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Limiting Curves for the Pascal Adic Transformation
Journal of Mathematical Sciences. 2016. Vol. 216. No. 1. P. 94-119.
Lodkin A. A., Minabutdinov A.
The paper generalizes results by E. Janvresse, T. de la Rue, and Y. Velenik and results by the second author on the fluctuations in the ergodic sums for the Pascal adic transformation in the case of an arbitrary ergodic invariant measure and arbitrary cylinder function.
Minabutdinov A., Лодкин А. А., Записки научных семинаров ПОМИ РАН 2015 Т. 437 С. 145-183
The paper generalizes the results by E. Janvresse, T. de la Rue and Y. Velenik on fluctuations in ergodic sums for the Pascal adic transformation in the case of any ergodic invariant measure and cylindric function. The result on non-discreteness of the spectrum of the Pascal adic is stated. ...
Added: October 14, 2015
Minabutdinov A., Записки научных семинаров ПОМИ РАН 2019 Т. 481 С. 74-86
A limiting curve of a stationary process in discrete time was defined by \'{E}. Janvresse, {T.} de~la Rue and {Y.} Velenik as the uniform limit
of the functions \[t\mapsto \big(S(tl_n) - tS(l_n)\big)/R_n \in C([0, 1]),\] where $S$ refers to the piecewise
linear extension of the partial sum, $R_n := \sup |S(tl_n) - tS(l_n))|$, and $(l_n) = (l_n(\omega))$ ...
Added: October 6, 2019
Minabutdinov A., Journal of Mathematical Sciences 2020 Vol. 247 No. 17 P. 688-695
A limiting curve of a stationary process in discrete time was defined by É. Janvresse, T. de la Rue, and Y. Velenik as the uniform limit of the certain renormalization of the process. We determine the limiting curves for the stationary sequence (f ∘ Tn(ω)) where T is the dyadic odometer and f is the weighted sum of digits ...
Added: November 21, 2020
Minabutdinov A., Journal of Mathematical Sciences 2016 Vol. 215 No. 6 P. 738-747
The paper extends a classical result on the convergence of the Krawtchouk polynomials to the Hermite polynomials. We provide a uniform asymptotic expansion in terms of Hermite polynomials and obtain explicit expressions for a few first terms of this expansion. The research is motivated by the study of ergodic sums of the Pascal adic transformation. ...
Added: July 8, 2016
Манаев И. Е., Лодкин А. А., Minabutdinov A., Записки научных семинаров ПОМИ РАН 2012 Т. 403 С. 95-102
A class of concatenation dynamical systems is introduced. Various automorphisms, including the Morse and Pascal authomorphisms, can be regarded as automorphisms of this class. In this realization, a natural number-theoretic interpretation of the problem whether the spectrum of an automorphisms is discrete arises. In particular, the known character of the asymptotic behavior of the function s 2(n) allows one ...
Added: November 8, 2014
Minabutdinov A., Journal of Mathematical Sciences 2017 Vol. 224 No. 2 P. 286-303
We prove the existence of and describe limiting curves resulting from deviations in the partial sums in the ergodic theorem for cylinder functions and polynomial adic systems. For a general ergodic measure-preserving transformation and a summable function, we give a necessary condition for a limiting curve to exist. Our work generalizes results by É. Janvresse, ...
Added: February 7, 2019
Лодкин А. А., Манаев И. Е., Minabutdinov A., Записки научных семинаров ПОМИ РАН 2010 Т. 378 С. 58-72
In this paper, we give an estimate on the growth of the scaling sequence of the Pascal adic transformation with respect to the sup-metric. We construct a special class of α-names of positive cumulative measure. The linear growth of its cardinality implies the logarithmic growth of the scaling sequence. Bibliography: 14 titles. ...
Added: November 10, 2014
Minabutdinov A., / Cornell University. Series arXiv "math". 2015. No. 1508.07421.
The paper extends the classical result on the convergence of the Krawtchouk polynomials to the Hermite polynomials. We provide the uniform asymptotic expansion in terms of the Hermite polynomials. We explicitly obtain expressions for a few initial terms of this expansion. The research is motivated by the study of ergodic sums of the Pascal adic ...
Added: September 12, 2015
Minabutdinov A., Лодкин А. А., Манаев И. Е., / Санкт-Петербургское математическое общество. Серия MSP "Preprints of the St. Petersburg Mathematical Society". 2014. № 11.
