Author

# Ilya Pershin

Bio: Ilya Pershin is an academic researcher from Kazan Federal University. The author has contributed to research in topics: Fractal dimension & Box counting. The author has an hindex of 2, co-authored 3 publications receiving 4 citations.

##### Papers

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01 Sep 2020TL;DR: The work’s goal is to establish the dependence of the base frequency on the dimension of the curve forming the antenna arm of the Koch type, and it is concluded that for the second and third iterations, the best correlation is a correlation between the base Frequency and the Higuchi dimension.

Abstract: A dipole wire antenna of the Koch type is considered. The antenna consists of a wire dipole with symmetrical arms with respect to the feed point with the geometry similar to the Koch prefractal. The curves forming the arms differ from the classical Koch fractal only by the position of the central vertex. The work’s goal is to establish the dependence of the base frequency on the dimension of the curve forming the antenna arm. Various dimensions as characteristics of the curve are considered. The dimensions are Minkowski dimension, information dimension, correlation dimension and Higuchi fractal dimension. The algorithm to calculate the Higuchi dimension for our curves is adapted. Also, algorithms for calculating the other dimensions are described. Relationships between the base frequency of the Koch-type wire dipole and the dimensions are explored. The correlation analysis for the first three Koch-type prefractals is carried out. The values of all correlation coefficients between the base frequency and the considered dimensions are given in the tables. It is concluded that for the second and third iterations, the best correlation is a correlation between the base frequency and the Higuchi dimension. The optimal one-parameter regression models for the base frequency in the case of the second and third iterations are constructed. The obtained regression model for the second iteration approximates the frequency values with an error of 1.17%. The model for the third iteration approximates the frequency values with an error of 1.46%.

4 citations

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TL;DR: In this paper, the authors considered a straight horizontal line with different thicknesses, and calculated the fractal dimension for different thickness values using the box-counting method (BCM).

Abstract: Fractal curves are found in various fields of science and technology, and the calculation of the dimensions of the curves is an actual direction. The fractal dimension (FD) is a metric used to characterize the filling of a plane with a curve. The choice of the thickness of the curve
line at calculating its FD using the box-counting method (BCM) is not obvious. This is the subject of the present paper. First, we consider a straight horizontal line with different thicknesses, and calculate FD for different thicknesses, using BCM. Using the exact dimensional value for a
straight line, the initial conclusion is made about the thicknesses that give a correct FD. In the next step, the dimensions of straight lines rotated by a certain angle in the range from to 90 degrees are calculated. At any angle of inclination of the line, the FD values should also remain
equal to unity. The range of FD values depending on the rotation angle is analyzed. The result is an “optimal” line thickness equal to 3 px. At this value, the FD values are the closest to one for any angle of inclination. As a result it is received that at dimensional calculation
by means of BCM, it is enough to choose the initial image of 200 on 200 pixels, and boxes to choose the sizes from 2 to 50 pixels with step of 2 pixels. The stability of dimension calculations on the grid offset has been verified. The algorithm’s error is estimated on the example of
the calculation of FD for the Koch fractal.

3 citations

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21 Sep 2020

TL;DR: In this article, the authors investigated the performance of parallel and serial implementations of the algorithm intended for calculating the number of boxes for evaluating the fractal dimension of analytical curves and concluded that the efficiency of using the GPU begins with three million boxes and grows with an increase in the size of curve points.

Abstract: Serial and parallel implementations of the algorithm intended for calculating the number of boxes for evaluating the fractal dimension of analytical curves are considered. The algorithm contains four stages: (1) preparing the data for calculations; (2) determining the boxes into which the curve fell; (3) counting the boxes that have an intersection with a curve; (4) counting the boxes of a larger size that intersect with a curve. The acceleration of computations performed by a parallel code (on OpenMP and CUDA) with respect to calculations performed by a serial code depending on the size of the box is investigated. Numerical experiments are carried out, the results of which exhibit a significant increase in performance for GPU calculations in the case of a large number of segments of the curve. A 100-fold increase in the computational speed is obtained for a curve containing a million segments with a billion boxes (box size is \( 2^{ - 15} \)). The graphs depicting an increase in acceleration of parallel code performance with decreasing the box size and increasing the number of curve segments are shown. It is concluded that the efficiency of using the GPU begins with three million boxes and grows with an increase in the number of curve points.

