ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • Springer  (823,867)
  • 1980-1984  (224,281)
  • 1975-1979  (211,911)
  • 1970-1974  (177,357)
  • 1965-1969  (146,830)
  • 1955-1959  (63,488)
Collection
Keywords
Publisher
Years
Year
  • 1
    Electronic Resource
    Electronic Resource
    Contributions to the theory of organismic sets, II: Aggressiveness and submissiveness (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 49-54 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In the theory of organismic sets (Bull. Math. Biophysics,31, 159–198, 1969) we considered organisms as sets endowed with certain “activities,” the latter’s resulting in a set of “products.” Those products may be of a material nature, like a hormone secreted by a cell, or of a non-material nature, like a feeling or an attitude. In the present paper aggressiveness and submissiveness are considered as such non-material products of the activities of the brain cells. A general description of aggressiveness and submissiveness is given in terms of organismic sets. Cycles in “peck order” are thus naturally explained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476664
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Contribution to the theory of organismic sets, III (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 55-66 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In line with previous studies on organismic sets, the division of all organismic sets intogeneral autotrophic and heterotrophic is introduced. The first produce their food themselves from some external source of energy, which in general may be an energy of any kind. The others use other organismic sets as the source of their food and energy. On earth we know only one kind of generalgeneral autotrophic organismic sets, namely, the autotrophic plants which use solar radiation as their source of energy and for production of their own food. It is shown why autotrophic animals do not exist on earth except as microorganisms like, e.g.,Euglena. A rigorous proof of the previously derived theorem that in an organismic set of ordern〉1 no element can be completely specialized is given. It requires the introduction of new postulates. Finally, in considering the organic world as a whole, the notion of organismic sets ofmixed order is introduced.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476665
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    “A stochastic solution of the 3-body problem in chemical kinetics. The termolecular stochastic process I” (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 67-81 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It appears to be axiomatic that termolecular and higher order reactions occur relatively rarely. The basis for this judgment seems to lie in the supposition that successful 3-Body collisions of 3 interactive species of molecules cannot occur frequently enought to account for chemical or biochemical transformation. In order to provide a more complete mathematical framework than now exists for examining this hypothesis the probability of effective termolecular “δ-collisions” as a function of time is derived. This amounts to adding to the class of reactions for which stochastic models are now available the termolecular reaction. In common with the unimolecular and bimolecular cases this process is seen to satisfy the criterion of consistency-in-the-mean with respect to deterministic formulations. It is planned next to use the termolecular process and the lower order processes in computer-assistedin numero experimental studies aimed at comparing alternative mechanisms of reaction.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476666
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Maximum likelihood estimation for stochastic first order reactions (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 83-96 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Small sample properties of the maximum likelihood estimator for the rate constant of a stochastic first order reaction are investigated. The approximate bias and variance of the maximum likelihood estimator are derived and tabulated. If observations of the system are made at timesiτ,i=1, 2, ...,N; τ〉0, the observational spacing τ which minimizes the approximate variance of the maximum likelihood estimator is found. The non-applicability of large sample theory to confidence interval derivation is demonstrated by examination of the relative likelihood. Bartlett’s method is employed to derive approximate confidence limits, and is illustrated by using simulated kinetic runs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476667
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    Organismic supercategories and qualitative dynamics of systems (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 339-354 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The representation of biological systems by means of organismic supercategories, developed in previous papers (Bull. Math. Biophysics,30, 625–636;31, 59–71;32, 539–561), is further discussed. The different approaches to relational biology, developed by Rashevsky, Rosen and by Băianu and Marinescu, are compared with Qualitative Dynamics of Systems which was initiated by Henri Poincaré (1881). On the basis of this comparison some concrete result concerning dynamics of genetic system, development, fertilization, regeneration, analogies, and oncogenesis are derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476778
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    Some realizations of (M, R)-systems and their interpretation (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 303-319 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Some years ago (Rosen 1958a, b; 1959) we described a class of metaphorical, relational paradigms for cellular activity which we termed (M, R)-systems. A sizable amount of subsequent work, to be itemized below, has been devoted to an exploration of some of the properties of these systems. The main purpose of the present paper is to put this class of paradigms into a general system-theoretic perspective, with a particular view to appraising the relation between the type of system description embodied in the (M, R)-system and other kinds of physical and mathematical descriptions of cellular systems. Thus, the principal aim is to establish the relationships and connections between the global relational formalism embodied in the (M, R)-systems and the empirical descriptions which still represent the bulk of our biological knowledge.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476776
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    Relational forces and structures produced by them (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 321-338 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract After giving a brief review of the theory of organismic sets (Bull. Math. Biophysics,29, 139–152, 1967;31, 159–198, 1969), in which the concept of relational forces, introduced earlier (Bull. Math. Biophysics,28, 283–308, 1966a) plays a fundamental role, the author discusses examples of possible different structures produced by relational forces. For biological organisms the different structures found theoretically are in general agreement with observation. For societies, which are also organismic sets as discussed in the above references, the structures can be described only in an abstract space, the nature of which is discussed. Different isomorphisms between anatomical structures, as described in ordinary Euclidean space, and the sociological structures described in an abstract space are noted, as should be expected from the theory of organismic sets.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476777
