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  • Springer  (45.561)
  • American Meteorological Society
  • 1990-1994
  • 1965-1969  (32.719)
  • 1950-1954  (13.748)
  • 1995
  • 1968  (32.719)
  • 1953  (8.024)
  • 1950  (5.724)
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Verlag/Herausgeber
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  • 1990-1994
  • 1965-1969  (32.719)
  • 1950-1954  (13.748)
  • 1995-1999  (72.282)
Jahr
  • 1
    Digitale Medien
    Digitale Medien
    Random walk with persistence and external bias (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 311-338 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The partial differential equation of the random walk problem with persistence of direction and external bias is derived. By persistence of direction or internal bias we mean that the probability a particle will travel in a given direction need not be the same for all directions, but depends solely upon the particle's previous direction of motion. The external bias arises from an anisotropy of the medium or an external force on the particle. The problem is treated by considering that the net displacement of a particle arises from two factors, namely, that neither the probability of the particle traveling in any direction after turning nor the distance the particle travels in a given direction need be the same for all directions. A modified Fokker-Planck equation is first obtained using the assumptions that the particles have a distribution of travel times and speeds and that the average time of travel between turns need not be zero. The fional equation incopporating the assumption of a persistence of direction and an external bias is then derived. Applications to the study of diffusion and to long-chain polymers are then made.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476407
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  • 2
    Digitale Medien
    Digitale Medien
    Methods of statistical analysis (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 383-383 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476411
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  • 3
    Digitale Medien
    Digitale Medien
    The transmission of excitation from the membrane to actomyosin (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 385-385 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476412
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  • 4
    Digitale Medien
    Digitale Medien
    On the spread of information with time and distance (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 367-381 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The transmission of some information or behavior pattern is treated as a flow of “particles” which execute random motions over a population of individuals and which may multiply or disappear. Equations are derived for the number density of these “particles” and from this is calculated the number of individuals through which the “particles” have passed. The results are applied to a number of situations such as 1) uniform spatial distribution with multiplication factor decreasing with time because of loss of interest or confusion of the information, 2) multiplication factor constant but the rate of spreal decreasing with multiple hearings, 3) one-dimensional region with a small starting region with or without an absorbing barrier 4) two-dimensional region with absorbing barrier, 5) continous sources of information within a small region in one dimension, 6) uniform spatial distribution in which individuals do not respond to more than one hearing.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476410
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  • 5
    Digitale Medien
    Digitale Medien
    A mathematical derivation of the exchange of a labeled substance between a liquid flowing in a vessel and an external compartment (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 387-394 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A situation is considered in which a fluid containing a substance flows through a vessel at a constant rate, the substance being permeable to the vessel wall. In the region outside the vessel there is supposed to be rapid mixing in the direction perpendicular to the axis of the vessel but no mixing longitudinally. The solution for the spatial distribution at any time is given for the case of an arbitrary initial distribution along the vessel length in the absence of an input. The solution is also given for the case of a single impulsive input, the concentration being initially zero everywhere.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476432
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  • 6
    Digitale Medien
    Digitale Medien
    A mathematical contribution to the study of orientation of organisms (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 431-476 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Organisms orient themselves to a stimulus by two general methods. One method is by directed orientation (taxis); the other is by undirected locomotory reaction (kinesis). An equation, and the methods for finding the necessary parameters of this equation, is derived for the distribution of organisms within a container, with the following limitations: (1) the organisms have no accommodation, (2) they are always active, and (3) the stimulus changes slowly with position. Necessary modifications of the equation are then derived, so that the last two limitations may be eliminated. The equation cannot be solved excatly because of its complexity; hence an approximation method must be used. This method is discussed, an approximate solution is found, and a time constant for equilibrium to be established is derived. Applications tovarious experiments in the literature are then made with fairly satisfactory results. A new interpretation of the theory of klino-kinesis with accommodation is found upon application of the equations developed to experimental work. Further limitations and uses of these equations are then discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476435
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  • 7
    Digitale Medien
    Digitale Medien
    Structural parameters of communication networks (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 501-507 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Certain parameters are defined which roughly characterize the internal structure of networks. A given network structure uniquely determines the values of the parameters, but the reverse is not true. The parameters therefore define certain classes of networks. One of the parameters, thedispersion D(S) gives an indication of the “compactness” of the internal structure. Addition theorems and inequalities are derived relating the dispersions of sub-systems to the dispersion of the complete structure.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476438
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  • 8
    Digitale Medien
    Digitale Medien
    Determination of diffusion and permeability coefficients in nerve trunks (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 489-500 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A mathematical theory is developed which permits the determination of certain parameters of an inhomogenous tissue, such as a nerve trunk without its epineurium. The parameters are the permeability coefficients for entrance into an exit of a substance from the nerve fibers, and the diffusion coefficient of the interstitial material. The experimental data required are the dimensions of the cross-section, the average diameter of the fibers, and the ratio of the cross-sectional are of the fibers to the total cross-section, as well as the time course of the decrease of the fraction of the substance left in the nerve trunk, when the trunk is immersed in a bathing solution containing none of it.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476437
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  • 9
    Digitale Medien
    Digitale Medien
    Enzyme localization as a mechanism of apparent active transport (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 509-522 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A model based on enzyme localization is developed which gives rise to an apparent active transport of a metabolite into or out of cells. The model is applied to three simple situations, using Fick's equation and the Rashevsky approximation. It is shown that the apparent efficiency can be made as large as desired if, for constant reaction, the outer cell region is made sufficiently small, or, for autocatalytic reaction, if the metabolite concentration in the outer region is sufficiently small. The physical limitations imposed by this mechanism are developed for all three situations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476439
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  • 10
    Digitale Medien
    Digitale Medien
    Spread of information through a population with socio-structural bias: I. Assumption of transitivity (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 523-533 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A previously derived iteration formula for a random net was applied to some data on the spread of information through a population. It was found that if the axon density (the only free parameter in the formula) is determined by the first pair of experimental values, the predicted spread is much more rapid than the observed one. If the successive values of the “apparent axon density” are calculated from the successive experimental values, it is noticed that this quantity at first suffers a sharp drop from an initial high value to its lowest value and then gradually “recovers”. An attempt is made to account for this behavior of the apparent axon density in terms of the “assumption of transitivity”, based on a certain socio-structural bias, namely, that the likely contacts of two individuals who themselves have been in contact are expected to be strongly overlapping. The assumption of transitivity leads to a drop in the apparent axon density from an arbitrary initial value to the vicinity of unity (if the actual axon density is not too small). However, the “recovery” is not accounted for, and thus the predicted spread turns out to beslower than the observed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476440
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  • 11
    Digitale Medien
    Digitale Medien
    Spread of information through a population with socio-structural bias: II. Various models with partial transitivity (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 535-546 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The assumption of transitivity treated in part I is modified in various ways to describe an information-diffusion process, in which a certain amount of randomness of contact does occur. In one model a parameter is introduced which is indicative of a tendency to go beyond one's immediate vicinity to spread the information as the vicinity becomes saturated with knowers. In another model the randomness appears in the assumption that new knowers are uniformly distributed among the knowers. Two of the equations thus derived, each with two free parameters are in good agreement with experimental results.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476441
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  • 12
    Digitale Medien
    Digitale Medien
    Note from the editor (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 1-1 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476935
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  • 13
    Digitale Medien
    Digitale Medien
    Erythrocyte distribution in arterial blood flow: IV. Simplification of the proposed equations (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 27-32 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In a previous paper (Bull. Math. Biophysics,29, 565–574, 1967) the author developed equations to represent velocity and hematocrit profiles in quasi-Poiseuille flow of blood. It was assumed that energy dissipation was minimized and that the viscosity depended on hematocrit and shear rate according to the Casson formula. These equations are simplified considerably, placed in a form more suitable for numerical solution and shown to depend on a single dimensionless parameter. Typicalin vivo values for this parameter are calculated.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476937
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  • 14
    Digitale Medien
    Digitale Medien
    Éléments d’une théorie générale de la croissance d’une population (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 33-46 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In this paper, discrete models of reproduction are studied. In part one, definitions are given, particularly on order of the reproduction; part two concerns the growth of the population; part three, the phenomena of delay or acceleration; and part four, the consequences of mortality.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476938
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  • 15
    Digitale Medien
    Digitale Medien
