User:Marc Goossens/Works by Günther Ludwig
THIS ARTICLE IS STILL IN SCAFFOLDING – PERSONAL DRAFT (intended for publication in 2008)
The following is an approximately chronological bibliography of publications by the German theoretical physicist and philosopher of science, Günther Ludwig (January 12, 1918 - June 8, 2007).
Ludwig contributed to fields as diverse as relativity, stellar formation, fluid dynamics, statistical and quantum mechanics with additions to pure mathematics along the way. His main interest lay in the foundations and (precise and no-nonsense) interpretation of physics as a whole, and quantum mechanics in particular. This is where one also finds his two most important achievements: (i) a systematic theory of the foundations of physics (or metatheory), and (ii) an application of these concepts to an extensive investigation of the foundations of quantum mechanics, including a derivation of its Hilbert space structure.
Günther Ludwig's post-war publications span a period of 60 years.
Publications
[edit]The publications by Günther Ludwig as listed below, slightly extend the catalogue compiled by M. Ziegler (ref). Items not mentioned in Ziegler's initial list are marked with (+).
For the titles of texts originally published in German, an English translation is appended, remaining faithful to the German original. This does not imply that a full translation of any of these texts is available.
Ziegler lists the 1948 article Ein Modell des Kosmos und der Sternentstehung as having been published in Annalen der Physik. However, the subsequent article with the same title in Archiv der Mathematik refers to the first one as "being published" in "Z. Physik" (footnote 1 on p 80), apparently indicating the Zeitschrift für Physik.
1947 – 1949
[edit]- Ludwig, Günther (1947). "Der Zusammenhang zwischen den Variationsprinzipien der projektiven und der vierdimensionalen Relativitätstheorie". Zeitschrift für Naturforschung. 2a: 3–5. doi:10.1515/zna-1947-0103. (The Connection between the Variational Principles of Projective and Fourdimensional Theory of Relativity)
- Ludwig, Günther (1947). "Skalares Materiefeld in der projektiven Relativitätstheorie mit variabler Gravitationsinvarianten". Zeitschrift für Naturforschung. 2a (9): 482–489. doi:10.1515/zna-1947-0902. (Scalar Matter Field in the Projective Theory of Relativity with Variable Gravitation Invariants)
- Ludwig, Günther (1948). "Ein Modell des Kosmos und der Sternentstehung". Annalen der Physik. 6. Folge (Bd 2). Leipzig: 76–84. doi:10.1002/andp.19484370106. (A Model of the Cosmos and of Stellar Formation)
- Ludwig, Günther (1948–1949). "Ein Modell des Kosmos und der Sternentstehung". Archiv der Mathematik. 1. Oberwolfach: Mathematisches Forschungsinstitut: 80–82. doi:10.1007/BF02038212.
{{cite journal}}
: Unknown parameter|coauthors=
ignored (|author=
suggested) (help) (A Model of the Cosmos and of Stellar Formation) (+)
- Ludwig, Günther (1948). "Zur projektiven Relativitätstheorie mit variabler Gravitationskonstanten, 1. Mitteilung: Beschreibung der projektiven Metrik durch Fünfbeine". Zeitschrift für Physik. 124: 450–457. doi:10.1007/BF01668883. (On the Projective Theory of Relativity with Variable Gravitation Constants, 1st Report: Description of the Projective Metric using 5-frames)
- Ludwig, Günther (1949). "Zur projektiven Relativitätstheorie mit variabler Gravitationskonstanten, 2. Mitteilung: Variationsprinzipien und Feldgleichungen für Gravitation und Materie". Zeitschrift für Physik. 125: 545–562. doi:10.1007/BF01331404. (On the Projective Theory of Relativity with Variable Gravitation Constants, 2nd Report: Variational Principles and Field Equations for Gravitation and Matter)
- Ludwig, Günther (1949). "Ansatz zu einer divergenzfreien Quantenelektrodynamik". Zeitschrift für Naturforschung. 5a: 637–641. (Ansatz towards a Divergence Free Quantum Electrodynamics)
1950 – 1959
[edit]- Ludwig, Günther (1951), Fortschritte der projektiven Reltivitätstheorie, Vieweg (Progress in Projective Theory of Relativity)
- Ludwig, Günther (1951). "Die erzwungenen Schwingungen des harmonischen Oszillators nach der Quantentheorie". Zeitschrift für Physik. 130 (4): 468–476. doi:10.1007/BF01328437. (The Forced Oscillations of the Harmonic Oscillator according to Quantum Theory)
- Ludwig, Günther (1952). "Wie kann die unitäre Feldtheorie Strahlungsemission, Selbstenergie und Lambshift erklären?". Zeitschrift für Naturforschung. 7a (3–4): 248–250. doi:10.1515/zna-1952-3-403. (How can the Theory of Unitary Fields explain Emission of Radiation, Self-energy and Lambshift?)
