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On the Structure of Graphs of Markoff Triples
Quarterly Journal of Mathematics. 2020. Vol. 71. No. 2. P. 637-648.
We sharpen the bounds of J. Bourgain, A. Gamburd and P. Sarnak (2016) on the possible number of nodes outside the ‘giant component’ and on the size of individual connected components in the suitably defined functional graph of Markoff triples modulo p. This is a step towards the conjecture that there are no such nodes at all.
Макарычев С. В., Vyugin I. V., Arnold Mathematical Journal 2019 Vol. 5 No. 1 P. 105-121
We present an upper bound on the number of solutions of an algebraic equation P(x,y)=0 where x and y belong to the union of cosets of some subgroup of the multiplicative group κ∗ of some field of positive characteristic. This bound generalizes the bound of Corvaja and Zannier (J Eur Math Soc 15(5):1927–1942, 2013) to the case of union of cosets. We also ...
Added: August 13, 2019
В. Л. Попов, Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2016 Т. 468 № 5 С. 499-501
A general theorem on the purity of of invariant field extensions
is proved. Using it, a criterion of rational triangulability of connected solvable
affine algebraic subgroups of the Cremona groups is obtained. This criterion is
applied for proving the existence of rationally nontriangulable subgroups of the
above form and for proving their stable rational triangulability. The latter property
answers in ...
Added: May 16, 2016
Vyugin I. V., Математические заметки 2019 Т. 106 № 2 С. 212-221
An upper bound for the number of field elements that can be taken to roots of unity of fixed multiplicity by means of several given polynomials is obtained. This bound generalizes the bound obtained by V'yugin and Shkredov in 2012 to the case of polynomials of degree higher than 1. This bound was obtained both over ...
Added: October 9, 2019
Popov V., / Centro Internazionale per la Ricerca Matematica. Series CIRM "Electronic preprint server". 2012. No. нет.
Some problems on the structure of the Cremona groups formulated (with comments) by the author at the International conference Birational and Affine Geometry, Levico Terme (Trento), 29.10.12--03.11.12 ...
Added: January 9, 2013
Vyugin I. V., Солодкова Е. В., Шкредов И. Д., Математические заметки 2016 Т. 100 № 2 С. 185-195
By means Stepanov's method the bound of cardinality of the intersection of additive shifts of several subgroups of multiplicative group of the finite field was obtained. This bound apply to some question of additive decomposition of subgroups. ...
Added: January 29, 2016
V. L. Popov, Doklady Mathematics 2016 Vol. 93 No. 3 P. 307-309
A general theorem on the purity of invariant field extensions is proved. Using it, a criterion of rational triangulability of connected solvable affine algebraic subgroups of the Cremona groups is obtained. This criterion is applied for proving the existence of rationally nontriangulable subgroups of the above form and for proving their stable rational triangulability. The ...
Added: June 29, 2016
Алешина С. А., Vyugin I. V., Математические заметки 2023 Т. 113 № 1 С. 3-10
We generalize two results in the papers [1:x003] and [2:x003] about sums of subsets of Fp to the more general case in which the sum x+y is replaced by P(x,y), where P is a rather general polynomial. In particular, a lower bound is obtained for the cardinality of the range of P(x,y), where the variables x and y belong to a subgroup G of the multiplicative group of the field Fp. We also prove that ...
Added: January 21, 2023
Vyugin I. V., Макарычев С. В., Arnold Mathematical Journal 2019
In this paper we present a new bound of the number of solutions of a polynomial equation $P(x,y)=0$ over the field $\overline{\mathbb{F}}_p$ that belong to a union of cosets $(x,y)\in\bigcup_{i=1}^hg_i'G\times g_i''G$.
This bound improves a case of the bound of Corvaja and Zannier (see \cite{C-Z}) in the case $h\gg 1$. Using this bound we obtain estimates ...
Added: December 14, 2017
Nabebin A. A., Tarasikov A. S., M. : -, 2012
The manual contains necessary data from homogeneous and inhomogeneous universal algebras, systems of axioms for the basic algebraic structures (arithmetics, monoids, subgroups, groups, partial ordering, rings, fields). It is described axiomatic programming language OBJ3 with examples of programs in this language. It is intended to students of universities of specialities: the applied mathematics, informatics, computer ...
Added: March 13, 2013
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
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
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
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
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
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
Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45
Added: October 17, 2014
Arzhantsev I., Journal of Lie Theory 2000 Vol. 10 No. 2 P. 345-357
Added: July 8, 2014
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
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
Кокоулина М. В., Епифанова А. С., Pelinovsky E. et al., Труды НГТУ им. Р.Е. Алексеева 2020 № 3 С. 28-41
Purpose: to analyze the dynamics of COVID-19 development using a generalized stochastic logistic equation to esti-mate the number of probable peaks in coronavirus incidence and to evaluate the nature of the scatter of the generalized logistic model coefficients.
Design/methodology/approach: we use a logistic model based on a generalized first-order logistic equation. The data on the incidence ...
Added: September 29, 2020