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  • Springer  (42,599)
  • 1980-1984
  • 1965-1969  (32,184)
  • 1955-1959  (10,415)
  • 1940-1944
  • 1925-1929
  • 1968  (32,184)
  • 1955  (10,415)
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  • 1980-1984
  • 1965-1969  (32,184)
  • 1955-1959  (10,415)
  • 1940-1944
  • 1925-1929
Year
  • 1
    Electronic Resource
    Electronic Resource
    Note from the editor (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 1-1 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476935
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  • 2
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    Erythrocyte distribution in arterial blood flow: IV. Simplification of the proposed equations (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 27-32 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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    URL: http://dx.doi.org/10.1007/BF02476937
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  • 3
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    Éléments d’une théorie générale de la croissance d’une population (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 33-46 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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    URL: http://dx.doi.org/10.1007/BF02476938
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  • 4
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    Neuroendocrine control of thyroid secretion in living systems: A feedback control system model (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 3-26 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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    URL: http://dx.doi.org/10.1007/BF02476936
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  • 5
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    Linear bulk diffusion into heterogeneous tissue (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 47-59 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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    URL: http://dx.doi.org/10.1007/BF02476939
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  • 6
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    The identification of recirculating systems in the frequency domain (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 87-104 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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    URL: http://dx.doi.org/10.1007/BF02476941
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  • 7
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    A systems-mathematical interpretation of psychoanalytic theory (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 61-86 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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    URL: http://dx.doi.org/10.1007/BF02476940
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  • 8
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    Cellular systems as sequential machines: Stability properties (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 117-122 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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    URL: http://dx.doi.org/10.1007/BF02476943
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  • 9
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    Cellular systems as graphs (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 105-116 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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).
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    URL: http://dx.doi.org/10.1007/BF02476942
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  • 10
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    A theoretical model for the control mechanisms in biochemical reactions (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 123-133 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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    URL: http://dx.doi.org/10.1007/BF02476944
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  • 11
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    A contribution to Rashevsky’s mathematical theory of development (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 135-151 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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  • 12
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    Mathematical biology of automobile driving: III (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 153-162 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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  • 13
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    Computer solution of the ultracentrifuge equation (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 205-213 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02476690
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  • 14
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    Organismic sets: II. Some general considerations (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 163-174 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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  • 15
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    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 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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).
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    URL: http://dx.doi.org/10.1007/BF02476948
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  • 16
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    Models of social structure (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 215-224 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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    URL: http://dx.doi.org/10.1007/BF02476691
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  • 17
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    The struggle for life: II. Three competitors (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 291-298 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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  • 18
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    Pulse velocities in initially stressed cylindrical rubber tubes (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 299-308 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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  • 19
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    A macroscopic formulation of electromagnetophoresis (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 309-318 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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  • 20
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    On relationships between various distribution functions in balanced unicellular growth (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 319-323 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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  • 21
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    The differential equations for specific activities in a distributed tracer system (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 325-331 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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  • 22
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    Properties of solution of the diffusion-reaction equation. II (1968)
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    Bulletin of mathematical biology 30 (1968), S. 333-340 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
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    Notes: 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.
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  • 23
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    Some possible theoretical implications of experiments on the chemical transfer of memory (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 341-349 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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    A remark on the possible use of nonoriented graphs in biology (1968)
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    Bulletin of mathematical biology 30 (1968), S. 351-353 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
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    Notes: 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).
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    A note on the development of organismic sets (1968)
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    Bulletin of mathematical biology 30 (1968), S. 355-357 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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  • 26
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    Entropy and the complexity of graphs: III. Graphs with prescribed information content (1968)
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    Bulletin of mathematical biology 30 (1968), S. 387-414 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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  • 27
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    Transient behavior of arterial systems in response to flow pulses (1968)
    Springer
    Bulletin of mathematical biology 30 (1968), S. 359-385 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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  • 28
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    Equations for the age structure of growing populations (1968)
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    Bulletin of mathematical biology 30 (1968), S. 427-435 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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    An axiomatic explanation of complete self-reproduction (1968)
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    Bulletin of mathematical biology 30 (1968), S. 415-425 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: 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.
