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  • Articles  (309,495)
  • Data  (329)
  • Springer  (266,707)
  • American Association for the Advancement of Science  (42,740)
  • PANGAEA
  • 1965-1969  (165,215)
  • 1960-1964  (104,597)
  • 1935-1939  (40,012)
Collection
Source
Keywords
Publisher
Years
Year
Journal
Topic
  • 1
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    Obernkirchener Sandstein - Ein Werkstoff des Weserlandes (1937)
    PANGAEA
    In:  EPIC3Bremerhaven, PANGAEA
    Details
    Publication Date: 2019-11-27
    Repository Name: EPIC Alfred Wegener Institut
    Type: PANGAEA Documentation , notRev
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  • 2
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    Figure 13-3 of Pratt (1967) (1967)
    PANGAEA
    In:  EPIC3Bremerhaven, PANGAEA
    Details
    Publication Date: 2016-08-18
    Repository Name: EPIC Alfred Wegener Institut
    Type: PANGAEA Documentation , notRev
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  • 3
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    Figures of: Manganese pavements on the Blake Plateau (1961)
    PANGAEA
    In:  EPIC3Bremerhaven, PANGAEA
    Details
    Publication Date: 2016-08-25
    Repository Name: EPIC Alfred Wegener Institut
    Type: PANGAEA Documentation , notRev
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  • 4
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    Visual observations of manganese deposits on the Blake Plateau (1969)
    PANGAEA
    In:  EPIC3Bremerhaven, PANGAEA
    Details
    Publication Date: 2015-11-27
    Repository Name: EPIC Alfred Wegener Institut
    Type: PANGAEA Documentation , notRev
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  • 5
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    Cruise Report - R/V GOSNOLD #74 (1965)
    PANGAEA
    In:  EPIC3Bremerhaven, PANGAEA
    Details
    Publication Date: 2015-12-14
    Repository Name: EPIC Alfred Wegener Institut
    Type: PANGAEA Documentation , notRev
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  • 6
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    Vema Cruise 16 - Preliminary Megascopic Descriptions of Split Cores (Unpublished) (1960)
    PANGAEA
    In:  EPIC3Bremerhaven, PANGAEA
    Details
    Publication Date: 2016-07-28
    Repository Name: EPIC Alfred Wegener Institut
    Type: PANGAEA Documentation , notRev
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  • 7
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    The bogs at Ballybetagh, near Dublin, with remarks on late-glacial conditions in Ireland (1938)
    PANGAEA
    In:  EPIC3Proceedings of the Royal Irish Academy, Dublin: Hodges, Figgis, & Co., XLIV Sect A, Bremerhaven, PANGAEA, pp. 205-260
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 8
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    Chat moss, Lancashire (1964)
    PANGAEA
    In:  EPIC3Manchester Literay and Philosophical Society, Bremerhaven, PANGAEA, 106, pp. 22-45
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 9
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    Eemian interglacial at Golkow near Warsaw (1966)
    PANGAEA
    In:  EPIC3Kwartalnik geologiczny Wydawn, Geologiczne Warszawa, Bremerhaven, PANGAEA, 10(2), pp. 453-461
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
    Type: PANGAEA Documentation , notRev
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  • 10
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    PÓZNOGLACJALNA I HOLOCEŃSKA HISTORIA ROŚLINNOŚCI GÓR ŚWIĘTOKRZYSKICH (The History of the Late Glacial and Holocene Vegetation of the Holy Cross Mountains (1961)
    PANGAEA
    In:  EPIC3Polska Akdademia Nauk, Instytut Botaniki, II(2), Bremerhaven, PANGAEA, 56 p.
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 11
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    Chemical composition of ferromanganese nodules of the Indian ocean. Lithology and Mineral Resources, 3, 43–56 (in Russian) (1967)
    PANGAEA
    In:  EPIC3Bremerhaven, PANGAEA
    Details
    Publication Date: 2015-10-23
    Repository Name: EPIC Alfred Wegener Institut
    Type: PANGAEA Documentation , notRev
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  • 12
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    Data on the geochemistry of manganese nodules from the Indian Ocean. Geokhimiya 5, 493-499 (1963)
    PANGAEA
    In:  EPIC3Bremerhaven, PANGAEA
    Details
    Publication Date: 2015-10-29
    Repository Name: EPIC Alfred Wegener Institut
    Type: PANGAEA Documentation , notRev
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  • 13
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    Figure 1 of: Pelagic sediments (1961)
    American Association for the Advancement of Science
    In:  EPIC3New York, American Association for the Advancement of Science
    Details
    Publication Date: 2016-01-07
    Repository Name: EPIC Alfred Wegener Institut
    Type: PANGAEA Documentation , notRev
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  • 14
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    Priroda bolot i metody ich issledovaniy [According to the question of the age of the bogs of the forest-steppe in Ukraine] (1967)
    PANGAEA
    In:  EPIC3In: The nature of bogs and methods of their investigations, The Academy of Sciences of the USSR, All-Union Botanical Society, 291 pp, Nauka, Moscow., Bremerhaven, PANGAEA
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 15
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    Late-glacial deposits near Lockerbie, Dumfriesshire (1964)
    PANGAEA
    In:  EPIC3Transactions of the Dumfriesshire ..., Bremerhaven, PANGAEA
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 16
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    Pollen Analysis of Four Samples from the River Annan, Dumfriesshire (1964)
    PANGAEA
    In:  EPIC3Bremerhaven, PANGAEA
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 17
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    Assimilatory pigments from subfossil fir needles (Abies alba Mill.) (1963)
    PANGAEA
    In:  EPIC3ACTA SOCIETATIS BOTANICORUM POLONTAE Vol. XXXII Nr 1., Bremerhaven, PANGAEA
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 18
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    Grafic presentation of size analysis data (1968)
    PANGAEA
    In:  EPIC3manuscript for teaching students., Bremerhaven, PANGAEA
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 19
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    Photo of manganese nodule (1968)
    PANGAEA
    In:  EPIC3Bremerhaven, PANGAEA
    Details
    Publication Date: 2015-10-31
    Repository Name: EPIC Alfred Wegener Institut
    Type: PANGAEA Documentation , notRev
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  • 20
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    The Earth Beneath the Sea (1963)
    PANGAEA
    In:  EPIC3Bremerhaven, PANGAEA
    Details
    Publication Date: 2015-11-13
    Repository Name: EPIC Alfred Wegener Institut
    Type: PANGAEA Documentation , notRev
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  • 21
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    Argo-3-65 expedition, core photos (1965)
