scholarly journals ABOUT ONE CLASS OF FUNCTIONS WITH FRACTAL PROPERTIES

2021 ◽  
Vol 9 (1) ◽  
pp. 273-283
Author(s):  
Ya. Goncharenko ◽  
M. Pratsiovytyi ◽  
S. Dmytrenko ◽  
I. Lysenko ◽  
S. Ratushniak
Keyword(s):  
Random Variables ◽  
Variational Integral ◽  
Numerical Series ◽  
Fractal Properties ◽  
Fractal Functions ◽  
Self Similar ◽  
Object Of Study ◽  
Class Of Functions

We consider one generalization of functions, which are called as «binary self-similar functi- ons» by Bl. Sendov. In this paper, we analyze the connections of the object of study with well known classes of fractal functions, with the geometry of numerical series, with distributions of random variables with independent random digits of the two-symbol $Q_2$-representation, with theory of fractals. Structural, variational, integral, differential and fractal properties are studied for the functions of this class.

scholarly journals Fractal functions of exponential type that is generated by the $\mathbf{Q_2^*}$-representation of argument

2021 ◽  
Vol 56 (2) ◽  
pp. 133-143
Author(s):  
M.V. Pratsovytyi ◽  
Ya. V. Goncharenko ◽  
I. M. Lysenko ◽  
S.P. Ratushniak
Keyword(s):  
Exponential Type ◽  
Variational Integral ◽  
Fractal Properties ◽  
Functions Of Exponential Type ◽  
Fractal Functions ◽  
Positive Series

We consider function $f$ which is depended on the parameters $0<a\in R$, $q_{0n}\in (0;1)$, $n\in N$ and convergent positive series $v_1+v_2+...+v_n+...$, defined by equality $f(x=\Delta^{Q_2^*}_{\alpha_1\alpha_2...\alpha_n...})=a^{\varphi(x)}$, where $\alpha_n\in \{0,1\}$, $\varphi(x=\Delta^{Q_2^*}_{\alpha_1\alpha_2...\alpha_n...})=\alpha_1v_1+...+\alpha_nv_n+...$, $q_{1n}=1-q_{0n}$, $\Delta^{Q_2^*}_{\alpha_1...\alpha_n...}=\alpha_1q_{1-\alpha_1,1}+\sum\limits_{n=2}^{\infty}\big(\alpha_nq_{1-\alpha_n,n}\prod\limits_{i=1}^{n-1}q_{\alpha_i,i}\big)$.In the paper we study structural, variational, integral, differential and fractal properties of the function $f$.

Prophet Inequalities for Independent and Identically Distributed Random Variables from an Unknown Distribution

2021 ◽  
Author(s):  
José Correa ◽  
Paul Dütting ◽  
Felix Fischer ◽  
Kevin Schewior
Keyword(s):  
Stopping Time ◽  
Random Variables ◽  
Optimal Solution ◽  
Random Order ◽  
Secretary Problem ◽  
Maximum Value ◽  
Optimal Stopping Theory ◽  
Long Time ◽  
Object Of Study ◽  
Independent And Identically Distributed

A central object of study in optimal stopping theory is the single-choice prophet inequality for independent and identically distributed random variables: given a sequence of random variables [Formula: see text] drawn independently from the same distribution, the goal is to choose a stopping time τ such that for the maximum value of α and for all distributions, [Formula: see text]. What makes this problem challenging is that the decision whether [Formula: see text] may only depend on the values of the random variables [Formula: see text] and on the distribution F. For a long time, the best known bound for the problem had been [Formula: see text], but recently a tight bound of [Formula: see text] was obtained. The case where F is unknown, such that the decision whether [Formula: see text] may depend only on the values of the random variables [Formula: see text], is equally well motivated but has received much less attention. A straightforward guarantee for this case of [Formula: see text] can be derived from the well-known optimal solution to the secretary problem, where an arbitrary set of values arrive in random order and the goal is to maximize the probability of selecting the largest value. We show that this bound is in fact tight. We then investigate the case where the stopping time may additionally depend on a limited number of samples from F, and we show that, even with o(n) samples, [Formula: see text]. On the other hand, n samples allow for a significant improvement, whereas [Formula: see text] samples are equivalent to knowledge of the distribution: specifically, with n samples, [Formula: see text] and [Formula: see text], and with [Formula: see text] samples, [Formula: see text] for any [Formula: see text].

