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  • Articles  (63,038)
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  • Articles  (63,038)
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  • 2000-2004
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  • 1980-1984  (27,850)
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  • 1
    Electronic Resource
    Electronic Resource
    A contribution to the search of general mathematical principles in biology (1958)
    Springer
    Bulletin of mathematical biology 20 (1958), S. 71-93 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A somewhat different approach to the principle of biotopological mapping, discussed in previous publications, is given. The organism is considered as a set of properties, each of which is in its turn a set of numerous subproperties which are logically included in the corresponding properties. Topology is introduced by an appropriate definition of neighborhoods, and four postulates are stated which concern the mapping of the spaces corresponding to higher organisms on those of lower ones. A number of conclusions are drawn from the postulates. Some of them correspond to well-known facts. For example, in man and some higher organisms appropriate emotional stimuli should produce gastrointestinal or cardiovascular disturbances; or some microorganisms should produce substances harmful to other microorganisms (antibiotics). Some other conclusions are still awaiting verification. One of them is, for example, that there must exist unicellular organisms which produce antibodies to appropriate antigens.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476561
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  • 2
    Electronic Resource
    Electronic Resource
    Beitrag zur Theorie der Wirkung Mineralischer Nährstoffe (1958)
    Springer
    Bulletin of mathematical biology 20 (1958), S. 25-32 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Zusammenfassung Für die Praxis der Pflanzenernährung ist es wichtig, zu wissen, in welcher Weise die Ertragsbildung von der Konzentration eines mineralischen Nährstoffes in der Umgebung der Pflanze abhängt. Da nur diejenigen Nährstoffmengen das physiologische Geschehen in der Pflanze unmittelbar zu beeinflussen vermögen, die sich in der Pflanze befinden, wird angenommen, dass das Wachstum zum Zeitpunktt, d.h. die Geschwindigkeit der Trockensubstanzzunahme zu diesem Zeitpunkt, eine Funktion der zur Zeitt in der Pflanze enthaltenen Nährstoffmenge ist. Diese Nährstoffmenge wird natürlich im Intervall vor dem Zeitpunktt aufgenommen. Deshalb und auch noch aus anderen Gründen hängt das Wachstum zur Zeitt davon ab, wie die in der Umgebung der Pflanze herrschende Konzentration des betrachteten Nährstoffes in demjenigen Zeitintervall verläuft, das sich von der Aussaat bis zum Zeitpunktt erstreckt. Die angegebene Annahme fürhrt zusammen mit einigen weiteren naheliegenden Annahmen zu einem Ansatz, der Ergebnisse liefert, die in verschiedener Hinsicht gut mit der Erfahrung übereinstimmen. Jedoch gibt es auch noch Widersprüche zwischen Theorie und Erfahrung. Durch weitere Ausgestaltung der Theorie lassen sich diese Widersprüche beseitigen. Es wird angeregt, Versuche durchzuführen, deren Resultate Hinweise für die weitere Ausgestaltung der Theorie liefern.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476559
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  • 3
    Electronic Resource
    Electronic Resource
    Kinetics of isotope incorporation into the desoxyribonucleic acid (DNA) of tissues: Life span and generation time of cells (1958)
    Springer
    Bulletin of mathematical biology 20 (1958), S. 33-70 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The dynamics of cell multiplication and differentiation in tissues in asteady state and the kinetics of isotope incorporation into the DNA have been theoretically analyzed. Equations have been derived, with the aid of which thegeneration time, thelife span, and the distribution or rate of death of the cells can be obtained if the tissue is in asteady state, i.e., if the number of cells is maintained constant by constant, equal rates of cell division and cell death and if the mean DNA content per cell is also constant. An equation has also been derived which gives thegeneration time in the case of logarithmic multiplication of cells. Two special cases have been analyzed: InCase 1, the isotope is considered as being introduced into the metabolic system at zero time only; inCase 2, the specific activity of the DNA precursor is considered as being maintained constant. The use of the method has been illustrated by an example in which thegeneration time and themean, themedian, and themode life span, as well as the curve of the rate of death of leukocytes in a patient with chronic leukemic granulocytic leukemia, have been obtained from the rate of P32 incorporation into the DNA. The merits and the limitations of the method are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476560
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  • 4
    Electronic Resource
    Electronic Resource
    Announcement by perspectives in biology and medicine (1958)
    Springer
    Bulletin of mathematical biology 20 (1958), S. 95-95 
    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/BF02476562
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  • 5
    Electronic Resource
    Electronic Resource
    Complementary variational principles for diffusion problems with Michaelis-Menten kinetics (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 131-135 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The theory of complementary variational principles is used to obtain maximum and minimum principles for diffusion problems with Michaelis-Menten kinetics. In an illustrative calculation we obtain an extremely accurate variational solution in good agreement with the numerical solution of McElwain (1978).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462371
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  • 6
    Electronic Resource
    Electronic Resource
    Structural order and partial disorder in biological systems (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 137-141 
    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/BF02462372
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  • 7
    Electronic Resource
    Electronic Resource
    Primitivity of the product of two Leslie matrices (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 181-189 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Necessary and sufficient conditions for primitivity of a product of two Leslie matrices are given. Such a product could be used in modeling the growth of a population governed alternately by two different sets of fertility and survival parameters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02464637
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  • 8
    Electronic Resource
    Electronic Resource
    Frequency analysis of time-varying elastance model of the left ventricle (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 173-180 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Zadeh's transfer function method for linear time-variable systems is used to apply frequency-domain analysis to a periodically time-varying elastance model of the left ventricle. Left ventricular pressure computed from the system function of the time-varying elastance and the phasors of aortic flow shows a typical waveform of the measured ventricular pressure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02464636
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  • 9
    Electronic Resource
    Electronic Resource
    The 9th Annual Northeast Biomedical Engineering Conference (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 901-901 
    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/BF02461068
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  • 10
    Electronic Resource
    Electronic Resource
    Fluctuation analysis in small chemically reacting systems (1980)
    Springer
    Bulletin of mathematical biology 42 (1980), S. 147-160 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A theory of noise fluctuations is developed which is applicable to systems of any size in which unimolecular or bimolecular reactions are occurring. The main difference between small and large reacting systems is that in the former the probability of finding a particle in a particular state does not obey a Gaussian distribution, but satisfies a distribution which reflects the mechanism of the chemical reaction. This difference is reflected in the main result of the theory: an autocorrelation function that is expressible as a sum of exponentials, the amplitudes of which are explicit functions of the moments of the distribution. Thus, by using small systems, the autocorrelation function,in principle, allows the elucidation of reaction mechanisms. Numerical simulations indicate that for reacting systems having ten or fewer particles, the deviation of the autocorrelation function from a single exponential should be easily detectable, and that estimates of the first four moments of the distribution should be possible. Accurate inference of the distribution, however, will require further mathematical and experimental advances.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02464634
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