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Interconnection of fractional indexes of dimensions of measurands and of fractal dimensions
https://doi.org/10.32446/0368-1025it.2023-5-4-9
Abstract
The possibility of the existence of an informal relationship between two concepts of dimension – the dimension of the measurand and the fractal dimension of objects, in particular, in relation to fractional values of dimension, is investigated. Measurement results with non-zero error probabilities of the fi rst and second kinds when comparing the measured value with measures can be considered as environmental impact. For quantum theory, it is impossible to reliably predict the outcome of a measurement due to the impact of a measuring instrument on an object (non-uniformly scaled), limited only by the probability of the outcome. Fractional dimensions of units of electrical and magnetic quantities are present in the GHS system of units (centimeter, gram, second). Non-integer, including fractional, fractal dimensions appear when considering the structure of complex nonlinear objects. The commonality of the two different concepts of dimension lies in the measurement procedure in both defi nitions. It is shown that the relationship between the fractional dimensions of the measured quantities and fractal dimensions is manifested as a result of the representation of the measurement process in the form of a generalized effect characterizing the interaction of objects. The results obtained can be used to expand the scope of the fractal approach in measurement practice.
About the Authors
L. K. Isaev
Russian Research Institute for Metrological Service
Russian Federation
Russian Federation
Lev K. Isaev
S. L. Chernyshev
K. E. Tsiolkovsky Russian State Technological University
Russian Federation
Russian Federation
Sergey L. Chernyshev
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Review
For citations:
Isaev L.K., Chernyshev S.L. Interconnection of fractional indexes of dimensions of measurands and of fractal dimensions. Izmeritel`naya Tekhnika. 2023;(5):4-9. (In Russ.) https://doi.org/10.32446/0368-1025it.2023-5-4-9
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