    Neuroendocrine control of thyroid secretion in living systems: A feedback control system model (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 3-26 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A model of the regulation of thyroid hormone in the bloodstream of living systems is formulated and analyzed. The portion of this model defined as theregulator includes components representing the thyroid, anterior pituitary and hypothalamic organs and their intercommunicating channels, that is, the peripheral plasma and hypophysial portal circulations and certain neuro-secretory connections. The loss of hormones from the plasma in the living system associated with physiological mechanisms within the peripheral tissue space and the excretory pathways is represented in the model by a lumpedload on the regulator. The model is reduced to a system of differential equations involving eleven parameters and variables, all of which are identified with certain physiological structures and states. Five of these are currently observable by available laboratory techniques and two others are computable explicity from the equations of the model; the remaining four can be computed in the same way to within a multiplicative constant. Procedires for carrying out ten of these measurements and calculations are suggested. On the basis of the equations and parameters of the model, a discussion of the normal behavior and the response of this system to certain types of disturbances is presented. A systematic effort has been made in the development of this model to include all relevant physiological data and relationships reported in the biological literature. A summary of this literature, reflecting the views and interpretations made by the authors of this paper, is included for completeness and ease of reference.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476936
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  • 16
    Digitale Medien
    Digitale Medien
    Linear bulk diffusion into heterogeneous tissue (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 47-59 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In this paper an expression is derived which describes the transient overall uptake of an inert solute by a section of tissue excised with parallel faces and placed upon an impermeable base. The approach diverges from the conventional analyses for perfused tissue (Morales and Smith,Bull. Math. Biophysics,6, 125–141, 1944;7, 47–99, 1945) because the extravascular zone is regarded as a heterogeneous diffusion medium. Account for this is taken by regarding tissue as effectively composed of two phases—a continuous (extracellular) phase similar to water, and a dispersed phase comprising cells of irregular profile. In both phases the relevant mode of uptake is taken as bulk diffusion rather than surface permeation, thus emphasizing the influence of the internal geometry of the tissue upon its overall exchange response.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476939
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  • 17
    Digitale Medien
    Digitale Medien
    The identification of recirculating systems in the frequency domain (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 87-104 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A method for the identification of flow systems by frequency domain analysis has been extended to include systems with recirculation and truncated data curves. Application of the technique to clinical indicator-dilution curves indicates that the method may be useful in the quantitation of intracardiac shunts. A number of numerical examples which demonstrate the accuracy of the method are included.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476941
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  • 18
    Digitale Medien
    Digitale Medien
    A systems-mathematical interpretation of psychoanalytic theory (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 61-86 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract By assigning time-varying coordinates to all environmental stimuli, it has been possible to axiomatize psychoanalytic theory on the five principles of multiple causation, growth-aging influence, genetic influence, historic influence and conscious-unconscious activity. The theorems of summation of response and the inevitability of conscious-unconscious conflict with their corollaries follow directly from the axiomatic foundations, as does the existence of an adaptation-defense mechanism. The interpretation of the defense mechanism in terms of an ego-id feedback system provides the basis for the structural existence of conscious-conscious and unconscious-unconscious conflict.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476940
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  • 19
    Digitale Medien
    Digitale Medien
    Cellular systems as sequential machines: Stability properties (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 117-122 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In previous studies of (M,R) (Rosen, 1961; Demetrius, 1966), it was assumed that changes in the structure of (M,R) which were induced by environmental alternations occurred without error. Here, the effect of both “genetic” and “metabolic” malfunctions on the behavior of (M,R) is examined and a subclass of these systems whose behavior is invulnerable to such errors is specified.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476943
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  • 20
    Digitale Medien
    Digitale Medien
    Cellular systems as graphs (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 105-116 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The definition of an (M,R) is formulated in a way that emphasizes its mathematical properties. Neglecting interactions between the components, it is shown that: (1) An (M,R) contains only one non-reestablishable component. (2) If an (M,R) contains only one non-reestablishable component, then that component is central. Examples are given to illustrate the biological significance of these two results. The notion of “lag-independence” is introduced, and it is shown that if a system possesses only one non-reestablishable component which is “lag-independent” then all components are lag-independent. The concepts of reestablishability, centrality and lag-independence are applied in order to suggest various criteria for optimal organization of (M,R).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476942
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  • 21
    Digitale Medien
    Digitale Medien
    A theoretical model for the control mechanisms in biochemical reactions (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 123-133 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A mathematical representation for the analysis of control mechanisms in biochemical reactions is presented. First, the theoretical concept of concentration in biological systems is developed. Then a system consisting of two functions λ and τ is constructed as a network of single output automata. The range of λ is taken to be formed by a set of twostates qualitatively different from the “repair function” Φ f of a mappingf: A→B in the stimulated Φ1 and unstimulated state Φ0. Likewise, the range of τ is formed by the set δ={f o ,f 1} wheref 1 means the mappingf in its stimulated state andf o in the unstimulated one. It is demonstrated that the mathematical structure described acts as a control mechanism over thef and Φ f , so that two biochemical components,A→B, are transformed at a controlled rate. Some of the biological applications of this model are briefly examined. The Jacob-Monod model, the enzymatic adaptation phenomenon, and the “rheon unit” hypothesis are discussed within our framework. Eventually, a concrete model for the RNA-polymerase mechanism, based on the above discussion, is presented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476944
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  • 22
    Digitale Medien
    Digitale Medien
    A contribution to Rashevsky’s mathematical theory of development (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 135-151 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The application of Rashevsky’s transformationT to a primordial graph yields a set of graphs corresponding to different stages in the development of the organism. However, sinceT is multiple-valued the graphs obtained are not ordered. To obtain an ordering, it is first shown that the set of graphs under consideration is equivalent to a well defined setO (for “organism”) ofn-tuples. A metric is then introduced which is based on a biological consideration discussed by Rashevsky (Bull. Math. Biophysics,16, 317–348, 1954). Since a metric implies an ordering of the setO, with a knowledge of the structure of the primordial, one can obtain the developmental sequence. Unfortunately, at present, the structure of the primordial graph is unknown which makes the direct application of the above principle impossible. Consequently, an indirect approach which makes use of more accessible biological phenomena is discussed as well. The hypothesis thatrate of development decreases exponentially and the implications this has with regard to the metric onO are discussed. It is shown that if the hypothesis is accepted the search for the developmental sequence is narrowed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476945
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  • 23
    Digitale Medien
    Digitale Medien
    The transmission of excitation from the membrane to actomyosin (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 1-13 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The impressed field, “Window Field” (WF), due to a half-wave action potential on a muscle fiber, has been calculated on the basis of potential theory. It has been shown that in spite of the small intensity of the field, its integrated action can transfer the energy needed to induce, contraction from the membrane to the interior of the fiber. The energy of polarization has been found to be sufficient to exceed the energy of, thermal agitation on that length of fiber, which can be identified as the length of a sarcomere. The changes of ion concentration, caused by the WF, if calculated on the assumption of the semipermeability of theZ membranes, was found to be equal to the changes necessary to induce contraction of actomyosinin vitro.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476362
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  • 24
    Digitale Medien
    Digitale Medien
    Nonlinear diffusion in metabolic systems (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 15-21 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Some general properties of the solution of the diffusion equation are deduced for the steady-state, spherically symmetric system. On the basis of these developments some results of N. Rashevsky (Bull. Math. Biophysics,11, 15, 1949) are discussed and the results of a previous investigation (Hearon,Bull. Math. Biophysics,12, 135, 1950b) are extended to more general conditions. In particular these extensions apply to the flow of a soluteagainst its concentration gradient, the nonzero gradient of an inert metabolite, and theaccumulation or exclusion of an inert metabolite in a metabolic system.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476363
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  • 25
    Digitale Medien
    Digitale Medien
    Comments on the approximate solution of the diffusion equation: I (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 23-31 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The approximation method of N. Rashevsky is discussed and reviewed. It is shown that in addition to theexplicit assumptions and approximations there is involved the assumption that the rate of metabolism is the same at every point in the cell and that theaverage rate of metabolism is different from zero. An expression is given for the error in the approximate method when the rate of metabolism is any function of the concentration. It is also shown that a solution in theform of that obtained by the approximate method is not possible if the generalized laws of diffusion are assumed to apply.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476364
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  • 26
    Digitale Medien
    Digitale Medien
    The kinetics of the succinoxidase (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 33-42 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Rate equations for the enzymatic oxidation of succinic acid are derived on the assumption that when a single molecule of substrate combines with an enzyme molecule, it can do so with either one or two sites on the enzyme, and that oxidation occurs only in the second case. In addition it is assumed that the product of the reaction, fumaric acid, combines reversibly with the enzyme. With certain enzyme preparations the data fitted such an equation satisfactorily. In others the rate was that of a first-order reaction, but addition of cytochrome changed it to the former type. It was concluded that the transfer of hydrogen to oxygen was a first-order reaction and dominated the whole rate when enzyme preparations were used which had been washed relatively free of cytochrome. When the limiting factor was succino-dehydrogenase the rates followed the new equation. Criteria for recognizing noncompetitive inhibition are given, and inhibition by di-tertiary butyl peroxide was shown to be of this type.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476365
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  • 27
    Digitale Medien
    Digitale Medien
    The interpretation of exponential dose-effect curves (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 43-47 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract This paper deals with the following question: Which distributions of radiosensitivity in a population can lead to an exponential survival curve? The problem is solved exactly, with statistical fluctuations in dose fully accounted for. It is shown that only an exponential distribution of sensitivities can give rise to an exponential survival curve.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476366