    PANGAEA
    In:  EPIC3Bremerhaven, PANGAEA
    Details
    Publication Date: 2016-06-13
    Repository Name: EPIC Alfred Wegener Institut
    Type: PANGAEA Documentation , notRev
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  • 22
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    Pollenanalytische Untersuchungen zur Vegetationsgeschichte des Hannoverschen Wendlandes (1969)
    PANGAEA
    In:  EPIC3Flora:, Bremerhaven, PANGAEA, 158, pp. 480-519
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 23
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    Scans of the original registration diagrams of the radiation measurements during the Wegener expedition 1930/1931 (1935)
    PANGAEA
    In:  EPIC3Nachlaß Georgi, Alfred Wegener Institute for Polar and Marine Research, Bremerhaven., Bremerhaven, PANGAEA
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 24
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    O vybore metodiki mineralogicheskogo analiza peschano-alevritovykh fraktsyj morskikh donnykh osadkov (On choice of a method for mineralogical analysis of sandy-aleuritic franctions of marine bottom sediments) (1961)
    PANGAEA
    In:  EPIC3Transactions (Trudy) of the P.P. Shirshov Institute of Oceanology USSR Acad. Sci., 1961. Vol. 50, p., Bremerhaven, PANGAEA, pp. 170-183
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 25
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    METEOR Cruise overview M17 (1969)
    PANGAEA
    In:  EPIC3Deutsches Hydrographisches Institut, Hamburg, Bremerhaven, PANGAEA
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 26
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    METEOR Cruise overview M18 (1969)
    PANGAEA
    In:  EPIC3Deutsches Hydrographisches Institut, Hamburg, Bremerhaven, PANGAEA
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 27
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    The Iceland-Faroe Ridge International (ICES) "Oberflow" Expedition, May-June, 1960 (1967)
    PANGAEA
    In:  EPIC3Rapports et Procès-Verbaux des Réunions, Bremerhaven, PANGAEA, 157, 274 p.
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 28
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    METEOR Cruise overview M06 (1966)
    PANGAEA
    In:  EPIC3Deutsches Hydrographisches Institut, Hamburg, Bremerhaven, PANGAEA
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    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 29
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    METEOR Cruise overview M16 (1969)
    PANGAEA
    In:  EPIC3Deutsches Hydrographisches Institut, Hamburg, Bremerhaven, PANGAEA
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 30
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    METEOR Cruise overview M12 (1967)
    PANGAEA
    In:  EPIC3Deutsches Hydrographisches Institut, Hamburg, Bremerhaven, PANGAEA
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 31
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    METEOR Cruise overview M05 (1966)
    PANGAEA
    In:  EPIC3Deutsches Hydrographisches Institut, Hamburg, Bremerhaven, PANGAEA
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    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 32
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    METEOR Cruise overview M14 (1968)
    PANGAEA
    In:  EPIC3Deutsches Hydrographisches Institut, Hamburg, Bremerhaven, PANGAEA
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    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 33
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    Open questions (1935)
    PANGAEA
    In:  EPIC3Nachlaß Georgi, Alfred Wegener Institute for Polar and Marine Research, Bremerhaven., Bremerhaven, PANGAEA
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 34
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    METEOR Cruise overview M02 (1965)
    PANGAEA
    In:  EPIC3Deutsches Hydrographisches Institut, Hamburg, Bremerhaven, PANGAEA
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 35
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    METEOR Cruise overview M03 (1966)
    PANGAEA
    In:  EPIC3Deutsches Hydrographisches Institut, Hamburg, Bremerhaven, PANGAEA
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 36
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    METEOR Cruise overview M01 (1965)
    PANGAEA
    In:  EPIC3Deutsches Hydrographisches Institut, Hamburg, Bremerhaven, PANGAEA
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 37
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    Forschungsschiff "Meteor" (1964)
    PANGAEA
    In:  EPIC3Ergänzungsheft Reihe A (8°), Nr. 5 zur Deutschen Hydrographischen Zeitschrift, Deutsches Hydrographisches Institut, Hamburg., Bremerhaven, PANGAEA
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
    Type: PANGAEA Documentation , notRev
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  • 38
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    METEOR Cruise overview M09 (1967)
    PANGAEA
    In:  EPIC3Deutsches Hydrographisches Institut, Hamburg, Bremerhaven, PANGAEA
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    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 39
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    METEOR Cruise overview M04 (1966)
    PANGAEA
    In:  EPIC3Deutsches Hydrographisches Institut, Hamburg, Bremerhaven, PANGAEA
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    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 40
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    METEOR Cruise overview M08 (1967)
    PANGAEA
    In:  EPIC3Deutsches Hydrographisches Institut, Hamburg, Bremerhaven, PANGAEA
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 41
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    METEOR Cruise overview M07 (1966)
    PANGAEA
    In:  EPIC3Deutsches Hydrographisches Institut, Hamburg, Bremerhaven, PANGAEA
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    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 42
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    METEOR Cruise overview M10 (1967)
    PANGAEA
    In:  EPIC3Deutsches Hydrographisches Institut, Hamburg, Bremerhaven, PANGAEA
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    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 43
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    METEOR Cruise overview M13 (1968)
    PANGAEA
    In:  EPIC3Deutsches Hydrographisches Institut, Hamburg, Bremerhaven, PANGAEA
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    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 44
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    METEOR Cruise overview M11 (1967)
    PANGAEA
    In:  EPIC3Deutsches Hydrographisches Institut, Hamburg, Bremerhaven, PANGAEA
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    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 45
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    METEOR Cruise overview M15 (1968)
    PANGAEA
    In:  EPIC3Deutsches Hydrographisches Institut, Hamburg, Bremerhaven, PANGAEA
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    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 46
