# Raoul Rashid NigmatullinKazan National Research Technical University | KSTU · Radio-Electronics and Informative-Measurements Technics depertment.

Raoul Rashid Nigmatullin

Full Professor of Physics

## About

294

Publications

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Introduction

Now I'm working intensively on the idea that covers all aspects of the BIG DATA treatment area. It becomes possible to prove that any random sequence has a deterministic image/projection in 2D and 3D spaces, correspondingly. For 2D space this idea expressed in the form of the Discrete Geometrical Invariant (DGI) has been published in the "New Journal of Chemistry". With the help of the new tool the olive oils from two producers have been differentiated.
The calculations related to prove of the existence of the DGIs in 3D-space become more complicated, but possible! However, I think that these important calculations will be finished soon and transformed into interesting publication.

Additional affiliations

Education

September 1972 - December 2014

## Publications

Publications (294)

We present the description of a quasi-spherical coordinate system that is introduced in a space of parameters of a multilayer perceptron with ReLU and Leaky ReLU activation functions. In this instance, a regression loss function that is given in these coordinates becomes the sum of functions that depend on a set of functions defined on a sphere and...

For the purposes of a food chemistry, it is important to differentiate of complex liquids (as gels, emulsions, juices etc.) from each other. This paper presents for the first time a temporal approach to the study of the voltammetric behavior of multicomponent mixtures with implicit peaks of oxidation/reduction of electroactive components in the ini...

We extend the scope of the unified factorization method to the solution of conditionally and unconditionally exactly solvable models of quantum mechanics, proposed in a previous paper [R.R. Nigmatullin, A.A. Khamzin, D. Baleanu, Results in Physics 41 (2022) 105945]. The possibilities of applying the unified approach in the factorization method are...

In this paper, the non-orthogonal amplitude-frequency analysis of smoothed signals (NAFASS) method) is used to approximate discrete aperiodic signals from various complex systems with the non-integer harmonic series (NIHS). When approximating by the NIHS, there is a problem in determining the dispersion law for harmonic frequencies. In the original...

The well-known power-law fractal element was determined to need several important revisions by the authors of this work. It is now possible to demonstrate that any scaling equation associated with a fractal element is actually K-fold degenerated and includes previously unknown but crucial adjustments. These new discoveries have the potential to sig...

This work was greatly influenced by the opinions of one of the authors (JS), who demonstrated in a recent book that it is important to distinguish between “fractal models” and “fractal” (power-law) behaviors. According to the self-similarity principle (SSP), the authors of this study completely distinguish between independent “fractal” (power-law)...

A personalized URL link provides 50 days' free access to the article before June 20, 2023:
https://authors.elsevier.com/a/1g-nbxsQaMHTn

In this paper the authors want to prove that the trendless sequences (TLS) can be transformed to 3D-surface having only 10 statistically-significant parameters. These ten parameters can be extracted from random noise with the help of the Comparative Analysis of Positive/Negative fluctuations (CAPoNeF) method. Actually, without using of a treatment...

For the first time, this chapter analyzes the evolution stages of an unblown bud (plumeria) while monitoring the temporal evolution by measuring the behavioral variations in the complex impedance. Owing to their overabundance in tropical and subtropical areas and the superior medicinal and aromatic values of plumeria flowers of the Apocynaceae fami...

In this paper, the possibility of applying the fractional moments (FM) method in selection of the best operational amplifier (OA) among the available ones is considered. This method can be defined as the statistical method because is based on analysis and quantitative “reading” of the measured “noise”/random fluctuations with the help of the statis...

The article proposes a new algorithm for applying the factorization method to the problem of calculating the spectrum of exactly and conditionally exactly solvable potentials. The proposed algorithm allows us to unify and extend the capabilities of the factorization method to construct exactly solvable potentials. The new approach is demonstrated b...

The article is devoted to issues related to the propagation and transformation of vortexes in the optical range of frequency. Within the framework of the traditional and modified model of slowly varying envelope approximation (SVEA), the process of converting vortex beams of the optical domain into vortex beams of the terahertz radio range based on...

In this paper the proposed theoretical model describing 3D-branching systems in the intermediate range of frequencies was applied in the first time for description and further fitting of the complex impedance in a living system, as unblown bud plumeria flower (Frangipani Plumeria). The proposed fitting function that follows from the applied model a...

Here, we show how to extend the possibilities of the conventional F-analysis and adapt it for quantitative description of multi-periodic signals recorded from different complex systems. The basic idea lies in filtration property of the Dirichlet function that allows finding the leading frequencies (having the predominant amplitudes) and the shortcu...