- Ludwig, Günther (1953), "Die Stellung des Subjekts in der Quantentheorie", 'Veritas, Justita, Libertas' (Festschrift der Freien Universtität Berlin zur 200-Jahr-Feier der Columbia University), Berlin: Colloquium-Verlag, pp. 262–272 (The Position of the Subject in Quantum Theory)
- Ludwig, Günther (1953). "Der Meßprozeß". Zeitschrift für Physik. 135 (5): 483–511. doi:10.1007/BF01338813. (The Measurement Process)
- Ludwig, Günther (1954), "Die Grundlangen der Quantenmechanik", Grundlehren der Mathematischen Wissenshaften, Band 70, Springer (The Foundations of Quantum Mechanics)
- Ludwig, Günther (1954). "Zur Deutung der Beobachtung in der Quantenmechanik". Physikalischen Blätter. Band 11: 489–494. (On the Conception of Observation in Quantum Mechanics)
- Ludwig, Günther (1957). "Zum Ergodensatz und zum Begriff der makroskopischen Observablen". Zeitschrift für Naturforschung. 12a: 662–663. doi:10.1515/zna-1957-0812. (On the Ergodic Theorem and on the Concept of Macrosopic Observables)
- Ludwig, Günther (1958). "Zum Ergodensatz und zum Begriff der makroskopischen Observablen I". Zeitschrift für Physik. 150 (3): 346–375. doi:10.1007/BF01322328. (On the Ergodic Theorem and on the Concept of Macrosopic Observables I)
- Ludwig, Günther (1958). "Zum Ergodensatz und zum Begriff der makroskopischen Observablen II". Zeitschrift für Physik. 152: 98–115. doi:10.1007/BF01322009. (On the Ergodic Theorem and on the Concept of Macrosopic Observables II)
1960 – 1969
[edit]- Ludwig, Günther (1960), "Axiomatic quantum statistics of macroscopic systems (Ergodic theory)", in Caldirola, P. (ed.), Proceedings of the International School of Physics 'Enrico Fermi', Course XIV, Academic Press, pp. 57–132
- Ludwig, Günther; Heil, M. (1960), "Boundary-layer theory with dissociation and ionization", in Dryden; Karman (eds.), Advances in Applied Mechanics Vol. 6, Academic Press, pp. 39–118
- Ludwig, Günther; Heil, M. (1960), "Raum- und Zeitvorstellung in der Physik", in Dryden; Karman (eds.), Universitätstage 1960, Veröffentlichung der Freien Universität Berlin, Berlin: Walter de Gruyter & Co., pp. 16–29 ('The notion of space and time in physics')
- Ludwig, Günther; Heil, M. (1961), "Gelöste und ungelöste Probleme des Meßprozesses in der Quantenmechanik", in Dryden; Karman (eds.), Werner Heisenberg und die Physik unserer Zeit, Berlin: Vieweg Braunschweig, pp. 150–181 (Solved and Unsolved Problems of the Measurement Process in Quantum Mechanics)
- Ludwig, Günther (July 15, 1961). "Theoretical Research Studies of Reacting Plasmas". (unknown). Presumably this work was published under contract to the US Defense Department; the TR Citation on the Scientific and Technical Information Network (STINET) of the Defense Technical Information Centre (DTIC) lists the contract numbers DA91 AF61 052 239 (AF61052239). (+)
- Ludwig, Günther (September 30, 1961). "Kinetic Theory of Rarified Gases and of Highly Heated Diatomic Gases". (unknown). Presumably this work was published under contract to the US Defense Department; the TR Citation on the Scientific and Technical Information Network (STINET) of the Defense Technical Information Centre (DTIC) lists the contract numbers DA91 591EUC1592 (DA91591EUC1592). (+)