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  • 28
    Digitale Medien
    Digitale Medien
    An approximation method for the solution of diffusion and related problems (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 49-61 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract An approximation method is introduced which enables a number of diffusion-type problems to be solved in an approximate but simple manner. Many cases require only the solution of a simple first-order differential equation. The method is applied to a number of cases in which the exact solutions are available. A comparison shows that the method is quite satisfactory in these cases. The method is applied to diffusion problems with rate of consumption proportional to concentration or to the square of the concentration. In the latter case, the result obtained is essentially the same as that found by H. G. Landau (1950) after elaborate calculations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476367
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  • 29
    Digitale Medien
    Digitale Medien
    On spontaneous discharge obtained from a physicochemical model of excitation (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 83-91 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is shown that a slight modification of a model of excitatory phenomena in irritable tissues, which has been treated before, exhibits spontaneous oscillations. The frequency of these oscillations and the time-course of the potential across the model membrane have been determined, together with the dependence of some of their characteristics on some important parameters, particularly (Ca++).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476370
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  • 30
    Digitale Medien
    Digitale Medien
    Cell division by swelling stresses (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 73-81 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is demonstrated that, if the variations of viscosity throughout a cell are considered, swelling stresses may produce elongation and division. To do this it is necessary to generalize Betti's theorem to cover systems containing viscosity gradients and such a generalization is presented. On the basis of two special assumptions it is shown that most of the results of the diffusion drag theory of cell division may be duplicated by the present theory.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476369
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  • 31
    Digitale Medien
    Digitale Medien
    Imitative behavior in nonuniformly spatially distributed populations (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 63-71 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The theory of imitative behavior, developed previously, is applied to the case of two social groups which are separated spatially. If the information of each group as to the behavior of the other is complete, the case reduces to that of a single group. When any information is lacking at all, the two groups are independent. If we have two mutually exclusive behaviorsA andB, all four combinationsAA, AB, BA, andBB are possible. If the mutual information gradually increases from zero, then for a certain value of it, the group which is more informed about the behavior of the other will change to that behavior if it did not already exhibit it. If for constant information the size of the group increases, then above a certain threshold value, the larger group imposes its behavior on the smaller.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476368
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  • 32
    Digitale Medien
    Digitale Medien
    Note on a theory of membrane permeability (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 103-104 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476372
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  • 33
    Digitale Medien
    Digitale Medien
    The limiting information capacity of a neuronal link (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 107-107 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476374
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  • 34
    Digitale Medien
    Digitale Medien
    Heredity in uterine cancer (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 105-106 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476373
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  • 35
    Digitale Medien
    Digitale Medien
    Some considerations on capillary adjustment to changing metabolism of tissue (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 93-101 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Local regulation of blood flow as determined by capillary diameter and the number of open capillaries in a region is considered. The local changes in capillary diameter and in the number of open capillaries are assumed to be due to concentration changes of a diffusible, nonspecified metabolite. This metabolite is produced in the tissue and carried away by the blood stream. Using these assumptions and applying pertinent data on capillaries, deductions are made concerning: (a) the law of blood flow as a function of temperature and capillary radius for the hyperemia of high temperature, (b) high flow as it depends on metabolism during strenuous exercise of muscle, and (c) a first approximation to the time duration of occlusion hyperemia.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476371
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  • 36
    Digitale Medien
    Digitale Medien
    Some Contributions to the Mathematical Biology of Blood Circulation. Reflections of pressure waves in the arterial system (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 109-109 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476375
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  • 37
    Digitale Medien
    Digitale Medien
    On dominance relations and the structure of animal societies: III The condition for a score structure (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 143-148 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The necessary and sufficient condition is given forn integers to be the score structure of a society with a dominance relation. A proof is also given for a theorem showing that there are members who dominate every other member either directly or indirectly through a single intermediate member.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476378
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  • 38
    Digitale Medien
    Digitale Medien
    Comments on the approximate solution of the diffusion equation: II (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 111-119 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract On the basis of a previous general formulation (Bull. Math. Biophysics,15, 21–29, 1953a) a discussion is given of the error in the approximation method of N. Rashevsky. This error, inherent in the method when the metabolic rate is different at each point in the cell, is discussed in detail and numerical values are presented for two particular cases: the rate proportional to the concentration and the rate a prescribed function of the spatial coordinates. It is shown that the formulation for the first case also applies to several other cases, that the error is negligible provided the rate is sufficiently small, and that the error is fairly sensitive to the cell size. If the rate depends upon the coordinatesalone a small rate is not sufficient to insure a negligible error. The relations between the exact method, the standard approximate method, an earlier approximate method (Physics,7 260, 1936), and a more recent refinement (Bull. Math. Biophysics,10, 201, 1948) of the standard method are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476376
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  • 39
    Digitale Medien
    Digitale Medien
    The kinetics of linear systems with special reference to periodic reactions (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 121-141 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is shown on the basis of (1) conservation of mass, (2) positive concentrations, and (3) the principle of detail balancing that periodic reactions cannot occur in a closed system described bylinear differential equations. The matrix,A, of the rate equations must be such that |A|=0,a ij〉0 fori≠j,a ii〈0, andVAV −1=B, whereV is diagonal andB is symmetric. These properties ofA imply that the latent roots are real and non-positive and that neither catalysis nor inhibition can be described bylinear equations. It is further shown that periodic reactions cannot occur in anopen system for which the matrix associated with the chemical reactions has the above properties and in which thesimple law of diffusion is obeyed. The relation of these results to Onsager's reciprocal relations and to previous work on periodic and cyclic chemical reactions is discussed. The utility of certain of these results for the treatment of isotope kinetics is indicated.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476377
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  • 40
    Digitale Medien
    Digitale Medien
    A note on the flow of blood in capillary tubes (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 149-152 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is demonstrated that an explanation of the small radius effect or the so-called sigma phenomenon may be obtained by noting that one of the effects of the presence of suspended particles in a flowing fluid is to increase the velocity of flow near the wall over that existing in the absence of particles. This effect may be considered equivalent to relaxing the boundary conditions at the wall. An expression for the viscosity is compared with data and fit is found to be good.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476379
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  • 41
    Digitale Medien
    Digitale Medien
    Note on the Donnan equilibrium (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 153-159 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The solution for the spatial distribution of ions in a Donnan equilibrium has been given by J. H. Bartlett and R. A. Kromhout (1952). The present note gives an explicit solution for the case in which the length of the region containing the membrane is large; in biological situations this requires only that the length considered should be greater than a few hundred Ångstrom units. The Donnan equilibrium may be considered to be a special case of a situation in which forces other than electrical act upon the ions; in particular, it represents the case in which only one ion is acted upon and the energy difference on the two sides of the membrane is infinite. An expression is given for the difference in energy of theith in terms of the electrical potential and of the ion concentrations. As an illustration, the results are applied to nerve membrane potentials.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476380
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  • 42
    Digitale Medien
    Digitale Medien
    Some considerations on a carrier mechanism as a model for ion accumulation (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 161-165 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A mechanism is described which accounts for the active transport of Na+ ions through a membrane. It is assumed that at one side of the membrane the ion combines with a carrier ion, the resulting carrier compound then diffuses through the membrane and decomposes at the other side of the membrane. The free diffusion of the ions is also taken into account. The time rate of accumulation of the ion in question at the latter side of the membrane is calculated in terms of the concentrations of the ion at both sides of the membrane.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476381
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  • 43
    Digitale Medien
    Digitale Medien
    Approximate treatment of the formation of a difference in the concentrations of an ion at the two sides of a membrane (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 167-171 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The recent extension of the approximation method is applied to enable us to arrive at the time course of the concentrations at both sides of a membrane. From the differential equations which govern these, the steady-state solution is obtained in terms of the parameters, which are determined by the thickness of the diffusion layers, the chemical composition and reactions, and the diffusion constant of the membrane.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476382
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  • 44
    Digitale Medien
    Digitale Medien
    Contribution to the mathematical theory of contagion and spread of information: I. Spread through a thoroughly mixed population (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 173-183 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract An equation is derived from the spread of a “state” by contact through a thoroughly mixed population, in which the probability of transmission depends both on the over-all duration of the process and on the time an individual has been in the “state.” Cases in which this probability is a function of only one or the other of the two “times” are worked out. It is shown that in the case of dependence on “private time” alone the asymptotic value of the fraction of the population effected is the same as that derived by the random net approach.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476383