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    Planktonic foraminifera (1969)
    PANGAEA
    In:  EPIC3Antarctic Map Folio Series, American Geographical Society, Bremerhaven, PANGAEA, pp. 9-12
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    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 47
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    Geological situation of the Eemian interglacial deposits (1966)
    PANGAEA
    In:  EPIC3Kwartalnik geologiczny Wydawn, Geologiczne Warszawa, Bremerhaven, PANGAEA, 10(2), pp. 442-452
    Details
    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 48
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    Standardpollendiagramme und C14-Datierungen aus dem Ageröds Mosse im mittleren Schonen (1964)
    PANGAEA
    In:  EPIC3LUNDS UNIVERSITETS ÄRSSKRIFT. N.F. Avd. 2. Bd 59. Nr 7., Bremerhaven, PANGAEA
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    Publication Date: 2019-07-17
    Repository Name: EPIC Alfred Wegener Institut
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  • 49
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    Botanisch-moorkundliche Untersuchungen in Nordfriesland - Ein Beitrag zur Frage nach dem zeitlichen Ablauf der Meeresspiegelschwankungen (1962)
    PANGAEA
    In:  EPIC3Bremerhaven, PANGAEA
    Details
    Publication Date: 2019-07-17
    Description: Die erneute moorkundlich-pollenanalytische Bearbeitung Nordfrieslands galten u.a. der Klärung folgender Fragen: 1. Sind die in größerer Entfernung von der Küste gewonnenen Erfahrungen über den Verlauf der Waldgeschichte der Nacheiszeit ohne weiteres auf die marschen zu Übertragen? 2. Welche Einflüsse der Meeresüberflutungen auf die Entwicklung der Moore und ihrer Vegetation lassen sich feststellen ? 3. Wie ist der zeitliche Ablauf der postglazialen Meeresspiegelschwankungen in Nordfriesland, und ist es möglich, Fehldatierungen auszuschließen, welche durch Abtragung, Umlagerung oder Durchmischung der in das Marschprofil eingeschlossenen pollenführenden Moorschichten bedingt sind?
    Repository Name: EPIC Alfred Wegener Institut
    Type: PANGAEA Documentation , notRev
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    Relationship between ion distribution and membrane potential during a steady state (1960)
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    Bulletin of mathematical biology 22 (1960), S. 323-349 
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    Notes: Abstract Equations were derived showing the relationship between the membrane potential and the quantities which influence it under steady state conditions. Essentially, the membrane potential is caused by the valence and concentration of the non-permeating ions. The permeating ions can modify the membrane potential by altering the relative concentration of the non-permeating ions with respect to the concentration of the permeating ions. For muscle, the sodium cations act as the non-permeating ions in the extracellular environment by the maintenance of some type of active metabolic process and large anions act as the non-permeating ions in the intracellular environment. Both of these non-permeating ions contribute about equally to the maintenance of the resting membrane potential. When the active metabolic process for sodium extrusion breaks down or when acids are added, the membrane potential should decrease. Water should enter the cell when the sodium metabolic process is diminished; water should leave the cell when acids are added. When acid is added, it is expected that the cations potassium and sodium will leave the cell with little or no shift of the chloride ions.
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    Life, information theory, probability, and physics (1960)
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    Bulletin of mathematical biology 22 (1960), S. 351-364 
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    Notes: Abstract A purely information-theoretical approach to the problem of self-replication of elementary living units implies that pure chance is the determining factor in the formation of the first living unit. The probability of such a spontaneous formation can be calculated from the minimum amount of information which an organism must possess in order to replicate itself. An estimation of this amount of information is made here by two different methods. First by a “paper and pencil experiment” which indicates the minimum amount of information needed on a printed page in order that with given tools the page could be reproduced. Second—by an analytical consideration of some hypothetical molecular mechanisms. A general method for handling such problems is suggested. On the basis of estimated information contents it is shown that under most favorable conditions the probability of a spontaneous generation by pure chance during the lifetime of the earth is vanishingly small. It is concluded that dynamic factors, which may reduce tremendously the information content, must play a role in the genesis of life on earth.
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    Some remarks on molecular biology (1960)
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    Bulletin of mathematical biology 22 (1960), S. 365-370 
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    Notes: Abstract The binding energy of a very long molecular chain, composed of different classes of molecules, depends in general on the order of the molecules. It is shown that under very general conditions there exists for a givenbrutto chemical composition of a chain, a class of chains which is characterized by a total binding energy which is equal to the total binding energy of any other prescribed chain of different composition within the limits of unsharpness of the energy level. This establishes a criterion formapping of a class of configurations of long chain molecules on another class. To the extent that a mapping constitutes a generalized code those results contribute to the theory of molecular codes. Applying to our results the results of a previous paper (1959,Bull. Math. Biophysics,21, 309–326), we arrive at the conclusion that the self-replication of a living molecule may be the property not of a particular structure but of classes of structures.
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    On the utilization of food by planktophage fishes (1960)
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    Bulletin of mathematical biology 22 (1960), S. 371-389 
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    Notes: Abstract Making some plausible assumptions about the over-all mechanism of food catching and consumption by fishes and evaluating in the light of those assumptions some available experimental data, it is possible to calculate from those data the variation of several important factors with the concentration of food. The factors considered are: total rate of metabolism, total diurnal energy expenditure in the process of feeding, average number of hours per day during which the fish feeds, average length of path traveled by a fish per day, and the so-called “energetic coefficient of growth.” A possible relation with the work of N. Rashevsky (Bull. Math. Biophysics,20, 299–308, 1959) is discussed.
