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In this paper, we suggest a new algorithm for description of complex beatings. Under the complex beating we understand a signal, which contains the high-frequency (HF) component that is located between two low-frequency (LF) envelopes having random origin. These beatings are associated with the so-called blow-like signals (BLS) and a typical example of the BLS can be associated with the registered earthquakes signals. For description of these signals, it becomes possible to separate two envelopes from the HF-component located between them and find their amplitude-frequency response (AFR) based on the non-orthogonal amplitude-frequency analysis of the smoothed signals (NAFASS) approach that was suggested earlier by one of the authors (RRN) in paper [1] . It was successfully applied for description of economic data having also multi-frequency structure. In order to separate these envelopes from the HF component one can notice that the most signals of such kind have a fractal (self-similar) structure. It means that under reasonable compression/scaling of these signals they keep approximately their initial structure. This scaling property can be tested on many types of the different signals. In the results of application of the NAFASS approach one can describe quantitatively the desired envelopes and obtain their AFRs. As an example, we considered the randomly taken data that were recorded from EQs station located in Kyrgyzstan. We deliberately chose the different types of the EQs signals in order to demonstrate the flexibility and wide applicability of the proposed algorithm. We expect that this algorithm can find a wide application for description of many BLS that are met frequently in many natural phenomena and engineering applications.

We propose two modified and rather “universal” methods for the quantitative evaluation of electrochemical noises registered in running voltammetric sensor systems in the presence of unremovable artefacts. One approach is based on the discrete geometrical invariant (DGI) method and another is based on the usage of modified Fourier transform. Both approaches did not use model suppositions and were free from the treatment errors. We discussed the reasons for the appearance of the artefacts and showed their applications for increasing the sensitivity and specificity in the detection of some complex organic fluids. As an example, we obtained olive oils from two different producers for their definite differentiation. The selected olive oils from two different countries (Italy and Spain) were placed in working tube electrode cells, and we realized the possibility for the extraction of some useful information from the large amount of nanocurrents. The obtained quantitative parameters allowed the differentiation of URA from possible random noises. These two treatment methods have been proven to be rather “universal” and can be used for the analysis of other URAs having different natures.

In this paper, we suggest a new method for the quantitative "reading" of different calibration curves with the help of the so-called procedure of optimal linear smoothing (POLS), and the fractal compression of the measured initial curve thanks to its reduction to three incident points ($y_{\max}(b)$, $y_{{\mathrm {mean}}}(b)$, $y_{{\mathrm {min}}}(b)$), depending on the chosen compression coefficient b from the interval [3, 10], and elimination of the smoothed trend. This procedure helps to obtain the trendless sequence (TLS). Then this sequence is split into positive/negative parts and the subsequent summation of the positive and negative amplitudes helps to obtain finally the "confidence tube" (CT) that determines the sensitivity of the measured calibration curve to different external factors. The range of the CT determines its quantitative value. The proposed method increases the sensitivity of the given equipment by two or three orders of magnitude because of the elimination of the calibration curve trend and allows to test stability and reproducibility of the equipment thanks to comparison of the ranges of CT during the measurement process. The proposed method was tested on "Agilent" equipment (in terms of the scattering parameter S 11 ) and the obtained results can lead to reconsideration of some concepts of the conventional metrological standards.

We report on the numerical simulations and experimental validation of a microwave planar sensor based on two coupled rings operating in the 4&ndash, 6 GHz range. The fabricated sensor is used to characterize the dielectric permittivity of vegetable oils. We optimized the geometrical parameters in order to improve the overlap between the oil samples under study and the electric field. The experimental results showed an excellent match with the simulation results. The fabricated sensor allowed to retrieve the oil permittivity with a sensitivity of about 35 MHz per permittivity unit in the frequency range of interest. This paves the way to the realization of compact and sensitive sensors for a wide plethora of fields ranging from industry and food to chemistry and biology.

