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## Problem of Erdos – Vershik for Golden Ratio

The Erwin Schrodinger International Institute for Mathematical Physics
,
2008.
No. 2087.

Bezhaeva Z., Oseledets V. I.

Properties of Erdos measure and the invariant Erdos measure for the golden ratio and all values of the Bernoulli parameter are studies. It is proved that a shift on the two-sided Fibonacci compact set with invariant Erdos measure is isomorphic to the integral automorphism for a Bernoulli shift with countable alphabet.

Bezhaeva Z., Oseledets V. I., Functional Analysis and Its Applications 2010 Vol. 44 No. 2 P. 83-91

Properties of Erdos measure and the invariant Erdos measure for the golden ratio and all values of the Bernoulli parameter are studies. It is proved that a shift on the two-sided Fibonacci compact set with invariant Erdos measure is isomorphic to the integral automorphism for a Bernoulli shift with countable alphabet. ...

Added: April 12, 2012

Bezhaeva Z., Oseledets V. I., Функциональный анализ и его приложения 2010 Т. 44 № 2 С. 3-13

Properties of Erdos measure and the invariant Erdos measure for the golden ratio and all values of the Bernoulli parameter are studies. It is proved that a shift on the two-sided Fibonacci compact set with invariant Erdos measure is isomorphic to the integral automorphism for a Bernoulli shift with countable alphabet. An effective algorithm for ...

Added: April 12, 2012

Bezhaeva Z., Oseledets V. I., Grazer Mathematische Berichte 2009 Vol. 354 P. 15-25

We study the ergodic properties of Erdos measure and the invariant Erdos measure for the golden ratio and all values of the Bernoulli parameter. We provide an new effective algorithm for the calculate of entropy of the Erdos measure. ...

Added: April 12, 2012

Bezhaeva Z., Oseledets V. I., Journal of Dynamical and Control Systems 2013 Vol. 19 No. 4 P. 569-573

Algorithm is given for computation of the Hausdorff dimension of the support of the Erdos measure for a Pisot number. ...

Added: November 11, 2013

Bezhaeva Z., Oseledets V. I., Theory of Probability and Its Applications 2013 Vol. 57 No. 1 P. 135-144

The formula for calculating the entropy and the Hausdorff dimension of an invariant Erdos measure for the pseudogolden ratio and all values Bernoulli parameter is obtained. This formula make possible calculating the entropy and the Hausdorff dimension with high accuracy. ...

Added: February 15, 2014

Bezhaeva Z., Oseledets V. I., Journal of Dynamical and Control Systems 2013 Vol. 19 No. 2 P. 301-308

Consider a sofic dynamical system. We obtain an explcit formula for the KS-entropy of sofic dynamicsl system of Blackwell's type. ...

Added: August 22, 2013

Bezhaeva Z., Куликов В. Л., Олехова Е. Ф. et al., В кн. : Материалы конференции «Современная математика и концепции инновационного математического образования». : М. : ООО "Издательский дом МФО", 2017. С. 15-23.

Рассматривается новый подход к получению общего вида автоморфизма группы Гейзенберга. Определена мера Эрдеша на группе Гейзенберга. Дано определение инвариантной меры Эрдеша и получен критерий абсолютной непрерывности меры Эрдеша. ...

Added: July 14, 2017

Bilinkis (Stavenko) J., Gromoff A., Far East Journal of Psychology and Business 2012 Vol. 8 No. 3 P. 38-49

Operational risk management (ORM) is considered as decision-making tool to systematically operational risk identification and determination of the best courses of action for any given situation. Here we made an attempt to analyse ORM from the position of system approach to the enterprise management. In this view, 4 interrelated subsystems were identified: beliefs, constraints, control ...

Added: September 14, 2012

Maksim D. Miroshnichenko, Russian Studies in Philosophy 2022 Vol. 60 No. 3 P. 205-230

The paper reconstructs the conception of the Soviet-American psychologist Vladimir Lefebvre as part of the neocybernetic movement. In particular, I propose to consider such components of his research of the 70s-90s as systemic vision, reflexive analysis, search for a holistic configuration, and Janus-cosmology as realizations of neocybernetics. Lefebvre's interest in the reflexive structures of cognition ...

Added: November 29, 2021

Karpenko I., Вопросы философии 2019 № 4 С. 58-68

The article focuses on an analysis of the possible connection between the second law of thermodynamics and time. The growth of entropy as a physical process - mostly its technical side - has been well studied but in fact there is no philosophical interpretation of this phenomenon according to the current research, in particular, regarding ...

Added: March 5, 2019

Zhukova G., Сметанин Ю. Г., Ulyanov M., , in : 2019 International Conference on Engineering Technologies and Computer Science (EnT). : IEEE, 2019. P. 43-47.

A qualitative analysis refers to the identification of the qualitative characteristics of a time series, such as its periodicity, final periodicity or near periodicity, convergence to the limit state, randomness, etc. For such an analysis, methods of symbolic dynamics are used, with the time series being represented as a sequence of symbols from a finite ...

Added: October 22, 2019

Kolachev N., Психологические исследования: электронный научный журнал 2023 Т. 16 № 88 Статья 1

The present articleis aimed to examine the applicability of the difficulty index within the framework of psychometric analysis of psychological tests. It is demonstrated that this index is often disregarded in traditional psychometric research due to its absence in the paradigm of confirmatory factor analysis, which is commonly employed by most psychologists. Analytical and empirical ...