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    A theoretical model of the cornea for use in studies of tonometry (1968)
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    Bulletin of mathematical biology 30 (1968), S. 437-453 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: 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.
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    The conservation of the biomass density and the age structure of the populations (1968)
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    Bulletin of mathematical biology 30 (1968), S. 553-563 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: 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.
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    A neural model for conditioned avoidance learning (1968)
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    Bulletin of mathematical biology 30 (1968), S. 565-579 
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    Topics: Biology , Mathematics
    Notes: 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.
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    Applications of a surface dipole model to biological cells rationale (1968)
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    Bulletin of mathematical biology 30 (1968), S. 581-614 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    Die Jagdwissenschaft in Deutschland (1955)
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    European journal of wildlife research 1 (1955), S. 1-7 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Summary The hunting-science has rounded off itself in the course of the last about 50 years from the junction of its natural and intellectual scientific foundations under joining of the technical, economical and political factors, concerning hunting. There are represented its knowledge got thereby, as well as the problems due for the near future, the difficulties and possibilities in organizing, personal and real consideration.
    Abstract: Résumé La science de chasse s'est arrondie dans le courant des dernières environ 50 années de la fusion de ses bases scientifiques naturelles et intellectuelles, y compris les facteurs techniques, économiques et politiques concernat la chasse. Ses connaissance gagnées de cette manière et les tâches échues à l'avenir proche, les difficultés et les possibilités à l'égard d'organisateur, de personnel et d'objet sont représentées.
    Notes: Zusammenfassung Die Jagdwissenschaft hat sich im Laufe der letzten etwa 50 Jahre aus der Zusammenfassung ihrer natur- und geisteswissenschaftlichen Grundlagen unter Hinzutreten der die Jagd betreffenden technischen, wirtschaftlichen und politischen Faktoren abgerundet. Ihre dadurch gewonnenen Erkenntnisse und für die nähere Zukunft fälligen Aufgaben, die Schwierigkeiten und Möglichkeiten in organisatorischer, persönlicher und sachlicher Hinsicht werden dargestellt.
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    Vom “Pfeifen” des Murmeltieres (1955)
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    European journal of wildlife research 1 (1955), S. 32-33 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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    URL: http://dx.doi.org/10.1007/BF02093150
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    Vergleich der Hasenstrecken von Vorsteh- und Kesseltreiben (1955)
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    European journal of wildlife research 1 (1955), S. 29-32 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Summary On the same hunting ground on 100 ha area had been killed 15 hares by driving them towards the shooters and 24 hares by circular beats. The bag on young hares has been the same in either hunting-manner, whereas more old ones escaped the kill by driving the hares towards the shooters.
    Abstract: Résumé Dans la même varenne on a tué sur un district de 100 ha des 15 lièvres par placer les chasseurs en face des batteurs et des 24 lièvres par battue concentrique. C'est le même nombre des jeunes lièvres, qui est tué par les deux manières de chasser. Les chausseurs placés en face des batteurs plus des lièvres vieux s'échappaient.
    Notes: Zusammenfassung Im gleichen Jagdgebiet wurden auf 100 ha abgejagter Fläche bei Vorstehtreiben 15 Hasen, bei Kesseltreiben 24 Hasen erlegt. Die Strecke an Junghasen war bei beiden Jagdarten gleich groß, während bei den Vorstehtreiben mehr Althasen dem Abschuß entgingen.