- Ludwig, Günther (1962), Das naturwissenschaftliche Weltbild des Christen, Osnabrück: Verlag A. Fromm (The Christian's Physical Sciences Conception of the World)
- Ludwig, Günther (1963). "Zur Begründung der Thermodynamik auf Grund der Quantenmechanik". Zeitschrift für Physik. 171 (3): 476–486. doi:10.1007/BF01377869. (On founding Thermodynamics on the Basis of Quantum Mechanics)
- Ludwig, Günther (1963). "Zur Begründung der Thermodynamik auf Grund der Quantenmechanik II, Masterequation". Zeitschrift für Physik. 173: 232–240. doi:10.1007/BF01377962. (On founding Thermodynamics on the Basis of Quantum Mechanics II, Masterequation)
- Ludwig, Günther (1964). "Versuch einer axiomatischen Grundlegung der Quantenmechanik und allgemeiner physikalischer Theorien". Zeitschrift für Physik. 181 (3): 233–260. doi:10.1007/BF01418533. (Attempt at an Axiomatic Foundation of Quantum Mechanics and of General Physical Theories)
- Ludwig, Günther (January 21, 1964). "Attempt of an Axiomatic Foundation of Quantum Mechanics and More General Theories". (unknown). Presumably this work was published under contract to the US Defense Department; the TR Citation on the Scientific and Technical Information Network (STINET) of the Defense Technical Information Centre (DTIC) lists the contract numbers AF61 052 658 (AF61052658). (+)
- Ludwig, Günther (February 29, 1964). "Methods to Solve the Equations for Fluctuation Phenomena in Low Density Gas". (unknown). Presumably this work was published under contract to the US Defense Department; the TR Citation on the Scientific and Technical Information Network (STINET) of the Defense Technical Information Centre (DTIC) lists the contract numbers DA91 591EUC2918 (DA91591EUC2918) . (+)
- Ludwig, Günther (1967), "An axiomatic foundation of quantum mechanics on a nonsubjective basis", in Bunge, Mario (ed.), Quantum Theory and Reality, Springer, pp. 98–104
- Ludwig, Günther (1967). "Hauptsätze über das Messen als Grundlage der Hilbert-Raum-Struktur der Quantenmechanik". Zeitschrift für Naturforschung. 22a (9): 1303–1323. doi:10.1515/zna-1967-0904. (Fundamental Laws on Measurement as a Basis of the Hilbert Space Structure of Quantum Mechanics)
- Ludwig, Günther (1967). "Ein weiterer Hauptsatz über das Messen als Grundlage der Hilbert-Raum-Struktur der Quantenmechanik". Zeitschrift für Naturforschung. 22a (9): 1324–1327. doi:10.1515/zna-1967-0905. (A further Fundamental Law on Measurement as a Basis of the Hilbert Space Structure of Quantum Mechanics)
- Ludwig, Günther (1967). "Attempt of an Axiomatic Foundation of Quantum Mechanics and More General Theories II". Communications in Mathematical Physics. 4 (5): 331–348. doi:10.1007/BF01653647.
- Ludwig, Günther (1968). "Attempt of an Axiomatic Foundation of Quantum Mechanics and More General Theories III". Communications in Mathematical Physics. 9: 1–12. doi:10.1007/BF01654027.
