares, Journal of Business 34 (1961).

  104. J. F. Nash & L. S. Shapley, A simple three-person poker game, in Contributions to the Theory of Games, Princeton University Press, 1950, pp. 105-116; MR 12,514d.

  105. A. Nordsieck, W. E. Lamb, Jr. & G. E. Uhlenbeck, On the theory of cosmic-ray showers. I. The Furry model and the fluctuation problem, Physica 7 (1940), 344-360; MR 4,152b.

  106. J. R. Oppenheimer & R. Serber, On the stability of stellar neutron cores, Phys. Rev. (2) 54 (1938), 540.

  107. J. R. Oppenheimer & H. Snyder, On continued gravitational contraction, Phys. Rev. (2) 56 (1939), 455-459.

  108. L. S. Ornstein & H. A. Kramers, Zur kinetischen Herleitung des Fermischen Verteilungsgesetzes, Zeit. Physik 42 (1927), 481-486.

  109. L. S. Ornstein & F. Zernike, Proc. K. Ak. Amsterdam 28 (1919), 280.

  110. David Pines & J. Robert Schrieffer, Collective behavior in solid-state plasmas, Phys. Rev. (2) 124 (1961), 1387-1400; MR 24#B776.

  111. Boris Podolsky & Linus Pauling, The momentum distribution in hydrogen-like atoms, Phys. Rev. (2) 34 (1929), 109-116.

  112. I. I. Rabi, N. F. Ramsey & J. Schwinger, Use of rotating coordinates in magnetic resonance problems, Rev. Modern Physics 26 (1954), 167-171.

  113. L. J. Rainwater & C. S. Wu, Nucleonics 1 (1947), 60.

  114. I. W. Roxburgh, J. S. Griffith & P. A. Sweet, On models of non spherical stars. I. The theory of rapidly rotating main sequence stars, Z. Astrophys. 61 (1965) 203-221; MR 32#1001.

  115. I. W. Roxburgh & P. G. Saffman, The growth of condensations in a Newtonian model of the steady-state universe, Monthly Notices Roy. Astronom. Soc. 129 (1965), 181-189; MR 31#5679.

  116. Abdus Salam & W. Gilbert, On generalized dispersion relations. II, Nuovo Cimento (10) 3 (1956), 607-611; MR 17,1163c.

  117. Abdus Salam & J. C. Ward, Weak and electromagentic interactions, Nuovo Cimento (10) 11 (1959), 568-577; MR 21#3238.

  118. E. E. Salpeter & H. A. Bethe, A relativistic equation for bound-state problems, Phys. Rev. (2) 84 (1951), 1232-1242; MR 14,707a.

  119. I. Schur & G. Szegö, Über die Abschnitte einer im Einheitskreise beschränkten Potenzreihe, Sitzungsberichte der Preussichen Akademie der Wissenschaften 1925, Physikalisch-Mathmatische Klasse, 545-560.

  120. G. T. Seaborg & E. Segrè, Nuclear isomerism in element 43, Phys. Rev. (2) 55 (1939), 808-814.

  121. C. E. Shannon, A mathematical theory of communication, Bell System Tech. J. 27 (1948), 379-423, 623-656; MR 10,133e.

  122. C. E. Shannon, R. G. Gallager & E. R. Berlekamp, Lower bounds to error probability for coding on discrete memoryless channels. I, Information and Control 10 (1967) 65-103; MR 35#1405.

  123. Claude E. Shannon & Warren Weaver, The Mathematical Theory of Communication, University of Illinois Press, 1949; MR 11,258e.

  124. Lloyd Shapley & Herbert Scarf, On cores and indivisibility, J. Math. Econom. 1 (1974), 23-37; MR 54#4601.

  125. G. E. Uhlenbeck & S. Goudsmit, Ersetzung der Hypothese vom unmechanischen Zwang durch eine Forderung bezüglich des inneren Verhaltens jedes einzelnen Elektrons, Naturwiss. 13 (1925), 953-954.

  126. John von Neumann & Oskar Morgenstern, Theory of Games and Economic Behaviour, Princeton University Press, 1944; MR 6,235k.

  127. John Archibald Wheeler & Richard Phillips Feynman, Classical electrodynamics in terms of direct inter-particle action, Rev. Modern Physics 21 (1949), 425-433; MR 11,293a.
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