-
2
-
-
0003640744
-
-
Springer, New York
-
J. Kevorkian and J. D. Cole, Perturbation Methods in Applied Mathematics (Springer, New York, 1981); A. Nayfeh, Perturbation Methods (Wiley, New York, 1973); D. R. Smith, Singular Perturbation Theory (Cambridge University Press, Cambridge, 1985); S. A. Lomov, Introduction to the General Theory of Singular Perturbation (American Mathematical Society, Providence, 1992).
-
(1981)
Perturbation Methods in Applied Mathematics
-
-
Kevorkian, J.1
Cole, J.D.2
-
3
-
-
0004229164
-
-
Wiley, New York
-
J. Kevorkian and J. D. Cole, Perturbation Methods in Applied Mathematics (Springer, New York, 1981); A. Nayfeh, Perturbation Methods (Wiley, New York, 1973); D. R. Smith, Singular Perturbation Theory (Cambridge University Press, Cambridge, 1985); S. A. Lomov, Introduction to the General Theory of Singular Perturbation (American Mathematical Society, Providence, 1992).
-
(1973)
Perturbation Methods
-
-
Nayfeh, A.1
-
4
-
-
0003647448
-
-
Cambridge University Press, Cambridge
-
J. Kevorkian and J. D. Cole, Perturbation Methods in Applied Mathematics (Springer, New York, 1981); A. Nayfeh, Perturbation Methods (Wiley, New York, 1973); D. R. Smith, Singular Perturbation Theory (Cambridge University Press, Cambridge, 1985); S. A. Lomov, Introduction to the General Theory of Singular Perturbation (American Mathematical Society, Providence, 1992).
-
(1985)
Singular Perturbation Theory
-
-
Smith, D.R.1
-
5
-
-
0004055207
-
-
American Mathematical Society, Providence
-
J. Kevorkian and J. D. Cole, Perturbation Methods in Applied Mathematics (Springer, New York, 1981); A. Nayfeh, Perturbation Methods (Wiley, New York, 1973); D. R. Smith, Singular Perturbation Theory (Cambridge University Press, Cambridge, 1985); S. A. Lomov, Introduction to the General Theory of Singular Perturbation (American Mathematical Society, Providence, 1992).
-
(1992)
Introduction to the General Theory of Singular Perturbation
-
-
Lomov, S.A.1
-
8
-
-
0004261332
-
-
Cambridge University Press, Cambridge
-
E. J. Hinch, Perturbation Methods (Cambridge University Press, Cambridge, 1991).
-
(1991)
Perturbation Methods
-
-
Hinch, E.J.1
-
10
-
-
0001226485
-
-
J. Carr, Applications of Center Manifold Theory (Springer, Berlin, 1981); J. Carr and R. M. Muncaster, J. Diff. Eq. 50, 260 (1983).
-
(1983)
J. Diff. Eq.
, vol.50
, pp. 260
-
-
Carr, J.1
Muncaster, R.M.2
-
11
-
-
77952528320
-
-
T. Taniuti and C. C. Wei, J. Phys. Soc. Jpn. 24, 941 (1968); A. C. Newell and J. A. Whitehead, J. Fluid Mech. 38, 279 (1969); Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984).
-
(1968)
J. Phys. Soc. Jpn.
, vol.24
, pp. 941
-
-
Taniuti, T.1
Wei, C.C.2
-
12
-
-
0014662728
-
-
T. Taniuti and C. C. Wei, J. Phys. Soc. Jpn. 24, 941 (1968); A. C. Newell and J. A. Whitehead, J. Fluid Mech. 38, 279 (1969); Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984).
-
(1969)
J. Fluid Mech.
, vol.38
, pp. 279
-
-
Newell, A.C.1
Whitehead, J.A.2
-
13
-
-
77952528320
-
-
Springer, Berlin
-
T. Taniuti and C. C. Wei, J. Phys. Soc. Jpn. 24, 941 (1968); A. C. Newell and J. A. Whitehead, J. Fluid Mech. 38, 279 (1969); Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984).