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    Probabilistic and multiple regression modeling of the biologist’s decision processes and its implications for medical diagnosis (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 439-449 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Current psychological research into the inference (diagnostic) process is briefly reviewed, using as a vehicle an investigation of the prediction of the probability of success of hypothetical applicants to a graduate program in biology. Brunswik’s lens model and multiple regression analysis are used, as is a Bayesian approach. Four judges’ (biologists’) predictions are analyzed. Some general conclusions about inference, drawn from the current data in psychology, are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476785
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    Anin numero study of glucose-insulin interaction (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 451-462 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical model has been developed to simulate the glucose-insulin interaction following a glucose load such as occurs in an IVGTT. This model differs from earlier models in that the insulin response to glucose loading is a recurring all or none threshold response. The model has been simulated on a digital computer using the digital analog simulation language CSMP.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476786
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    Wave propagation in bone media (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 463-479 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The composite nature of bone dictates the use of a model for bone which is transversely isotropic. We solve the associated sets of partial differential equations governing the dynamic elastic behavoor of a two-layered cylindrical-shaped bone. The solution is analyzed for long, short, and intermediate length waves. The special case of compact bone is treated for long and short wave lengths and a numerical example is worked out to determine the wave speeds (for short wave lengths) given a set of elastic constants, determined by ultrasonic methods, and the bone density, wave frequency, and radius.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476787
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 11
    Electronic Resource
    Electronic Resource
    Fourth International Biophysics Congress (1971)
    Springer
    Bulletin of mathematical biology 33 (1971), S. 481-481 
    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/BF02476788
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 12
    Electronic Resource
    Electronic Resource
    Obituary of Nicolas Rashevsky (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. i 
    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/BF02477019
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 13
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 14
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 15
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 16
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 17
    Electronic Resource
    Electronic Resource
    On the stochastic theory of compartments: I. A single-compartment system (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 53-63 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A stochastic model is developed for a compartment with a single time-dependent input, and generalized to include inputs from several sources. With the number of particles of a given molecular species in the compartment as the random variable, the mean, variance and third central moment of this variable are calculated from its generating function, and compared with previous results. The behavior of the calculated moments is discussed, and the possibility of applying the model to chemical and biological systems is considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02477024
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 18
    Electronic Resource
    Electronic Resource
    Mathematical formulation of cardiovascular dynamics by use of the laplace transform (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 1-11 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract By means of the Laplace transform, the behavior of a simplified model of the cardiovascular system is mathematically formulated. This formulation allows mathematical expression of the periodicity of the cardiac output and the systemic response. With the cardiac output represented as half of a sine function cycle, the systolic aortic pressure becomes the sum of a sine term and exponential terms, while the sum of the exponential terms alone represents the diastolic pressure. The characteristics of the mathematical expressions for systole and diastole are analyzed, and some relationships of potentially practical value are derived. Variation in the parameters of the system yields mathematical results consistent with the expected physical ones.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476454
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 19
    Electronic Resource
    Electronic Resource
    A quasi-steady-state approximation method for diffusion problems: I. Concentration dependent diffusion coefficients (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 19-32 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A generalization of Landahl's approximation method (H. D. Landahl,Bull. Math. Biophysics,15, 49–61, 1953) for non-linear diffusion problems is suggested. The method is applied to sorption, desorption, and free diffusion problems involving concentration-dependent diffusion coefficients. With some limitations, the results compare favorably with those obtained by numerical methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476456
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 20
    Electronic Resource
    Electronic Resource
    Multipole representation of an eccentric dipole and an eccentric double-layer (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 33-60 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Recently a theorem for representing current generators in a volume conductor by the superposition of a central dipole, quadrupole, octopole, etc., has been established by G. C. K. Yeh, J. Martinek, and H. de Beaumont (Bull. Math. Biophysics,20, 203–16, 1958). This theorem makes possible the representation of any discrete or line, surface- or volume-distributed current source by a unique model which can be determined for each given case by surface potential measurements and closed form analysis. In this paper the multipole representations of an eccentric dipole and an eccentric double-layer are obtained in terms of the various parameters of the assumed singularities, and the contributions to surface potentials due to each of the multipoles are compared. Certain numerical results corresponding to those of E. Frank (Amer. Heart J.,46, 364–78, 1953) are carried out and compared. Furthermore, the multipole representation of a partially damaged double-layer is also determined and compared with that of an undamaged one. It is concluded that within the range of parameters corresponding to human subjects the higher-order multipoles can contribute significantly to the surface potentials compared with the dipole.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476457
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 21
    Electronic Resource
    Electronic Resource
    A note on topological biology (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 97-100 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In line with a recent suggestion by the author (Bull. Math. Biophysics,20, 267–73, September, 1958) that not only does the organism as a whole map on the primordial, but that each organ can also be thus mapped, it is shown that the previously introduced abstract spaces, which represent an organism, contain subspaces which map continuously on the space of the primordial. Several theorems about those subspaces are proven.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476460