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    Das Kruckenwachstum beim jungen Gams (1955)
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    European journal of wildlife research 1 (1955), S. 22-29 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Summary The growth of horns of the first three years is decisive for the size of the ripe trophy; from this reason the form of the horns during youth is especialy fit to draw from it conclusions as to the quality of the ripeness-form of the horns. The first two classes of age being to be recognized with security with regard to their age, the shooting off according the size of horns in the class of the yearlings and two years old ones, should be furthered. For this purpose there are given directions, according to the local experiences, for the distinction of males to be shot off and those promising for the time to come, within these two classes of age.
    Abstract: Résumé La croissance des cornes du chamois pendant les premières trois années c'est décicive pour la vigueur du trophée mûr; c'est pourquoi c'est la forme du corne pendant le jeune âge, qui est particulièrement propre à en tirer des conclusions à l'égard de la qualité de la forme de maturité du corne. Les premières deux classes d'âge étant connaissables avec certitude eu égard à leur âge, on devrait favoriser la chasse relectif dans la classe des animaux d'un et de deux ans. A cela d'après les expériences locales, des directions sont données pour la distinction des mâles à abattre et ceux-ci qui promettent des trophées forts pour le temps à venir dans ces deux classes d'âge.
    Notes: Zusammenfassung Das Kruckenwachstum der ersten drei Jahre ist entscheidend für die Stärke der reifen Trophäe; deshalb ist die Jugendform der Krucke besonders geeignet, aus ihr Rückschlüsse auf die Qualität der Reifeform der Krucke zu ziehen. Da die ersten beiden Altersklassen mit Sicherheit auf ihr Alter anzusprechen sind, sollte man den Wahlabschuß in der Klasse der Jährlinge und Zweijährigen fördern. Dazu werden nach den örtlichen Erfahrungen Richtlinien für die Unterscheidung von Abschuß- und Zukunftsböcken in diesen beiden Altersklassen gegeben.
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    Wildverluste durch Hochwasser (1955)
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    European journal of wildlife research 1 (1955), S. 33-35 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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    Aufzucht von Rehkitzen (1955)
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    European journal of wildlife research 1 (1955), S. 35-36 
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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    Nachrichten (1955)
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    European journal of wildlife research 1 (1955), S. 36-36 
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    Referate (1955)
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    European journal of wildlife research 1 (1955), S. 36-48 
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    Erstes internationales Treffen der Jagdwissenschaftler (1955)
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    European journal of wildlife research 1 (1955), S. 49-50 
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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    Über das regelmäßige Vorkommen von Gänsegeier und Bartgeier in den salzburgischen Alpen (1955)
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    European journal of wildlife research 1 (1955), S. 78-79 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Résumé Du territoire de Salzbourg (Tauern) on a pû constater que le vautour fauve (Gyps fulvus fulvus) soit devenu un oiseau d'été qui revient régulièrement. La limite inférieure de diffusion d'altitude est rapportée à 1000 m NN. Le nombre, annuel des vautours habitant ce territoire de Mai à September (en moyen 200 vautours d'oie) dépend directement du temps de départs des moutons pour les Alpes et du nombre départi. Les vautours fauve n'airent pas dans les Alpes de Salzbourg, ils viennent des Balkans après la couvaison au mois de Février. Les gypaètes barbus sont par contre devenus depuis 25 ans oiseaux de demeure dans ce territoire.
    Notes: Summary In the Tauern area near Salzburg the griffon-vulture (Gyps fulvus fulvus) is observed as a regular summer bird. The lowest limit of its occurrence is reported to be about 1000 m NN. The number of vultures living from Mai to September in this area (averagely about 200) shows an immediate dependence on the date of the departure of sheep for the Alpine pastures and the quantity of sheep to be found there. The griffon-vultures do not build their eyries in the Salzburg mountains, but they immigrate into this area after their hatching time in February, coming from the Balcans. The bearded vulture (Gypaetus barbatus), however, returned to keep to these same grounds since about 1930.
