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  • 11
    Electronic Resource
    Electronic Resource
    Mathematical models of conception and birth (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 455-456 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02464621
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  • 12
    Electronic Resource
    Electronic Resource
    Why are there so many species? (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 477-488 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is shown from the statistical-mechanical overview of Volterra's ecological model how to reckon the fluctuations of collective variables such as the total population of a genus: and that these fluctuations are much decreased (or that the collective populationsteadiness is enhanced) as the speciation is increased. (A niching of species in time, or phase-niching, is entailed here.) Secondly, it is shown how Preston's log-normal distribution describing the species-abundance relationship, as well as a generalization of such distributions, come forth simply and naturally from the statistical-Volterra-dynamics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02463261
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  • 13
    Electronic Resource
    Electronic Resource
    The epileptic neuron: II (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 1-16 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Conditions under which a neuron can maintain repetitive discharges are studied with the view that some light may be shed on the problem of epilepsy. It is shown that if there are excitatory and inhibitory substances as well as binding substances in volved, then for repetitive discharges to occur, the formation of the substances must be intracellular. The geometric physical characteristics of the system are also determining factors. The role of a fatigue factor is considered in an attempt to understand the frequency and duration of mild and severe epileptic attacks.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461186
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  • 14
    Electronic Resource
    Electronic Resource
    On the number of phenotype structures in genetic systems (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 325-338 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Phenotype structures in genetic systems are carefully defined in an abstract setting so that a considerable amount of enumerative theory can be brought to bear on the problem of enumerating them. Recent results can be used to simplify the computations, and a natural correspondence is suggested which changes the problem of finding the number of phenotype structures to the problem of determining the numbers of certain graphs with colored points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02461332
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  • 15
    Electronic Resource
    Electronic Resource
    The interaction of diffusion and perfusion in homogeneous tissue (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 505-526 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical model is proposed to examine the interaction between blood perfusion and gas diffusion in the uptake of inert gases in tissue. The standard Haldane perfusion model is contrasted with the Hills radial bulk diffusion model in a variety of homogeneous tissue types used in decompression theory. It is the intention of the present analysis to fix ideas on the role of diffusion, perfusion and axial concentration and quantitative studies are given and seem to show that Haldane's perfusion theory is at best a poor approximation even at asymptotic times. It is shown that a strong interaction exists between diffusion and perfusion in muscle tissue and neither approach adequately describes the actual uptake half-time of an inert gas.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02463263
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  • 16
    Electronic Resource
    Electronic Resource
    Necessary and sufficient condition for a model insect population to go to extinction (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 527-533 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A necessary and sufficient condition on the parameters for a model population to become extinct is presented. The mathematical model describes an insect population with overlapping generations where the females are polyandrous and the males are subject to autosterilization. The relationship between the values of the parameters of the model and the time to extinction is illustrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02463264
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  • 17
    Electronic Resource
    Electronic Resource
    D'Arcy Thompson's theorems and the shape of the molluscan shell (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 567-575 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The paper deals with properties of mathematical models of biological systems. It is shown that under suitable conditions the number of parameters employed in the model depends only on the biological system and not on the particular model chosen. As an application the mathematical description of the formation of molluscan shells is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02463268
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  • 18
    Electronic Resource
    Electronic Resource
    Molecular control systems: I—Temporal organization in cells revisited (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 595-599 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An analysis of Goodwin's fundamental nonlinear oscillator in the light of the requirement that concentrations must be intrinsically non-negative reveals that most of the phase plane is “forbidden”, and that there is one distinguished closed curve that has some of the properties of a limit cycle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02463271
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  • 19
    Electronic Resource
    Electronic Resource
    Note on oscillations of turbidity in a precipitation reaction system of thyroxine (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 601-604 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A model for a precipitation reaction system is presented in which all steps are reversible monomolecular or bimolecular reactions. Under certain conditions, quasi-stable oscillations in turbidity can occur, as has been observed in the precipitation of thyroxine.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02463272
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  • 20
    Electronic Resource
    Electronic Resource
    Stabilité structurelle et morphogénèse (1974)
    Springer
    Bulletin of mathematical biology 36 (1974), S. 611-613 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02463275
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