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News Academy of Engineering Sciences A.M. Prokhorov Annotation << Back
Computer and number asymmetry
in engineering sciences |
A.D. Izotov
F.I. Mavrikidi
Present paper discusses the problem of adequacy of classical
physico-mathematical tools in the realm of engineering problems
in their vast spectra.. The main problem is discrepancy
between classical notion of space-time and fractal reality of
engineering systems environment, that causes different problems
in basic mathematical structures – smooth functions,
differential equations, definability, categoricity of results, etc.
As a sequence this leads to unlimited processes of approximation
of different kind. Due to high financial, material, social
and even political responsibility of engineering solutions
such instability of scientific results is unacceptable. It is argued
that the space-time of engineering problems is fractal, rigged
with number asymmetry. Number asymmetry is combination
of real and p-adic numbers. It has justification in pure mathematics
and fractal empirical results and is suitable both for
physico-technical and systems problems. Such shift in theoretical
basis is supported by modern computer science via
fractal, 2-adic space-time of computer. This enables transfer
and extend mathematical tools from those parts of mathematics,
which were applicably latent. Computer-based mathematics
saves classical results but its models become much more
adequate to complementarity structure of natural sciences,
reflected by fractals.
Key words: Mathematical modeling, Engineering science, Fractals,
computer, p-adic numbers.
Contacts: E-mail: izotov@igic.ras.ru
Pp. 03-13. |
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