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  4. Analysis of measurement systems mathematical models by using the comparison of functions

Analysis of measurement systems mathematical models by using the comparison of functions

MMC.
2019;
Volume 6, Number 2
: pp. 268–275
https://doi.org/10.23939/mmc2019.02.268
Received: May 18, 2019
Revised: October 10, 2019
Accepted: October 10, 2019

Mathematical Modeling and Computing, Vol. 6, No. 2, pp. 268–275 (2019)

Authors:
  1. V. S. Ilkiv
  2. Z. M. Nytrebych
  3. P. Ya. Pukach
  4. I. V. Kohut
  5. B. B. Pakholok
1
Lviv Polytechnic National University
2
Lviv Polytechnic National University
3
Lviv Polytechnic National University
4
Lviv Polytechnic National University
5
Lviv Polytechnic National University

We propose an approach to mathematical modeling for a system on the basis of comparing scalar products in spaces of real functions integrable on the segment.  This approach may be used in discrete and continuous measurement systems and some combinatorial systems, in which comparison problem of function exists in the process of synthesis and optimal choice of their parameters.  In theory, such problems are characteristic of boundary value problems for equations of mathematical physics, in particular for multi-point problems that describe oscillatory processes in mechanisms.  We have found the necessary and sufficient conditions for such a comparison.  We use special transformations of sums and integrals that appear in the corresponding scalar products for vectors and functions.

measurement systems
optimization
scalar product
integration by parts
integrable functions
polynomials
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