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 22
    Electronic Resource
    Electronic Resource
    The DNA-protein coding problem (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 71-95 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The DNA-protein coding problem is given a general algebraic formulation, the consequences of which are then explored by standard mathematical methods. To keep the treatment self-contained, the mathematical techniques to be used are explained in detail. It is demonstrated that there exista priori a countably infinite number of different abstract DNA-protein codes, thereby showing that inductive attempts to construct such a code will most likely be fruitless. A notion of ergodicity is then introduced, which imposes a number of restrictions on the admissible codes, and, in fact, these considerations enable us toderive a small portion of a code which, if our hypothesis of ergodicity is correct, must occur in nature. Finally, we discuss briefly the problem as to whether there can exist more than one DNA-protein code in nature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476459
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 23
    Electronic Resource
    Electronic Resource
    The inconsistencies of present-day mathematical-physical methods pertaining to current generators in volume conductors used in electrocardiography (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 61-70 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The present-day practices of electrocardiography and vectorardiography are based upon the theory that the surface potential differences can be assumed to be due to a single dipole inside the body. It is shown in this paper that a dipole cannot account for all the surface potentials due to realistic current generators, and hence the determination of the current generator from surface potential measurements based upon such a theory will lead to inconsistent representations of the heart for one and the same subject. To demonstrate this point two eccentric dipoles of different strengths and locations representing two muscle fibers are taken to be the current generator in a homogeneous spherical conductor. The exact surface potentials are then expressed by means of the “interior sphere theorem” of the authors. With these expressions the magnitude, direction, and location of the resultant dipole are determined by the method of D. Gabor and C. V. Nelson (J. App. Physics,25, 413–16, 1954). The surface potentials due to this resultant dipole are again exactly expressed by means of the “interior sphere theorem” and compared with those due to the eccentric dipoles assumed. It can be seen that the differences can be considerable. It is suggested that the multipole model of the authors (Bull. Math. Biophysics,20, 203–16, 1958) be used as a more accurate and the only unique representation of the heart.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476458
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 24
    Electronic Resource
    Electronic Resource
    A set-theoretical approach to biology (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 101-106 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In a preceding paper (Bull. Math. Biophysics 20, 71–93, 1958) the principle of biotopological mapping was formulated in terms of a continuous mapping of an abstract space, made from the set of biological properties which characterize the organism, by an appropriate definition of neighborhoods. In this paper it is shown that we may consider directly the mappings of the different sets of properties which characterize different organisms without taking recourse to abstract spaces. All the verificable conclusions made in the preceding paper remain valid. A serious difficulty mentioned previously is, however, avoided and the possibility of more general predictions is established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476461
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 25
    Electronic Resource
    Electronic Resource
    Statistical research monographs (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 107-107 
    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/BF02476462
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 26
    Electronic Resource
    Electronic Resource
    A relational theory of biological systems II (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 109-128 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The general Theory of Categories is applied to the study of the (M, R)-systems previously defined. A set of axioms is provided which characterize “abstract (M, R)-systems”, defined in terms of the Theory of Categories. It is shown that the replication of the repair components of these systems may be accounted for in a natural way within this framework, thereby obviating the need for anad hoc postulation of a replication mechanism. A time-lag structure is introduced into these abstract (M, R)-systems. In order to apply this structure to a discussion of the “morphology” of these systems, it is necessary to make certain assumptions which relate the morphology to the time lags. By so doing, a system of abstract biology is in effect constructed. In particular, a formulation of a general Principle of Optimal Design is proposed for these systems. It is shown under what conditions the repair mechanism of the system will be localized into a spherical region, suggestive of the nuclear arrangements in cells. The possibility of placing an abstract (M, R)-system into optimal form in more than one way is then investigated, and a necessary and sufficient condition for this occurrence is obtained. Some further implications of the above assumptions are then discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476354
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 27
    Electronic Resource
    Electronic Resource
    A note on the transient stage of the random dispersal of logistic populations (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 141-151 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The transient stage of the random dispersal of logistic populations is investigated, using a Sturm-Liouville series leading to an infinite system of non-linear integral equations. These equations are then solved via a successive approximation scheme. R. A. Fisher's (steady-state) velocity of advance paradox is discussed. An illustrative example is worked to the second order of approximation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476356
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 28
    Electronic Resource
    Electronic Resource
    A note on population growth under random dispersal (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 153-159 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An approximation method using a sine function is used to solve the second degree growth equation for the case in which an organism may simultaneously become dispersed throughout a uniform region. The resulting expression for a special case is compared with the expression obtained by R. Barakat (1959,Bull. Math. Biophysics,21, 141–51), giving the first two terms, by an iterative, procedure. The agreement is satisfactory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476357
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 29
    Electronic Resource
    Electronic Resource
