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Закон больших чисел для суммы неполных частных рационального числа с фиксированным знаменателем
Математические заметки. 2011. Т. 90. № 3. С. 431-444.
Рукавишникова М. Г.
We obtain a nontrivial estimate of the variance of the sum of bounded partial quotients appearing in the continued-fraction expansion of a rational number with fixed denominator. As a consequence, we obtain a law of large numbers for the sum of all partial quotients.
M. G. Rukavishnikova, Mathematical notes 2011 Vol. 90 No. 3 P. 418-430
We obtain a nontrivial estimate of the variance of the sum of bounded partial quotients appearing in the continued-fraction expansion of a rational number with fixed denominator. As a consequence, we obtain a law of large numbers for the sum of all partial quotients. ...
Added: July 20, 2015
Рукавишникова М. Г., Чебышевский сборник 2006 Т. 7 № 4 С. 113-121
a ...
Added: July 20, 2015
Makarov I., Mathematical notes 2014 Vol. 95 No. 6 P. 795-805
The convex hull of all integer points of a noncompact polyhedron is closed and is a generalized polyhedron only under certain conditions. It is proved that if only the integer points in the interior of the polyhedron are taken, then most of the conditions can be dropped. Moreover, the object thus obtained has properties resembling ...
Added: June 9, 2014
Кан И. Д., Frolenkov D., Известия РАН. Серия математическая 2014 Т. 78 № 2 С. 87-144
We prove that the set of positive integers contains a positive proportion of numbers satisfying Zaremba’s conjecture withA= 7. This result strengthens a similar theorem of Bourgain and Kontorovich obtained for A= 50. ...
Added: October 23, 2014
Frolenkov D., Kan I. D., Moscow Journal of Combinatorics and Number Theory 2014 Vol. 4 No. 1 P. 78-117
Zaremba's conjecture (1971) states that every positive integer number can be represented as a denominator (continuant) of a finite continued fraction with all partial quotients being bounded by an absolute constant A. Recently (in 2011) several new theorems concerning this conjecture were proved by Bourgain and Kontorovich. The easiest of them states that the set of ...
Added: November 1, 2014
Gutnik L., / Cornell University Library. 2013. No. 1307.1125.
We present here continued fraction for Zeta(3) parametrized by some family of points (F,G) on projective line. This family of points can be obtained if from full projective line would be removed some no more than countable nowhereмножество dense exeptional set of finite points. countable nowhere dense set, which contains the above exeptional set of ...
Added: January 8, 2014
Gutnik L., International Mathematical Forum 2013 Vol. 17 No. 6 P. 771-781
We found a series of continued fractions for zeta(3), parametrized by some family of pairs of sequences F,G. Two members of this series are present here; they are different from Apery-Nesterenko continued fraction. ...
Added: May 17, 2013
Gutnik L., International Mathematical Forum 2013 Vol. 8 No. 28 P. 1385-1396
This is continuation of our article [4]. When F and G in [4] are constant sequences, we obtain continued fraction for zeta(3) parametrized by some family of points (F,G) on projective line. This family of points can be obtained if from full projective line would be removed some no more than countable nowhere dense exeptional ...
Added: January 8, 2014
Nesterenko A., Математические вопросы криптографии 2014 Vol. 5 No. 2 P. 99-102
In this article we present an algorithm for constructing an elliptic curve endomorphism for given complex irrationality. This endomorphism can be used for speeding up a group operation on elliptic curve. ...
Added: February 2, 2015
Feigin E., European Journal of Combinatorics 2012 Vol. 33 No. 1 P. 1913-1918
It has been shown recently that the normalized median Genocchi numbers are equal to the Euler characteristics of the degenerate flag varieties. The q-analogues of the Genocchi numbers can be naturally defined as the Poincare polynomials of the degenerate flag varieties. We prove that the generating function of the Poincare polynomials can be written as ...
Added: July 18, 2012
Frolenkov D., Математический сборник 2012 Т. 203 № 2 С. 143-160
В работе рассматриваются первые моменты для числа шагов в различных алгоритмах Евклида. Для них, используя улучшенные оценки сумм дробных долей и идеи из элементарного доказательства А.Сельберга асимптотического закона распределения простых чисел, получены асимптотические формулы с новыми остаточными членами ...
Added: November 3, 2014
Kan I. D., Izvestiya. Mathematics 2014 Vol. 78 No. 2 P. 293-353
We prove that positive integers contains a positive proportion of numbers, satisfying Zaremba's conjecture with A=7.
This result is a strengthening of a similar theorem of Bourgain-Kontorovich, obtained for A=50. ...
Added: April 28, 2015
Gutnik L., Advances in Difference Equations 2010 No. Article ID 143521 P. 1-11
Yu. V. Nesterenko has proved that ζ_3_ _ b0 _ a1|/|b1 _ · · · _ aν|/|bν _ · · · , b0 _ b1 _ a2 _ 2,
a1 _ 1, b2 _ 4, b4k_1 _ 2k _ 2, a4k_1 _ k_k _ 1_, b4k_2 _ 2k _ 4, and a4k_2 _ _k _ 1__k ...
Added: November 11, 2013
Smirnov E., Квант 2020 № 5 С. 15-24
В статье рассказывается о числовых фризах Конвея-Кокстера и обсуждаются их основные свойства. ...
Added: September 19, 2020
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
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
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