Intermittency and related issues in 16O-Ag/Br collision at 200A GeV/c

2010 ◽  
Vol 88 (8) ◽  
pp. 575-584 ◽  
Author(s):  
M. K. Ghosh ◽  
P. K. Haldar ◽  
S. K. Manna ◽  
A. Mukhopadhyay ◽  
G. Singh
Keyword(s):  
Particle Density ◽  
Simulated Data ◽  
Space Distribution ◽  
Monte Carlo Code ◽  
Final State ◽  
Data Set ◽  
Fractal Properties ◽  
Self Similar ◽  
Singly Charged ◽  
Almost All

In this paper we present some results on the nonstatistical fluctuation in the 1-dimensional (1-d) density distribution of singly charged produced particles in the framework of the intermittency phenomenon. A set of nuclear emulsion data on 16O-Ag/Br interactions at an incident momentum of 200A GeV/c, was analyzed in terms of different statistical methods that are related to the self-similar fractal properties of the particle density function. A comparison of the present experiment with a similar experiment induced by the 32S nuclei and also with a set of results simulated by the Lund Monte Carlo code FRITIOF is presented. A similar comparison between this experiment and a pseudo-random number generated simulated data set is also made. The analysis reveals the presence of a weak intermittency in the 1-d phase space distribution of the produced particles. The results also indicate the occurrence of a nonthermal phase transition during emission of final-state hadrons. Our results on factorial correlators suggests that short-range correlations are present in the angular distribution of charged hadrons, whereas those on oscillatory moments show that such correlations are not restricted only to a few particles. In almost all cases, the simulated results fail to replicate their experimental counterparts.

scholarly journals Self-similar extrapolation of nonlinear problems from small-variable to large-variable limit

2020 ◽  
Vol 34 (21) ◽  
pp. 2050208
Author(s):  
V. I. Yukalov ◽  
E. P. Yukalova
Keyword(s):  
Asymptotic Series ◽  
Nonlinear Problems ◽  
Numerical Convergence ◽  
Physical Problems ◽  
Variable Limit ◽  
Small Parameters ◽  
Self Similar ◽  
Similar Approximation ◽  
Similar Factor ◽  
Class Of Functions

Complicated physical problems are usually solved by resorting to perturbation theory leading to solutions in the form of asymptotic series in powers of small parameters. However, finite, and even large values of the parameters, are often of main physical interest. A method is described for predicting the large-variable behavior of solutions to nonlinear problems from the knowledge of only their small-variable expansions. The method is based on self-similar approximation theory resulting in self-similar factor approximants. The latter can well approximate a large class of functions, rational, irrational, and transcendental. The method is illustrated by several examples from statistical and condensed matter physics, where the self-similar predictions can be compared with the available large-variable behavior. It is shown that the method allows for finding the behavior of solutions at large variables when knowing just a few terms of small-variable expansions. Numerical convergence of approximants is demonstrated.

scholarly journals MULTIFRACTALITY OF NETWORK MEDIACOMMUNICATIONS IN THE INFORMATION CIVILIZATION: PHILOSOPHICAL ASPECT

2020 ◽  
Vol 30 (4) ◽  
pp. 333-343
Author(s):  
I.A. Latypov
Keyword(s):  
Social Philosophy ◽  
Point Of View ◽  
Philosophical Theory ◽  
Main Hypothesis ◽  
Subject Field ◽  
Philosophy Of Culture ◽  
Social Communications ◽  
Philosophical Aspect ◽  
Self Similar ◽  
Object Of Study