-
(1984)
Chemical Oscillations, Waves, and Turbulence
-
-
Kuramoto, Y.1
-
14
-
-
5544318075
-
-
edited by I. Prigogine and S. A. Rice Wiley, New York, Chap. 5
-
Y. Oono, Advances in Chemical Physics, edited by I. Prigogine and S. A. Rice (Wiley, New York, 1985), Vol. 6, Chap. 5.
-
(1985)
Advances in Chemical Physics
, vol.6
-
-
Oono, Y.1
-
15
-
-
5544296111
-
-
Y. Oono, Butsuri 42, 311 (1987).
-
(1987)
Butsuri
, vol.42
, pp. 311
-
-
Oono, Y.1
-
17
-
-
43949154200
-
-
L.-Y. Chen, N. Goldenfeld, Y. Oono, and G. Paquette, Physica A 204, 111 (1994); G. Paquette, L.-Y. Chen, N. Goldenfeld, and Y. Oono, Phys. Rev. Lett. 72, 76 (1994); G. C. Paquette and Y. Oono, Phys. Rev. E 49, 2368 (1994); L.-Y. Chen, N. D. Goldenfeld, and Y. Oono, ibid. 49, 4502 (1994).
-
(1994)
Physica A
, vol.204
, pp. 111
-
-
Chen, L.-Y.1
Goldenfeld, N.2
Oono, Y.3
Paquette, G.4
-
18
-
-
0002200283
-
-
L.-Y. Chen, N. Goldenfeld, Y. Oono, and G. Paquette, Physica A 204, 111 (1994); G. Paquette, L.-Y. Chen, N. Goldenfeld, and Y. Oono, Phys. Rev. Lett. 72, 76 (1994); G. C. Paquette and Y. Oono, Phys. Rev. E 49, 2368 (1994); L.-Y. Chen, N. D. Goldenfeld, and Y. Oono, ibid. 49, 4502 (1994).
-
(1994)
Phys. Rev. Lett.
, vol.72
, pp. 76
-
-
Paquette, G.1
Chen, L.-Y.2
Goldenfeld, N.3
Oono, Y.4
-
19
-
-
0000056645
-
-
L.-Y. Chen, N. Goldenfeld, Y. Oono, and G. Paquette, Physica A 204, 111 (1994); G. Paquette, L.-Y. Chen, N. Goldenfeld, and Y. Oono, Phys. Rev. Lett. 72, 76 (1994); G. C. Paquette and Y. Oono, Phys. Rev. E 49, 2368 (1994); L.-Y. Chen, N. D. Goldenfeld, and Y. Oono, ibid. 49, 4502 (1994).
-
(1994)
Phys. Rev. E
, vol.49
, pp. 2368
-
-
Paquette, G.C.1
Oono, Y.2
-
20
-
-
0000005970
-
-
L.-Y. Chen, N. Goldenfeld, Y. Oono, and G. Paquette, Physica A 204, 111 (1994); G. Paquette, L.-Y. Chen, N. Goldenfeld, and Y. Oono, Phys. Rev. Lett. 72, 76 (1994); G. C. Paquette and Y. Oono, Phys. Rev. E 49, 2368 (1994); L.-Y. Chen, N. D. Goldenfeld, and Y. Oono, ibid. 49, 4502 (1994).
-
(1994)
Phys. Rev. E
, vol.49
, pp. 4502
-
-
Chen, L.-Y.1
Goldenfeld, N.D.2
Oono, Y.3
-
21
-
-
0024795190
-
-
N. Goldenfeld, O. Martin, and Y. Oono, J. Sci. Comp. 4, 355 (1989); N. Goldenfeld, O. Martin, Y. Oono, and F. Liu, Phys. Rev. Lett. 64, 1361 (1990).