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    Symposium on Mathematical Theories of Biological Phenomena (1960)
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    Bulletin of mathematical biology 22 (1960), S. 425-425 
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    On the theory of indicator-dilution methods under varying blood-flow conditions (1960)
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    Bulletin of mathematical biology 22 (1960), S. 417-424 
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    Notes: Abstract The theory of measurement of flow and volume by indicator dilution techniques is given in conditions of time-variable flow rates. It is shown that the usual Hamilton (1932,Am. J. Physiol.,99, 534–551) methods can be misleading if the flow changes at a rate of close to that of the transport function.
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    An hypothesis of freese and the DNA-protein coding problem (1961)
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    Bulletin of mathematical biology 23 (1961), S. 305-318 
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    Notes: Abstract Freese’s Hypothesis states that a single specific alteration in the sequence of nucleotides of an information-bearing DNA molecule results in a specific mutational effect. Within the framework of the DNA-protein coding problem developed elsewhere, and assuming the quasi-ergodicity of the general coding process, it is shown that Freese’s Hypothesis allows us to derive expressions for the length of the smallest mutable DNA molecule and to obtain a bound for the maximal number of allelic molecules of fixed length. To illustrate these ideas, calculations are carried out on appropriate data from bacternophage and man, and the results are shown to differ by a factor of 10 (modulo the rather crude approximations used). It is further shown that, if ρ(N) and ϱ(N) are respectively the number of information-bearing words of lengthN in a given code and the number of words of lengthN, then the number lim ρ(N)/ϱ(N) depends sensitively on the parameter ∈ which specifiesN→∞ the given code. The implications of this result for the spontaneous aggregation of a sufficient number of information-bearing words to characterize an organism are discussed.
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    Post-and predoctoral fellowships in mathematical biology (1961)
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    Bulletin of mathematical biology 23 (1961), S. 319-319 
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    The perfect learner (1961)
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    Bulletin of mathematical biology 23 (1961), S. 321-335 
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    Notes: Abstract As a “base line” of memorization performance, the behavior of a “perfect learner” is considered. He is characterized by a perfect memory and by the ability to choose the best search procedure in problems where the correct response from a given repertoire is to be found to each of several stimuli under the condition of “right” and “wroing” promptings by the experimenter. Expected learning curves are derived for the case of disjoint response repertoires associated with the stimuli under cyclic and random presentation of the stimuli and for the case of a single response repertoire (a one-to-one matching problem) under cyclic presentation.
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    A method for the computation of aortic distensibility in the living human patient and its use for the determination of the aortic effects of aging, drugs, and exercise (1961)
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    Bulletin of mathematical biology 23 (1961), S. 337-353 
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    Notes: Abstract Detailed equations are given for the computation of aortic distensibility in the intact living human patient from measurements of systolic and diastolic arterial pressures, heart rate and cardiac output. From these equations, the aortic characteristics of a large series of normal men of different ages were computed. Comparing these results with measurements on excised aortas, a more pronounced trend toward increasing aortic stiffness with increasing age is evident in living than in dead aortas. Nor-epinephrine and exercise apparently cause the living aortas to constrict but to become more distensible. The same change occurs after 30 minutes of high spinal anesthesia. The ganglionic blocking agents hexamethonium, pentamethonium, and tetraethylammonium usually cause the living aorta to become stiffer, presumably due to dilatation. The aortas of patients with pulmonary disease usually react in different fashion to exercise or tetraethylammonium. The increased aortic distensibility that occurs with the hypertension induced by nor-epinephrine or exercise acts as a compensatory mechanism by decreasing systolic pressure.
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    Dimensional analysis in mathematical biology I. General discussion (1961)
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    Bulletin of mathematical biology 23 (1961), S. 355-376 
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    Notes: Abstract Dimensional analysis is discussed from the viewpoint of its basic group properties and shown to be an algebraic Abelian group that is useful for analysis of physical measurements. The application of the method to various types of equations and the formulation of previously unclassified dimensions are discussed. Functional dimensional analysis is applied to the problems of cell size and biomass proliferation; future applications are also noted. A number of dimensionless terms have been formulated for cellular physiochemical phenomena. They apparently represent the first systematic study of biological dimensionless numbers recorded in the literature. A dimensionless proliferation law is suggested. A brief analysis of the physical dimensionality associated with information measures is carried out. Entropy and “information” are shown to be completely different in their dimensional meaning; other informational measures of possible interest in biology are proposed. The dimensional coding and computor analysis of biomathematical equations is suggested.
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    A minimal principle in biomechanics (1961)
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    Bulletin of mathematical biology 23 (1961), S. 377-391 
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    Notes: Abstract Expenditure of energy under several simultaneous forms (mechanical, chemical, etc.) is associated with all muscular activity. The energy is directly related to what is commonly called exertion or effort. This paper defines “muscular effort” quantitatively in terms of some of the elements of the dynamics of the human (and animal) body. It postulates that in all likelihood the individual will, consciously or otherwise, determine his motion (or his posture, if at rest) in such a manner as to reduce his total muscular effort to a minimum consistent with imposed conditions, or “constraints”. The principle, formulated in mathematical terms, is sufficient to ascribe to the moments at all body joints—a matter generally of free choice on the part of the individual—their most likely magnitudes. It therefore renders the equations of human (and animal) motion determinate within this context. The paper also describes briefly an iteration method for the solution of these equations, once they have been made determinate. A simple illustrative application of the principle is included.
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    On the role of chemical systems in the microphysical aspects of primary genetic mechanisms (1961)
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    Bulletin of mathematical biology 23 (1961), S. 393-403 
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    Notes: Abstract It is pointed out that two fundamentally different views of primary genetic processes occur in the literature which are frequently confused. The first is a true communication-theoretic view, which regards the genetic apparatus as containing a real information-source and a transducer which converts that information to useful form. The second view is generally expressed as a template scheme based on the Watson-Crick model; it is shown that in this model there is actually no such thing as genetic information in a communication-theoretic sense. Both views are then discussed on the basis of microphysical principles developed in previous work of the author (Bull. Math. Biophysics,22, 227–255, 1960) in an attempt to find which approach is in closer accord with the biological facts. It is shown that, if the communication-theoretic view is correct, then the information-bearing object must act as a “catalyst,” but it is pointed out that the type of catalysis involved must be of a fundamentally different nature than that occurring in familiar enzyme-catalyzed reactions. On the basis of general considerations of irreversible changes in microphysical measuring systems, it is shown that any type of template must suffer a gradual and irreversible denaturation, which seems to make it unlikely that a template could play a primary role in fundamental genetic processes.