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    Eine europäische Zentralstelle für Gamsräudebekämpfung (1955)
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    European journal of wildlife research 1 (1955), S. 80-81 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Résumé L'apparition de la gale des chamols s'est accrue d'une telle façon qu'on ne peut plus computer sur son extirpation complet. On peut seulement essayer d'empecher qu'elle ne se répande pas plus loin ou que des foyers de contagion neuf se forment. On a proposé d'installer un bureau central pour l'Autriche, la Bavière, la Suisse, l'Italie et la Yougoslavie et de rendre de rigueur la notification de l'apparition, de la gale de chamois aux autres pays.
    Notes: Summary The scab of the chamois has grown to such an extend that we cannot hope to exterminate it, but can only try to prevent further extension and the formation of new centres of contagion. With this end in view it has been recommended to create a common centre for the countries of Austria, Bavaria, Switzerland, Italy and Yugoslavia, together with an obligation to report new cases to all the countries above mentioned.
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    Produktivität und Qualität der Hasenstrecken 1953 (Kurzreferat) (1955)
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    European journal of wildlife research 1 (1955), S. 75-77 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Résumé Depuis 1946 on a fait des recherches relatives au menu gibier le plus important de la Pologne le lièvre de champs (lepus europ. Pall.) dans les districts gouvernementaux de Gdansk et de Bydgoszcz à l'aide des butins de la chasse aux lièvres et au lièvres vivant. L'index moyen de rendement (lièvres tués sur 100 ha) est entre 15 et 50 pièces par 100 ha. La proportion moyenne entre hases et lièvres est de 50,7% ♂ et 49,3% ♀. Le poids moyen de 1404 lièvres tués en 1953 était de 4,2 kos, le poids maximal est 5 kos. Quoique l'été fût assez sec et qu'on suppose que la réproductibilité d'une paire de lièvres soit de 10 jeunes lièvres, on a pû constater par une hase tuée seulement 0,54 jeune lièrre. Il fut pour le moment impossible de trouver une raison objective pour cette proportion très base. Pour les autres parts de la Pologne l'année 1953 était une année de lièvres très mauvaise, et seulement les districts du Nord avaient une population satisfaisante. La part de la venaison par lièvre est en moyen 35,4% par poids moyen de 4,1 kos. La viande très maigre du lièvre contient 0,2% de graisse mais par contre approximativement 25% d'albumine.
    Notes: Summary Since 1946 there have been realized investigations about the most important small game of Poland, the field hare (Lepus europ. Pall.), uitilizing bagged and living hares in the administrative districts of Gdansk and Bydgoszcz. Results: Average index of production (=number of pieces of bagged hares on 100 ha) fluctuates between 15 and 50 hares/100 ha. The average proportion of sex is 50.7% of ♂ hares and 49.3% of ♀ hares. The average weight of 1404 hares shot in 1953 was 4.2 kilos; the maximum weight was 5 kilos. Although the summer of 1953 was dry in the district of Gdansk, only 0.54 young hares fell from 1 shot old, female hare in spite of the supposed average propagation of 10 young hares out of 1 couple of old hares. This small number may at present not be interpreted objectively. In other parts of Poland 1953 has been a really bad hare year, only the Northern districts had a good stock. The average eatable game part of a hare amounts to 35.4% of an average total weight of 4.1 kilos. The very lean hare meat contains 0.2% of fat, but about 25% of albumen.
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    Jagdwissenschaft und Praxis (1955)
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    European journal of wildlife research 1 (1955), S. 81-84 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Résumé L'eploration de la science de chasse est malheureusement peu soutenue par les gens de profession. Les appels faits en vue de recevoir le matériel nécessaire aux recherches, ont eu trés peu de succès. L'exploration doit de ce fait essayer d'avoir à sa disposition cantons d'essai, grilles et enclos pour pouvoir s'occuper sur une plus large échelle des bêtes vivantes. Cependant, il ne faut pas s'attendre d'avoir sous peu des résultats.