In this paper, ideal boundary conditions have been created for recording instrument noises and their fluctuations at the level of pico-currents to describe quantitatively the voltammetric behavior of trace components...

In the first time we apply the statistics of the complex moments for selection of an optimal pressure sensor (from the available set of sensors) based on their statistical/correlation characteristics. The complex moments contain additional source of information and, therefore, they can realize the comparison of random sequences registered for almos...

In this paper, the authors propose a theory to describe the behavior of the new type of fractal element which exihibit complex-conjugated power-law exponents. To explain the impedance behaviour of these elements, log-periodic corrections are employed. So far, the impedance of fractal elements are studied which shows power law behaviour in a limited...

The article is devoted to issues related to the propagation and transformation of vortexes in the optical range of frequency. Within the framework of the traditional and modified model of slowly varying envelope approximation (SVEA), the process of converting vortex beams of the optical domain into vortex beams of the terahertz radio range based on...

The proposed method as CAPoNeF (Comparative Analysis of Positive and Negative Fluctuations) allows to “read” any trendless sequence quantitatively irrespective of the imposed model and treatment errors that inevitably accompany random sequence. This method will have a wide possibility because of its generality and simplicity in possible application...

In this paper, a theoretical-model has been proposed for the first-time to illustrate the living Tulsi (Holy Basil) leaf-evolution in describing the branching-systems. The proposed fitting-function following the applied model portrays the whole stages of the temporal-evolution of Tulsi (Holy Basil, Ocimumtenuiflorum") leaf during the six days of im...

Non-Orthogonal Combined Fourier Analysis of the Smoothed Signals (NOCFASS) helps to extract the reduced/invariant spectrum from the total Fourier-spectrum that contains a small number of frequencies with the linear dispersion law Ωk =a⋅k+b. The paper presents a new technique to treat original data of natural processes like seismic ambient noise, me...

The work presents data treatment methods aimed at eliminating the noise in the strain sensor data induced by vibrations of the helicopter blade in flight conditions. The methods can be applied in order to enhance the metrological performance of the helicopter weight estimation system based on the deformation measurement of the main rotor blades. Th...

In this paper, we consider the mechanism of a memory effect based on linear or nonlinear systems of balance equations. By considering a chain of balance equations, connecting each particle to the next by means of a memory kernel, it becomes possible to derive generalised expressions for the overall memory kernel that connects the initial particle t...

In this paper, we focus on the generalization of the Hurst empirical law and suggest a set of reduced parameters for quantitative description of long-time series. These series are usually considered as a specific response of a complex system (economic, geophysical, electromagnetic and other systems), where successive fixations of external factors b...

In this paper, we concentrate on encrypted traffic detection and characterization and analyze the popular ISCXVPN2016 dataset. The detection of encrypted traffic and further characterization of its content is crucial both for securing the required Quality of Service and for Network Intrusion Detection. We introduce Accumulated Generalized Mean Valu...

We propose a new approach to traffic preprocessing called Differentiation of Sliding Rescaled Ranges (DSRR) expanding the ideas laid down by H.E. Hurst. We apply proposed approach on the characterizing encrypted and unencrypted traffic on the well-known ISCXVPN2016 dataset. We deploy DSRR for flow-base features and then solve the task VPN vs nonVPN...

This paper demonstrates that highly accurate radiometric identification is possible using CAPoNeF feature engineering method. We tested basic ML classification algorithms on experimental data gathered by SDR. The statistical and correlational properties of suggested features were analyzed first with the help of Point Biserial and Pearson Correlatio...

This paper demonstrates that highly accurate radiometric identification is possible using CAPoNeF feature engineering method. We tested basic ML classification algorithms on experimental data gathered by SDR. The statistical and correlational properties of suggested features were analyzed first with the help of Point Biserial and Pearson Correlatio...

In this paper, based on the "fuzzy" calculus covering the continuous range of operations between two couples of arithmetic operations (+, −) and (×,:), a new form of the fractional integral is proposed occupying an intermediate position between the integral and derivative of the first order. This new form of the fractional integral satisfies the C...

This chapter represents the logical continuation of Chap. 5. Assuming that any set of reproducible/repeatable measurements can be considered as a quasi-periodic process, it is possible to derive the fitting function that strives to describe every experiment in which measurements of the same variable or quantity can be repeated many times. Here, it...