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  • 45
    Digitale Medien
    Digitale Medien
    Comments on the approximate solution of the diffusion equation: I (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 235-235 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476386
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  • 46
    Digitale Medien
    Digitale Medien
    Contributions to the mathematical biophysics of the cardiovascular system (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 185-195 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The reflection of pressure waves in a fluid enclosed within a tube with an elastic wall is studied for the case of a localized change in diameter of the tube. The concept of impedance is introduced. The relation of the reflection characteristics of the parts of the tube at either side of the change is derived on the basis of the continuity of pressure and mass flow at the site of the change. This relations is used to derive the expression for the ratio of the pressure oscillations measured in front of, and behind, the constriction in terms of the constants of the system. As a result, a method is indicated to locate the coarctation from measurements of the pressures in front of, and behind it.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476384
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  • 47
    Digitale Medien
    Digitale Medien
    On the subnormal variance in the counts of randomly distributed particles: I. Approximate treatment of the three-dimensional case and discussion of experiments (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 237-244 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The question is raised concerning the possible causes of abnormally small standard deviations found in counting samples in which particles are distributed at random (e.g., blood cells, fat globules in milk, etc.). The effect of discarding abnormal samples is discounted inasmuch as small standard deviations occur even when all samples are counted. An approximation method is used to calculate the effect of finite particle size, of known repulsive forces between particles and of convection currents. This calculation shows that neither finite size nor the known repulsive forces are sufficient to account for the observed abnormality of standard deviation, but that convection currents can possibly account for it. The possible presence of long-range repulsive forces cannot, however, be excluded.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476399
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  • 48
    Digitale Medien
    Digitale Medien
    On the subnormal variance in the counts of randomly distributed particles: II. Exact treatment of the one-dimensional case (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 245-250 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The effect of finite particle size on the standard deviation in sample counts is computed for the one-dimensional case. To a first order of approximation the correction is found to be identifical with that found by H. de Vries (1953) using a general approximation method.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476400
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  • 49
    Digitale Medien
    Digitale Medien
    Outlines of a new theory of photoreception (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 251-260 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A critical examination of the “classical” theories of photoreception in view of more recent experimental findings yields the result that these theories do not possess the property to describe all the more significant phenomena of photoreception correctly, and to some extent suffer the lack of more general applicability. The basis for a new and presumably more general theory of photoreception based on dynamical aspects is laid out. Emphasis is put on the time course of afferent and efferent excitation in the photoreception model, consisting of a receptor element, an afferent and an efferent neuron of the one-factor Rashevsky-type, and an effector organ.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476401
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  • 50
    Digitale Medien
    Digitale Medien
    Outline of a mathematical approach to history (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 197-234 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A mathematical model for the development of human society, beginning with the earliest stages of urban cultures, is outlined. In the early stages of history, behavior was characterized largely by adherence to a number of beliefs and prejudices of diffeirent kinds, which were accepted on faith and not subject to critical rational analysis. Due to psychobiological variability a very small number of individuals spontaneously appear at all times who challenge the accepted beliefs and prejudices and do not follow the accepted patterns of social behavior. The effect of these individuals upon the rest of the society, especially upon the younger generation, depends on the facilities with which information spreads in society. In earliest societies, when modern methods of mass communication were unknown, the channels of communication were practically identical with the channels of economic transport. The latter in its turn depended on the nature of the roads, and especially on the presence of waterway, which facilitated transportation. The sizes of the earliest cities and the distances between them were largely determined by relative ease of transporation. Expressions are derived for the average size of the earliest cities and for the average distance between them. The calculated average populations of the earliest cities are of the order of 103; the distance of the order of 102 km. Both are in agreement with some archaeological findings. An expression for the time spaon required for the development from the earliest stages of urban cultures to the present time is derived and shown to depend on the specific shoreline of the country, that is, the length of the shorline divided by the area of the country. It is pointed out that western Europe's specific shoreline, including land bordering both seas and rivers, is ten times as large as the shoreline area of other parts of the world. It is shown that this greater specific shoreline may account quantitatively for the faster social and technological development of western Europe in the last few centuries. The calculated total span of time of development from earliest urban cultures to our days is found to be of the order of magnitude of ten thousand years. It is shown that the model accounts for the existence at the present time of primitive cultures. A number of suggestions is made in regard to other possible applications of mathematics to history.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476385
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  • 51
    Digitale Medien
    Digitale Medien
    A note on the integral-equation description of metabolizing systems (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 269-276 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The assumptions latent in the derivation of the integral equation of Branson are rendered explicit and discussed. It is shown that the equation is valid only for systems in which the substance disappears according to a linear rate law.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476403
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  • 52
    Digitale Medien
    Digitale Medien
    A critical investigation of the integral description of metabolizing systems (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 261-268 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is shown that the validity of Branson's integral description of metabolizing systems is subject to severe limitations. The validity is insured only in cases where the reaction is of first order, or quasi of first order. In all other cases Branson's equation has to be modified to insure general applicability. The consequences of a different definition of the metabolizing functionF have also been investigated. With the new definitionF describes the pure effect of metabolization. It is found that in this case the integral equation is only capable of describing first-order reactions. With a slight modification of the integral equation it is possible to describe metabolites “with age”, which do not have reactions of definite order, but which satisfy the superposition principle.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476402
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  • 53
    Digitale Medien
    Digitale Medien
    On the statistical distribution of mutant bacteria (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 277-292 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A problem in probability is stated with included the problem of the distribution of bacterial mutants as a special case. This problem is solved exactly but since the resulting expressions are too complicated for practical use, various approximate expressions for the distribution are considered, especially for the bacterial mutation case.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476404
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  • 54
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    Digitale Medien
    Note on the neurobiophysical interpretation of imitative behavior (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 293-300 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Simple reaction and discrimination reaction, under the influence of imitation, are considered for the situation in which the stimulus or the stimuli vary slowly with time. The result is analogous to hysteresis under certain conditions. The calculations are facilitated by the solution of $$x = \int_{ - \infty }^{a + \beta x} {g\left( \xi \right)d} \xi ,$$ g(ξ) being the normal error function. Values ofx(α, β) are given in a table.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476405
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  • 55
    Digitale Medien
    Digitale Medien
    Blood flow in branching circulatory systems during rest and activity (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 301-309 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract On the basis of simple physical considerations the blood flow in a branching circulatory system is studied. The case of two groups of parallel vessels is treated. The vessels of the same group are supposed to be identical. The resistance of each group is determined by the resistance of each vessel in the group and by the number of vessels in the group. From the dependence of the resistance of each vessel on its radius an expression is obtained for the blood flow through each group of vessels in terms of the numbers and sizes of the vessels in each group. The number of open vessels in an organ and the radius of each of those vessels are assumed to depend on the metabolic rate of that organ. The relations so obtained, together with the expression above, are applied to derive the blood flow through an organ as a function of the metabolic rate of that organ. It is indicated that the relations obtained might describe the shifting of blood from one organ to another if the activity of one of them changes. A way is pointed out to treat neural regulation of this phenomenon.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476406
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  • 56
    Digitale Medien
    Digitale Medien
    An age-dependent stochastic model of population growth (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 361-365 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A stochastic model of population growth is treated using the Bellman-Harris theory of agedependent stochastic branching processes. The probability distribution for the population size at any time and the expectation are obtained when it is assumed that there is probability (1−σ), 0≤σ〈1, of the organism dividing into two at the end of its lifetime, and probability σ that division will not take place.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476409
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  • 57
    Digitale Medien
    Digitale Medien
    Some quantitative aspects of history (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 339-359 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In a previous paper, in which a possible mathematical approach to history was outlined, it was shown that urbanization plays an important part in the propagation of new ideas. The rate of such propagation influences the rate of historical developments. The present paper deals in more detail with possible mechanisms of formation of earliest cities. Equations are derived which give the limiting size of such cities and their rate of growth. Of particular importance for the spread of new ideas is the spread of information. The latter largely depends on the fraction of individuals who travel between city and country. Expressions for this quantity are derived. An approach is outlined to the mathematical study of the earliest social classes, which may have been formed as a result of military, religious, or economic stratifications.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476408
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  • 58