    Notes: Summary The research in the section of game management does not receive much support from practice. Appeals to provide material which is wanted for purposes of examination do not meet with much success. Therefore research has to attempt to organize special districts of investigation, enclosures, and preserves in order to be able to observe live animals to a greater extend. Results may not be anticipated within a short period of time.
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    Über die europäische Jagdliteratur des 12. bis 15. Jahrhunderts (1955)
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    European journal of wildlife research 1 (1955), S. 84-92 
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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    Über bemerkenswerte Zerlegungsbefunde beim Schwarzwild (1955)
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    European journal of wildlife research 1 (1955), S. 104-106 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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    Um ein System der Jagdwissenschaft (1955)
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    European journal of wildlife research 1 (1955), S. 101-104 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Résumé La science de chasse a subi pendant le dernier siècle un tel élargissement et une telle consolidation, qu'il y faut maintenant apporter un examen, un ordre et une élimination. La manière d'envisager les faits varie selon les besoins et est différente s'il s'agit d'établir un exposé pour l'enseignement par exemple, ou d'établir la structure d'une matière bibliographique, ou de donner la description logique et mentale d'une continuité des problèmes.
    Notes: Summary The science of Game Management (or knowledge of Game Management) has experienced such an extension and consolidation in the course of the last century that this field requires to be sifted, ordered, and limited. According to circumstances, if a classification of matters for teaching purposes or for bibliographical purposes is intended, or if a representation of the logical and ideal relations of the problem is to be given, the results will always differ.
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    Organisation der Wildforschung in Schweden (1955)
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    European journal of wildlife research 1 (1955), S. 99-100 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Résumé L'Union des Chasseurs Suèdois fondée il y a 100 ans a entamée pour la primière fois l'exploration du gibier en Suède. Ce fut cependant la Loi de Chasse de 1938 qui a rendu possible la création d'une organisation plus solide, ayant à sa disposition des moyens suffisants. Après un développement de plusieurs années le Gouvernement Suèdois vient d'installer cette année un Conseil indépendant pour l'exploration du gibier. Ce Conseil a les buts suivants: Suivre de près sur son domaine d'activité au développement tant à l'intérieur du pays qu'à l'extérieur. Créer une collaboration entre les diverses Organisations d'exploration et avoir soins d'éléver l'efficacité des recherches. Le Conseil doit soutenir en outre l'initiative importante de chaque Organisation pour l'exploration du gibier et au besoin saisir lui-même l'initiative pour encourager une telle exploratation. L'exploratation du gibier a lieu maintenant principalement à l'Université d'Economie Forestière à Stockholm sous la direction de M. le ProfesseurNotini et à l'Institut National vétérinaire de M. le Docteur med. vet.Borg. Certaines explorations pratiques seront l'objet des recherches faites par l'aide de champ de l'Union des Chasseurs,M. Nils Höglund.
    Notes: Summary Game Research in Sweden has been taken up in the first place by the “Swedish Union of Hunters”, founded over 100 years ago. Only the Shooting Law of 1938 made a firmer organization and the disposition of means possible. After several years' development there has been appointed by the Swedish Government in this year an independent Council for Game Research, which has the following tasks: The Council has to follow the development in its sphere of activity as well within its native country as in foreign countries. It has to act for a co-operation in research, which is carried through by different research organs, and to take care of the raise of research effectivity. Besides the Council has to support the initiative of every research, which is important for the care of game, and it has to seize the initiative for the promotion of such research itself, if required. At present game research is carried through chiefly by the “Academy of Forestry” at Stockholm (under direction of ProfessorNotini) and in the “National Veterinary College” (by Dr. med. vet.Borg). Besides there exists a certain practical investigation of the subject in the “Union of Hunters” by Field-AssistentNils Höglund.