- Ludwig, Günther, ed. (1968), Wave Mechanics, Pergamon Press
- Ludwig, Günther (1969), Wellenmechanik: Einführung und Originaltexte. (Wissenschaftliche Taschenbücher Band 55), Berlin, Braunschweig, Oxford: Akademie Verlag / Vieweg und Sohn / Pergamon Press (Wave Mechanics: Introduction and Original Texts)
1970 – 1979
[edit]- Ludwig, Günther (1970), "Zur Deutung der Beobachtung in der Quantenmechanik (reprinted from Phys Blätter 11, 1954)", in Krüger (ed.), Erkenntnisprobleme der Naturwissenschaften: Texte zur Einführung in die Philosophie der Wissenschaft", Band 38 von Neue Wissenschaftliche Bibliothek: Philosophie, Kiepenheuer & Witsch, pp. 428–434
- Ludwig, Günther (1970), "Deutung des Begriffs «physikalische Theorie» und axiomatische Grundlegung der Hilbertraumstruktur der Quantenmechanik durch Hauptsätze des Messens", in Ehlers; Hepp; Zurich (eds.), Lecture Notes in Physics 4, Springer (Understanding the Concept "Physical Theory" and an Axiomatic Foundation of the Hilbert Space Structure of Quantum Mechanics through the Fundamental Laws of Measurement)
- Ludwig, Günther (1971), "The measuring process and an axiomatic foundation of quantum mechanics", in D'Espagnat, B. (ed.), Foundations of Quantum Mechanics (Proceedings of the International School of Physics 'Enrico Fermi', Course IL), Academic Press
- Ludwig, Günther (1971), "A physical interpretation of an axiom within an axiomatic approach to quantum mechanics and a new formulation of this axiom as a general covering condition", Notes in Math.Phys. 1, Marburg
{{citation}}
: CS1 maint: location missing publisher (link)
- Ludwig, Günther (1971), "Transformationen von Gesamtheiten und Effekten", Notes in Math.Phys. 4, Marburg
{{citation}}
: CS1 maint: location missing publisher (link) (Transformation of Ensembles and Effects)
- Ludwig, Günther (1972), "Makroskopische Systeme und Quantenmechanik", Notes in Math.Phys. 5, Marburg
{{citation}}
: CS1 maint: location missing publisher (link) (Macroscopic Systems and Quantum Mechanics)
- Ludwig, Günther (1972), "Meß- und Präparierprozesse", Notes in Math.Phys. 6, Marburg
{{citation}}
: CS1 maint: location missing publisher (link) (Measuring and Preparing Processes)
- Ludwig, Günther (1972), "An improved formulation of some theorems and axioms in the axiomatic foundation of the Hilbert space structure of quantum mechanics", Communications in Mathematical Physics 26, pp. 78–86
- Ludwig, Günther (1973), "Why a new approach to found quantum theory?", in D'Espagnat, B. (ed.), The Physicist's Conception of Nature, Reidel, pp. 702–708
- Ludwig, Günther (1974), "Measurement as a Process of Interaction Between Macroscopic Systems", Notes in Math.Phys. 14, Marburg
{{citation}}
: CS1 maint: location missing publisher (link)
- Ludwig, Günther (1974), Einführung in die Grundlagen der Theoretischen Physik; Band II: Elektrodynamik, Zeit, Raum, Kosmos, Vieweg, ISBN 3-571-09182-5 (An Introduction into the Principles of Theoretical Physics, Vol II: "Electrodynamics, Time, Space, Cosmos")
- Ludwig, Günther (1976, 1984), Einführung in die Grundlagen der Theoretischen Physik; Band III: Quantentheorie, Vieweg, ISBN 3-528-09183-5
{{citation}}
: Check date values in:|year=
(help)CS1 maint: year (link) (An Introduction into the Principles of Theoretical Physics, Vol III: "Quantum Theory")
- Ludwig, Günther (1974), "Measuring and Preparing Processes", in Hartkämper; Neumann (eds.), Foundations of Quantum Mechanics and Ordered Linear Spaces, Springer Lecture Notes in Physics 29, Springer, pp. AAAAAAAAA
- Ludwig, Günther (1976), "A Theoretical Description of Single Microsystems", in Price; Chissick (eds.), The Uncertainty Principle and Foundations of Quantum Mechanics: A Fifty Years Survey, Wiley&Sons, pp. 189–226
- Ludwig, Günther (1978), Einführung in die Grundlagen der Theoretischen Physik; Band I: Raum, Zeit, Mechanik, Vieweg (An Introduction into the Principles of Theoretical Physics, Vol I: "Space, Time, Mechanics")
- Ludwig, Günther (1978, 1990), Die Grundstrukturen einer physikalischen Theorie, Springer
{{citation}}
: Check date values in:|year=
(help)CS1 maint: year (link) (The Fundamental Structures of a Physical Theory)
- Ludwig, Günther (1979), Einführung in die Grundlagen der Theoretischen Physik; Band IV: Makrosysteme, Physik und Mensch, Vieweg, ISBN 3-528-09184-3 (An Introduction into the Principles of Theoretical Physics, Vol IV: "Macrosystems, Physics and Man")
- Ludwig, Günther (1979). "Wie kann man durch Physik etwas von der Wirklichkeit erkennen?". Akad. Wiss. Mainz, Abhn. Math.-Nat. Kl. Nr. 2: 3–16.
