|
Mathematics and physics
Author:
Peter D. Lax
Journal:
Bull. Amer. Math. Soc. 45 (2008), 135-152
MSC (2000):
Primary 35-XX, 76-XX, 46-XX
Posted:
October 30, 2007
MathSciNet review:
2358380
Full-text PDF
References |
Similar Articles |
Additional Information
- 1.
G.
D. Birkhoff, What is the ergodic theorem?, Amer. Math. Monthly
49 (1942), 222–226. MR 0006619
(4,15b)
- 2.
Ludwig
Boltzmann, Wissenschaftliche Abhandlungen von Ludwig Boltzmann. I.
Band (1865–1874); II. Band (1875–1881); III. Band
(1882–1905), Herausgegeben von Fritz Hasenöhrl, Chelsea
Publishing Co., New York, 1968 (German). MR 0237281
(38 #5571)
- 3.
Demetrios
Christodoulou and Sergiu
Klainerman, The global nonlinear stability of the Minkowski
space, Princeton Mathematical Series, vol. 41, Princeton
University Press, Princeton, NJ, 1993. MR 1316662
(95k:83006)
- 4.
Louis
de Branges, A proof of the Bieberbach conjecture, Acta Math.
154 (1985), no. 1-2, 137–152. MR 772434
(86h:30026), http://dx.doi.org/10.1007/BF02392821
- 5.
Dyson, F., Statistical theory of the energy levels of complex systems, I, II, III, J. Math. Physics 3 (1962), 140-175.
- 6.
Freeman
J. Dyson, Missed opportunities, Bull. Amer. Math. Soc. 78 (1972), 635–652. MR 0522147
(58 #25442), http://dx.doi.org/10.1090/S0002-9904-1972-12971-9
- 7.
Gibbs, J. W., The Collected Works of J. Willard Gibbs, Longman's, Green and Co., 1931.
- 8.
James
Glimm, Solutions in the large for nonlinear hyperbolic systems of
equations, Comm. Pure Appl. Math. 18 (1965),
697–715. MR 0194770
(33 #2976)
- 9.
David
Gottlieb and Chi-Wang
Shu, On the Gibbs phenomenon and its resolution, SIAM Rev.
39 (1997), no. 4, 644–668. MR 1491051
(98m:42002), http://dx.doi.org/10.1137/S0036144596301390
- 10.
Edwin
Hewitt and Robert
E. Hewitt, The Gibbs-Wilbraham phenomenon: an episode in Fourier
analysis, Arch. Hist. Exact Sci. 21 (1979/80),
no. 2, 129–160. MR 555102
(81g:01015), http://dx.doi.org/10.1007/BF00330404
- 11.
David
Hilbert, Begründung der kinetischen Gastheorie, Math.
Ann. 72 (1912), no. 4, 562–577 (German). MR
1511713, http://dx.doi.org/10.1007/BF01456676
- 12.
Songming
Hou and Xu-Dong
Liu, Solutions of multi-dimensional hyperbolic systems of
conservation laws by square entropy condition satisfying discontinuous
Galerkin method, J. Sci. Comput. 31 (2007),
no. 1-2, 127–151. MR 2304273
(2008f:65176), http://dx.doi.org/10.1007/s10915-006-9105-9
- 13.
Koestler, A., and Butterfield, H., The Sleepwalkers, Peregrine Books, 1959.
- 14.
Jean
Leray, Sur le mouvement d’un liquide visqueux emplissant
l’espace, Acta Math. 63 (1934), no. 1,
193–248 (French). MR
1555394, http://dx.doi.org/10.1007/BF02547354
- 15.
Peter
D. Lax and Xu-Dong
Liu, Solution of two-dimensional Riemann problems of gas dynamics
by positive schemes, SIAM J. Sci. Comput. 19 (1998),
no. 2, 319–340 (electronic). MR
1618863, http://dx.doi.org/10.1137/S1064827595291819
- 16.