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    Ein Erklärungsversuch der bei Rotwild in Westdeutschland anzutreffenden Unterschiede im Körpergewicht (1955)
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    European journal of wildlife research 1 (1955), S. 92-98 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Résumé Les interprétations données parM. Beninde sur les différences dans le poids des fauves ne sont pas satisfaisantes. On a surtout pas assez pris en considération les facteurs concernant la paisson. En 33 administrations de cantons on vient de vérifier les rélations entre le poids moyen des fauves et celles des conditions dans les cantons, la qualité de populations était entre 51,7 et 72,8 kos. Il était impossible d'établir une rélation quelconque entre les conditions de vie dans le canton et le poids de la venaison. Il était en particulier impossible de reconnaitre une influence exercé par le climat. De ces recherches on doit conclure, que les différences des mésures corporelles dépendent des dispositions de la race. La profusion des fauves, d'abord ferme, s'est relâcher en ilots isolés. Par l'abattement sans plan, une diminution des allèles dans ces groupes isolées a eu lieu, qui a amené une formation des différences raciales. Il en suit pour le pratique que, lièrement la qualité de l'état du gibier peur être seulement corrigé dans une mésure limitée par l'amélioration du paisson et 2ièmement, qu'on peut seulement avoir un succès par l'élimination, s'il y a encore des bonnes qualités héréditaire et que, 3ièmement il faut amener les bêtes ayant ces qualités héréditaire requises, si la population en est dépourvu.
    Notes: Summary The explanations given byBeninde for the differences in the body weight of red deer are not satisfactory, above all the factor of browsing has not been considered sufficiently. Rherefore the relation between the average weight of grown animals and the conditions of the district have been examined in 33 Forestry Districts of Western Germany. The quality of populations was between 51.7 and 72.8 kilos. There could not be proved relations between the conditions of the living space and the weight of game within larger areas, especially there could not be recognized any climatical influence. The investigations permit the conclusion that differences are caused by racial particularities concerning size of bodies. The originally close distribution of red deer has been dissolved into isolated isles. By arbitrary shooting a diminution of alleles within the isolated populations has taken place which is the cause of the formation of racial differences. For practical purposes we may draw the following conclusions: 1. the quality of a stock may be improved by improved browsing only up to certain limit, 2. the method of selective shooting may lead to good results if there are still hereditary qualities of good condition, 3. it is necessary to introduce heads of deer of better hereditary qualities, if such have disappeared out of the population.
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    Zur Biologie der Wildschweinlaus (1955)
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    European journal of wildlife research 1 (1955), S. 145-148 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Description / Table of Contents: Summary The first scientific prove of the occurrence of the louse of the wild boar (Haematopinus apri Goureau) in Germany was established in 1942. The auther investigates the occurence, development, nourishment, expressions of life, contagion, and the extent of seizure.
    Abstract: Résumé La présence du pou de sanglier (Haematopinus apri Goureau) en Allemagne fut pour la première fois établie en 1942. L'auteur traite ici l'habitat, le développement, la nourriture, la condition de vie, la transmissibilité et la force du saisissement.
    Notes: Zusammenfassung Der erste wissenschaftliche Nachweis des Vorkommens der Wildschweinlaus (Haematopinus apri Goureau) in Deutschland erfolgte 1942. Verfasser befaßt sich mit dem Vorkommen, der Entwicklung, der Nahrung, den Lebensäußerungen, der Übertragung und der Befallsstärke.
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    Ein Beitrag zum abdominalen Kryptorchismus beim Rehbock (1968)
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    European journal of wildlife research 14 (1968), S. 28-30 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: 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.
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    Pansenstein beim Reh (1968)
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    European journal of wildlife research 14 (1968), S. 30-31 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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    Zu einigen Jagdverfahren auf Hirsche im Altertum (1968)
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    European journal of wildlife research 14 (1968), S. 31-34 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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    Bericht über den VIII. Kongreß des Internationalen Ringes der Jagdwissenschaftler in Helsinki/Finnland vom 22.–27. VIII. 1967 (1968)
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    European journal of wildlife research 14 (1968), S. 34-40 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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    Einfache Methode zur Darstellung der Altersklassenverhältnisse in Schalenwildbeständen (1968)
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    European journal of wildlife research 14 (1968), S. 88-90 
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    ISSN: 1439-0574
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
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    A theory of speech perception: II (1968)
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    Bulletin of mathematical biology 30 (1968), S. 455-479 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: 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.