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    On imitative behavior. II. Time course of change from one behavior to another (1961)
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    Bulletin of mathematical biology 23 (1961), S. 405-411 
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    Notes: Abstract The theory developed in previous papers and based on distribution curves of definite form is generalized to any form of unimodel distributions. The time course of the change from one behavior to another is discussed and a general theorem about the time course is established.
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    Abstract mathematical molecular biology (1961)
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    Bulletin of mathematical biology 23 (1961), S. 417-417 
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    Training program in computer use for biomedical scientists (1963)
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    Bulletin of mathematical biology 25 (1963), S. 471-471 
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    Reflexes et centres analyseurs dans les microstructures isotropes (1963)
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    Bulletin of mathematical biology 25 (1963), S. 421-469 
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    Notes: Résumé Nous appliquons le modèle de neurone introduit dans un article antérieur à l’étude d’une microstructure isotrope. La stabilité de cette microstructure implique l’existence d’une régulation d’activité que le principe de construction adéquate permet de définir entièrement. Nous aboutissons à une conception stratifiée du cerveau. Un réseau de neurones spécialisés exercerait, grâce à certains médiateurs chimiques, une action diffuse qui modulerait les propriétés du réseau localisé classique. Les lois de Pavlov peuvent être retrouvées à partir des propriétés de la microstructure et de celles de la régulation. La microstructure isotrope peut également fonctionner comme analyseur. Un certain nombre de temps caractéristiques apparaissent alors, qui semblent jouer un grand rôle en psychologie.
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    Tissue blood flow and the sympathomimetic amines (1964)
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    Bulletin of mathematical biology 26 (1964), S. 1-7 
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    Notes: Abstract In the arteries, blood flow and blood pressure are pulsatile in nature (Roston, 1962a; Roston 1962b). The patterns of blood movement and mural distension in the arteries are important because they may be associated with life-threatening degenerative changes in the arterial walls. As the vascular channels narrow, the pulsation decreases. At the level of the capillaries, almost no pulsation exists (Best and Taylor, 1961). The tissues are affected by the direct flow in the capillaries and not by the pulsation in the arteries. Thus, such quantities as pulse pressure, systolic pressure, and diastolic pressure which characterize blood movement in the arteries are not important as far as the tissues are concerned. Rather, the average pressure and flow in the capillaries are the quantities significant for tissue blood flow. The present study analyzes the local blood circulation in a typical tissue. Logical extension of this analysis results in insights into the physiological behavior of the circulation which integrate a considerable body of experimental data.
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    A multidimensional birth process and its application to some problems in the dynamics of biological populations (1966)
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    Bulletin of mathematical biology 28 (1966), S. 333-345 
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    Notes: Abstract This paper is a sequel to a paper by the author entitled “Restricted Transition Probabilities and Their Applications to Some Problems in the Dynamics of Biological Populations” (Bull. Math. Biophysics, 1966,28, 315–331). The paper is divided into two parts. In part one some aspects of the maximum size attained by the population during a finite time interval are studied for the case the stochastic process underlying the evolution of the population is a birth process. Two interesting by-products emerge from the study presented in part one; namely a combinatorial method of finding solutions to the Kolmogorov differential equations in special cases, and secondly, a set of criteria for the optimum allocation of genotypes in the host population of a host-pathogen system. The optimum allocation of genotypes in the host population is a problem of practical importance in controlling plant pathogens. In part two the theory of restricted transition probabilities developed in the companion paper is applied in finding the distribution of the time to the appearance of the first mutation for the case of a two dimensional birth process. The distribution of the time to the appearance of the first mutation is of importance in understanding the role mutation plays in the evolution of a population, particularly in the pathogen population of a host-pathogen system.
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    The motion of the left ventricle. I (1966)
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    Bulletin of mathematical biology 28 (1966), S. 355-362 
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    Notes: Abstract The complex arrangement of the muscle fibers in the ventricular wall and the nonsymmetric contraction and expansion of the ventricle preclude the writing of a differential equation of motion for the ventricle as a whole. We can, however, describe the motion of the ventricle by describing the motion of the dimensional parameters length and diameter; the radius, circumference, cross-sectional area, and volume following naturally from these. The ventricle is assumed to be an ellipsoid of revolution and the dimensional parameters to be periodic functions of time. Each of the parameters is expressed as a Fourier series.
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    Comparaison des modeles de neurone de Hodgkin-Huxley et de Nelson (1966)
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    Bulletin of mathematical biology 28 (1966), S. 347-354 
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    Notes: Abstract Le modèle de Nelson peut-être considéré comme une approximation du modèle de Hodgkin-Huxley. Moins précis, il est plus maniable. Le modèle de Nelson peut également être considéré comme une généralisation du modèle de Hodgkin-Huxley. En effet, il introduit des liaisons synaptiques localisées ou diffusantes, et un processus de facilitation. Le mécanisme des liaisons synaptiques ne se traduit pas facilement dans le langage de Hodgkin-Huxley. Par contre, le processus de facilitation s'interprète facilement. Nelson's model can be taken as an approximation of Hodgkin-Huxley's model. Its precision is lesser, but it is more usable. Nelson's model can also be taken as a generalization of Hodgkin-Huxley's one; for it introduces localized or diffusing synaptic connexions and a facilitating process. The mechanism of synaptic connexions cannot be easily translated into Hodgkin-Huxley's language. On the contrary, the facilitating process is easily interpreted.
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    The theory of the left ventricular aneurysm (1966)
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    Bulletin of mathematical biology 28 (1966), S. 363-370 
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    Notes: Abstract A spherical model for the human left ventricle with two different types of aneurysms, circular and rectangular-square, is proposed and meaningful relations are derived between the parameters of the aneurysms and ventricle. Such ventricular parameters as stroke volume, end-diastolic volume, and end-systolic volume are given normal human values to compute values for end-systolic radius and percentage shortening of muscle for various sized circular and rectangular-square aneurysms.