A new method based on the so-called discrete geometrical invariants (DGIs) is proposed to highlight the statistical differences between random sequences that can be presented in the form of two dimensions curves. The effectiveness of the proposed method is validated experimentally. Different complex fluids (i.e. sunflower and olive oils from different producers, isopropanol (IPA), sodium chloride, glucose, and distilled water) are considered to carry out a set of measurements for identifying the differences between fluids. The experimental results are obtained by two different approaches that are based on microwave and optical characterization. Moreover, an algorithm is provided to apply the DGIs method to both types of results and, in general, to implement the identification method in an automatic way also to other fluids. The new methodology is specified by the combination of the peculiar statistical analysis with the employed experimental technique. It opens a wide scenario of practical applications in detection and identification of hidden differences between complex fluids like vegetable and industrial oils, wines, milk, etc., without having a detailed knowledge of the complicated chemical content. It is expected that the proposed methodology can be applied to different technologies and systems, such as in production of different beverages, chemical fluids and solutions.

Based on the new method (defined below as the discrete geometrical invariants—DGI(s)), one can show that it enables to find the statistical differences between random sequences that can be presented in the form of 2D curves. We generalized and considered the Weierstrass–Mandelbrot function and found the desired invariant of the fourth order that connects the WM-functions with different fractal dimensions. Besides, we consider an example based on real experimental data. A high correlation of the statistically significant parameters of the DGI obtained from the measured data (associated with reflection optical spectra of olive oil) with the sample temperature is shown. This new methodology opens wide practical applications in differentiation of the hidden interconnections between measured by the environment and external factors.

In this paper, we want to demonstrate a set of “universal” parameters that help to read quantitatively any trendless sequence (TLS). This set will be very useful in order to select the “pattern” noise from the tested one and thereby to solve the problem of calibration of random fluctuations and express some qualitative inputs in terms of these “universal” parameters. This set of quantitative parameters allows to compare the TLS(s) of different nature (acoustic, mechanical, electrochemical, vibrational, etc.) with each other. The model example based on different random sequences generated by different distributions and the TLS(s) based on real data justify this approach and confirm its universal character. Besides, using the same algorithm we analyzed the acoustic noise recorded from the frictionless bearings (FB) in a normal state and the distorted noise from the FBs with artificially created defects. The proposed algorithm allows detecting the desired defect that initially had a qualitative description only. We do suppose that the proposed “universal” scheme free from uncontrollable errors can find a wide application in the solution of many practical problems.

In this paper, we propose a general mathematical method for the detection of electrochemical additives in a given solute with the help of discrete geometrical invariants (DGI). This idea is based on the generalization of Pythagor&rsquo, s theorem that can be proved for two random sets located in the two-dimensional (2D) plane. This statement follows from the previous ideas proposed by Babenko, who essentially modernized the well-known theorem and propagated it on a wide class of &ldquo, right&rdquo, discrete sets with different symmetry. However, attentive analysis of these results shows that there is a possibility for their further generalization. For practical purposes, it is important to have discrete and deterministic curve(s) with the limited number of parameters that enables comparing two random sets of any nature if their quantitative description expressed in terms of the &ldquo, best-fit&rdquo, model is absent. Under the best-fit model, we imply the microscopic model that enables describing the measured data in terms of the minimal set of the fitting parameters. We propose at least two invariants: (a) the curve of the second order that coincides with the classical ellipse oriented at an arbitrary direction relative to the X- and Y-axes, and (b) the curve of the fourth order that has eight quantitative parameters and includes the cross-combination of the integer moments. In this paper, the DGIs of both types were used. These curves are made useful for the solution of a key problem in electrochemistry, i.e., the detection of small concentrations of d-tryptophan (6.54 &divide, 38.7) 10&minus, 5 mol&middot, L&minus, 1 in a given solute (phosphate buffer solution (Na2HPO4 + KH2PO4) with pH = 6.86) that was activated by electrodes of two types&mdash, Pt (platinum) and C (carbon). The DGI method is free from treatment errors and model suppositions, therefore, it can be applied for the detection of small additives in a given solute and a further description can be attained with the help of a monotone/calibration curve expressed by means of parameters associated with the DGI.

Graphene is a material with exceptional optical, electrical and physicochemical properties that can be combined with dielectric waveguides. To date, several optical devices based on graphene have been modeled and fabricated operating in the near-infrared range and showing excellent performance and broad application prospects. This paper covers the main aspects of the optical behaviour of graphene and its exploitation as electrodes in several device configurations. The work compares the reported optical devices focusing on the wavelength tuning, showing how it can vary from a few hundred up to a few thousand picometers in the wavelength range of interest. This work could help and lead the design of tunable optical devices with integrated graphene layers that operate in the NIR.