    Digitale Medien
    Digitale Medien
    On the propagation of a disturbance through a viscous liquid flowing in a distensible tube of appreciable mass (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 395-409 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The velocity of propagation of a disturbance wave in a liquid flowing in a distensible tube is computed. The mathematical model is more general than those used in previous analyses: the tube wall properties are realistic; the convective part of the axial inertia forces is taken into account; radial inertia forces of both the fluid and tube wall are present; viscous stresses are present. Four parameters influencing the velocity of propagation are obtained and discussed. Curves are plotted illustrating the effects of the parameters. Contrary to the results of previous analyses, viscous effects are shown to be appreciable in blood flow. It is also shown that radial inertia effects can be important in laboratory set-ups.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476433
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  • 59
    Digitale Medien
    Digitale Medien
    Theory of the vacuum drying of frozen tissues (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 411-429 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A general theory of the drying of frozen tissue is developed and applied to the measurement of the drying rate of frozen guinea pig liver. It is shown that for a given temperature of the subliming ice crystals the mininum drying time of a piece of guinea pig liver is greater than the minimum sublimation time of a piece of ice of the same size and shape by a factor of the order of one thousand. This fact has many implications in the design of freeze-dry apparatus which will be developed in a following paper.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476434
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  • 60
    Digitale Medien
    Digitale Medien
    The time course of capillary exchange (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 477-488 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The equations governing the time course of the exchange of substances between the blood in the capillaries and the extracellular space are solved for the case of substances which do not penetrate the cells. The equations given relate the time course of the exchange process to the various tissue and circulation parameters such as the specific capillary wall area, the pore area, the inter-capillary distance, the size of the extra-vascular, extra-cellular space, the diffusion coefficient in this space, and the velocity of blood in the capillaries. Some experimental work on capillary exchange is discussed in relation to the theory and estimates are made of the relative importance of the various tissue and circulation parameters in the exchange of substances in different tissues.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476436
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  • 61
    Digitale Medien
    Digitale Medien
    The excitation of the heart and its modification under the influence of the chemical mediators and the cardiac nerves: II. A particular case of the one-factor theory (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 547-559 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Previous work (Macey, 1952) in the application of the one-factor theory to the heart is extended. The rate of production of the excitatory state is assumed to be linear. Two possible mechanisms are indicated whereby such a situation might arise. Assumptions are made regarding the mode of action of the chemical mediators on the heart, and an equation is derived relating the heart rate to the frequency of nerve impulses traveling along the cardiac nerves. This result compares favorably with the experimental findings of A. Rosenblueth and F. A. Simeone (1934). Other experimental results are interpreted in terms of the theory.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476442
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  • 62
    Digitale Medien
    Digitale Medien
    Symposium on Radiobiology. The Basic Spects of Radiation Effects on Living Systems (1953)
    Springer
    Bulletin of mathematical biology 15 (1953), S. 561-563 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476443
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  • 63
    Digitale Medien
    Digitale Medien
    Mathematical biology of automobile driving: III (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 153-162 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In a previous paper (Bull. Math. Biophysics,22, 257–262, 1960), an expression for the probability that a car jumps off a road as a function of the speed and the size of the car was derived mostly from geometric and kinematic considerations, introducing only the reaction time as a biological parameter. In subsequent papers (Bull. Math. Biophysics,29, 181–186, 187–188, 1967) a more detailed study was made of the exact shape of the tracking curve of the car which involved several biological parameters of the driver. In the present paper the results of the previous studies are combined, and a more general equation for the probability of jumping off the road is obtained. This probability, as in the earlier study, increases with the speedv, widths o and lengthl o of the car, and decreases with widths of the lane. However, this probability also depends on several parameters which characterize the psychobiological constitution of the driver. Unpublished experiments by Ehrlich, which corroborate the general conclusions, are briefly described.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476946
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  • 64
    Digitale Medien
    Digitale Medien
    Computer solution of the ultracentrifuge equation (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 205-213 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476690
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  • 65
    Digitale Medien
    Digitale Medien
    Organismic sets: II. Some general considerations (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 163-174 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The theory of organismic sets, developed in previous papers (Bull. Math. Biophysics,29, 139–152; 389–393; 643–647) is further generalized. To conform better with some biological and sociological facts the basic definitions are made more general. The conclusion is reached that every organismic setS o is in general the union of three disjoined subsetsS o1 ,S o2 andS o3 . Of these the subsetS o1 , called the “core” is equivalent to an organismic set defined in previous publications. Its functioning is essential for the functioning ofS o . The subsetsS o2 andS o3 , taken alone, are not organismic sets. The first of them is responsible for such biological or sociological functions which are not necessary for the “immediate” survival ofS o but which are important for adaptation to changing environment and are therefore essential for a “long range survival.” The second one,S o3 , is responsible for biological or social functions which are irrelevant for the survival ofS o . Biological and sociological examples ofS o2 andS o3 are given. In addition to the fundamental theorem established in the first of the above mentioned papers, three new conclusions are derived. One is that in organismic sets of order higher than zero not all elements are specialized. The second is that every organismic set of order higher than zero is mortal. The third is that with increasing specialization the intensities of some activities in some elements ofS o are reduced. Again the biological and sociological examples are given. At the end some very general speculations are made on the possible relation between biology and physics and on the possibility of “relationalizing” physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476947
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  • 66
    Digitale Medien
    Digitale Medien
    Entropy and the complexity of graphs: I. An index of the relative complexity of a graph (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 175-204 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The structural information content (Rashevsky, 1955; Trucco 1956a, b)I g (X) of a graphX is defined as the entropy of the finite probability scheme constructed from the orbits of its automorphism groupG(X). The behavior ofI g on various graph operations—complement, sum, join, cartesian product and composition, is examined. The principal result of the paper is the characterization of a class of graph product operations on whichI g is semi-additive. That is to say, conditions are found for binary operations o and ∇ defined on graphs and groups, respectively, which are sufficient to insure thatI g (X o Y)=I g (X)+I g (Y)−H XY , whereH XY is a certain conditional entropy defined relative to the orbits ofG(X o Y) andG(X) ∇G(Y).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476948
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  • 67
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    Digitale Medien
    Models of social structure (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 215-224 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The mathematical treatment of three models of possible development of a society with a dominance relationship is discussed. The conclusion is reached that social factors as well as inherent characteristics need to be introduced to account for near-hierarchical structures. This is not a surprising conclusion; however, deriving it from mathematical considerations should be of interest to the mathematical sociologist since it puts the problem into theoretical perspective. Also these considerations may suggest quantitative observations or experimental tests and given indications as to their analysis.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476691
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  • 68
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    Digitale Medien
    The struggle for life: II. Three competitors (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 291-298 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Some of the properties of the equations describing three species living in competition in the same environment are analysed. In particular it is found that, under certain conditions, the size of the three populations can oscillate.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476696
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  • 69
    Digitale Medien
    Digitale Medien
    Pulse velocities in initially stressed cylindrical rubber tubes (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 299-308 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Expressions are obtained for the pulse velocities in cylindrical tubes of rubber-like materials which are under a state of initial stress. The development is based on the theory of finite elastic deformations and a Mooney materials is considered for illustrative purposes. Numerical results are given in terms of dimensionless parameters which involve the stretch ratio and lumen volume ratio. For the thoracic aorta, a value for the pulse velocity is obtained which is lower than the experimental value.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476697
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  • 70
    Digitale Medien
    Digitale Medien
    A macroscopic formulation of electromagnetophoresis (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 309-318 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A macroscopic conservation equation is derived for electromagnetophoresis of a dilute suspension. The governing equation and auxiliary conditions are formulated for transport in a rectangular cell, these being reduced to standard form by dimensional methods.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476698
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  • 71
    Digitale Medien
    Digitale Medien
    On relationships between various distribution functions in balanced unicellular growth (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 319-323 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The relationships between various size distributions in balanced exponential growth of a batch culture of microorganisms are presented. Starting from the partial differential integral equations (Eakmanet al., 1966; Fredricksonet al., 1967) derived for the growth of a microbial culture expressions are obtained for the growth rate of organisms of specific size and size range. These expressions were first obtained by Collins and Richmond (1962) by an entirely different method. Also derived are equations which link probability functions, which are basic to the growth of a microbial culture, with other size distributions that can be estimated experimentally.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476699
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  • 72
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    Digitale Medien
    The differential equations for specific activities in a distributed tracer system (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 325-331 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Under the assumption of simple Fick-law diffusion with convection and/or imposed force fields, the flux law for tagged molecules in a tracer system is derived, and the Sheppard-Householder interfusion coefficient identified. The partial differential equations for concentrations of tagged species and for specific activities in an open distributed reaction system are derived and compared.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476700