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    A note on crime control (1966)
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    Bulletin of mathematical biology 28 (1966), S. 375-378 
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    Notes: Abstract The Volterra theory of two competing populations is extended to the contemporary social problem of crime control. Domains of stability for the time dependence of the numbers in the criminal and enforcement groups are exposed by a numerical example. Both augmentation and reduction of enforcement can produce a stable system. Average values of the ratio of members in each group show great sensitivity to the control policies adopted by the remaining sector of the total population.
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    Interactions in enzymatic reactions (1966)
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    Bulletin of mathematical biology 28 (1966), S. 379-390 
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    Notes: Abstract The paper deals with interactions of substances via an enzymatic reaction (Bull. Math. Biophysics,25, 141–154, 1963). The substances are the activators, inhibitors and/or substrates of the reaction. Due to the bimolecularity of the processes in the reaction, the quantitative relation between the steady state amount of complexes and the amounts of the substances assumes a typical form. In multiple enzymatic reactions this form is more complicated, though basically similar. Because the substances may influence the steady state amounts of the complexes in opposite directions, the compensation and blocking effects are the properties of enzymatic reactions. The substances with the same direction of influence may potentiate each other. In the enzymatic reaction here considered, the potentiation is always non-negative.
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    Decay of cell synchronization: Solutions of the cell-growth equation (1966)
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    Bulletin of mathematical biology 28 (1966), S. 391-409 
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    Notes: Abstract Growth-rate functions in analytic form have been obtained for cell cultures in which the doubling times follow the Gaussian and Poisson distributions. The growth-rate functions are calculated by using Laplace transforms to solve an integral equation previously presented. Oscillatory solutions result if a substantial fraction of the cells in a culture are synchronized to divide at some particular time. The synchrony and, hence, the oscillatory character of the growth-rate function eventually disappear because of the non-zero variance of the doubling-time distribution. If their variances are sufficiently small, the Gaussian and Poisson doubling-time distributions lead to growth-rate functions that become identical in the limit of large time.
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    On the derivation of a mean growth equation for cell cultures (1966)
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    Bulletin of mathematical biology 28 (1966), S. 411-416 
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    Notes: Abstract IfN(t) is the expected number of cells in a culture at timet, $$\dot N(t)$$ the corresponding time derivative, andf(t−τ)dt the probability that a cell of aget−τ at timet will divide in the succeeding time intervaldt, then according to Hirsch and Engelberg (this issue) there obtains the integral equation $$\dot N(t) = 2\int_{ - \infty }^t {f(t - \tau )\dot N(\tau )d\tau }$$ for describing the dynamics of the cell population. It is the purpose of this note to give two alternative derivations of this equation, one based on the age density equation of Von Foerster, and the other based on a generalized form of the Harris-Bellman equation describing the first moment of an age dependent, branching process. In addition, a probability model is posed from which the Von Foerster equation and, hence, the Hirsch-Engelberg equation readily follows.
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    A mathematical theory of enamel solubility and the onset of dental caries: I. The kinetics of dissolution of powdered enamel in acid buffer (1966)
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    Bulletin of mathematical biology 28 (1966), S. 417-432 
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    Notes: Abstract A model of the dissolution kinetics of powdered enamel is developed based on the kinetic rate termq, $$q = K'H - k'C \cdot P_1$$ , whereH=[H +],C=[Ca ++] andP 1=[HPO 4 = ]. The differential equations describing the rate of mineral dissolution (and the linearly related rate of appearance of calcium and phosphate in solution) have been derived and solved for three basic cases: (1) when thepH of the solution and surface area of the enamel are considered constant, (2) when thepH is assumed constant, but the reduction in surface area during dissolution is considered, and (3) when the rise ofpH resulting from the buffering effect of the dissolved enamel is considered along with the change in surface area. Analytical solutions have been obtained for cases (1) and (2), while a numerical solution has been found for case (3). Data from a study on enamel dissolution are presented that agree with the theory of case (3), and it is noted that apH rise as large as 0.5 can occur, as has been shown elsewhere in the literature.
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    Reward and punishment in learning with possible reference to punishment for crime (1966)
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    Bulletin of mathematical biology 28 (1966), S. 477-481 
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    Notes: Abstract On the basis of Landahl's theory of two-choice learning it is shown that application of punishment for wrong responses, without giving award for correct ones, does not lead to complete learning, no matter how many trials are used. If initially a “wrong response” was learned, then an attempt to inhibit it by punishment alone will in a class of cases lead only to a 50% suppression of that wrong response. Possible connection with the problem of effectiveness of punishment as a deterrent for crime is mentioned.
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    The use of two radiotracers for transfer-rate determinations in closed two compartment systems (1966)
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    Bulletin of mathematical biology 28 (1966), S. 483-483 
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    Cooperative specific adsorption of iona at charged sites in an electric field (1966)
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    Bulletin of mathematical biology 28 (1966), S. 483-483 
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    Operations research around the world meetings (1966)
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    Bulletin of mathematical biology 28 (1966), S. 485-485 
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    Dimensional anlaysis and the equations of electrophoresis (1966)
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    Bulletin of mathematical biology 28 (1966), S. 501-510 
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    Notes: Abstract A set of characteristic parameters is given for electrophoresis accompanied by diffusion, followed by a method of simplification of the transport equation. The concept of electrophoretic similarity is introduced in connection with the presentation of solutions and the final section contains some dimensional considerations of the potential equation.
