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Regular version of the site
Of all publications in the section: 55
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Article
Borodin A., Olshanski G. Journal of Mathematical Sciences. 2014. Vol. 421. P. 47-57.

We discuss a stochastic particle system consisting of a two-dimensional array of particles living in one space dimension. The stochastic evolution bears a certain similarity to Hammersley's process, and the particle interaction is governed by combinatorics of the Young tableaux.

Article
Lytvynov E., Olshanski G. Journal of Mathematical Sciences. 2012. Vol. 403. P. 81-94.
Article
Hirsch E. A., Melanich O., Nikolenko S. I. Journal of Mathematical Sciences. 2012. Vol. 399. P. 32-64.

In 1992, A. Hiltgen provided first constructions of provably (slightly) secure cryptographic primitives, namely feebly one-way functions. These functions are provably harder to invert than to compute, but the complexity (viewed as the circuit complexity over circuits with arbitrary binary gates) is amplified only by a constant factor (in Hiltgen’s works, the factor approaches 2).   In traditional cryptography, one-way functions are the basic primitive of private-key schemes, while public-key schemes are constructed using trapdoor functions. We continue Hiltgen’s work by providing examples of feebly secure trapdoor functions where the adversary is guaranteed to spend more time than honest participants (also by a constant factor). We give both a (simpler) linear and a (better) non-linear construction.

Article
Olshanski G. Journal of Mathematical Sciences. 2010. Vol. 378. P. 81-110.
Article
Kalinin N. Journal of Mathematical Sciences. 2018. Vol. 476. P. 92-110.

We prove that the number o fLegendrian rational cubics in CP^3 through three generic points and a line is three. Also, we classify all Legendrian curves on a quadric surface. Additionally, several computations are verified using Macaulay2 computer algebra system.

Article
Rudenko D. Journal of Mathematical Sciences. 2012. Vol. 403. P. 142-157.

In this paper we show that a lattice balanced polygon of odd area cannot be cut into an odd number of triangles of equal areas. First result of this type was obtained by Paul Monsky in 1970. He proved that a square cannot be cut into an odd number of triangles of equal areas. In 2000 Sherman Stein conjectured that the same holds for any balanced polygon.

We also show connections between the equidissection problem and tropical geometry.

Article
Amosov G., Zhdanovskiy I. Journal of Mathematical Sciences. 2015. Vol. 436. P. 49-75.

We study the noncommutative operator graph ${\mathcal L}_{\theta }$ depending on complex parameter $\theta$ recently introduced by M.E. Shirokov to construct channels with positive quantum zero-error capacity having vanishing n-shot capacity. We define the noncommutative group $G$ and the algebra ${\mathcal A}_{\theta }$ which is a quotient of ${\mathbb C}G$with respect to the special algebraic relation depending on $\theta$ such that the matrix representation $\phi$ of ${\mathcal A}_{\theta }$ results in the algebra ${\mathcal M}_{\theta }$ generated by ${\mathcal L}_{\theta }$. In the case of $\theta =\pm 1$ $\phi$ is degenerated to the faithful representation of ${\mathbb C}K_4$, where $K_4$ is the Klein group. Thus, ${\mathcal L}_{\theta }$ can be considered as a noncommutative deformation of the graph associated with the Klein group.

Article
Bondal A. I., Zhdanovskiy I. Journal of Mathematical Sciences. 2015. Vol. 437. P. 35-61.