The paper describes the philosophical context of multifractal characteristics of network mediacommunications development trends. The analysis of these trends shapes the contours of new subject field of not only socio-philosophical or cultural studies, but also inter-disciplinary researches of the multifractality phenomenon as a whole. Consideration of the multifractal prospects from the point of view of social philosophy of culture of an informational society is a kind of inter-disciplinary research in a sphere of philosophical works. The paper forms a discourse of the multifractal mediacommunications in a global networking space. Mediacommunications in this research are defined as a kind of social communications in a media sphere. The main problem of the research may be reduced to the question: is it possible to characterize the issue of multifractality of network mediacommunications in a philosophical context? The purpose of the research is the analysis of the philosophical aspect of multifractality of network mediacommunications in the information civilization. The object of study is a variety of processes of social communications development connected to the prospects of modern mediacommunications. The main hypothesis formulated in the research is that elaboration of the philosophical theory of global networking mediacommunications may be of a fractal-like nature. The concept of multifractality is defined as a process and result of designing complex self-similar structures based on the consistent use of several algorithms to create different fractals.

Fractal Models and the Structure of Materials

MRS Bulletin ◽  
1988 ◽  
Vol 13 (2) ◽  
pp. 22-27 ◽  
Author(s):  
Dale W. Schaefer
Keyword(s):  
Fractal Geometry ◽  
Materials Science ◽  
Rotational Symmetry ◽  
Disordered Materials ◽  
Growth Processes ◽  
Fractal Models ◽  
Kinetic Growth ◽  
Fractal Properties ◽  
New Ideas ◽  
Self Similar

Science often advances through the introdction of new ideas which simplify the understanding of complex problems. Materials science is no exception to this rule. Concepts such as nucleation in crystal growth and spinodal decomposition, for example, have played essential roles in the modern understanding of the structure of materials. More recently, fractal geometry has emerged as an essential idea for understanding the kinetic growth of disordered materials. This review will introduce the concept of fractal geometry and demonstrate its application to the understanding of the structure of materials.Fractal geometry is a natural concept used to describe random or disordered objects ranging from branched polymers to the earth's surface. Disordered materials seldom display translational or rotational symmetry so conventional crystallographic classification is of no value. These materials, however, often display “dilation symmetry,” which means they look geometrically self-similar under transformation of scale such as changing the magnification of a microscope. Surprisingly, most kinetic growth processes produce objects with self-similar fractal properties. It is now becoming clear that the origin of dilation symmetry is found in disorderly kinetic growth processes present in the formation of these materials.

Jessen–Wintner type random variables and fractal properties of their distributions

2006 ◽  
Vol 279 (15) ◽  
pp. 1619-1633 ◽  
Author(s):  
Sergio Albeverio ◽  
Yana Gontcharenko ◽  
Mykola Pratsiovytyi ◽  
Grygoriy Torbin
Keyword(s):  
Random Variables ◽  
Fractal Properties

SELF SIMILARITY IN SWELLING SYSTEMS: FRACTAL PROPERTIES OF PEAT

Fractals ◽  
1994 ◽  
Vol 02 (01) ◽  
pp. 45-52 ◽  
Author(s):  
A. V. NEIMARK ◽  
E. ROBENS ◽  
K. K. UNGER ◽  
Yu. M. VOLFKOYICH
Keyword(s):  
Fractal Dimension ◽  
Water Adsorption ◽  
The Self ◽  
Self Similarity ◽  
Sphagnum Peat ◽  
Fractal Properties ◽  
Wide Range ◽  
Capillary Equilibrium ◽  
Scale Range ◽  
Self Similar

Sphagnum peat gives an example of a swelling system with a self-similar structure in sufficiently wide range of scales. The surface fractal dimension, dfs, has been calculated by means of thermodynamic method on the basis of water adsorption and capillary equilibrium measurements. This method makes possible the exploration of the self-similarity in the scale range over at least 4 decimal orders of magnitude from 1 nm to 10 μm. In a sample explored, two ranges of fractality have been observed: dfs ≈ 2.55 in the range 1.5–80 nm and dfs ≈ 2.42 in the range 0.25–9 µm.

Some fractal properties of a class of self-similar Markov processes

1997 ◽  
Vol 2 (3) ◽  
pp. 257-262
Author(s):  
Huang Lihu ◽  
Li Bingzhang ◽  
Liu Luqin
Keyword(s):  
Markov Processes ◽  
Fractal Properties ◽  
Self Similar
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