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  • 73
    Digitale Medien
    Digitale Medien
    Properties of solution of the diffusion-reaction equation. II (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 333-340 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Two theorems relating to properties of the solutions of the equations of continuity for the concentrations of the chemical species in a diffusion-reaction system are proved. The theorems concern boundary conditions under which the flux of a specified species can be guaranteed to be directed into the reaction region and the circumstances under which any two of the conditions (i) stationarity, (ii) flux equilibrium, and (iii) chemical equilibrium, imply the third. Application of these theorems to apparent active transport and to the properties of the differential equations for specific activities in a distributed tracer system are noted.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476701
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  • 74
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    Digitale Medien
    Some possible theoretical implications of experiments on the chemical transfer of memory (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 341-349 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Recent experiments on so-called chemical transfer of memory may indicate at first glance that the possibility of transfer of the memory of a large number of reaction patterns in this manner requires the assumption of a correspondingly large number of specific chemical substances. It is shown that this is not necessarily the case. A mechanism is conceivable in which a single substance is responsible for “memory” transfer for a large number of distinct patterns. Mechanisms involving only about one hundred different specific substances could conceivably be responsible for chemical transfer of memory of some 1050 spatial patterns.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476702
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  • 75
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    Digitale Medien
    A remark on the possible use of nonoriented graphs in biology (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 351-353 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is suggested how nonoriented graphs may be used to representn-ary relations in organisms and to study the changes in variousn-ary relations under the transformation proposed in a previous paper (Bull. Math. Biophysics,16, 317–348, 1954).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476703
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  • 76
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    Digitale Medien
    A note on the development of organismic sets (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 355-357 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract It is suggested that the development of organismic sets is governed not by the maximalization of the integral survival value, as suggested previously (Bull. Math. Biophysics,28, 283–308, 1966;29, 139–152, 1967;30, 163–174, 1968), but by maximizing the number of new relations which appear as an organismic set develops.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476704
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  • 77
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    Digitale Medien
    Entropy and the complexity of graphs: III. Graphs with prescribed information content (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 387-414 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The connection between the adjacency matrix and the automorphisms of a digraph is used to develop a method for studying the automorphism group and, thus, the information content (Mowshowitz 1968a, b) of a digraph. An algorithm is given for constructing digraphs with zero information content, and the properties of such digraphs are examined. Moreover, an algorithm for computing the automorphism group of a digraph is presented and is used to find conditions which insure that two digraphs have the same information content. This algorithm is further used to determine the information content of digraphs whose adjacency matrices have prescribed properties.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476603
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  • 78
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    Digitale Medien
    Transient behavior of arterial systems in response to flow pulses (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 359-385 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The arterial system is characterized geometrically as a system of branched elastic fluid lines whose frequency response is then known in the sense of the Fourier transform. For convenience of visualization the transient response of the individual tube to an input pressure-flow pair is represented in the time domain by kernel functions indicating the hybrid effect of viscosity and momentum on the line impedance and damping characteristics. The system as a whole is then divided into a zone of smaller tubes (below 3 mm) and a zone of larger tubes extending up to the aorta. It is shown that as a system each labyrinth of tubes below the 3 mm size may be replaced by a single impedance transformation which is dominantly resistive-capacitive. In the larger tubes, the transformation of the pulse wave at different stations is considered a point of interest. Therefore hand calculated examples are worked to derive the response of a system involving some of the larger vessels to a pressure or flow pulse of the typical shape seen near the heart. The result suggests that the dicrotic wave seen in the pressure pulse of mammals is due to the hybrid viscosity-momentum nature of the longer fluid lines in relation to the gradation of unmatched terminal impedances with which they are terminated. Damping of the higher frequency components is also accounted for.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476602
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  • 79
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    Digitale Medien
    Equations for the age structure of growing populations (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 427-435 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Generalized equations are developed for the age structure of growing cell populations when other parameters besides chronological age are taken into account. These are summarized in a parameter which we call “chronological age”. The theory is Markovian in spirit and leads to an integro-differential equation for population density which generalizes several equations now appearing in the literature. Approximations to the fundamental equation are suggested.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476605
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  • 80
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    Digitale Medien
    An axiomatic explanation of complete self-reproduction (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 415-425 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A similarity between the concepts of reproduction and explanation is observed which implies a similarity between the less well understood concepts of complete self-reproduction and complete self-explanation. These latter concepts are shown to be independent from ordinary logical-mathematical-biological reasoning, and a special form of complete self-reproduction is shown to be axiomatizable. Involved is the question whether there exists a function that belongs to its own domain or range. Previously, Wittgenstein has argued, on intuitive grounds, that no function can be its own argument. Similarly, Rosen has argued that a paradox is implied by the notion of a function which is a member of its own range. Our result shows that such functions indeed are independent from ordinary logical-mathematical reasoning, but that they need not imply any inconsistencies. Instead such functions can be axiomatized, and in this sense they really do exist. Finally, the introduced notion of complete self-reproduction is compared with “self-reproduction” of ordinary biological language. It is pointed out that complete self-reproduction is primarily of interest in connection with formal theories of evolution.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476604
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  • 81
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    Digitale Medien
    A theoretical model of the cornea for use in studies of tonometry (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 437-453 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A theoretical model of the cornea based on corneal dimensions and reported properties is presented in this paper. It is shown that because of large differences in the thicknesses of the Bowman’s and Descemet’s membranes and the stroma, and because of the reported large differences in the elastic properties of the layers, a sandwich-shell model is a good approximation for the study of corneal deformation. The theory is applicable for applanation tonometry. A set of equilibrium equations based on Reissner’s theory is given. Shell parameters which determine the behavior of shells are expressed in terms of the corneal properties and dimensions. Numerical examples which show the effects of corneal parameters on the stress resultants due to intraocular pressure are also given.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476606
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  • 82
    Digitale Medien
    Digitale Medien
    The conservation of the biomass density and the age structure of the populations (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 553-563 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A study was made of populations in stationary equilibrium that satisfy the following conditions: (1) The birth rate is very large in relation to the capacity of the habitat. (2) The part of the mortality which is independent of age is easily measured and is found to be very high. For these populations the following conclusions were drawn from the experimental observations: (1) The populations in steady state show an inversely proportional relation between the maximum average age of its components and the mortality. (2) The biomass of a population in a steady state saturating a habitat remains constant in spite of changes in the mortality. (3) The population of organisms continually growing through life, whose steady-state equilibria are reached under conditions of high mortality are composed of great numbers of individuals with a small average size. The equilibria which are reached under conditions of low mortality are characterized by a small number of individuals with large average size.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476675
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  • 83
    Digitale Medien
    Digitale Medien
    A neural model for conditioned avoidance learning (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 565-579 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A mathematical model for learning of a conditioned avoidance behavior is presented. An identification of the net excitation of a neural model (Rashevsky, N., 1960.Mathematical Biophysics. Vol. II. New York: Dover Publications, Inc.) with the instantaneous probability of response is introduced and its usefulness in discussing block-trial learning performances in the conditioned avoidance situation is outlined for normal and brain-operated animals, using experimental data collected by the author. Later, the model is applied to consecutive trial learning and connection is made with the approach of H. D. Landahl (1964. “An Avoidance Learning Situation. A Neural Net Model.”Bull. Math. Biophysics,26, 83–89; and 1965, “A Neural Net Model for Escape Learning.”Bull. Math. Biophysics,27, Special Edition, 317–328) wherein lie further data with which the model can be compared.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476676
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  • 84
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    Digitale Medien
    Applications of a surface dipole model to biological cells rationale (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 581-614 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476677
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  • 85
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    Digitale Medien
    Ein Beitrag zum abdominalen Kryptorchismus beim Rehbock (1968)
    Springer
    European journal of wildlife research 14 (1968), S. 28-30 
    Details
    ISSN: 1439-0574
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Land- und Forstwirtschaft, Gartenbau, Fischereiwirtschaft, Hauswirtschaft
    Notizen: Zusammenfassung Es wird über einen vollständigen, beiderseitigen abdominalen Kryptorchismus beim Rehbock berichtet. Der pathologisch-anatomische sowie der histologische Untersuchungsbefund der atrophierten Hoden zeigen eine fehlende Spermiogenese. Die Stummelgehörnbildung läßt Rückschlüsse auf die mangelnde Hormonproduktion der Leydigschen Zwischenzellen zu.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01892684
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  • 86
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    Digitale Medien
    Pansenstein beim Reh (1968)
    Springer
    European journal of wildlife research 14 (1968), S. 30-31 
    Details
    ISSN: 1439-0574
