# Epidemics of Plant Diseases: Mathematical Analysis and by J. Kranz (auth.), Professor Dr. Jürgen Kranz (eds.) By J. Kranz (auth.), Professor Dr. Jürgen Kranz (eds.)

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For the probable flight line Schrodter expands Schmidt's equation, on condition that at time t = and at place x=O, a number N of spores is dispersed in the open space z=O, the number of spores n' found above z at time t is given by ° n' = j n dz = _2-=N=- exp (t/4nat _c2_t ) j exp ( _ 4a. _ Z_2_ _ _ c_ z) dz 4at 2a (44) with a = A/~ . 4769 -AX -~ <5 U c _·x U (45) as the equation of the probable flight line. Cutting out the shape of the flight line which here proved to be a parabola (see SCHRODTER, 1960, p.

This is justified as long as we really have ample data in hand, or believe we know exactly enough the sizes of the populations involved, and the rates of their change. It may also be justified as long as we are satisfied with the present accuracy of predictions. However, the values for variables and constants derived from measurements are, in fact, limited by their accuracy, and are on each occasion restricted in number. For these reasons each value necessarily carries an element of a probability distribution.

E. 37-41. Berkeley, Los Angeles, London: Univ. of California Press 1970. : Beitrage zur Epidemiologie von Cercospora beticola Sacco an Zuckerriiben. D. Thesis Univ. Bonn (1971).