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    On possible reversible changes between arational and rational behavior of society (1968)
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    Bulletin of mathematical biology 30 (1968), S. 519-525 
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    Topics: Biology , Mathematics
    Notes: 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.
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    Remarks on Weissenberger’s Comments Concerning “Stability Analysis of a Mathematical Neuron Model” (1968)
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    Bulletin of mathematical biology 30 (1968), S. 529-529 
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    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
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    A suggestion of a new approach to the theory of some biological periodicities (1968)
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    Bulletin of mathematical biology 30 (1968), S. 751-760 
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    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: 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.
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    On the numerical solution of higher order nonlinear parabolic equations (1968)
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    Computing 3 (1968), S. 139-150 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: 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.
    Notes: 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.
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    The behavior of jet streams in potential fallout situations (1968)
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    Meteorology and atmospheric physics 17 (1968), S. 8-16 
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    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: 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.
    Abstract: 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”.
    Notes: 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.
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    Results of investigation on precipitation and cloud electricity based on 15 years of observation (1968)
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    Meteorology and atmospheric physics 17 (1968), S. 17-29 
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    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: 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.
    Abstract: 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.
    Notes: 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.
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    Remarks concerning the “ten-year-period” of atmospheric electricity (1968)
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    Meteorology and atmospheric physics 17 (1968), S. 88-89 
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    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
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    Beschreibung des Stromfeldes im Alpenbereich mittels Windmatrizen (1968)
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    Meteorology and atmospheric physics 17 (1968), S. 61-77 
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    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: 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.
    Abstract: 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.
    Notes: 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.
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    The formation of crevasses in relation to the measured distribution of strain-rates and stresses (1968)
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    Meteorology and atmospheric physics 17 (1968), S. 78-87 
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    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: 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.
    Abstract: 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.
    Notes: 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.
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    Eddy flux of sensible heat at different levels in the stratosphere (1968)
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    Meteorology and atmospheric physics 17 (1968), S. 101-113 
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    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: 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.
    Abstract: 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.
    Notes: 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.
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    Endliche Abbildungsscharen in kompakten topologischen Mannigfaltigkeiten (1955)
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    Monatshefte für Mathematik 59 (1955), S. 1-21 
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    Topics: Mathematics
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    Zur Theorie der Hermiteschen Kreise (1955)
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    Monatshefte für Mathematik 59 (1955), S. 22-26 
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    Beziehungen zwischen den Koeffizienten einer analytischen Funktion und ihrer Umkehrfunktion (1955)
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    Monatshefte für Mathematik 59 (1955), S. 27-33 
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    Überall unlösbare lineare partielle Differentialgleichungen (1955)
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    Monatshefte für Mathematik 59 (1955), S. 34-42 
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    Über die Summe $$\mathop \Sigma \limits_{p \leqq N} e(\alpha p)$$ (1955)
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    Monatshefte für Mathematik 59 (1955), S. 43-44 
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    Quadriken als Bewegflächen (1955)
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    Monatshefte für Mathematik 59 (1955), S. 45-63 
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    Buchbesprechungen (1955)
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    Monatshefte für Mathematik 59 (1955), S. 64-72 