    A contribution to the study of diffusion of neutral particles through pores (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 129-140 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Diffusion through a flat pore into a large open region is proportional to the linear dimension of the pore and not to its area. This was first explained by Brown and Escombe (1900) for a circular pore and is here generalized, by means of a dimensional argument, to include any type of regular opening. The problem is further generalized to include diffusion through pores of finite thickness, finite distance apart, and into finite regions. Since this problem cannot be solved exactly, an approximation method is introduced. Reasons for the credibility of the approximation are presented. It is then shown, by means of the approximation method, that the diffusive flow through a pore is equal to the total concentration difference divided by the resistance of the system. The resistance, in turn, is the sum of the resistances of all portions of the system, each of which is calculated. The result is compared with results which have been calculated exactly for limiting cases and found to agree very well. The results are then applied to a standard method of computing pore size in membranes, and it is shown that the correction factor is negligible.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476355
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 30
    Electronic Resource
    Electronic Resource
    Some remarks on the mathematical theory of nutrition of fishes (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 161-183 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract V. S. Ivlev [Experimental Ecology of Nutrition of Fishes, 1955, Moscow (in Russia)] has shown that the food uptake by fishes during a fixed interval of time is an exponential function of the concentration of food. Ivlev's equation is derived here, and it is shown that it can hold only for non-stationary conditions, such as prevailed in Ivlev's experiments. For a stationary state, the rate of food uptake should tend asymptotically to a limiting value as the concentration increases, but the variation is not exponential. Different other aspects of the problem are investigated, and definite new experimental procedures suggested. The implications of Ivlev's findings on the effect of non-uniformity of food distribution upon the rate of food consumption are studied from a mathematical point of view. The conclusion is reached that whereas a fish does not, in the process of eating, move directly to an individual food particle which it perceives, it does move more or less directly to large aggregates of particles, if the latter are distributed nonuniformly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476358
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 31
    Electronic Resource
    Electronic Resource
    A note on the nature and origin of life (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 185-193 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Some relational aspects of the property of self-reproduction of biological systems are studied. If in addition to the requirement of the property of self-reproduction we add also the requirement of adaptability of the organism to changing environment, this imposes certain conditions on the topology of the graphs which represent such systems. A further study of the relational properties of such systems seems to offer the possibility of deriving the principle of biological mapping from the requirement of self-reproduction and adaptability. An examination of the problem of the original formation of such self-reproducing systems in connection with the established fact of impossibility of spontaneous generation leads to the conclusion that an organism must inhibit such processes which, in the absence of organisms, would lead to spontaneous generation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476359
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 32
    Electronic Resource
    Electronic Resource
    Feedback in physiological systems: An application of feedback analysis and stochastic models to neurophysiology (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 195-216 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In the human, the antagonistic, extensor-flexor system of the leg is an example of a common type of neurophysiological feedback system. After a brief introduction to the neuroanatomy and physiology of this feedback system, the paper formulates transfer functions from temporal response data available in the literature. A feedback stability analysis, based on the extension of Nyquist's stability criteria to multiple-loop systems and utilizing flow-graph techniques, demonstrates the stable behavior of the system. Expressions are given relating the sensitivity of the system to variations in muscle response and Golgi tendon organ (tension receptor) response. By considering the events taking place at synapses and end-plates during “isometric tension-small knee angle excursion” conditions as stationary stochastic processes, an external “noise” input to the system is given, whose spectrum is derived from the statistics of a shot-process representation of these events. The paper concludes with some correlations between the analytical results and clinical syndromes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476360
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 33
    Electronic Resource
    Electronic Resource
    Further considerations on the statistical mechanics of biological associations (1959)
    Springer
    Bulletin of mathematical biology 21 (1959), S. 217-255 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this continuation of a previous report it is shown how the Volterra population dynamics, which underlies the statistical theory, can be based on a variational principle; how the dynamics can be generalized as regards both the behavior of total populations and migration phenomena; and how many directly observable data, such as amplitudes and frequencies of oscillation of a population, fit into the statistical theory and can test it. Such a test is carried out in some detail using the fox-catch data of Elton, with a clear indication that the theory is capable of comprehending the major statistical properties of population-time curves. A final section sketches an extension of the theory to cover secular variations of external conditions such as temperature of the environment.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476361
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 34
    Electronic Resource
    Electronic Resource
    A remark on sensory deprivation from the point of view of organismic sets (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 439-441 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is shown that from the definition of organismic sets (Rashevsky,Organismic Sets. Some Reflections on the Nature of Life and Society, Holland, Michigan, Mathematical Biology, Inc. and Grosse Pointe, Michigan, J. M. Richards Laboratory) a complete sensory deprivation of an organismic set of ordern=2 should result in malfunctioning of the set. A generalization to higher order sets is suggested.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476706
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 35
    Electronic Resource
    Electronic Resource
    Optimal branching structure of the vascular tree (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 431-438 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Optimality in branching structure of the vascular tree was studied. Analysis on its physiological roles as the duct system for blood supply to the capillaries predicted that the vascular tree should be constructed with minimum volume under restriction of determinant pressure, flow and location at the origin and the terminals. Mathematical derivations of this conditional extremum problem yielded some equations expressing the relations between the radii of the branches and their branching angles, which provided numerical solutions for branching points of bi- and poli-terminal minimum volume trees. Comparison of the peritoneal vascular tree in a dog with the minimum volume one computed under the same restrictive conditions showed good agreement in their branching structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476705