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    Categories of (ℓ, ℛ)-systems (1966)
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    Bulletin of mathematical biology 28 (1966), S. 511-517 
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    Notes: Abstract We show that when we represent (ℓ, ℛ)-systems with fixed genome as automata (sequential machines), we get automata with output-dependent states. This yields a short proof that ((ℓ, ℛ)-systems from a subcategory of automata—and with more homomorphisms than previously exhibited. We show how ((ℓ, ℛ)-systems with variable genetic structure may be represented as automata and use this embedding to set up a larger subcategory of the category of automata. An analogy with dynamical systems is briefly discussed. This paper presents a formal exploration and extension of some of the ideas presented by Rosen (Bull. Math. Biophyss,26, 103–111, 1964;28, 141–148;28 149–151). We refer the reader to these papers, and references cited therein, for a discussion of the relevance of this material to relational biology.
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    The origin of lift forces in fluttering flight (1966)
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    Bulletin of mathematical biology 28 (1966), S. 487-500 
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    Notes: Abstract A two-dimensional nonlinear integro-differential equation with time-varying coefficients describing the behavior of the fluttering wing-body systems typical of natural flight mechanisms has been deduced from the Navier-Stokes equation which generalizes local pressure and velocity distributions in the externally oscillating air field. The resulting equation for the wing forces is combined with an analogous expression for the forces of gravitation and acceleration associated with the body. The air acceleration force, not previously considered in bio-physical models of insect and bird flight, is shown to arise from a formal analysis of unsteady or time-varying contributions to the velocity field, while the square form of the conventional steady state aerodynamic forces is derived from the intertial terms in the Navier-Stokes equation with the aid of the approximations of Newtonian impact theory. Previous calculations (Houghton, 1964) have indicated that the contribution to gravitational stability of air acceleration and aerodynamic life are roughly in the ratio of 3:1.
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    Evoked potentials arising from neural population elements excited at different times on a warped surface (1966)
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    Bulletin of mathematical biology 28 (1966), S. 519-536 
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    Notes: Abstract Certain types of cortical electrical events are non-propagated so that the associated electric fields must have standing wave characteristics. However, cortical electric events typically are generated by neurone populations which cannot be activated simultaneously on impulse driving. Hence the sum of the standing wave fields due to asynchronous activation of adjoining regions of cortical neurones must give the appearance of a traveling wave. Analysis of cortical waveforms is further complicated by curvature in cortical surfaces. A model is presented that shows the effects of curvature and time lag in activation on the form of the potential at points in space around a laminar array of elements simulating a population of cortical neurones. The results are compared with waveforms evoked by single-shock stimulation of the prepyriform cortex in cats.
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    A continuity equation for cell populations (1966)
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    Bulletin of mathematical biology 28 (1966), S. 545-554 
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    Notes: Abstract A continuity equation for cell-number density in a population of cells is derived, and a system of equations for eliminating parameters between the general solution and the initial distribution obtained.
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    The behavior of the weakening and failing myocardium (1966)
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    Bulletin of mathematical biology 28 (1966), S. 537-544 
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    Notes: Abstract Use of an electrical model of the left ventricle of the heart and the arterial system permits analysis of the changes which take place as the capacity of the myocardium for generation of force decreases. The model is simple in structure, and its construction and practical testing would not be difficult. It demonstrates that, as the heart muscle weakens, the peak of intracardiac force occurs later in systole, and the difference between the intracardiac pressure and the aortic pressure in the second half of systole is much greater than for the normal heart. The feedback mechanisms which are proposed to affect myocardial contractility would affect this compensation for cardiac weakening. Indices to categorize the behavior of the normal, compensated though weakened, and decompensated myocardium are proposed.
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    The frequency distribution of chromosome constituents in cells with chromosome-number dispersion (1966)
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    Bulletin of mathematical biology 28 (1966), S. 555-566 
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    Notes: Abstract The frequency distribution in a population of cells of the quantityCD (defined as the amount of some chromosomal substance in a cell which containsC chromosomes) is calculated using the distribution in the population of the amount per chromosome,D, and the distribution of chromosome number,C.
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    Calculation of rate of synthesis of chromosomal DNA in cells with chromosome-number dispersion (1966)
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    Bulletin of mathematical biology 28 (1966), S. 567-574 
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    Notes: Abstract The rate of chromosomal DNA synthesis in an exponentially growing population of cells having chromosome-number dispersion is calculated using DNA histogram data, chromosome-number distribution data, and the assumptions that the synthesis rate is constant and DNA double exactly.
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    Estimation of rate of synthesis of chromosomal DNA in ehrlich ascites tumor cells (1966)
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    Bulletin of mathematical biology 28 (1966), S. 575-584 
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    Notes: Abstract An estimate is made of the rate coefficient for linear DNA synthesis with exact doubling in an exponentially growing population of Ehrlich ascites tumor cells having chromosome-number dispersion. Comparison of calculated and experimental results suggest that the assumptions used in the calculation are tenable, but further experimental evidence is needed to prove this.
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    A sociological approach to biology (1966)
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    Bulletin of mathematical biology 28 (1966), S. 655-661 
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    Notes: Abstract The paper develops further some suggestions made previously (Bulletin of Mathematical Biophysics,28, 283–308, 1966) that certain biological phenomena may be more easily interpreted from a “sociological” point of view by considering the organism as a social aggregate of cells and a cell as a social aggregate of genes. In this light the problems of origin of life on earth, of aging, and of parasitism and symbiosis are discussed. The notion of social aggregates of different orders is introduced.
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    Theorems on random evolution (1966)
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    Bulletin of mathematical biology 28 (1966), S. 663-663 
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    A theoretical and experimental study of the mechanical behavior of the cornea with application to the measurement of intraocular pressure (1966)
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    Bulletin of mathematical biology 28 (1966), S. 585-643 
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    Notes: Abstract A theoretical and experimental study was made of the mechanical behavior of the cornea. The theoretical analysis included an analytical solution for the symmetrical constraint of a thin, shallow, spherical shell by a rigid indenter. The experimental study investigated the rheology of the cornea with particular emphasis on its compliance with the requirements of the Boltzmann Superposition Principle. Representative results of tests on twenty enucleated hog eyes and two human eyes have been reported. The corneas of the human and hog eyes behaved as linear viscoelastic solids; the human eyes differed from the hog eyes in having a long term creep component. Several eyes were tested at the site of procurement, six to seven minutes after the animal's death, and it was established that creep is not an artifact due to aging or enucleation. The analytical and experimental results were combined to study some instruments used to detect the level of pressure in the eye. The theoretical analysis predicted that a type of elastic instability occurs during the process of flattening a small portion of the cornea; this is discussed with reference to the Goldmann and Mackay-Marg tonometers. The role of corneal creep was considered with reference to the response of the Schiøtz indentation tonometer during the time dependent process known as tonography.
