## Guest lecture by R. R. Nigmatullin

This Thursday at 10:00 on scientific seminar Ravil Rashidovich Nigmatullin will present his latest work titled

## «General theory of experiment containing reproducible data: The reduction to an ideal experiment»

by **R.R. Nigmatullin**, proff at KNRTU-KAI, PhD

The authors suggest a general theory for consideration of all experiments associated with measurements of reproducible data in one unified scheme. The suggested algorithm does not contain unjustified suppositions and the final function that is extracted from these measurements can be compared with hypothesis that is suggested by the theory adopted for the explanation of the object/phenomenon studied. This true function is free from the influence of the apparatus (instrumental) function and when the ‘‘best fit’’, or the most acceptable hypothesis, is absent, can be presented as a segment of the Fourier series. The discrete set of the decomposition coefficients describes the final function quantitatively and can serve as an intermediate model that coincides with the amplitude-frequency response (AFR) of the object studied. It can be used by theoreticians also for comparison of the suggested theory with experimental observations. Two examples (Raman spectra of the distilled water and exchange by packets between two wireless sensor nodes) confirm the basic elements of this general theory. From this general theory the following

important conclusions follow:

1. The Prony’s decomposition should be used in detection of the quasi-periodic processes and for quantitative description of reproducible data.

2. The segment of the Fourier series should be used as the fitting function for description of observable data corresponding to an ideal experiment. The transition from the initial Prony’s decomposition to the conventional Fourier transform implies also the

elimination of the apparatus function that plays an important role in the reproducible data processing.

3. The suggested theory will be helpful for creation of the unified metrological standard (UMS) that should be used in comparison of similar data obtained from the same object studied but in different laboratories with the usage of different equipment. 4. Many cases when the conventional theory confirms the experimental data obtained from equipment (where the apparatus function was not taken into account) should be remeasured and some of the competitive theoretical hypothesis can be reconsidered, as

well.

*Communications in Nonlinear Science and Numerical Simulation*,

**27**, (2015), pp 175-192.