The goal of our arti le is a study of related mathemati al and physi al ob je ts: orthogonal pairs in sl(n) and mutually unbiased bases in Cn . An orthogonal pair in a simple Lie algebra is a pair of Cartan subalgebras that are orthogonal with respe t to the Killing form. The des ription of orthogonal pairs in a given Lie algebra is an important step in the lassi ation of orthogonal de- ompositions, i.e., de ompositions of the Lie algebra into a dire t sum of Cartan subalgebras pairwise orthogonal with respe t to the Killing form. One of the important notions of quantum me hani s, quantum information theory, and quantum teleportation is the notion of mutually unbiased bases in the Hilbert spa e C n . Two orthonormal bases {ei } n i=1 ; {fj } n j=1 are mutual ly unbiased if and only if |hei |fj i|2 = 1 n for any i; j = 1; : : : ; n. The notions of mutually unbiased bases in C n and orthogonal pairs in sl(n) are losely related. The problem of lassi ation of orthogonal pairs in sl(n) and the losely related problem of lassi ation of mutually unbiased bases in C n are still open even for the ase n = 6. In this arti le, we give a sket h of our proof that there is a omplex four-dimensional family of orthogonal pairs in sl(6). This proof requires a lot of algebrai geometry and representation theory. Further, we give an appli ation of the result on the algebrai geometri family to the study of mutually unbiased bases. We show the existen e of a real fourdimensional family of mutually unbiased bases in C 6 , thus solving a long-standing problem.

Article
Takebe T., Takasaki K. Journal of Mathematical Sciences. 1996. Vol. 235. P. 295-303.

This paper deals with the dispersionless KP hierarchy from the point of view of quasi-classical limit. Its Lax formalism, W-infinity symmetries and general solutions are shown to be reproduced from their counterparts in the KP hierarchy in the limit of hbar->0. Free fermions and bosonized vertex operators play a key role in the description of W-infinity symmetries and general solutions, which is technically very similar to a recent free fermion formalism of c=1 matrix models.

Article
Деркачев С. Э., Белоусов Н. Записки научных семинаров ПОМИ РАН. 2018. Т. 473. С. 34-65.
Article
Derkachov S., Валиневич П. А. Journal of Mathematical Sciences. 2018. Vol. 473. P. 110-146.

The quantum SL(3, C) invariant spin magnet with infinite-dimensional principal series representation in local spaces is considered. We construct eigenfunctions of Sklyanin’s B-operator which define the representation of separated variables of the model

Article
Лодкин А. А., Манаев И. Е., Минабутдинов А. Р. 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.

Article
Минабутдинов А. Р. 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 adic transformation.

Article
Полотовский Г. М. Записки научных семинаров ПОМИ РАН. 2020. Т. 498. С. 157-167.

The story of the friendship and cooperation between Vladimir Abramovich Rokhlin and the Nizhny Novgorod mathematician Dmitry Andreevich Gudkov during the last period of Rokhlin’s mathematical biography, when he worked in the topology of real algebraic varieties, in which he received remarkable results. The paper is based on the correspondence of 1971–1982 preserved in Gudkov’s archive containing 15 letters by V.A.Rokhlin and 8 letters by D.A.Gudkov.

Article
Широков Н.А. Записки научных семинаров ПОМИ РАН. 2019. Т. 480. С. 206-213.

We introduce classes of analytic functions in a disc and holomorphic functions in a ball that satisfy a H¨older condition in a Lebesgue norm with variable exponent. We describe outer functions in the disc and state the drop of the smoothness of a function in comparison with the smoothness of its modulus on the boundary in the case of the disc and the ball

Article
Савченко А. В. Записки научных семинаров ПОМИ РАН. 2021. Т. 499. С. 267-283.

In this paper fast image recognition techniques based on statistical sequential analysis are discussed. We examine the possibility to sequentially process the principal components and organize a convolutional neural net- work with early exits. Particular attention is paid to sequentially learn multi-task lightweight neural network model to predict several facial at- tributes (age, gender and ethnicity) based on preliminary training on the face classification task. It is highlighted that the whole above-mentioned model should be fine-tuned in order to deal with emotion recognition problem. Experimental study on several datasets demonstrate that the proposed approach is rather accurate and has very low run-time and space complexity when compared to known state-of-the-art methods.

Article
Н. А. Широков Записки научных семинаров ПОМИ РАН. 2016. Т. 416. С. 123-128.
Article
Широков Н. А. Записки научных семинаров ПОМИ РАН. 2017. Т. 456. С. 172-176.