Karl
Löwner, Untersuchungen über schlichte konforme
Abbildungen des Einheitskreises. I, Math. Ann. 89
(1923), no. 1-2, 103–121 (German). MR
1512136, http://dx.doi.org/10.1007/BF01448091
- 17.
James
Clerk Maxwell, A dynamical theory of the electromagnetic
field, Scottish Academic Press, Edinburgh, 1982. With an appreciation
by Albert Einstein; Edited and with an introduction by Thomas F. Torrance.
MR 778034
(87i:01032)
- 18.
McCoy, B. M., Introductory Remarks to Szegö's Paper ``On Certain Hermitean Forms Associated with the Fourier Series of a Positive Function'', in Gabor Szegö Collected Papers, R. Askey, ed., Vol. 1, 47-51, Birkhäuser, 1982.
- 19.
O.
Neugebauer, Notes on Kepler, Comm. Pure Appl. Math.
14 (1961), 593–597. MR 0131339
(24 #A1191)
- 20.
Odlyzko, A., On the distribution of the spacing between the zeros of the
 function, Math. Comp. 48 (1989), 273-308.
- 21.
L.
Onsager, Statistical hydrodynamics, Nuovo Cimento (9)
6 (1949), no. Supplemento, 2(Convegno Internazionale
di Meccanica Statistica), 279–287. MR 0036116
(12,60f)
- 22.
Riemann, B., Über die Fortpflanzung ebener Luftwellen von endlicher Schwingingsweite, 188-207, Collected Papers, Springer Verlag, 1990.
- 23.
E.
Schrödinger, Collected papers on wave mechanics, Chelsea
Publishing Co., New York, 1982. Translated from the second German edition
by J. F. Shearer and W. M. Deans; Including Four lectures on wave
mechanics. MR
750301 (85k:01057)
- 24.
Carsten
W. Schulz-Rinne, James
P. Collins, and Harland
M. Glaz, Numerical solution of the Riemann problem for
two-dimensional gas dynamics, SIAM J. Sci. Comput. 14
(1993), no. 6, 1394–1414. MR 1241592
(94j:76062), http://dx.doi.org/10.1137/0914082
- 25.
Logic, methodology and philosophy of science, Proceedings of the
1960 International Congress, Stanford University Press, Stanford, Calif.,
1962. MR
0166069 (29 #3347)
- 26.
G.
Szegö, On certain Hermitian forms associated with the Fourier
series of a positive function, Comm. Sém. Math. Univ. Lund
[Medd. Lunds Univ. Mat. Sem.] 1952 (1952), no. Tome
Supplementaire, 228–238. MR 0051961
(14,553d)
Gábor
Szegő, Collected papers. Vol. 3, Contemporary
Mathematicians, Birkhäuser Boston, Mass., 1982. 1945–1972;
Edited by Richard Askey. MR 674484
(84d:01082c)
- 27.
John
von Neumann, Collected works. Vol. I: Logic, theory of sets and
quantum mechanics, General editor: A. H. Taub, Pergamon Press, New
York, 1961. MR
0157871 (28 #1100)
- 28.
John
von Neumann, Collected works. Vol. I: Logic, theory of sets and
quantum mechanics, General editor: A. H. Taub, Pergamon Press, New
York, 1961. MR
0157871 (28 #1100)
- 29.
John
von Neumann, Collected works. Vol. V: Design of computers, theory
of automata and numerical analysis, General editor: A. H. Taub. A
Pergamon Press Book, The Macmillan Co., New York, 1963. MR 0157875
(28 #1104)
- 30.
Wendelin
Werner, Random planar curves and Schramm-Loewner evolutions,
Lectures on probability theory and statistics, Lecture Notes in Math.,
vol. 1840, Springer, Berlin, 2004, pp. 107–195. MR 2079672
(2005m:60020), http://dx.doi.org/10.1007/978-3-540-39982-7_2
- 31.
Wigner, E., On the statistical distribution of the width and spacing of nuclear resonance levels, Proc. Cambridge Phil. Soc. 47 (1951), 790-798.