The paper generalizes the results by \'E. Janvresse, T. de la Rue and Y. Velenik [22] and the work [9] of the third author on fluctuations in ergodic sums for the Pascal adic in the case of arbitrary ergodic invariant measures. In particular, we answer several questions from [22] and [9]. ...
Added: March 28, 2015
Minabutdinov A., Манаев И. Е., Записки научных семинаров ПОМИ РАН 2013 Т. 411 С. 135-147
Interrelations between the Kruskal–Katona function, Conway sequence, Takagi curve, and Pascaladic are investigated. Using the obtained results and, particularly, the convergence of the sequence 2a(n) – n, where a(n) is the Conway sequence, to the family of generalized Takagi curves, we prove the same for the Kruskal–Katona function. Moreover, an inductive method of calculating the values of ...
Added: November 8, 2014
Minabutdinov A., Записки научных семинаров ПОМИ РАН 2015 Т. 432 С. 224-260
The paper generalizes the results by E. Janvresse, T. de la Rue and Y. Velenik [18] on fluctuations in ergodic sums for the Pascal adic transformation in the case of Lebesgue measure for a wide class of functions. In particular, we answer several questions from [18]. ...
Added: March 15, 2015
Minabutdinov A., Записки научных семинаров ПОМИ РАН 2015 Т. Том 436 С. 174-189
The paper extends the classical result on the convergence of the Krawtchouk polynomials to the Hermite polynomials. We provide the uniform asymptotic expansion in terms of the Hermite polynomials. We explicitly obtain expressions for a few initial terms of this expan- sion. The research is motivated by the study of ergodic sums of the Pascal ...
Added: October 14, 2015
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017
Красноярск : ИВМ СО РАН, 2013
Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...
Added: November 18, 2013
Grines V., Gurevich E., Pochinka O., Russian Mathematical Surveys 2017 Vol. 71 No. 6 P. 1146-1148
In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed. ...
Added: May 17, 2017
Okounkov A., Aganagic M., Moscow Mathematical Journal 2017 Vol. 17 No. 4 P. 565-600
We associate an explicit equivalent descendent insertion to any relative insertion in quantum K-theory of Nakajima varieties.
This also serves as an explicit formula for off-shell Bethe eigenfunctions for general quantum loop algebras associated to quivers and gives the general integral solution to the corresponding quantum Knizhnik Zamolodchikov and dynamical q-difference equations. ...
Added: October 25, 2018
Danilov B.R., Moscow University Computational Mathematics and Cybernetics 2013 Vol. 37 No. 4 P. 180-188
The article investigates a model of delays in a network of functional elements (a gate network) in an arbitrary finite complete basis B, where basis elements delays are arbitrary positive real numbers that are specified for each input and each set of boolean variables supplied on the other inputs. Asymptotic bounds of the form τ ...
Added: December 2, 2019
Beklemishev L. D., Оноприенко А. А., Математический сборник 2015 Т. 206 № 9 С. 3-20
We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano arithmetic PA. Thus, the termination of such systems is unprovable in PA. These systems are derived from an independent combinatorial result known as the Worm ...
Added: March 13, 2016
Levashov M., Кухаренко А. В., Вопросы защиты информации 2018 № 2 С. 66-71
Рассматривается статистическая модель одного этапа системы фрод-мониторинга транзакций в интернет-банкинге. Построен и рассчитан близкий к отношению правдоподобия критерий отсева мошеннических транзакций. Для выборочных распределений, полученных на выборке объема в 1 млн реальных транзакций, вычислены параметры эффективности этого критерия. ...
Added: June 14, 2018
Amerik E., Verbitsky M., / Cornell University. Series arXiv "math". 2021.
An MBM locus on a hyperkahler manifold is the union of all deformations of a minimal rational curve with negative self-intersection. MBM loci can be equivalently defined as centers of bimeromorphic contractions. It was shown that the MBM loci on deformation equivalent hyperkahler manifolds are diffeomorphic. We determine the MBM loci on a hyperkahler manifold ...
Added: April 7, 2022
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Litvin Y. V., Абрамов И. В., Технологии техносферной безопасности 2016 № 66
Advanced approach to the assessment of a random time of arrival fire fighting calculation on the object of protection, the time of their employment and the free combustion. There is some quantitative assessments with the review of analytical methods and simulation ...
Added: August 27, 2016