{{cite journal}}
:|volume=
has extra text (help) (How can one find out Something about Reality through Physics?)
1980 – Retirement in 1983
[edit]- Ludwig, Günther (1980), "Axiomatische Basis der Quantenmechanik, Kap. I-III", Notes in Math.Phys. 16, Marburg
{{citation}}
: CS1 maint: location missing publisher (link) (Axiomatic Basis of Quantum Mechanics, Ch I-III)
- Ludwig, Günther (1980), "Axiomatische Basis der Quantenmechanik, Kap. IV-VII", Notes in Math.Phys. 17, Marburg
{{citation}}
: CS1 maint: location missing publisher (link) (Axiomatic Basis of Quantum Mechanics, Ch IV-VII)
- Ludwig, Günther (1980), "Axiomatische Basis der Quantenmechanik, Kap. VIII-X", Notes in Math.Phys. 18, Marburg
{{citation}}
: CS1 maint: location missing publisher (link) (Axiomatic Basis of Quantum Mechanics, Ch VIII)
- Ludwig, Günther (1980), "Das Problem der Ja-Nein-Messung in der Quantenmechanik", Grundlagen der exakten Naturwissenschaften, Band 1: "Grundlagen der Quantentheorie", Mannheim, pp. 9–21
{{citation}}
: CS1 maint: location missing publisher (link) (The Problem of the Yes-no Measurement in Quantum Mechanics)
- Ludwig, Günther (1981), "An Axiomatic Basis of Quantum Mechanics", in Neumann, H. (ed.), Grundlagen der exakten Naturwissenschaften, Band 5: "Interpretations and Foundations of Quantum Theory", B.I.-Wissenschaftsverlag, pp. 49–70
- Ludwig, Günther; Neumann, Holger (1981), "Connections between Different Approaches to the Foundations of Quantum Mechanics", in Neumann, H. (ed.), Grundlagen der exakten Naturwissenschaften, Band 5: "Interpretations and Foundations of Quantum Theory", B.I.-Wissenschaftsverlag, pp. 133–143
- Ludwig, Günther (1981). "Axiomatische Basis einer physikalischen Theorie und theoretische Begriffe". Zeitschriftt für allgemeine Wissenschaftstheorie. Band XII/1. Franz Steiner Verlag: 55–74. doi:10.1007/BF01811304. (Axiomatic Basis of a Physical Theory and Theoretical Concepts)
- Ludwig, Günther (1981), "Imprecision in Physics", in Hartkämper, A.; Schmidt, H.-J. (eds.), Structure and Approximation in Physical Theories, Plenum
- Ludwig, Günther (1981). "Quantum theory as a theory of interactions between macroscopic systems which can be described objectively". Erkentniss. 16: 359–387.
- Ludwig, Günther (1981), "Eigenschaften und Pseudoeigenschaften von Mikrosystemen", in Nitsch, J.; Pfarr, J.; Stachow, E.-W. (eds.), Grundlagenprobleme der modernen Physik, Festschrift für Peter Mittelstaedt zum 50. Geburtstag, B.I.-Wissenschaftsverlag, pp. 217–242 (Properties and Pseudoproperties of Microsystems)
- Ludwig, Günther. "The Objective Description of Preparation and Registration as a Basis of Quantum Theory". Nuovo Cimento.
- Ludwig, Günther (1983), "The Connection between the Objective Description of Macrosystems and Quantum Mechanics of 'Many Particles'", in van der Merwe, A. (ed.), Old and New Questions in Physics, Cosmology, Philosophy and Theoretical Biology: Essays in Honor of Wolfgang Yourgrau, Plenum, pp. 243–263, ISBN 0306409623
- Ludwig, Günther (1983), "Is the Geometry of Physical Space a Form of Pure Sensible Intuition? A Technical Construction? Or a Structure of Reality?", in Mayr; Süssmann (eds.), Space, Time, and Mechanics, Reidel Publishing Company, pp. 1–20
- Ludwig, Günther (1983), "Was entspricht Möglichkeitsaussagen im Mathematischen Bild einer Physikalischen Theorie?", Erkenntnis- und Wissenschaftstheorie, Akten des 7. Internationalen Wittgenstein Symposiums, 22. bis 29. August 1982, Kirchberg/Wechsel (Österreich), Hölder-Pichler-Tempsky (What corresponds to Statements on Possibility in the Mathematical Image of a Physical Theory?)