- 32.
Wigner, E., Random Matrices in Physics, SIAM Review 9 (1967), 1-23.
- 33.
Wilbraham, H., On certain periodic functions, Cambridge Dublin Math. J. 3 (1848), 198-204.
- 34.
Edward
Witten, Magic, mystery, and matrix, Mathematics: frontiers and
perspectives, Amer. Math. Soc., Providence, RI, 2000,
pp. 343–352. MR
1756796
- 1.
- Birkhoff, G. D., What is the ergodic theorem? Amer. Math. Monthly 49 (1942), 222-226. MR 0006619 (4:15b)
- 2.
- Boltzmann, L., Wissenschaftliche Abhandlungen, Chelsea Pub. Co., New York, 1968. MR 0237281 (38:5571)
- 3.
- Christodoulou, D., and Klainerman, S., The Global Nonlinear Stability of the Minkowski Space, Princeton University Press, Princeton, NJ, 1993. MR 1316662 (95k:83006)
- 4.
- de Branges, L., A proof of the Bieberbach conjecture, Acta Math. 154 (1985), 137-152. MR 772434 (86h:30026)
- 5.
- Dyson, F., Statistical theory of the energy levels of complex systems, I, II, III, J. Math. Physics 3 (1962), 140-175.
- 6.
- Dyson, F., Missed opportunities, Bull. Amer. Math. Soc. 78 (1972), 635-652. MR 0522147 (58:25442)
- 7.
- Gibbs, J. W., The Collected Works of J. Willard Gibbs, Longman's, Green and Co., 1931.
- 8.
- Glimm, J., Solutions in the large for nonlinear hyperbolic systems of equations, CPAM 18 (1965), 697-715. MR 0194770 (33:2976)
- 9.
- Gottlieb, D., and Shu, C.-W., On the Gibbs phenomenon and its resolution, SIAM Review 39 (1997), 644-668. MR 1491051 (98m:42002)
- 10.
- Hewitt, E., and Hewitt, R. E., The Gibbs-Wilbraham phenomenon: an episode in Fourier analysis, Archive for History of Exact Sciences 21 (1979), 129-160. MR 0555102 (81g:01015)
- 11.
- Hilbert, D., Begründung der kinetischen Gastheorie, Math. Ann. 72 (1912), 562-577. MR 1511713
- 12.
- Hou, S., and Liu, X.-D., Solutions of multi-dimensional hyperbolic systems of conservation laws by square entropy condition satisfying discontinuous Galerkin method, J. Sci. Computing 31 (2007), 127-151.MR 2304273
- 13.
- Koestler, A., and Butterfield, H., The Sleepwalkers, Peregrine Books, 1959.
- 14.
- Leray, J., Sur le mouvement d'un fluide visqueux emplissant l'espace, Acta Math. 63 (1934), 193-248. MR 1555394
- 15.
- Liu, X. D., and Lax, P. D., Solution of two-dimensional Riemann problems of gas dynamics by positive schemes, SIAM J. Sci. Comp. 19 (1998), 319-340 (electronic). MR 1618863
- 16.
- Loewner, C., Untersuchungen über schlichte konforme Abbildungen des Einheitskreises, I. Math. Ann. 89 (1923), 103-121. MR 1512136
- 17.
- Maxwell, J. C., A dynamical theory of the electromagnetic field, Royal Soc. Trans. 155 (1865), The Scientific Papers of James Clerk Maxwell, Scottish Acad. Press, 1982, 526-597. MR 0778034 (87i:01032)
- 18.
- McCoy, B. M., Introductory Remarks to Szegö's Paper ``On Certain Hermitean Forms Associated with the Fourier Series of a Positive Function'', in Gabor Szegö Collected Papers, R. Askey, ed., Vol. 1, 47-51, Birkhäuser, 1982.
- 19.
- Neugebauer, O., Notes on Kepler, CPAM 14 (1961), 593-597. MR 0131339 (24:A1191)
- 20.