This chapter provides essential information about the fitting procedure. Everybody should know the conventional linear least squares method (LLSM), which was proposed by K. F. Gauss in the 18th century and later modified by other mathematicians. This method is very efficient when dealing with linear fitting coefficients. On the contrary, nonlinear...

This chapter considers the application of the eigen-coordinates (ECs) method to the nontrivial example of the analysis of blow-like signals (BLS). These signals show a typical behaviour that starts in some segment of time, then rises and achieves the peak value, and finally decreases, and can originate in very different scenarios, e.g. the propagat...

This chapter analyses in detail the concept of fractional moments. The modern mathematical statistics widely uses only four integer moments: the arithmetic mean, the standard deviation (based on the second moment), the measure of asymmetry, and the measure of skewness associated with the value of the fourth moment. Why not increase the moments conc...

This chapter shows how to combine the methods outlined in the previous chapters for application to electrochemistry. The first adopted method, which can be considered as original, is based on the ideas of Yu. Babenko, who generalised the Pythagorean theorem for a wide class of geometrical figures with high symmetry. By applying this method is possi...

This chapter deals with non-reproducible experiments and contains the answer to the following question: is it possible to find a “universal” fitting function for some non-reproducible and random results from an experiment/observation? There are a lot of examples of such kind of experiments producing various types of data: economic data, medical dat...

This chapter demonstrates how to obtain a quantitative description of noise samplings or, more precisely, of trendless sequences containing clearly expressed fluctuations only. Besides the mean value, standard deviation and range, it is shown that it is possible to find up to ten more parameters useful for a quantitative reading of a wide class of...

Any young researcher is accustomed to the conventional Fourier transform (F-transform). However, it would be useful to think about the meaning of this transformation and its purpose. Is it just for detecting the harmonic components in the input signal? This chapter tries to answer this question, such that the reader will be acquainted with not only...

This chapter considers two unexpected applications of the fractional moments. The first application is associated with the distribution of stable points, which are described by defining the quantitative universal label (QUL). The “universal” distribution of stable points that exists in some random sequence can be expressed in the form of the genera...

Previous work has determined the discrete geometrical invariant (DGI) in 2D space, which allows the analysis of a pair of random sequences ([r1k, r2k], k = 1,2,…N) containing an equal number of data points to be reduced to eight “universal” parameters that present different inter-correlations between the two compared sequences. These eight paramete...

This book is intended as a manual on modern advanced statistical methods for signal processing. The objectives of signal processing are the analysis, synthesis, and modification of signals measured from different natural phenomena, including engineering applications as well. Often the measured signals are affected by noise, distortion and incomplet...

Based on the new method (defined below as the discrete geometrical invariants-DGI(s)) one can show that it enables to differentiate 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 4-th order t...

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 co...

In this paper it is demonstrated a new set of “universal” parameters that help to read quantitatively any trendless sequence (TLS). This method is applied for solving the problem of selection of the “pattern” noise from the tested one and for calibration of random fluctuations expressing some qualitative inputs in terms of these quantitative parame...

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 (ymax(b), ymean(b), ymin(b)), depending on the chosen compressio...

We report on the numerical simulations and experimental validation of a microwave planar sensor based on two coupled rings operating in the 4–6 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...

In the present work, a new type granular core has been studied and implemented to a mechanically excited electromagnetic harvester. The system mainly consists of a linear fluid core and a surrounding winding. The system entirely depends on the vibration of the fluid core indicating a highly fluid dynamical feature, whereas the winding component of...

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 "univ...

Polyaniline (PANI) represents itself a class of polymers having ionic and electronic conductivities. The polymer has wide application as chemical modifier of electrodes for voltammetry. Electrochemical polymerization of aniline includes in itself some oxidation/reduction stages of electroactive groups. In the result of this process, polyaniline str...

The so-called intermediate model (IM) was applied in the paper to quantitatively describe
complex trajectories. Using this model it was possible to find the proper fitting function for
describing random trajectories that were recorded during the walking process performed by
a volunteer. Experimental data were acquired using a three-dimensional Moti...

We propose two modified and rather “universal” methods for quantitative evaluation of electrochemical noises registered in the running voltammetric sensor systems in the presence of unremovable artefacts. One approach is based on the discrete geometrical invariants (DGI)-method and another one is based on the usage of the modified Fourier transform...

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’s theorem that can be proved for two random sets located in the two-dimensional (2D) plane. This statement follows from...