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Land- und Forstwirtschaft, Gartenbau, Fischereiwirtschaft, Hauswirtschaft
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01892685
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  • 87
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    Digitale Medien
    Zu einigen Jagdverfahren auf Hirsche im Altertum (1968)
    Springer
    European journal of wildlife research 14 (1968), S. 31-34 
    Details
    ISSN: 1439-0574
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Land- und Forstwirtschaft, Gartenbau, Fischereiwirtschaft, Hauswirtschaft
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01892686
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  • 88
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    Digitale Medien
    Bericht über den VIII. Kongreß des Internationalen Ringes der Jagdwissenschaftler in Helsinki/Finnland vom 22.–27. VIII. 1967 (1968)
    Springer
    European journal of wildlife research 14 (1968), S. 34-40 
    Details
    ISSN: 1439-0574
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Land- und Forstwirtschaft, Gartenbau, Fischereiwirtschaft, Hauswirtschaft
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01892687
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  • 89
    Digitale Medien
    Digitale Medien
    Einfache Methode zur Darstellung der Altersklassenverhältnisse in Schalenwildbeständen (1968)
    Springer
    European journal of wildlife research 14 (1968), S. 88-90 
    Details
    ISSN: 1439-0574
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Land- und Forstwirtschaft, Gartenbau, Fischereiwirtschaft, Hauswirtschaft
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01902648
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  • 90
    Digitale Medien
    Digitale Medien
    A theory of speech perception: II (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 455-479 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract The author’s theory of speech perception, as applied to time-dependent speech sounds, leads to many testable predictions. While some of these predictions are consistent with conventional knowledge, others are new and quite unexpected. A few are in contradiction to long accepted experimental results. A computer-aided experimental program, designed to test the theory, wholly supported these predictions. In view of this outcome, it seems desirable to test other predictions of the theory and to reexamine some conventionally accepted views in order to arrive at a more comprehensive theory of speech. The present findings indicate that, apart from categorization, consonants are similar to vowels: they exhibit parallel organizations and transformation properties.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476607
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  • 91
    Digitale Medien
    Digitale Medien
    On possible reversible changes between arational and rational behavior of society (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 519-525 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract In our recent book,Looking at History Through Mathematics (MIT Press, 1968), we discussed two possible mechanisms of a transition of a society from an “arational” behavior, in which most things are accepted uncritically on faith, to a rational behavior, characterized by a critical appraisal of everything. Both mechanisms lead to irreversible changes, which eventually result asymptotically in a complete rationalization of society. In the present paper it is shown that a generalization of the second mechanism may lead to alternations between rational and arational behavior of a society. The reversal from rational to arational behavior is due to the circumstance that for some people hard thinking is either impossible or at least highly unpleasant. It appears, on the basis of the model discussed here, that acomplete rationalization of any society is unattainable.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476611
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  • 92
    Digitale Medien
    Digitale Medien
    Remarks on Weissenberger’s Comments Concerning “Stability Analysis of a Mathematical Neuron Model” (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 529-529 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476613
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  • 93
    Digitale Medien
    Digitale Medien
    A suggestion of a new approach to the theory of some biological periodicities (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 751-760 
    Details
    ISSN: 1522-9602
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract Previous studies of L. Danziger and G. Elmergreen (Bull. Math. Biophysics,16, 15–21, 1954;18, 1–13, 1956) of possible biochemical periodicities in organisms assumed non-linear biochemical interaction between different metabolites, because linear systems do not lead to undamped ocsillations. They treated homogeneous systems. Later N. Rashevsky generalized their results to a more realistic case where the non-homogeneity due to the histological structure is considered. (Some Medical Aspects of Mathematical Biology, Springfield, Illinois: Charles C. Thomas, Publisher, 1964;Bull. Math. Biophysics,29, 389–393, 1967.) As long as the histological structure remains constant, the existence of sustained periodicities requires the assumption of non-linearity of biochemical interactions. If, however, the secretions of an endocrine gland affect the histological structure of the target organ, notably as in the menstrual cycle, and if there is a feed-back, the equations become non-linear and may admit sustained periodic solutions even if the purely biochemical interactions are linear.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02476689
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  • 94
    Digitale Medien
    Digitale Medien
    On the numerical solution of higher order nonlinear parabolic equations (1968)
    Springer
    Computing 3 (1968), S. 139-150 
    Details
    ISSN: 1436-5057
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik
    Beschreibung / Inhaltsverzeichnis: Zusammenfassung Diese Arbeit behandelt die numerische Approximation von schwachen Lösungen der ersten Anfangs-Randwertaufgabe für die nichtlineare parabolische Gleichung höherer Ordnung $$\sum\limits_{|\alpha | , |\beta | \leqq p} {D^\alpha (a_{\alpha \beta } (x,t)) \leqq D^\beta u - \partial u/\partial t = f} $$ wof=f(x, t, D v u), |v|≤p−1, p≥1 ganz, und wo α, β,v multi-Indices sind.
    Notizen: Summary This paper deals with the numerical approximation of weak solutions of the first initial, boundary value problem for the higher order, nonlinear parabolic equation $$\sum\limits_{|\alpha | , |\beta | \leqq p} {D^\alpha (a_{\alpha \beta } (x,t)) \leqq D^\beta u - \partial u/\partial t = f} $$ wheref=f(x, t, D v u), |v|≤p−1, p≥1 is an integer and α, β,v are multi-indices.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02277456
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  • 95
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    Digitale Medien
    The behavior of jet streams in potential fallout situations (1968)
    Springer
    Meteorology and atmospheric physics 17 (1968), S. 8-16 
    Details
    ISSN: 1436-5065
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geographie , Physik
    Beschreibung / Inhaltsverzeichnis: Zusammenfassung An Hand eines konkreten Falles wird gezeigt, daß die Aufspaltung des Jet Streams in mehrere Äste, wie dies häufig über den Vereinigten Staaten an der Vorderseite intensiver Jet Maxima beobachtet wird, mit der Erhaltung der potentiellen Vorticity innerhalb einer Luftschicht, die sich über ein Hindernis bewegt, erklärt werden kann. Ein derartiges Hindernis kann einerseits durch ein Gebirge gegeben sein, wie etwa die Rocky Mountains, andererseits aber auch durch eine sich nur langsam fortbewegende Kaltluftmasse in der unteren Troposphäre. Eine solche ist für Kaltluftausbrüche im Zusammenhang mit intensiven Strahlströmen charakteristisch.
    Kurzfassung: Résumé En se basant sur un cas particulier, on montre que la subdivision d'un courant “jet” en plusieurs bras distincts — fait souvent observé au dessus des Etats Unis d'Amérique à l'avant de la zone d'intensité maximum — peut s'expliquer par la conservation de l'énergie tourbillonnaire potentielle d'une couche d'air se déplaçant sur un obstacle. Un tel obstacle peut être soit une importante chaîne de montagnes telles que les Rocheuses, soit une masse d'air froid se déplaçant lentement dans la basse troposphère, comme c'est typiquement le cas lorsqu'une invasion d'air froid est liée à un fort courant “jet”.
    Notizen: Summary It is shown from a case study that the splitting of jet streams into several branches, which is frequently observed over the United States on the leading edges of intense maxima, may be explained by conservation of potential vorticity within an atmospheric layer moving over an obstacle. Such an obstacle may be a large mountain barrier, such as the Rocky Mountains, or a slowmoving dome of cold air in the lower troposphere, as is typical for cold outbreaks associated with strong jet streams.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02250789
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  • 96
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    Digitale Medien
    Results of investigation on precipitation and cloud electricity based on 15 years of observation (1968)
    Springer
    Meteorology and atmospheric physics 17 (1968), S. 17-29 
    Details
    ISSN: 1436-5065
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geographie , Physik
    Beschreibung / Inhaltsverzeichnis: Zusammenfassung Es wird eine systematische Phänomenologie der luftelektrischen Erscheinungen innerhalb und in der Umgebung von Wolken und Niederschlägen, soweit sie nicht mit Gewittern verbunden sind, entwickelt. Sie erstreckt sich auf niedrige Schichtwolken, Cumulus humilis, Cumuli im Wachstumsstadium sowie Cu congestus und schließt typische stabile Aufgleitprozesse mit Übergang von Altocumulus über Altostratus in Nimbostratus bei absinkender Basis ein. Die schlüsselhafte Bedeutung des Aggregatzustandes der Niederschläge und des Turbulenzgrades innerhalb der Wolken für das Verständnis der atmosphärisch-elektrischen Prozesse und ihrer Systematisierung im Rahmen einer Phänomenologie wird dargestellt.
    Kurzfassung: Résumé On développe ici un système des phénomènes électriques atmosphériques au voisinage et à l'intérieur des nuages et des précipitations, pour autant que ces deux catégories d'hydrométéores ne soient pas liées à des orages. Cette classification s'étend aux nuages stratiformes bas, aux cumulus humilis, aux cumulus en plein développement ainsi qu'aux cumulus congestus, Elle englobe en outre des processus de glissement ascendant stables et typiques tels que le passage de l'altocumulus au nimbus en passant par l'altostratus et cela par abaissement de la base du nuage. On souligne la signification de l'état des précipitations et du degré de turbulence à l'intérieur du nuage pour la compréhension des processus électriques atmosphériques et leur systématisation.
    Notizen: Summary An attempt is made to develop a systematic, phenomenological classification of non-thunderstorm clouds based on the electrical characteristics of such clouds, and to derive a similar classification of precipitation from the electrical properties of hydrometeors. The system, as proposed, will cover low stratus, cumulus humilis, convective cumulus and cumulus congestus, and also the cloud configuration associated with stable upslide situations characterized by a continuous transition, in time and space, from altocumulus to altostratus and nimbostratus, with the bases of the latter steadily losing altitude. The significance of the physical state of hydrometeors and of the intensity of turbulence in clouds as a key to atmospheric-electrical phenomena, and the interpretation and phenomenological classification thereof, is stressed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02250790
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  • 97
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    Digitale Medien
    Remarks concerning the “ten-year-period” of atmospheric electricity (1968)
    Springer
    Meteorology and atmospheric physics 17 (1968), S. 88-89 
    Details
    ISSN: 1436-5065
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geographie , Physik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02250794
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  • 98
    Digitale Medien
    Digitale Medien
    Beschreibung des Stromfeldes im Alpenbereich mittels Windmatrizen (1968)
    Springer
    Meteorology and atmospheric physics 17 (1968), S. 61-77 
    Details
    ISSN: 1436-5065
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geographie , Physik
    Beschreibung / Inhaltsverzeichnis: Summary In the present paper the authors investigate the stream field over the Alpine region. For the comparison of the wind frequencies observed at two stations the representation of the frequencies of wind direction in matrix notation proved to be very useful. From such a matrix one can immediately read off the frequencies of the simultaneous wind directions at the stationB, when the direction at the stationA is held fast. The frequency distributions of the wind directions at the single stationsA andB result as the sums of the columns and of the rows of the wind matrix. The matrix allows to specify index numbers (e. g. the trace of the matrix) which characterize the simultaneous wind conditions at a pair of stations,AB, the change of direction from one station to the other and so on.
