Dynamical Measurements in the View of the Group Operators Theory
| Autor: | Georgy A. Sviridyuk, Alexander L. Shestakov, Yurii V. Khudyakov |
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| Rok vydání: | 2014 |
| Předmět: |
Physics
Theoretical computer science Dynamical systems theory Stochastic process media_common.quotation_subject Mathematical analysis Degenerate energy levels Inertia System of linear equations symbols.namesake Operator (computer programming) Wiener process symbols Initial value problem media_common |
| Zdroj: | Springer Proceedings in Mathematics & Statistics ISBN: 9783319121444 |
| Popis: | The mathematical model (MM) of the measuring transducer (MT) is discussed. The MM is intended for restoration of deterministic signals distorted by mechanical inertia of the MT, resonances in MT’s circuits and stochastic perturbations. The MM is represented by the Leontieff type system of equations, reflecting the change in the state of MT under useful signal, deterministic and stochastic perturbations; algebraic system of equations modelling observations of distorted signal; and the Showalter–Sidorov initial condition. In addition the MM of the MT includes a functional. The minimum point of the functional is a required optimal measurement. Qualitative research the MM of MT is conducted by the methods of the degenerate operator group’s theory. Namely, the existence of the unique optimal measurement is proved. This result corresponds to input signal without deterministic and stochastic perturbation. |
| Databáze: | OpenAIRE |
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