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    Discrete analogs of inequalities of Wirtinger (1955)
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    Monatshefte für Mathematik 59 (1955), S. 73-90 
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    Über die Anzahl der Teiler einer natürlichen Zahl, welche die Formp−1 haben (1955)
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    Monatshefte für Mathematik 59 (1955), S. 91-97 
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    Über die Lösungszahl eines Systems von Gleichungen in Primzahlen (1955)
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    Monatshefte für Mathematik 59 (1955), S. 98-103 
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    Über den Typus eines Zerlegungsringes (1955)
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    Monatshefte für Mathematik 59 (1955), S. 104-110 
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    Über Loxodromen auf Zylindern 2. Grades (1955)
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    Monatshefte für Mathematik 59 (1955), S. 111-117 
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    Gruppen von Restklassen nach Restpolynomidealen in mehreren Unbestimmten (1955)
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    Monatshefte für Mathematik 59 (1955), S. 118-145 
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    Über unwesentliche eindimensionale Singularitäten (1955)
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    Monatshefte für Mathematik 59 (1955), S. 165-177 
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    Circuits in critical graphs (1955)
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    Monatshefte für Mathematik 59 (1955), S. 178-187 
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    The coefficients of certain power series (1955)
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    Monatshefte für Mathematik 59 (1955), S. 188-193 
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    Buchbesprechungen (1955)
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    Monatshefte für Mathematik 59 (1955), S. 146-164 
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    Gruppen von Restpolynomidealrestklassen nach Primzahlpotenzen (1955)
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    Monatshefte für Mathematik 59 (1955), S. 194-202 
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    Zur Abschätzung der Wurzeln algebraischer Gleichungen (1955)
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    Monatshefte für Mathematik 59 (1955), S. 203-216 
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    Konkave Eikörperfunktionale (1955)
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    Monatshefte für Mathematik 59 (1955), S. 230-237 
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    Über die Einbettung hyperbolischer Räume in euklidische Räume (1955)
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    Monatshefte für Mathematik 59 (1955), S. 217-229 
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    Buchbesprechungen (1955)
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    Monatshefte für Mathematik 59 (1955), S. 238-252 
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    Über die Projektion mittels der Sehnen einer Raumkurve 3. Ordnung (1955)
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    Monatshefte für Mathematik 59 (1955), S. 258-273 
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    Über höhere kritische Determinanten von Sternkörpern (1955)
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    Monatshefte für Mathematik 59 (1955), S. 274-304 
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    On the sums of certain series of Bessel functions (1955)
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    Monatshefte für Mathematik 59 (1955), S. 253-257 
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    Topics: Mathematics
    Notes: Summary Though many forms of series of Bessel functions of increasing order appear in the literature, they all seem to involve a term by term increase in the order by unity, possibly by 1/2, or by some integer greater than unity, usually 2. InWatson's “Bessel Functions” (1) no case appears in which the increase in the order is not an integer or 1/2. The purpose of this note is to give the sums of series of the form $$\mathop \Sigma \limits_{n = 0}^\infty J{}_s(z) and \mathop \Sigma \limits_{n = 0}^\infty ( - 1)^n J{}_s(z)$$ and similar series involvingI s , wheres is of the form 2kn+v andk is any positive real number. Such series have occurred in the theory of heat conduction and fluid flow (2). The method is to replace the function by a contour integral of Schläfli type.
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    Über die Formengruppe (1955)
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    Monatshefte für Mathematik 59 (1955), S. 305-317 
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    Über die Anzahl der Lösungen von [p−1,q−1]≤x (1955)
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    Monatshefte für Mathematik 59 (1955), S. 318-319 
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    An extremal theorem for N-simplexes (1955)
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    Monatshefte für Mathematik 59 (1955), S. 320-322 
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    On orthogonal polynomials with extrema at the ends of the orthogonality interval (1955)
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    Monatshefte für Mathematik 59 (1955), S. 323-330 
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    Buchbesprechungen (1955)
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    Monatshefte für Mathematik 59 (1955), S. 331-348 
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    Die diophantische Gleichungx 2+4D=y p im Zusammenhang mit Klassenzahlen (1968)
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    Monatshefte für Mathematik 72 (1968), S. 1-5 
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    On pseudo-proper values of a linear transformation (1968)
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    Monatshefte für Mathematik 72 (1968), S. 6-8 
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