-
(1989)
J. Sci. Comp.
, vol.4
, pp. 355
-
-
Goldenfeld, N.1
Martin, O.2
Oono, Y.3
-
22
-
-
0000062672
-
-
N. Goldenfeld, O. Martin, and Y. Oono, J. Sci. Comp. 4, 355 (1989); N. Goldenfeld, O. Martin, Y. Oono, and F. Liu, Phys. Rev. Lett. 64, 1361 (1990).
-
(1990)
Phys. Rev. Lett.
, vol.64
, pp. 1361
-
-
Goldenfeld, N.1
Martin, O.2
Oono, Y.3
Liu, F.4
-
25
-
-
21144479301
-
-
J. Bricmont and A. Kupiainen, Commun. Math. Phys. 150, 193 (1992); J. Bricmont, A. Kupiainen, and G. Lin, Commun. Pure Appl. Math. 47, 893 (1994); J. Bricmont and A. Kupiainen; J. Bricmont, A. Kupiainen, and J. Xin (unpublished).
-
(1992)
Commun. Math. Phys.
, vol.150
, pp. 193
-
-
Bricmont, J.1
Kupiainen, A.2
-
26
-
-
84990739185
-
-
J. Bricmont and A. Kupiainen, Commun. Math. Phys. 150, 193 (1992); J. Bricmont, A. Kupiainen, and G. Lin, Commun. Pure Appl. Math. 47, 893 (1994); J. Bricmont and A. Kupiainen; J. Bricmont, A. Kupiainen, and J. Xin (unpublished).
-
(1994)
Commun. Pure Appl. Math.
, vol.47
, pp. 893
-
-
Bricmont, J.1
Kupiainen, A.2
Lin, G.3
-
27
-
-
21144479301
-
-
unpublished
-
J. Bricmont and A. Kupiainen, Commun. Math. Phys. 150, 193 (1992); J. Bricmont, A. Kupiainen, and G. Lin, Commun. Pure Appl. Math. 47, 893 (1994); J. Bricmont and A. Kupiainen; J. Bricmont, A. Kupiainen, and J. Xin (unpublished).
-
-
-
Bricmont, J.1
Kupiainen, A.2
Bricmont, J.3
Kupiainen, A.4
Xin, J.5
-
29
-
-
5544273243
-
-
For a pedagogical account of the relationship between the anomalous dimensions of the quantum field theory and those of partial differential equations, see Ref. [10], Chap. 10
-
For a pedagogical account of the relationship between the anomalous dimensions of the quantum field theory and those of partial differential equations, see Ref. [10], Chap. 10.
-
-
-
-
34
-
-
5544259870
-
-
See Ref. [1], p. 554
-
See Ref. [1], p. 554.
-
-
-
-
36
-
-
26144461489
-
-
K. G. Wilson, Phys. Rev. B 4, 3174 (1971); 4, 3184 (1971).
-
(1971)
Phys. Rev. B
, vol.4
, pp. 3184
-
-
-
38
-
-
36149023949
-
-
M. Gell-Mann and F. E. Low, Phys. Rev. 95, 1300 (1954); see also the presentations by K. Wilson, Phys. Rev. 179, 1499 (1969), and by J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1966).
-
(1954)
Phys. Rev.
, vol.95
, pp. 1300
-
-
Gell-Mann, M.1
Low, F.E.2
-
39
-
-
36049055863
-
-
M. Gell-Mann and F. E. Low, Phys. Rev. 95, 1300 (1954); see also the presentations by K. Wilson, Phys. Rev. 179, 1499 (1969), and by J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1966).
-
(1969)
Phys. Rev.
, vol.179
, pp. 1499
-
-
Wilson, K.1
-
40
-
-
36149023949
-
-
McGraw-Hill, New York
-
M. Gell-Mann and F. E. Low, Phys. Rev. 95, 1300 (1954); see also the presentations by K. Wilson, Phys. Rev. 179, 1499 (1969), and by J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields (McGraw-Hill, New York, 1966).