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 36
    Electronic Resource
    Electronic Resource
    First order kinetics in a distributed model (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 443-456 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In order to determine the kinetics of passage of a substance through an organ containing a tangle of vessels, we study the response of a tube to various inflows (perfusion, brief injection, ...). The introduction of the catabolic terms and of the spatial dependence between bulk concentration and surface concentration allows one to account for the difference of arteriovenous concentrations observed experimentally for many metabolites. The relationships between the physico-chemical parameters of the organ and the operational parameters of the model demonstrate the importance of the transit time through the considered vessels. If one considers the different pathways as independent, the introduction of the transit time distribution for an inert substance enables one to compute the response of the organ analytically or by recurrence, using convolution. The parameters of the model can be obtained by the moments method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476707
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 37
    Electronic Resource
    Electronic Resource
    Stochastic simulation of the gas diffusion in the air phase of the human lung (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 457-466 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The solution of the diffusion equation in the gas phase of the human lung is very difficult because of the structure of the bronchial tree. It is shown by means of physical arguments, how one can reduce the diffusion equation to a simple one-dimensional form. The solution is then obtained by a stochastic simulation, which is easily realized on a digital computer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476708
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 38
    Electronic Resource
    Electronic Resource
    A new mathematical model of the respiratory center (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 467-481 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A new mathematical model of the oscillatory behavior of the respiratory center has been developed based upon published records of neuronal activity during respiration in the pons and medulla. In contrast with a previous model, four, rather than two, networks are assumed to interact in the respiratory center so as to produce the respiratory oscillation. A mathematical description of this interaction, in the form of a set of four first-order, nonlinear, coupled differential equations, is derived; the behavior of the solutions of this system is studied qualitatively, and expressions for the durations of the inspiratory and expiratory phases are obtained in terms of some parameters. It is found that central and chemical influences drive the medullar neurons to a position somewhere between saturation and full cutoff, and the pontine neurons deeply into cutoff. The control of the duration of the different phases by these chemical and central means is discussed. In order to effect a decrease in the magnitude of the various times, the neurons have to be driven towards operating points of higher central facilitation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476709
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 39
    Electronic Resource
    Electronic Resource
    A mathematical model for calcium homeostasis (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 483-502 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In vivo control of calcium is analysed under the assumption that hormonal influences via plasma levels of parathormone and calcitonin are of prime (but not absolutely dominating) importance. A brief review concerning the physiological significance of body calcium and the mode of action of these two hormones is presented as an introduction to the basic philosophy of the study. A theoretical quasi-linear lumped-parameter model is developed to describe variations in ionic calcium, parathormone and calcitonin plasma concentrations to specific input stimuli. Formal evaluation of the system response requires the determination of ten constants, together with quantitation of ingested calcium entry into the plasma compartment which isindependent of hormonal influences. Values for various parameters are deduced from published data and experimental procedures are outlined to facilitate determination of the remaining unknowns. It is suggested that the proposed model should prove useful for investigations concerning general hormonal actions on calcium homeostatic mechanisms in both normal and diseased states, with particular reference to calcitonin.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476710
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 40
    Electronic Resource
    Electronic Resource
    The struggle for life: III. A predator-prey chain (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 521-532 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Ann species predator-prey chain is analyzed to determine what oscillations occur in population sizes. It is found that only the populations of the first and second species in the chain must necessarily oscillate around the point of equilibrium if they do not come to equilibrium. The other species may or may not oscillate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476712
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 41
    Electronic Resource
    Electronic Resource
    Mathematical models for exchange of substances in regional vascular beds— Measurement of the rates within vivo counters (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 503-520 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Sangren and Sheppard developed a mathematical model for first-order processes taking place in the regional circulation, applicable—for example—to tracer studies of potassium transport. It permits calculation of specific activity at any point along a “tube of flow” or in the cuff of tissue surrounding it as a function of time following a spike injection of tracer. In efforts to relate to the exchange a rate curves obtained within vivo counters pointed at the region of interest, we developed a compartment-system model of the process. In investigating the properties of the Sangren and Sheppard model integrated over an entire circulatory bed, as thein vivo counter would see it, we found that when the distribution of transit times of the “tubes of flow” can be approximated by an exponential sum, the solution reduces to that of the compartment system model. This results in an important simplification in the calculation, and insight into the assumptions underlying the two different models. A curve-fitting computer program for the compartment model has been written and applied to double-isotope studies of potassium transport in the hind leg of the dog.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476711
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 42
    Electronic Resource
    Electronic Resource
    A numerical experiment on the determination of kinetic rate constants in the presence of diffusion (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 547-558 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Two chemicals,A andB, are allowed to diffuse together and a reaction described by $$A + B\mathop \rightleftharpoons \limits_{K_{ - 1} }^{K_1 } C$$ is allowed to proceed. This system is described mathematically by a system of partial differential equations. A numerical procedure is presented to find the rate constants ofK 1 andK −1. A systematic analysis of the effects of errors is also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476714