Added: June 23, 2023

Apenko S.M., Physica A: Statistical Mechanics and its Applications 2012 Vol. 391 No. 1-2 P. 62-77

We present a possible approach to the study of the renormalization group (RG) flow based
entirely on the information theory. The average information loss under a single step of
Wilsonian RG transformation is evaluated as a conditional entropy of the fast variables,
which are integrated out, when the slow ones are held fixed. Its positivity results in the
monotonic ...

Added: October 23, 2014

Bilinkis (Stavenko) J., Gromoff A., Качество. Инновации. Образование 2012 № 7 С. 80-87

The article includes an example of a system approach to managing operational risk in the procurement process. According this approach, 4 interrelated subsystems were identified: beliefs, constraints, control and monitoring. Therefore the operational risk management is a Meta process embedded into business processes and set requirements to the above subsystems. ...

Added: December 13, 2012

Sandlersky Robert, Krenke Alexander, Entropy 2020 Vol. 22 No. 10 Article 1132

The hypothesis of an increase in free energy (exergy) by ecosystems during evolution is tested on direct measurements. As a measuring system of thermodynamic parameters (exergy, information, entropy), a series of measurements of reflected solar radiation in bands of Landsat multispectral imagery for 20 years is used. The thermodynamic parameters are compared for different types ...

Added: March 21, 2022

Bufetov A. I., Mkrtchyan S., Scherbina M. et al., Journal of Statistical Physics 2013 Vol. 152 No. 1 P. 1-14

We show that beta ensembles in Random Matrix Theory with generic real analytic potential have the asymptotic equipartition property. In addition, we prove a Central Limit Theorem for the density of the eigenvalues of these ensembles. ...

Added: March 13, 2014

В.Н. Азаров, Бойцов Б. В., Ю.И. Гудков et al., Компетентность 2017 № 9-10 С. 46-57

We have examined the main new competencies that should be matched by the specialist — managers of complex techno-technological and socio-economic systems in the era of information (digital) and industrial revolutions. We have also investigated what kind of overprofessional competencies the expert should have and what the system of its preparation includes. Having outlined and ...

Added: January 29, 2018

Rubchinskiy A., / Высшая школа экономики. Series WP7 "Математические методы анализа решений в экономике, бизнесе и политике". 2015. No. WP7/2015/09.

An algorithm of solution of the Automatic Classification (AC for brevity) problem is set forth in the paper. In the AC problem, it is required to find one or several partitions, starting with the given pattern matrix or dissimilarity / similarity matrix. The three-level scheme of the algorithm is suggested. The output of the procedure ...

Added: October 19, 2017

Rubchinskiy A., , in : Models, Algorithms, and Technologies for Network Analysis. Springer Proceedings in Mathematics & Statistics. Vol. 197.: Springer, 2017. P. 127-152.

A new approach to network decomposition problems (and, hence, to classification problems, presented in network form) is suggested. Opposite to the conventional approach, consisting in construction of one, “the most correct” decomposition (classification), the suggested approach is focused on construction of a family of classifications. Basing on this family, two numerical indices are introduced and ...

Added: October 20, 2017

Gromoff A., Bilinkis (Stavenko) J., Информационные технологии в проектировании и производстве 2011 № 3 С. 28-35

This article discusses and applies an approach to solution of business process monitoring task on the basis of study of entropy characters of an acting business system information field, which is considered from a view of behavior and modeling of open systems. Process flow continuity in time is taken to account. A method of stability ...

Added: December 10, 2012

Kiyatkina A., Shadrikov V., Вестник Ярославского государственного университета им. П.Г. Демидова. Серия Гуманитарные науки 2021 Т. 5 № 3 С. 434-443

The article discusses understanding as a human tendency to remove uncertainty through the phenomenon of «entropy». The learning process initially puts the student in a situation of constant movement from a disordered
environment to an ordered one, which occurs due to the constant interruption of the student’s inner world balance. Studies of understanding through entropy allow ...

Added: November 10, 2021

Bezhaeva Z., Oseledets V. I., Теория вероятностей и ее применения 2012 Т. 57 № 1 С. 1-10

В работе для псевдозолотого сечения и для произвольного параметра Бернулли получена формула для вычисления энтропии инвариантной меры Эрдеша. Формула позволяет производить вычисление энтропии и хаусдорфовой размерности инвариантной меры Эрдеша с высокой точностью. ...

Added: May 21, 2012

Skripchenko A., Troubetzkoy S., / Cornell University. Series math "arxiv.org". 2015. No. 1501.04584.

We prove that a polygonal billiard with one-sided mirrors has zero
topological entropy. In certain cases we show sub exponential and for other
polynomial estimates on the complexity. ...

Added: January 26, 2015

Popkov Y., Popkov A., Dubnov Y. A., Автоматика и телемеханика 2020 № 7 С. 148-172

A randomized forecasting method based on the generation of ensembles of entropy-optimal forecasting trajectories is developed. The latter are generated by randomized dynamic regression models containing random parameters, measurement noises, and a random input. The probability density functions of random parameters and measurement noises are estimated using real data within the randomized machine learning procedure. ...

Added: October 31, 2020