From Ludwig's retirement until 1989
[edit]- Ludwig, Günther (1984), "Restriction and Embedding", in Balzer (ed.), Reduction in Science -- Structure, Examples, Philosophical Problems, Reidel Publishing Company, pp. 17–31
- a Ludwig, Günther (1983), Foundations of Quantum Mechanics I, Springer
- a Ludwig, Günther (1985), Foundations of Quantum Mechanics II, Springer
- Ludwig, Günther (1985), "Construction of a Formal Language and Logic 'a priori' or 'a posteriori'?", in Mittelstaedt, P.; Stachow, E.-W. (eds.), Grundlagen der exakten Naturwissenschaften, Band 6: Recent Developments in Quantum Logic (Proceedings of the International Symposium on Quantum Logic, Cologne, Germany, June 13-16, 1984), B.I. Wissenschaftsverlag, pp. 105–110
- Ludwig, Günther (1985). "Das EPR-Paradoxon als makroskopisches Experiment und seine Auswirkungen auf unsere Vorstellung von Physik". Annalen der Physik, Folge 7. 42 (2): 150–168. doi:10.1002/andp.19854970209. (The EPR-Paradox as a Macroscopic Experiment and its Effect on our Conception of Physics)
- Ludwig, Günther (1985), An Axiomatic Basis for Quantum Mechanics, Vol I: "Derivation of Hilbert Space Structure", Springer
- Ludwig, Günther (1986). "Theory of Quantum Mechanical Measurements". Metrologia. 22 (3). Springer: 128–133. doi:10.1088/0026-1394/22/3/002.
- Ludwig, Günther (1987), An Axiomatic Basis for Quantum Mechanics, Vol II: "Quantum Mechanics and Macrosystems", Springer
- Ludwig, Günther (1989). "Atoms: Are They Real or Are They Objects?". Foundations of Physics. 19 (8). Plenum: 971–983. doi:10.1007/BF01883151.
From 1990 until Ludwig's death in 2007
[edit]- Ludwig, Günther (1990), "Die Katze ist tot", in Audretsch, J.; Mainzer, K. (eds.), Wieviele Leben hat Schrödingers Katze?, B.I. Wissenschaftsverlag, pp. 183–208 (The Cat is Dead (in: How many Lives does Schrödinger's Cat have?)
- Ludwig, Günther (1990). "Concepts of States in Physics". Foundations of Physics. 20 (6). Plenum: 621–633. doi:10.1007/BF01889451.
- Ludwig, Günther (1990). "Intertheory relations and the striving for a unique and uniform theory". (reprint).
- Ludwig, Günther (1993), "Die Stellung des Subjekts in einer physikalischen Theorie", in Geyer, B.; Herwig, H.; Rechenberg, H. (eds.), Werner Heisenberg, Physiker und Philosoph (Verhandlungen der Konferenz 'Werner Heisenberg als Physiker und Philosoph in Leipzig' vom 9.-12. Dez. 1991 an der Univ. Leipzig), Spektrum, pp. 244–250 (The Position of the Subject in a Physical Theory (in: "W. Heisenberg, Physicist and Philospher)
- Ludwig, Günther, "The Minimal Interpretation of Quantum Mechanics and the Objective Description of Macrosystems", in Busch, P.; Lahti, P.; Mittelstaedt, P. (eds.), Symposium on the Foundations of Modern Physics, Quantum Measurement, Irreversibility and the Physics of Information, World Scientific (Cologne, Germany, 1-5 June 1993, pp. 242–250
- Ludwig, Günther (1994). "Die Methode der Physik und ihre Grenzen". Ethik und Sozialwissenschaften. 5: 458–460. (The Method of Physics and its Limitations)
- Ludwig, Günther (1994), "The Relations between various Spacetime Theories", in Mayr, Ulrich; Schmidt, Heinz-Jürgen (eds.), Semantical Aspects of Spacetime Theories
- a Ludwig, Günther; Thurler, Gérald (2006), A New Foundation of Physical Theories, Berlin: Springer
References
[edit]Reichenbach ref http://www.iep.utm.edu/r/reichenb.htm#H2