One-Dimensional Hard-Rod Caricature of Hydrodynamics: “Navier–Stokes Correction” for Local Equilibrium Initial States
Abstract: A one-dimensional system, consisting of identical hard-rod particles of length $a$ is studied in the hydrodynamical limit. A “Navier–Stokes correction” to the Euler equation is found for an initial local equilibrium family of states \documentclass[12pt]{minimal} \usepackage{amsmath} \usepa...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Boldrighini, C. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1997 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 1997 |
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| Übergeordnetes Werk: |
Enthalten in: Communications in mathematical physics - Springer-Verlag, 1965, 189(1997), 2 vom: Nov., Seite 577-590 |
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| Übergeordnetes Werk: |
volume:189 ; year:1997 ; number:2 ; month:11 ; pages:577-590 |
| Links: |
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| DOI / URN: |
10.1007/s002200050218 |
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| Katalog-ID: |
OLC2038869286 |
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| 520 | |a Abstract: A one-dimensional system, consisting of identical hard-rod particles of length $a$ is studied in the hydrodynamical limit. A “Navier–Stokes correction” to the Euler equation is found for an initial local equilibrium family of states \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, of constant density. The correction is given, at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, by a non-linear second order differential operator acting on f(q,v), the hydrodynamical density at a point \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} of the “species” of fluid with velocity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. | ||
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10.1007/s002200050218 doi (DE-627)OLC2038869286 (DE-He213)s002200050218-p DE-627 ger DE-627 rakwb eng 530 510 VZ Boldrighini, C. verfasserin aut One-Dimensional Hard-Rod Caricature of Hydrodynamics: “Navier–Stokes Correction” for Local Equilibrium Initial States 1997 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 1997 Abstract: A one-dimensional system, consisting of identical hard-rod particles of length $a$ is studied in the hydrodynamical limit. A “Navier–Stokes correction” to the Euler equation is found for an initial local equilibrium family of states \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, of constant density. The correction is given, at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, by a non-linear second order differential operator acting on f(q,v), the hydrodynamical density at a point \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} of the “species” of fluid with velocity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. Local Equilibrium Equilibrium Initial State Suhov, Y.M. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 189(1997), 2 vom: Nov., Seite 577-590 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:189 year:1997 number:2 month:11 pages:577-590 https://doi.org/10.1007/s002200050218 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 AR 189 1997 2 11 577-590 |
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10.1007/s002200050218 doi (DE-627)OLC2038869286 (DE-He213)s002200050218-p DE-627 ger DE-627 rakwb eng 530 510 VZ Boldrighini, C. verfasserin aut One-Dimensional Hard-Rod Caricature of Hydrodynamics: “Navier–Stokes Correction” for Local Equilibrium Initial States 1997 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 1997 Abstract: A one-dimensional system, consisting of identical hard-rod particles of length $a$ is studied in the hydrodynamical limit. A “Navier–Stokes correction” to the Euler equation is found for an initial local equilibrium family of states \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, of constant density. The correction is given, at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, by a non-linear second order differential operator acting on f(q,v), the hydrodynamical density at a point \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} of the “species” of fluid with velocity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. Local Equilibrium Equilibrium Initial State Suhov, Y.M. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 189(1997), 2 vom: Nov., Seite 577-590 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:189 year:1997 number:2 month:11 pages:577-590 https://doi.org/10.1007/s002200050218 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 AR 189 1997 2 11 577-590 |
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10.1007/s002200050218 doi (DE-627)OLC2038869286 (DE-He213)s002200050218-p DE-627 ger DE-627 rakwb eng 530 510 VZ Boldrighini, C. verfasserin aut One-Dimensional Hard-Rod Caricature of Hydrodynamics: “Navier–Stokes Correction” for Local Equilibrium Initial States 1997 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 1997 Abstract: A one-dimensional system, consisting of identical hard-rod particles of length $a$ is studied in the hydrodynamical limit. A “Navier–Stokes correction” to the Euler equation is found for an initial local equilibrium family of states \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, of constant density. The correction is given, at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, by a non-linear second order differential operator acting on f(q,v), the hydrodynamical density at a point \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} of the “species” of fluid with velocity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. Local Equilibrium Equilibrium Initial State Suhov, Y.M. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 189(1997), 2 vom: Nov., Seite 577-590 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:189 year:1997 number:2 month:11 pages:577-590 https://doi.org/10.1007/s002200050218 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 AR 189 1997 2 11 577-590 |