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 43
    Electronic Resource
    Electronic Resource
    Observations on cardiac energetics: I. Theoretical introduction (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 533-546 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Equations are developed to describe the energy expenditure of the human heart. As well as the external potential and kinetic energy terms, general consideration is given to other possible avenues of energy consumption. Emphasis is placed upon using mathematical variables which are readily available for experimental verification. The errors involved in assuming that mean values for the physiological parameters give reasonable estimations for the external mechanical performance are examined, and a theoretical estimation for the discrepancy in the kinetic component is presented. Logical extension of the mathematical derivation leads to a determination of cardiac external mechanical efficiency and clearly demonstrates the significance of the ventricular pressure-volume loop in this context. Finally, experimental procedures are suggested to clarify further some of the conclusions reached through the theoretical analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476713
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 44
    Electronic Resource
    Electronic Resource
    Organismic sets. Sex in animal and human societies (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 559-563 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The question is discussed as to the reason why some animal societies, such as bees or ants, are sexually differentiated, that is, onlysome of its members are exhibiting reproducing activities. It is indicated that human society may be on its way to such a sexual differentiation which may eventually come.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476715
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 45
    Electronic Resource
    Electronic Resource
    Some biochemical threshold mechanisms (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 565-565 
    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/BF02476716
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 46
    Electronic Resource
    Electronic Resource
    Announcement (1972)
    Springer
    Bulletin of mathematical biology 34 (1972), S. 567-567 
    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/BF02476717
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 47
    Electronic Resource
    Electronic Resource
    The structure of DNA as deduced from fiber X-ray crystallography (1973)
    Springer
    Bulletin of mathematical biology 35 (1973), S. 301-311 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract X-ray diffraction patterns obtained experimentally for fibers, together with their chemical structures, can be analyzed theoretically in terms of an integral equation. The partially unknown electron density function can be solved by iteration. This mathematical technique has been applied with success to study the secondary structures of DNA fibers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02458338
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 48
    Electronic Resource
    Electronic Resource
    Comment on biomass diversity in ecology (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 967-969 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is observed that a dynamical continuity equation for biomass distribution yields the asymptotic steady-state exponential dependencen=A exp( $$ - m/\bar m$$ ) exhibited by certain fishery data, wherem is the biomass of an individual,n is the number of individuals per unit biomass interval, andA, $$\bar m$$ are positive constants. This dynamical approach to biomass distribution is an alternative to the global maximization principle proposed recently by Lurié and Wagensberg.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462083
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 49
    Electronic Resource
    Electronic Resource
    Physik der Selbstorganization und Evolution (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 971-972 
    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/BF02462084
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 50
    Electronic Resource
    Electronic Resource
    Announcements (1984)
    Springer
    Bulletin of mathematical biology 46 (1984), S. 973-974 
    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/BF02462085
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 51
    Electronic Resource
    Electronic Resource
    Modeling of biological tree structures (1979)
    Springer
    Bulletin of mathematical biology 41 (1979), S. 893-898 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Biological tree-like structures, such as mammalian tracheobronchial airways, are complicated branching systems. One problem in modeling such systems is the reassignment of the number of segments at a given generation in the model being constructed. A hypothesis is proposed which has successfully been used in modeling mammalian lung airways.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462385
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 52
    Electronic Resource
    Electronic Resource
    A multidimensional birth process and its application to some problems in the dynamics of biological populations (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 333-345 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476814
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 53
    Electronic Resource
    Electronic Resource
    The motion of the left ventricle. I (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 355-362 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476816
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 54
    Electronic Resource
    Electronic Resource
    Comparaison des modeles de neurone de Hodgkin-Huxley et de Nelson (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 347-354 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476815
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 55
    Electronic Resource
    Electronic Resource
    The theory of the left ventricular aneurysm (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 363-370 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476817
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 56
    Electronic Resource
    Electronic Resource
    A note on crime control (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 375-378 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476819
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 57
    Electronic Resource
    Electronic Resource
    Interactions in enzymatic reactions (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 379-390 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476820
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 58
    Electronic Resource
    Electronic Resource
    Decay of cell synchronization: Solutions of the cell-growth equation (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 391-409 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476821
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 59
    Electronic Resource
    Electronic Resource
    On the derivation of a mean growth equation for cell cultures (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 411-416 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476822
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 60
    Electronic Resource
    Electronic Resource
    A mathematical theory of enamel solubility and the onset of dental caries: I. The kinetics of dissolution of powdered enamel in acid buffer (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 417-432 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476823