The paper presents a new approach to the description of earthquake seismic signals based on the nonorthogonal amplitude-frequency analysis of the smoothed signals (NAFASS) method. The authors consider an example of the processing of one of earthquake’s records that occurred in the Tien Shan territory. The earthquake signals were recorded at the Kar...

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 com plex fluids (i.e. sunflower and olive oils from diffe...

In this paper, the exact relationships between the averaging procedure of a smooth function over 1D-fractal sets and the fractional integral of the RL-type are found. The numerical verifications are realized for confirmation of the analytical results and the physical meaning of these obtained formulas is discussed. Besides, the generalizations of t...

In this paper we want to show some original solutions of the functional equations that can be considered as a main “bridge” connecting the fractional calculus with fractal geometry. This bridge should justify a wide application of the fractional calculus in many important applications and, from another side, increase the possibilities of the fracti...

Authors develop new nonparametric methods for verification and monitoring for quantum randomness based on the ranged correlation function (RCF) and a sequence of the ranged amplitudes (SRA). We carried out RCF-analysis of different topology subsamples from raw data of the prototype of a quantum random number generator on homodyne detection. It is s...

Accurate detection of faults of induction motors is an important challenge for industry. Often only stator currents/voltages are measurable and, hence, can be analyzed for fault detection. Among current analysis methods, the most attractive ones have low computational cost and little memory requirement for treatment of the measured data. Motor curr...

Accurate detection and identification of faults
of induction motors is an important challenge for industry.
Often only stator currents/voltages are measurable and, hence,
can be analyzed for fault detection. Among current analysis
methods, the most attractive ones have low computational cost
and little memory requirement for treatment of the measur...

Accurate detection and identification of faults of induction motors is an important challenge for industry. Often only stator currents/voltages are measurable and, hence, can be analyzed for fault detection. Among current analysis methods, the most attractive ones have low computational cost and little memory requirement for treatment of the measur...

Lithium batteries are currently used as the main energy storage for electronic devices. Progress in the field of portable electronic devices is significantly determined by the improvement of their weight/dimensional characteristics and specific capacity. In addition to the high reliability required of lithium batteries, in some critical application...

In the paper, the percolation model (PM) developed earlier for description of data associated with complex fluids was successfully applied. As an example, we analyzed the virgin olive oil electrochemical data. In spite of the fact that this complex fluid as olive oil contains more than 100 different chemical components, it becomes possible to descr...

A comparative analysis of the method of histograms and the sequence of the ranged amplitudes (SRA) for statistical parametrization of the operation regime of a single-photon avalanche photodetector has been performed. It was shown that in addition to providing all the information that can be obtained using the histogram method, the SRA method also...

The general mesoscopic theory pretending on the quantitative description of the interfacial surface and the self-similar structure of the double electric layer in the vicinity of solid electrodes is suggested. It takes into account the fact that the fractal dimension can be complex and depends on the applied potential. In the frame of the suggested...

Single-photon detectors based on avalanche photodiodes (SPADs) are key elements of many modern highly sensitive optical systems. One of the bottlenecks of such detectors is an afterpulsing effect, which limits detection rate and requires an optimal hold-off time. In this paper, we propose a novel approach for statistical analysis of SPAD dark count...

A comparative analysis of the method of histograms and the sequence of the ranged am-plitudes (SRA) for statistical parametrization of the operation regime of a single-photon avalanche photodetector is carried out. It is shown that the SRA method contains all the information, which can be obtained using the method of histograms, and also allows to...

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) a...

A microscopic theory of dielectric relaxation of the hexagonal ice (Ih) is proposed based on the multiple-trapping model. The theory explains the distinctive peculiarities of the relaxation time temperature behavior and the peak broadening parameter in a wide temperature range from the unified positions.

The results of quantitative reading of the cyclic voltammetry behavior of the tryptophan (Trp) enantiomers deposited on the electrochemically activated glassy carbon electrode (GCE) are presented. The combined method for “reading” of analytical signals based on the modified Fourier transform and the GPCA was applied. It allows describing a derivati...

In this paper the accurate relationships between the averaging procedure of a smooth function over 1D-fractal sets and the fractional integral of the RL-type are established. The numerical verifications are realized for confirmation of the analytical results and the physical meaning of these obtained formulas is discussed. Besides, the generalizati...

The authors suggest an effective scheme for quantitative description of complex systems, when the number of measurements is relatively small. It has a great importance for quantitative description of expensive and rare experiments when the volume of the sampling is small. They proposed a simple theory that is based on the previous results associate...