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  • Springer  (20,569)
  • MDPI Publishing
  • 1960-1964  (20,569)
  • 1964  (20,569)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 26 (1964), S. 1-7 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In the arteries, blood flow and blood pressure are pulsatile in nature (Roston, 1962a; Roston 1962b). The patterns of blood movement and mural distension in the arteries are important because they may be associated with life-threatening degenerative changes in the arterial walls. As the vascular channels narrow, the pulsation decreases. At the level of the capillaries, almost no pulsation exists (Best and Taylor, 1961). The tissues are affected by the direct flow in the capillaries and not by the pulsation in the arteries. Thus, such quantities as pulse pressure, systolic pressure, and diastolic pressure which characterize blood movement in the arteries are not important as far as the tissues are concerned. Rather, the average pressure and flow in the capillaries are the quantities significant for tissue blood flow. The present study analyzes the local blood circulation in a typical tissue. Logical extension of this analysis results in insights into the physiological behavior of the circulation which integrate a considerable body of experimental data.
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 26 (1964), S. 25-29 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Error-detecting codes have been known to mathematicians and to electrical engineers for over ten years. In general, such codes utilize an additional orparity bit for purposes of detecting errors by the addition of all positive binary bits or “1’s” occurring in any code word. However, since the process of addition is required for such code detection, it is not surprising that these codes have not been applied to the nucleic acid molecule. In 1962, P. I. Hershberg (Trans. I.R.E., CS-10, 280–4, 1962) outlined a categorical constraint which permitted the realization of a class of error-detecting codes which did not require parity bits. This class of codes is applied to the nucleic acid molecule in the present paper.
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  • 3
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    Springer
    Bulletin of mathematical biology 26 (1964), S. 31-38 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Compartment systems are often used as models for tracer and drug kinetics. The structure of a compartment system is here analyzed by means of theory of graphs methods. In particular the precursor-successor relationship between any two compartments is classified according to the structure of the graph of the system and to the values of the elements of the matrix associated with it.
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  • 4
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    Springer
    Bulletin of mathematical biology 26 (1964), S. 39-43 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract An application of a bifurcation theorem shows the existence of periodic solutions of a system of differential equation used to describe competition between two species. It is then shown that the results are more general than those previously established.
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  • 5
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    Springer
    Bulletin of mathematical biology 26 (1964), S. 9-24 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The 2o and 10o field color-matching functions are independent: one specification is not a linear transformation of the other, even after correcting for macular pigment effects. Therefore, the “true” color-matching functions which directly describe the linear responses of the eye must be different for the two field sizes. This means that a given stimulus will, in general, have a different chromaticity depending upon the field size, regardless of the choice of any one colorimetric co-ordinate system for all field sizes. However, in spite of these chromaticity differences, a large uniform field usually appears nearly uniform. Such color uniformity implies that even though chromatic differences occur as a function of retinal position or field size, these differences are small. If this is the case, then the underling “true” color-matching functions determining the observed color-matching functions must be nearly, but not quite, identical. These differences vanish as identity between the sets of color-matching functions is approached. This property suggests a method of calculating the “true” color-matching functions. The “true” color-matching functions must approximate those obtained by minimizing the chromaticity differences between two independent sets of data. This can be done by assuming that the coefficients of transformation should be adjusted so as to produce as nearly identical chromaticities for spectrum stimuli as possible. In this paper, it is also assumed that the “true” color-matching functions have no negative values, as if they were based on actual absorption spectra. This article describes the calculation of the “true” 2o and 10o field color-matching functions satisfying these two conditions. For both field sizes, the maxima of the three functions are near 435, 540, and 585 mμ, after correcting for the filtering effects of the ocular media and macular pigment.
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  • 6
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    Springer
    Bulletin of mathematical biology 26 (1964), S. 45-47 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In this note the principal convergence theorem (F. Rosenblatt,Principles of Neurodynamics, Spartan Books, Washington D.C., 1962, 111–116) is proved by a new method.
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  • 7
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    Bulletin of mathematical biology 26 (1964), S. 49-55 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Considering only nearest neighbor interactions, an expression is obtained for the grand partition function for the adsorption of two kinds of monovalent positive ions at a long chain of one type of monovalent negative fixed sites in an electric field. Expressions are obtained for the fractions of sites which are occupied by each kind of ion as well as of those which are unoccupied as a function of the potential of the electric field.
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  • 8
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    Springer
    Bulletin of mathematical biology 26 (1964), S. 57-61 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract In connection with a series of previous papers by this author (Bulletin of Mathematical Biophysics,21, 299–308, 375–385;22, 257–262, 263–267;23, 19–29;24, 319–325) results obtained by A. Crawford (Economics 5, 417–428) on the effects of irrelevant lights on reaction times toward a given light stimulus are discussed. The conclusions from a previous paper of this author (Bulletin of Mathematical Biophysics,23, 19–29) are elaborated.
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  • 9
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    Springer
    Bulletin of mathematical biology 26 (1964), S. 77-81 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A mathematical model has been constructed to describe experimental data recorded in a study of a simple avoidance situation. The theoretical description makes use of the concept of the effective number of shocks. The model explains the existence of oscillations encountered in previous experiments.
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  • 10
    Electronic Resource
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    Springer
    Bulletin of mathematical biology 26 (1964), S. 63-75 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Response probabilities are interpreted from two points of view. One corresponds to fluctuations in physical parameters suggestive of a neurological basis, and the other corresponds to fluctuations in stimulus sample constitution. The two interpretations are shown to be equivalent under rather general conditions, giving the same type of relation between response and training states. This relation is different from that obtained via the response strength concept used in Part I. As a step toward evaluating the difference in predicted behavior for these different response-training relations, a general functional-difference equation is derived that describes the moments of the corresponding stochastic process in experimenter-subject controlled experiments. As an immediate application, it is used to obtain the continuity condition for the solution of the functional equation treated in Part I, and to justify the differentiability conditions assumed in establishing asymptotic properties of the solution as a function of the reinforcement parameter.
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