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 61
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 62
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 63
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 64
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 65
    Electronic Resource
    Electronic Resource
    Reward and punishment in learning with possible reference to punishment for crime (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 477-481 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476827
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 66
    Electronic Resource
    Electronic Resource
    The use of two radiotracers for transfer-rate determinations in closed two compartment systems (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 483-483 
    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/BF02476828
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 67
    Electronic Resource
    Electronic Resource
    Cooperative specific adsorption of iona at charged sites in an electric field (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 483-483 
    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/BF02476829
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 68
    Electronic Resource
    Electronic Resource
    Operations research around the world meetings (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 485-485 
    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/BF02476830
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 69
    Electronic Resource
    Electronic Resource
    Dimensional anlaysis and the equations of electrophoresis (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 501-510 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476857
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 70
    Electronic Resource
    Electronic Resource
    Categories of (ℓ, ℛ)-systems (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 511-517 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476858
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 71
    Electronic Resource
    Electronic Resource
    The origin of lift forces in fluttering flight (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 487-500 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476856
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 72
    Electronic Resource
    Electronic Resource
    Evoked potentials arising from neural population elements excited at different times on a warped surface (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 519-536 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476859
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 73
    Electronic Resource
    Electronic Resource
    A continuity equation for cell populations (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 545-554 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476861
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 74
    Electronic Resource
    Electronic Resource
    The behavior of the weakening and failing myocardium (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 537-544 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476860
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 75
    Electronic Resource
    Electronic Resource
    The frequency distribution of chromosome constituents in cells with chromosome-number dispersion (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 555-566 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476862
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 76
    Electronic Resource
    Electronic Resource
    Calculation of rate of synthesis of chromosomal DNA in cells with chromosome-number dispersion (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 567-574 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476863
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 77
    Electronic Resource
    Electronic Resource
    Estimation of rate of synthesis of chromosomal DNA in ehrlich ascites tumor cells (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 575-584 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476864
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 78
    Electronic Resource
    Electronic Resource
    A sociological approach to biology (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 655-661 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476867
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 79
    Electronic Resource
    Electronic Resource
    Theorems on random evolution (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 663-663 
    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/BF02476868
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 80
    Electronic Resource
    Electronic Resource
    A theoretical and experimental study of the mechanical behavior of the cornea with application to the measurement of intraocular pressure (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 585-643 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476865
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 81
    Electronic Resource
    Electronic Resource
    Further studies on the shape of the tracking curve of an automobile and its dependence on biological parameters of the driver (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 645-654 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476866
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 82
    Electronic Resource
    Electronic Resource
    The motion of thhe left ventriele: I (1966)
    Springer
    Bulletin of mathematical biology 28 (1966), S. 663-663 
    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/BF02476869
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 83
    Electronic Resource
    Electronic Resource
    Bimolecular systems: I. Linear systems of complexes (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 1-16 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476958
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 84
    Electronic Resource
    Electronic Resource
    DNA histograms of irradiated cells: The case of prophase-trapping (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 17-32 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476959
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 85
    Electronic Resource
    Electronic Resource
    A note on the mathematical biology of automobile driving (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 187-188 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476971
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 86
    Electronic Resource
    Electronic Resource
    Mathematical biology of automobile driving (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 181-186 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476970
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 87
    Electronic Resource
    Electronic Resource
    Angles of branching and diameters of branches in the human bronchial tree (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 245-259 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476898
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 88
    Electronic Resource
    Electronic Resource
    Finite linnaean structures (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 191-206 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476893
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 89
    Electronic Resource
    Electronic Resource