-
(1966)
Relativistic Quantum Fields
-
-
Bjorken, J.D.1
Drell, S.D.2
-
41
-
-
5544234301
-
-
N. N. Bogoliubov and D. V. Shirkov, Usp. Fiz. Nauk 55, 149 (1955); 57, 3 (1955); Zh. Eksp. Teor. Fiz. 30, 77 (1956) [Sov. Phys. JETP 3, 57 (1956)]; for a pedagogical discussion of the connection with Lie groups, see N. N. Bogoliubov and D. V. Shirkov, Introduction to the Theory of Quantized Fields, 3rd ed. (Wiley, New York, 1980).
-
(1955)
Usp. Fiz. Nauk
, vol.55
, pp. 149
-
-
Bogoliubov, N.N.1
Shirkov, D.V.2
-
42
-
-
5544223466
-
-
N. N. Bogoliubov and D. V. Shirkov, Usp. Fiz. Nauk 55, 149 (1955); 57, 3 (1955); Zh. Eksp. Teor. Fiz. 30, 77 (1956) [Sov. Phys. JETP 3, 57 (1956)]; for a pedagogical discussion of the connection with Lie groups, see N. N. Bogoliubov and D. V. Shirkov, Introduction to the Theory of Quantized Fields, 3rd ed. (Wiley, New York, 1980).
-
(1955)
Usp. Fiz. Nauk
, vol.57
, pp. 3
-
-
-
43
-
-
5544232601
-
-
N. N. Bogoliubov and D. V. Shirkov, Usp. Fiz. Nauk 55, 149 (1955); 57, 3 (1955); Zh. Eksp. Teor. Fiz. 30, 77 (1956) [Sov. Phys. JETP 3, 57 (1956)]; for a pedagogical discussion of the connection with Lie groups, see N. N. Bogoliubov and D. V. Shirkov, Introduction to the Theory of Quantized Fields, 3rd ed. (Wiley, New York, 1980).
-
(1956)
Zh. Eksp. Teor. Fiz.
, vol.30
, pp. 77
-
-
-
44
-
-
5544239440
-
-
N. N. Bogoliubov and D. V. Shirkov, Usp. Fiz. Nauk 55, 149 (1955); 57, 3 (1955); Zh. Eksp. Teor. Fiz. 30, 77 (1956) [Sov. Phys. JETP 3, 57 (1956)]; for a pedagogical discussion of the connection with Lie groups, see N. N. Bogoliubov and D. V. Shirkov, Introduction to the Theory of Quantized Fields, 3rd ed. (Wiley, New York, 1980).
-
(1956)
Sov. Phys. JETP
, vol.3
, pp. 57
-
-
-
45
-
-
0003432713
-
-
Wiley, New York
-
N. N. Bogoliubov and D. V. Shirkov, Usp. Fiz. Nauk 55, 149 (1955); 57, 3 (1955); Zh. Eksp. Teor. Fiz. 30, 77 (1956) [Sov. Phys. JETP 3, 57 (1956)]; for a pedagogical discussion of the connection with Lie groups, see N. N. Bogoliubov and D. V. Shirkov, Introduction to the Theory of Quantized Fields, 3rd ed. (Wiley, New York, 1980).
-
(1980)
Introduction to the Theory of Quantized Fields, 3rd Ed.
-
-
Bogoliubov, N.N.1
Shirkov, D.V.2
-
48
-
-
85088621736
-
-
1 may depend upon R, because R is dimensionless. This is analogous to the renormalization of a dimensionless coupling constant in field theory
-
1 may depend upon R, because R is dimensionless. This is analogous to the renormalization of a dimensionless coupling constant in field theory.
-
-
-
-
49
-
-
5544253610
-
-
See Ref. [1], p. 560
-
See Ref. [1], p. 560.
-
-
-
-
50
-
-
5544223467
-
-
See Ref. [1], p. 567
-
See Ref. [1], p. 567.