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01 Jan 2016

TL;DR: Chaotic vibrations as mentioned in this paper is an introduction for applied scientists and engineers, but it is not suitable for the general public and it cannot be used in a classroom environment due to its infectious nature.

Abstract: Thank you for downloading chaotic vibrations an introduction for applied scientists and engineers. As you may know, people have look numerous times for their favorite readings like this chaotic vibrations an introduction for applied scientists and engineers, but end up in infectious downloads. Rather than enjoying a good book with a cup of coffee in the afternoon, instead they are facing with some infectious virus inside their desktop computer.

30 citations

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01 Sep 2020TL;DR: The work’s goal is to establish the dependence of the base frequency on the dimension of the curve forming the antenna arm of the Koch type, and it is concluded that for the second and third iterations, the best correlation is a correlation between the base Frequency and the Higuchi dimension.

Abstract: A dipole wire antenna of the Koch type is considered. The antenna consists of a wire dipole with symmetrical arms with respect to the feed point with the geometry similar to the Koch prefractal. The curves forming the arms differ from the classical Koch fractal only by the position of the central vertex. The work’s goal is to establish the dependence of the base frequency on the dimension of the curve forming the antenna arm. Various dimensions as characteristics of the curve are considered. The dimensions are Minkowski dimension, information dimension, correlation dimension and Higuchi fractal dimension. The algorithm to calculate the Higuchi dimension for our curves is adapted. Also, algorithms for calculating the other dimensions are described. Relationships between the base frequency of the Koch-type wire dipole and the dimensions are explored. The correlation analysis for the first three Koch-type prefractals is carried out. The values of all correlation coefficients between the base frequency and the considered dimensions are given in the tables. It is concluded that for the second and third iterations, the best correlation is a correlation between the base frequency and the Higuchi dimension. The optimal one-parameter regression models for the base frequency in the case of the second and third iterations are constructed. The obtained regression model for the second iteration approximates the frequency values with an error of 1.17%. The model for the third iteration approximates the frequency values with an error of 1.46%.

4 citations

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TL;DR: In this paper , the authors investigated electrical treeing with a needle-plane geometry in low-density polyethylene (LDPE) under a high negative dc voltage superimposed with ac ripples (−60 kV dc ± 7 kV ac).

Abstract: Understanding the role of power quality in the aging of HVdc cable systems is critical to the reliable connection of offshore renewable energy sources, and hence global ambitions to reduce carbon emissions. This work investigates electrical treeing with a needle-plane geometry in low-density polyethylene (LDPE) under a high negative dc voltage superimposed with ac ripples (−60 kV dc ± 7 kV ac). Tree initiation showed behavior similar to that widely reported under pure power frequencies. Subsequent tree growth, however, was observed to be confined in a smaller area with limited length and width than seen under pure ac voltages, even after long periods of voltage application. Traditional 2-D imaging showed overlapped tree channels which developed to cover the whole area within the tree outline. A distinguishing tree shape resulted, which we have named a “slim bouquet” shape. The volume rendering from X-ray computed tomography (XCT) showed the structure had a 3-D fractal dimension greater than 2, considerably larger than its 2-D representation. PD signals during the growth had wing-like phase-resolved partial discharge (PRPD) clusters and signal phase concentrations between 10°–45° appeared after hours of growth. There was a comb-like appearance in maximum partial discharge (PD) magnitude variation, which is typical in pure high negative dc fields. Consideration is given to both space charge distribution controlled by high dc fields and continuous degradation by ac fields to explain the slim bouquet tree formation.

3 citations

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21 Aug 2022

TL;DR: In this paper , a miniaturized log-periodic Koch dipole array (LPKDA) antenna is proposed, where the T-shaped top construction and the novel Koch bifurcated folding dipole are used to reduce the length of the single dipole element.

Abstract: A miniaturized log-periodic Koch dipole array (LPKDA) antenna is proposed in this paper. With the T-shaped top construction and the novel Koch bifurcated folding dipole, the length of the single dipole element is reduced to the minimum, which immensely reduce the antenna size. The antenna operates in the frequency band of 195 ~ 848 MHz. The characteristics of compact structure, simple structure and wide band are achieved by the proposed antenna.