    Abstract power structures (APS) and related bumping orders (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 207-216 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Generalizing an idea of M. Richardson (Fundamentals of Mathematics, New York: Macmillan Co., 1958), an APS on a given populationP is a non-empty collection of non-empty subsets ofP such that ifA is in the collection andA⊆B, thenB is in the collection. From a structure of this kind a partial ordering ofP, called therelated bumping order, is derived. The question is raised as to what kinds of partial orderings can be so obtained. For structures determined by voting weights of the members of the population, a complete characterization of all possible bumping orders is obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476894
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 90
    Electronic Resource
    Electronic Resource
    Stability analysis of a mathematical neuron model (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 217-226 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The “second method” of Liapunov is used to perform a stability analysis of a mathematical model of the neuron. This analysis is based on the hypothesis that the firing of the neuron coincides with a temporary state of instability of the system, and that the initiation of all-or-none process depends on the magnitude of membrane depolarization and its first time derivative. It is found that the stability (and hence the possibility of a second firing) is restored approximately when the rate of membrane repolarization is at a maximum. This result predicts that the duration of the period of absolute refractoriness in neurons would be about 75 per cent of the spike duration, and thus shorter than the value usually obtained from experimental measurements.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476895
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 91
    Electronic Resource
    Electronic Resource
    A neural net model for masking phenomena (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 227-232 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Some aspects of masking phenomena are considered in terms of the simplest possible model of two-factor neural elements. The effect of a number of variables can be accounted for, but the introduction of an internuncial element results in a masking function which need not be symmetric about zero delay interval. As an illustration, the results for a special case are compared with available data. In general, such a model results in a masking function which depends on the intensity, area, and duration of the stimuli, as well as on the temporal and spatial separation between them.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476896
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 92
    Electronic Resource
    Electronic Resource
    The struggle for life: I. Two species (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 377-388 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The general equations are discussed describing two species in competition or in symbiosis or feeding one on the other.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476909
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 93
    Electronic Resource
    Electronic Resource
    A note on Rashevsky’s postulate of relational forces (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 403-404 
    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/BF02476912
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 94
    Electronic Resource
    Electronic Resource
    Organismic sets and biological epimorphism (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 389-393 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract It is shown that the principle of biological epimorphism (Rashevsky,Mathematical Principles in Biology and Their Applications, Springfield, Ill.: Charles Thomas, 1960) is contained in the theory of organismic sets (Bull. Math. Biophysics,29, 139–152, 1967) if an additional postulate not directly connected to mappings is made.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476910
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 95
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 96
    Electronic Resource
    Electronic Resource
    Out-of-print volumes and back issues of the Bulletin of Mathematical Biophysics (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 407-407 
    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/BF02476914
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 97
    Electronic Resource
    Electronic Resource
    Model of urethra under uniform circumferential tension (1967)
    Springer
    Bulletin of mathematical biology 29 (1967), S. 409-409 
    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/BF02476915
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 98
    Electronic Resource
    Electronic Resource
    Multibreath tracer species dynamics in the lung (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 1-19 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract By studying the behavior of various tracer species in the lungs, one can assess many important characteristics which distinguish normal and abnormal function. Quantitative evaluation of function depends on the use of an appropriate model in conjunction with experimental data. A multi-compartment model is derived from mass balances to describe dynamic as well as (breath-averaged) steady-state transport processes between the environment and pulmonary capillary blood. The breathing cycle is divided into three time periods (inspiration, expiration, and pause) so that the model equations are discrete in time. No other model of tracer species transport in the lungs deals simultaneously with species dynamics, variable breathing pattern, distribution inhomogeneities, and non-equilibrium between alveolar gas and capillary blood. Models currently in the literature are shown to be special cases of the model presented here.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460935
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 99
    Electronic Resource
    Electronic Resource
    Global stability of population models (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 47-58 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Local stability seems to imply global stability for population models. To investigate this claim, we formally define apopulation model. This definition seems to include the one-dimensional discrete models now in use. We derive a necessary and sufficient condition for the global stability of our defined class of models. We derive an easily testable sufficient condition for local stability to imply global stability. We also show that if a discrete model is majorized by one of these stable population models, then the discrete model is globally stable. We demonstrate the utility of these theorems by using them to prove that the regions of local and global stability coincide for six models from the literature. We close by arguing that these theorems give a method for demonstrating global stability that is simpler and easier to apply than the usual method of Liapunov functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02460938
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 100
    Electronic Resource
    Electronic Resource
    The logistic equation with a diffusionally coupled delay (1981)
    Springer
    Bulletin of mathematical biology 43 (1981), S. 125-140 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The asymptotic behaviour of a logistic equation with diffusion on a bounded region and a diffusionally coupled delay is investigated. An equivelent parabolic system is derived for certain types of delays. Using a Layapunov functional, sufficient conditions for the global asymptotic stability of the constant steady state are obtained. When the global stability is lost, using Hopf's bifurcation theory, existence of travelling waves is shown for ring-like and periodic one dimensional habitats.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459438
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...