- Odlyzko, A., On the distribution of the spacing between the zeros of the function, Math. Comp. 48 (1989), 273-308.
- 21.
- Onsager, L., Statistical hydrodynamics, Nuovo Cimento 6, Suppl. 261 (1949). MR 0036116 (12:60f)
- 22.
- Riemann, B., Über die Fortpflanzung ebener Luftwellen von endlicher Schwingingsweite, 188-207, Collected Papers, Springer Verlag, 1990.
- 23.
- Schrödinger, E., Collected Papers on Wave Mechanics, Blackie and Son, Ltd., London, 1928. MR 0750301 (85k:01057)
- 24.
- Schultz-Rinne, C. W., Collins, J. P., and Glaz, H. M., Numerical solution of the Riemann problem for two-dimensional gas dynamics, SIAM J. Sci. Comp. 14 (1993), 1394-1414. MR 1241592 (94j:76062)
- 25.
- Schwartz, J., The pernicious influence of mathematics on science, in Logic, Methodology and Philosophy of Science, Nagel, Suppes and Tarski, eds., Stanford University Press, 1962. MR 0166069 (29:3347)
- 26.
- Szegö, G., On certain Hermitean forms associated with Fourier series of a positive function, Comm. Sem. Math. Univ. Lund, Tome Supplementaire, Festshrift Marcel Riesz, Lund (1952), 228-238; also Gabor Szegö Collected Papers, E. Askey, ed., Vol. 3, 270-280, Birkhäuser, 1982. MR 0051961 (14:553d), MR 0674484 (84d:01082c)
- 27.
- von Neumann, J., Proof of the Quasi-ergodic Hypothesis, NAS Proc. 186 (1932), 70-82; see also Vol. I, Collected Works, Pergamon Press, 1961. MR 0157871 (28:1100)
- 28.
- -, Mathematische Begründung der Quantenmechanic, Goett. Nach. 1927, 1-57; see also Vol. I, Collected Works, Pergamon Press, 1961. MR 0157871 (28:1100)
- 29.
- -, with Burke, A. W., and Goldstine, H. H., Preliminary Discussion of the Logical Design of an Electronic Computing Instrument, Vol. V, Collected Works, Pergamon Press, 1963. MR 0157875 (28:1104)
- 30.
- Werner, W., Random planar curves and Schramm-Loewner evolutions, Lectures on Probability Theory and Statistics, 107-195, in Lecture Notes in Math. 1840, Springer Verlag, 2004. MR 2079672 (2005m:60020)
- 31.
- Wigner, E., On the statistical distribution of the width and spacing of nuclear resonance levels, Proc. Cambridge Phil. Soc. 47 (1951), 790-798.
- 32.
- Wigner, E., Random Matrices in Physics, SIAM Review 9 (1967), 1-23.
- 33.
- Wilbraham, H., On certain periodic functions, Cambridge Dublin Math. J. 3 (1848), 198-204.
- 34.
- Witten, E., Magic, Mystery and Matrix, 343-352, in Mathematics: Frontiers and Perspectives, Arnold, Atiyah et al., eds., Amer. Math. Soc., Providence, RI, 2000. MR 1756796
Similar Articles
Retrieve articles in Bulletin of the American Mathematical Society
with MSC (2000):
35-XX,
76-XX,
46-XX
Retrieve articles in all journals
with MSC (2000):
35-XX,
76-XX,
46-XX
Additional Information
Peter D. Lax
Affiliation:
Courant Institute, New York University, 251 Mercer Street, New York, New York 10012-1110
DOI:
http://dx.doi.org/10.1090/S0273-0979-07-01182-2
PII:
S 0273-0979(07)01182-2
Received by editor(s):
May 7, 2007
Posted:
October 30, 2007
Additional Notes:
This article is based on the author’s Gibbs Lecture at the Joint Mathematics Meetings in New Orleans in 2007.
Article copyright:
© Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
|
