Raoul Rashidovich Nigmatullin

This paper is a first step toward providing answers to the question of whether fractal pattern formation gives rise to power-law (fractional) kinetics and how such kinetics relate to geometric properties such as fractal dimension. The study focuses on Lichtenberg figures produced by high-voltage discharges on wood, a heterogeneous dielectric medium with anisotropic conductivity and variable moisture content. During breakdown, the discharge propagates through branching streamers and carbonization fronts, exhibiting scale-free growth, long-tailed waiting times, and memory effects. The associated current signals are analyzed using the theory of fractal elements developed by Nigmatullin and Chen. This framework allows complex self-similar waveforms to be decomposed into elementary fractal modes characterized by power-law exponents and amplitudes. The results show that the electrical response is governed by fractional dynamics encoded in these modes. However, no direct one-to-one relationship is found between the fractal dimension of the discharge patterns and the kinetic power-law exponents. This decoupling is attributed to the influence of the heterogeneous medium and the percolation pathways through which the discharge propagates.

В работе представлены результаты анализа наиболее известных генераторов псевдослучайных чисел методом дискретных геометрических инвариантов (ДГИ). Показано, что данный метод позволяет сопоставлять различные типы генераторов псевдослучайных чисел, классифицировать генераторы по временным реализациям псевдослучайных последовательностей и найти их различия друг с другом (в рамках параметров ДГИ), которые обусловлены их малыми физическими различиями (на уровне их приборных реализаций). The paper presents the results of the analysis of the most famous pseudorandom number generators by the method of discrete geometric invariants (DGI). It is shown that this method makes it possible to compare different types of pseudorandom number generators, classify generators by time realizations of pseudorandom sequences and find their differences with each other (within the parameters of the DG), which are due to their small physical differences (at the level of their instrument implementations).

This paper proposes a novel method for describing earthquake waveforms based on the transformation of seismic waveforms to mesofluctuations (MSF). These cumulative MSF representations ignore high-frequency (fine-scale) oscillations but effectively preserve the waveform envelope and enable accurate detection of the onset, amplitude, and decay duration of P- and S-waves. These key features serve as the foundation for the architecture of the proposed neural network RSNet (Russian Seismic Net) designed for automatic detection of body wave onsets (P- and S-phases) using computed mesofluctuation metrics. In contrast to existing neural network models that rely on raw three-component seismograms, the proposed method operates on reduced and intermediate-scale (mesoscale) metric representations derived from mesofluctuation analysis – specifically, signal range and its first derivative. This approach enhances interpretability and robustness under noise, while reducing the dimensionality of the input data. The model was trained and validated using the STEAD database, which includes over 1 million labeled seismograms. The mean absolute error (MAE) of wave onset detection was 0.04 s for P-waves and 0.13 s for S-waves. When benchmarked against phase picks generated by the PhaseNet neural network, the MAE for S-waves decreased to 0.10 s. These results are comparable to the accuracy of the state-of-the-art neural-network models, while RSNet offers distinct advantages in interpretability and resilience to external noise factors.

In this paper, the authors propose the foundations of an original theory of quasi-reproducible experiments (QREs) based on the testable hypothesis that the

In this paper, the authors identify a transformation that is valid for any arbitrary signal. This transformation is strictly periodical and therefore it al

БЕЗМОДЕЛЬНАЯ ОБРАБОТКА ДАННЫХ МИКРОТОКОВ ДИОДОВ, ЗАДАННЫХ В ВИДЕ БЕСТРЕНДОВЫХ ПОСЛЕДОВАТЕЛЬНОСТЕЙ (Селекция диодов по критерию соответствия эталонной группе)

Structure of integral curves obtained by processing chronopotentiograms (CPG) of an aluminum anode polarized by a weak (at the level of one to several μA/cm²) current in a chloride-containing environment is self-similar in nature. This universal property allows us to find their fitting function and calculate the reduced (compressed dependence; the initial number of points is 1000, described by the number of frequency response modes is 14). The initial curve is invariant with respect to its transformed analogue after fivefold compression. For two different types of data obtained in open circuit and in metal polarization with microcurrent, a common fitting platform can be obtained related to its parameters. There are various methods of detrending: i.e., obtaining a trend from the original non-trending noise. The simplest way to obtain a trend that does not give computational errors is obtained from the formula for numerical integration using the trapezoidal method. It is this trend, obtained from the original trendless sequence without additional data processing errors, that makes sense to define as a clear trend. The approximation parameters can be used to compare various random processes, including those caused by reactions on the metal surface with changes in its microrelief during oxidation-reduction processes.

In this paper, the authors found a transformation that is valid for any arbitrary signal. This transformation is strictly periodical and therefore it allows to apply the ordinary F-transformation for the fitting of the transformed signal. The most interesting application (in accordance with the author's opinion) is the fitting of the frequency-phase modulated signals that actually located inside the found transformation. This new transformation will be useful for application of the responses of different complex systems when an ordinary model is absent. As an available data we consider meteo-data corresponding to measurements of methane concentration (CH4) in atmosphere during 4 weeks of its observation. For us it is important to consider the integral (cumulative) data and find their amplitude-frequency response (AFR). If one considers each column as frequency-phase modulated signal, then AFR can be evaluated with the help of F-transformation that has the period equals 2p that is valid for any analyzed random signal. This "universal" F-transformation allows to fit a wide set of random signals and compare them with each other in terms of their AFRs. Concluding the abstract one can say that these new possibilities of the traditional F-analysis will serve as a common tool in the armory of the methods used by researchers in data processing area.

In this paper, the authors propose the foundations of an original theory of quasi-reproducible experiments (QRE) based on the testable hypothesis that there exists an essential correlation (memory) between successive measurements. Based on this hypothesis, which the authors define for brevity as the verified partial correlation principle (VPCP), it can be proved that there exists a universal fitting function (UFF) for quasi-reproducible (QR) measurements. In other words, there is some common platform or "bridge" on which, figuratively speaking, a true theory (claiming to describe data from first principles or verifiable models) and an experiment offering this theory for verification measured data, maximally "cleaned" from the influence of uncontrollable factors and apparatus/software function, meet. Actually, the proposed theory gives a potential researcher the method of purification of initial data and finally suggests the curve that periodic and cleaned from a set of uncontrollable factors. The final curve corresponds to an ideal experiment. The proposed theory has been tested on eddy covariance ecologic data related to the content of CH4, CO2 and water vapors of H2O in the local atmosphere where the corresponding detectors for measuring of the desired gases content are located. For these tested eddy covariance data associated with the presence in atmosphere two gases CH4, CO2 and H2O vapors there is no simple hypothesis containing a minimal number of the fitting parameters, and, therefore, the fitting function that follows from this theory can serve as the only and reliable quantitative description of this kind of data belonging to the tested complex system. We should note also that the final fitting function removed from uncontrollable factors becomes pure periodic and corresponds to an ideal experiment. Applications of this theory to practical applications, the place of this theory among other alternative approaches, (especially touching the professional interests of ecologists) and its further development are discussed in the paper. The paper examines the phenomenon of joint creativity of several authors, and provides examples from various fields of activity. The main attention is paid to information technologies: inventions made at the end of the 20th century are analyzed. Their authors are pairs of outstanding specialists who combined the talents of a programmer and a manager. They determined the further development of the IT industry and radically changed the quality of mankind’s way of life. The stories of the emergence of famous computers, operating systems, the World Wide Web, and network navigation tools are briefly described.