    Kurzfassung: Résumé Dans le présent travail, on étudie le champ des courants dans la région des Alpes. Pour comparer la fréquence du vent à 2 stations, il est apparu que la représentation de la fréquence des directions du vent sous forme de matrice était parfaitement utilisable. Il est possible de tirer immédiatement d'une telle matrice la direction du vent dans une stationB en partant de la direction du vent observée au même moment en une stationA. La répartition des fréquences de la direction du vent aux stationsA etB résulte de la somme des colonnes, respectivement des lignes de la matrice. Une telle matrice permet également de tirer des grandeurs caractéristiques de la paire des stationsA etB. Ces grandeurs expliquent mieux l'apparition simultanée des mêmes directions (trace de la matrice), les rotations du vent d'une station par rapport à l'autre, etc.
    Notizen: Zusammenfassung In der vorliegenden Arbeit wird das Strömungsfeld im Bereich der Alpen untersucht. Für einen Vergleich der Windhäufigkeiten zwischen zwei Stationen stellte sich eine Darstellung der Häufigkeiten der Windrichtungen in Matrixform als sehr brauchbar heraus. Man kann aus einer solchen Windmatrix bei einer festgehaltenen Windrichtung in der StationA sofort die Häufigkeiten der gleichzeitigen Windrichtungen in der StationB ablesen. Die Häufigkeitsverteilungen der Windrichtungen an den einzelnen StationenA undB ergeben sich aus der Summe der Spalten bzw. der Zeilen der Windmatrix. Mittels einer solchen Windmatrix ist man auch in der Lage, für das betreffende StationspaarAB charakteristische Kenngrößen anzugeben, die das gleichzeitige Auftreten von Windrichtungen (Spur der Matrix), die Drehung des Windes und dergleichen mehr beschreiben.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02250792
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  • 99
    Digitale Medien
    Digitale Medien
    The formation of crevasses in relation to the measured distribution of strain-rates and stresses (1968)
    Springer
    Meteorology and atmospheric physics 17 (1968), S. 78-87 
    Details
    ISSN: 1436-5065
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geographie , Physik
    Beschreibung / Inhaltsverzeichnis: Zusammenfassung Auf einer Fläche von etwa 0,3 km2 wurde am Hintereis- und Langtaufererjochferner (Ötztaler Alpen) die Verteilung der Deformationen und der Spannungen an der Oberfläche bestimmt. Dazu wurde in den Jahren von 1957 bis 1963 ein Pegelnetz, bestehend aus 30 Pegeln in etwa 2750 m Seehöhe, vermessen. Die Gletscheroberfläche zeigt beim Zusammenfluß beider Gletscher ein Gebiet ohne Spalten, bedingt durch hohe Kompressionen, und ein Gebiet mit Querspalten, die durch seitliche Quetschung in Verbindung mit kleinen Zugspannungen entstehen. Die Spaltenbildung stimmt mit der Spannungsverteilung in bezug auf Größe und Richtung des Spannungszustandes überein.
    Kurzfassung: Résumé On a déterminé la répartition des déformations et des tensions à la surface des glaciers du Hintereis et du Langtaufererjoch (Alpes de l'Ötztal, Autriche) et cela sur, une surface de 0.3 km2. Ces mesures furent effectuées de 1957 à 1963 et on s'est servi pour cela d'un, réseau de 30 échelles nivométriques situées à environ 2750 m d'altitude. La surface présente, au confluent des deux glaciers une zone sans crevasses due à de hautes compressions et une zone zébrée de crevasses transversales dues à des forces de compression, latérale liées à de petites tensions. La formation des crevasses correspond à la répartition des tensions et cela aussi bien en ce qui concerne leur direction que leur importance.
    Notizen: Summary The distribution of strain-rates and stresses was determined in an area of approximately 0.3 km2. For this purpose a network of 30 stakes was established on the Hintereisferner and Langtaufererjochferner (Oetztal Alps, Austria) in an altitude of approximately 2750 m in the years between 1957 and 1963. The region of the confluence of the Hintereisferner and the Langtaufererjochferner shows both, an area without crevasses, where high compressing strainrates and stresses occur, and an area with transverse crevasses formed by high lateral compressive stresses in combination with small tensile stresses. The formation of crevasses is a good agreement with the distribution of stresses concerning direction and magnitude.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02250793
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  • 100
    Digitale Medien
    Digitale Medien
    Eddy flux of sensible heat at different levels in the stratosphere (1968)
    Springer
    Meteorology and atmospheric physics 17 (1968), S. 101-113 
    Details
    ISSN: 1436-5065
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geographie , Physik
    Beschreibung / Inhaltsverzeichnis: Zusammenfassung Die Kovarianz zwischen Temperatur und meridionaler Windkomponente wurde für 18 Stationen der nördlichen Hemisphäre für 2km-Intervalle vom Boden bis 28 km berechnet. Diese Kovarianzen sind dem nach Norden gerichteten mittleren Strom der Wärme proportional, verursacht durch wandernde Wirbel. Für 80°W wurden Querschnitte der Kovarianz zwischen Temperatur und meridionaler Windkomponente konstruiert. In diesem Meridianschnitt tritt ein Minimum des turbulenten Wärmeflusses in nahezu 20 km Höhe in allen Breiten im Januar auf; in höheren Breiten beginnt eine plötzliche Zunahme mit der Höhe zwischen 18 und 22 km. Dieser turbulente Wärmefluß ist im allgemeinen in der unteren Stratosphäre unterhalb 20 km ziemlich klein. Ein ähnliches Verhalten wird bei der französischen Station Chateauroux gefunden. Die Schicht, welche die Regionen des kleinen und des großen turbulenten Wärmeflusses trennt, scheint mit einer vonFaust besprochenen Nullschicht zusammenzufallen. Diese scharfe Trennungslinie zwischen unterer Stratosphäre mit kleinem turbulenten Wärmefluß und der oberen Stratosphäre mit größeren Wirbelköpern der Wärme tritt jedoch nicht an allen Längengraden auf. Über Alaska findet man einen maximalen turbulenten Wärmestrom zwischen 20 und 22 km; auch die Werte in der unteren Stratosphäre sind dort viel größer als diejenigen um 80°W.
    Kurzfassung: Résumé On a calculé la covariance existant entre la température et la composante méridionale du vent. Ces calculs, ont été effectués pour des intervalles de 2 km du sol à 28 km et cela pour 18 stations, de l'hémisphère nord. Ces nord et provoqués par des tourbillons mobiles. On a construit des sections de la covariance entre température et composante méridionale du vent à 80° de longitude W. Sous cette longitude, on constate en janvier un minimum du flux turbulent de chaleur à environ 20 km d'altitude et cela sous toutes les latitudes. Dans les latitudes élevées, on constate en outre une brusque augmentation de ce flux avec l'altitude et cela entre 18 et 22 km. Ce flux turbulent de chaleur est en général assez faible dans les basses couches de la stratosphère, c'est à dire au-dessous de 20 km. On trouve des conditions similaires, à la station française de Chateauroux. La couche qui sépare les régions présentant des flux turbulents de chaleur faible et important semble coïncider avec la “couche nulle” deFaust. Cette nette ligne de séparation entre la stratosphère inférieure présentant un faible flux turbulent de chaleur et la stratosphère supérieure comportant des corps tourbillonnaires de chaleur importants ne se rencontre cependant pas sous toutes les longitudes. Au-dessus de l'Alaska, on rencontre un courant turbulent de chaleur maximum entre 20 et 22 km. Les valeurs de la stratosphère inférieure y sont aussi beaucoup plus grandes que celles trouvées à 80° de longitude ouest.
    Notizen: Summary Covariances of temperature and meridional wind component at 18 stations in the Northern Hemisphere were computed at 2km-intervals from the surface to 28 km. These covariances are proportional to the northward flux of sensible heat resulting from transient eddies. Cross sections of covariance of temperature and meridional wind component during January and July were constructed for 80°W. At this longitude during January a minimum of eddy heat flux occurred near an altitude of 20 km at all latitudes, and in the higher latitudes a sharp increase began somewhere between 18 km and 22 km. Eddy heat fluxes were generally quite small, in the part of the stratosphere below 20 km. A similar pattern was found at the French station of Chateauroux. The layer which separates the regions of small and large eddy heat fluxes appears to coincide with a null layer described byFaust. However, this sharp dividing line between a lower stratosphere with small eddy heat fluxes and an upper stratosphere with large eddy heat fluxes does not appear at all longitudes. Over Alaska one finds maximum eddy heat fluxes between 20 km and 22 km, and values in the lower stratosphere are much larger than those near 80° W.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02247078
    Standort Signatur Erwartet Verfügbarkeit
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