-
-
-
-
51
-
-
0004335478
-
-
Wiley, New York
-
For example, see L. Allen and J. H. Eberly, Optical Resonance and Two-level Atoms (Wiley, New York, 1975); P. Meystre and M. Saregent III, Elements of Quantum Optics (Springer-Verlag, New York, 1990).
-
(1975)
Optical Resonance and Two-level Atoms
-
-
Allen, L.1
Eberly, J.H.2
-
52
-
-
84892319049
-
-
Springer-Verlag, New York
-
For example, see L. Allen and J. H. Eberly, Optical Resonance and Two-level Atoms (Wiley, New York, 1975); P. Meystre and M. Saregent III, Elements of Quantum Optics (Springer-Verlag, New York, 1990).
-
(1990)
Elements of Quantum Optics
-
-
Meystre, P.1
Saregent III, M.2
-
55
-
-
5544314166
-
-
See Ref. [1], p. 442
-
See Ref. [1], p. 442.
-
-
-
-
56
-
-
5544320874
-
-
See Ref. [1], p. 463
-
See Ref. [1], p. 463.
-
-
-
-
57
-
-
5544277597
-
-
See Ref. [5], p. 103
-
See Ref. [5], p. 103.
-
-
-
-
58
-
-
5544221699
-
-
See Ref. [3], p. 388, example 7.6.1
-
See Ref. [3], p. 388, example 7.6.1.
-
-
-
-
59
-
-
0002519912
-
-
J. Liouville J. Math. Pure Appl. 2, 16 (1837); G. Green, Trans. Camb. Philos. Soc. 6, 457 (1837).
-
(1837)
J. Math. Pure Appl.
, vol.2
, pp. 16
-
-
Liouville, J.1
-
62
-
-
84968466174
-
-
R. E. Langer, Trans. Am. Math. Soc. 33, 23 (1931); 36, 90 (1934); 37, 397 (1935).
-
(1934)
Trans. Am. Math. Soc.
, vol.36
, pp. 90
-
-
-
63
-
-
84927746419
-
-
R. E. Langer, Trans. Am. Math. Soc. 33, 23 (1931); 36, 90 (1934); 37, 397 (1935).
-
(1935)
Trans. Am. Math. Soc.
, vol.37
, pp. 397
-
-
-
64
-
-
5544296110
-
-
See Ref. [5], p. 74 and 77
-
See Ref. [5], p. 74 and 77.
-
-
-
-
68
-
-
5544271276
-
-
private communication
-
G. Paquette (private communication).
-
-
-
Paquette, G.1
-
70
-
-
5544271275
-
-
edited by S. Tanveer Plenum, New York
-
N. Goldenfeld, O. Martin, and Y. Oono, Proceedings of the NATO Advanced Research Workshop on Asymptotics Beyond All Orders, edited by S. Tanveer (Plenum, New York, 1992).
-
(1992)
Proceedings of the NATO Advanced Research Workshop on Asymptotics Beyond All Orders
-
-
Goldenfeld, N.1
Martin, O.2
Oono, Y.3
-
72
-
-
0012163533
-
-
unpublished
-
L.-Y. Chen and N. Goldenfeld, Phys. Rev. E 51, 5577 (1995); M. Baisera, and Y. Oono (unpublished).
-
-
-
Baisera, M.1
Oono, Y.2
-
75
-
-
5544275907
-
-
T. de Grand, A. Hasenfratz, P. Hasenfratz, and F. Niedermayer, Report No. hep-lat/9506030
-
Related perfect operator methods have been used with some success in lattice gauge theory by P. Hasenfratz and F. Niedermayer, Nucl. Phys. B 414, 785 (1994); T. de Grand, A. Hasenfratz, P. Hasenfratz, and F. Niedermayer, Report No. hep-lat/9506030.
-
(1994)
Nucl. Phys. B
, vol.414
, pp. 785
-
-
Hasenfratz, P.1
Niedermayer, F.2
|