Abstract
A closed solution of the integral equation obtained by N. Rashevsky, with the assumption that the inhibitory influence between centers is a constant, i.e., independent of the distance apart, is obtained. Furthermore, a more general kernel, representing a variable inhibitory influence, which in our case is a monotonic (increasing or decreasing) function of the distance between centers, is introduced. The resulting integral equation is solved and some properties of the solution discussed.
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References
N. Rashevsky, “Mathematical Biophysics and Psychology,”Psychometrika, 1936,1, pp. 1–26.
N. Rashevsky, “Mathematical Biophysics of Delayed Reflexes in Connection with the Theory of Error Elimination.”Psychometrika, 1936,1, 265–273. We shall refer to this paper as II.
In fact ifK is expressible as a sum of finite number of such products. See,e. g., Courant-Hilbert,Methoden der Mathematischen Physik, pp. 99–101, 1931 (Berlin).
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Householder, A.S., Amelotti, E. Some aspects of Rashevsky's theory of delayed reflexes. Psychometrika 2, 255–262 (1937). https://doi.org/10.1007/BF02287897
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DOI: https://doi.org/10.1007/BF02287897