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10.1007/s002200050218 doi (DE-627)OLC2038869286 (DE-He213)s002200050218-p DE-627 ger DE-627 rakwb eng 530 510 VZ Boldrighini, C. verfasserin aut One-Dimensional Hard-Rod Caricature of Hydrodynamics: “Navier–Stokes Correction” for Local Equilibrium Initial States 1997 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 1997 Abstract: A one-dimensional system, consisting of identical hard-rod particles of length $a$ is studied in the hydrodynamical limit. A “Navier–Stokes correction” to the Euler equation is found for an initial local equilibrium family of states \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, of constant density. The correction is given, at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, by a non-linear second order differential operator acting on f(q,v), the hydrodynamical density at a point \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} of the “species” of fluid with velocity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. Local Equilibrium Equilibrium Initial State Suhov, Y.M. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 189(1997), 2 vom: Nov., Seite 577-590 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:189 year:1997 number:2 month:11 pages:577-590 https://doi.org/10.1007/s002200050218 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 AR 189 1997 2 11 577-590 |
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10.1007/s002200050218 doi (DE-627)OLC2038869286 (DE-He213)s002200050218-p DE-627 ger DE-627 rakwb eng 530 510 VZ Boldrighini, C. verfasserin aut One-Dimensional Hard-Rod Caricature of Hydrodynamics: “Navier–Stokes Correction” for Local Equilibrium Initial States 1997 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 1997 Abstract: A one-dimensional system, consisting of identical hard-rod particles of length $a$ is studied in the hydrodynamical limit. A “Navier–Stokes correction” to the Euler equation is found for an initial local equilibrium family of states \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, of constant density. The correction is given, at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, by a non-linear second order differential operator acting on f(q,v), the hydrodynamical density at a point \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} of the “species” of fluid with velocity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. Local Equilibrium Equilibrium Initial State Suhov, Y.M. aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 189(1997), 2 vom: Nov., Seite 577-590 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:189 year:1997 number:2 month:11 pages:577-590 https://doi.org/10.1007/s002200050218 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4012 GBV_ILN_4028 GBV_ILN_4046 GBV_ILN_4082 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4313 GBV_ILN_4318 GBV_ILN_4319 AR 189 1997 2 11 577-590 |
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one-dimensional hard-rod caricature of hydrodynamics: “navier–stokes correction” for local equilibrium initial states |
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One-Dimensional Hard-Rod Caricature of Hydrodynamics: “Navier–Stokes Correction” for Local Equilibrium Initial States |
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Abstract: A one-dimensional system, consisting of identical hard-rod particles of length $a$ is studied in the hydrodynamical limit. A “Navier–Stokes correction” to the Euler equation is found for an initial local equilibrium family of states \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, of constant density. The correction is given, at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, by a non-linear second order differential operator acting on f(q,v), the hydrodynamical density at a point \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} of the “species” of fluid with velocity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. © Springer-Verlag Berlin Heidelberg 1997 |
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Abstract: A one-dimensional system, consisting of identical hard-rod particles of length $a$ is studied in the hydrodynamical limit. A “Navier–Stokes correction” to the Euler equation is found for an initial local equilibrium family of states \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, of constant density. The correction is given, at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, by a non-linear second order differential operator acting on f(q,v), the hydrodynamical density at a point \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} of the “species” of fluid with velocity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. © Springer-Verlag Berlin Heidelberg 1997 |
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Abstract: A one-dimensional system, consisting of identical hard-rod particles of length $a$ is studied in the hydrodynamical limit. A “Navier–Stokes correction” to the Euler equation is found for an initial local equilibrium family of states \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, of constant density. The correction is given, at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, by a non-linear second order differential operator acting on f(q,v), the hydrodynamical density at a point \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document} of the “species” of fluid with velocity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. © Springer-Verlag Berlin Heidelberg 1997 |
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