Application of the Discrete Geometrical Invariants to the Quantitative Monitoring of the Electrochemical Background


Application of the Discrete Geometrical Invariants to the Quantitative Monitoring of the Electrochemical Background


R. R. Nigmatullin1, H. C. Budnikov2, A. V. Sidelnikov3, E. I. Maksyutova3

1Radioelectronic and Informative-Measurements Techniques Department, Kazan National Research Technical University (KNRTU-KAI)K. Marx str. 10. , 420011, Kazan, Tatarstan, Russian Federation;
2A.M. Butlerov Institute of Chemistry, Kazan Federal University (KFU), Kazan, Russian Federatio;
3Chemistry Department, Bashkir State University, Ufa, Russian Federation


Research Journal of Mathematics and Computer Science

In this paper, we apply the statistics of the fractional moments (SFM) and discrete geometrical sets/invariants (DGI) for explain of the temporal evolution of the electrochemical background. For analysis of this phenomenon, we apply the internal correlation factor (ICF) and proved that integral curves expressed in the form of voltammograms (VAGs) are more sensitive in comparison with their derivatives. For analysis of the VAGs (integral curves), we propose the set of the quantitative parameters that form the invariant DGI curves of the second and the fourth orders, correspondingly. The method of their calculation based on the generalization of the well-known Pythagor’s theorem is described. The quantitative parameters that determine these DGI allow monitoring the background of the electrochemical solution covering the period of 1-1000 measurements for two types of electrode (Pt and C) and notice the specific peculiarities that characterize each electrode material. The total set of 1000 measurements was divided on 9 parts (1-100, 101-200, 201-300, …, 901-1000) and the duration of each hundred set was 1300 sec. The proposed algorithm is sensitive and has a “universal” character. It can be applied for a wide set of random curves (experimental measurements) that are needed to be compared in terms of a limited number of the integer moments. The qualitative peculiarities of the background behavior for two types of electrodes (Pt and C) based on the DGI can be explained quantitatively.


Keywords: Application of the Discrete Geometrical Invariants, Quantitative Monitoring, Electrochemical Background

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How to cite this article:
R. R. Nigmatullin et al., Application of the Discrete Geometrical Invariants to the Quantitative Monitoring of the Electrochemical Background. Research Journal of Mathematics and Computer Science, 2017; 1:7


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