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    Further studies on the shape of the tracking curve of an automobile and its dependence on biological parameters of the driver (1966)
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    Bulletin of mathematical biology 28 (1966), S. 645-654 
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    Notes: Abstract Following previous studies, differential equations are established which determine the variation of the stimulus towards a corrective turn of the steering wheel and its effect on the excitation of the centers in the brain which results in the production of the corrective turn. The equations are derived under the highly oversimplified assumption that all excitation thresholds are so small that they can be neglected. Under these assumptions it is found that the tracking curve of a car is a sinusoid with negative damping, that is, with an ever increasing amplitude. Driving under these assumptions is imposible since the car will always eventually jump off the road. The possible effects of the threshold as well as stimuli towards corrective turns other than the distance from the edge of the lane are very briefly discussed. In spite of the negative results of the paper, its interest lies in the circumstance that with the complication of the model, we find that driving depends not only on the reaction times as the only “purely biological” parameter, but on three other neurobiophysical constants. In a subsequent paper (Rashevsky, 1967) it is shown how the introduction of one or more purely biological parameters of the driver makes a stable driving regime possible.
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    The motion of thhe left ventriele: I (1966)
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    Bulletin of mathematical biology 28 (1966), S. 663-663 
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    Bimolecular systems: I. Linear systems of complexes (1967)
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    Bulletin of mathematical biology 29 (1967), S. 1-16 
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    Notes: Abstract A vast number of biologically important processes are based upon bimolecular systems. In these systems intermediate complexes are formed. Bimolecular systems in which no complex-complex interactions occur are called linear systems of complexes. A definition and some characteristic properties of these systems are given here. There may exist a contradiction of Onsager's principle of detailed balancing in these systems; however, no principal differences are found between the steady state behavior of an open system and that of a closed system. It is shown that the steady state behavior of a linear system of complexes of arbitrary complexity has some similarities with the steady state behavior of a simple bimolecular system, e.g., Michaelis-Menten enzymatic reaction. Multiplicity of action of the substances participating in biomolecular processes may produce some qualitative differences in the steady state behavior of the system.
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    DNA histograms of irradiated cells: The case of prophase-trapping (1967)
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    Bulletin of mathematical biology 29 (1967), S. 17-32 
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    Notes: Abstract A time-dependent DNA histogram is calculated for an irradiated population of cells under the limiting assumption that the cells cannot pass through prophase due to the effects of the radiation. The population is assumed to increase exponentially prior to irradiation, but after irradiation to neither gain nor lose cells. Chromosome-number dispersion is taken into account in the calculation. The qualitative behavior of the calculated and experimental histograms are in reasonable agreement. The quantitative agreement between the two is relatively good at short post-irradiation times but is poor at long post-irradiation times (say, greater than half the doubling time). This suggests that recovery phenomena cannot be neglected at long post-irradiation times.
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    A note on the mathematical biology of automobile driving (1967)
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    Bulletin of mathematical biology 29 (1967), S. 187-188 
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    Notes: Abstract It is pointed out that the three different stimuli for a corrective turn, namely the distance from the edge of the lane, the rate of approach to the edge, and the angle between the direction of the car and the direction of the lane (Bull. Math. Biophysics,28, 645–654, 1966,29, 181–186, 1967) may act all three simultaneously. It is found that in that case the tracking curve of the car is stable below a critical speed and becomes unstable above it.
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    Mathematical biology of automobile driving (1967)
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    Bulletin of mathematical biology 29 (1967), S. 181-186 
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    Notes: Abstract Continuing a previous study (Bull. Math. Biophysics, 28, 645–654, 1966), the biophysical mechanism of a corrective turn is investigated for the case where the stimulus for the corrective turn is produced not only by the perception of the nearness of an edge of the lane, but also by the rate of approach of the car towards the edge. In that case it is found that the tracking curve of the car may consist of a series of damped sinusoids and safe driving would be possible at any speed if it were not for the endogenous fluctuation in the driver's central nervous system. If the effect of the rate of approach increases sufficiently rapidly as the distance to the edge of the lane decreases, then a stable undamped oscillating tracking curve is possible. The case is also studied where the driver makes a corrective turn in response to a direct perception of the angle between the direction of the lane and the longitudinal axis of the car.
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    Angles of branching and diameters of branches in the human bronchial tree (1967)
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    Bulletin of mathematical biology 29 (1967), S. 245-259 
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    Notes: Abstract The principle of minimal work requires that the conducting airways of the human lung should have a maximum radius for minimal resistance to gas flow. At the same time there is a requirement that the airways should have a minimal volume for economy of space. These two opposing requirements have been investigated mathematically, and a method for calculating the angle of branching which produces minimal volume has been derived. The relationship of the radii of the parent and daughter branches to produce minimal resistance has been similarly defined. By measurement of a bronchial cast from a human lung the extent to which the predicted optimum structure is realized in practice has been shown. The change in structure associated with change of function at the transition from conducting airway to diffusion zone has been demonstrated.
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    Finite linnaean structures (1967)
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    Bulletin of mathematical biology 29 (1967), S. 191-206 
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    Notes: Abstract This paper considers a class of set-theoretical entities, calledn-rank Linnaean structures, which are intended as abstract models of the taxonomic classificatory systems of biology. In the first part, devoted to formalism, finite Linnaean structures are discussed in complete generality; but, in addition, eight distinct subclasses are noted and some of the properties of their elements are explored. In the second part, concerned with applications, it is shown that taxonomic systems may be recast in the form of finite Linnaean structures, and an effort is made to show that some undesirable features of earlier models are avoided without artificiality and without abandoning extensional mathematics.
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