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Algebraically integrable bodies and related properties of the Radon transform
P. 1–36.
Algebraic geometric properties of functions defined by integral representations are studied by the methods of monodromy theory
De Gruyter, 2023.
Algebraic geometrical properties of functions defined by integral transformations are studied ...
Added: October 31, 2025
Ilyashenko Y., Nonlinearity 2024 Vol. 37 No. 10 Article 105017
Consider a germ of a holomorphic vector field at the origin on the coordinate complex plane. This germ is called a saddle-node if the origin is its singular point, one of its eigenvalues at zero is zero, and the other is not. A saddle-node germ is real if its restriction to the real plane is ...
Added: January 25, 2025
Serge Lvovski, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze 2024 Vol. XXIV No. 2 P. 941–963
Using an adjunction-theoretic result due to A. J. Sommese together with a proposition from SGA7, we obtain a complete list of smooth threefolds for which the monodromy group, acting on the second cohomology group of its smooth hyperplane section, is Z/2Z. The possibility of such a classification was announced by F. L. Zak in 1991. ...
Added: July 11, 2024
Vyugin I. V., Дудникова Л. А., Математический сборник 2024 Т. 215 № 2 С. 3–20
The paper is devoted to the study of holomorphic vector bundles with logarithmic connections on a compact Riemann surface and the application of the results obtained to the study of the question of positive solvability of the Riemann–Hilbert problem on a Riemann surface. We give an example of a representation of the fundamental group of a ...
Added: March 5, 2024
Salnikov A., Stepanova I., Gudkova T. et al., , in: 2021 14th International Conference Management of large-scale system development (MLSD).: IEEE, 2021. P. 1–3.
We have constructed an analytical model of the magnetic field over a region of the Martian surface using satellite raw data and S-approximations within the modified structural-parametric approach. The method mentioned above implies considering the environment features as a function included in an integral. We approximated the anomalous field by the sum of simple and ...
Added: October 30, 2022
Gudkova T. V., Stepanova I. E., Batov A. et al., Inverse Problems in Science and Engineering 2021 Vol. 29 No. 6 P. 790–804
The connection of different modifications of the method of linear integral representation is studied. Solutions of the related inverse problems based upon a ‘hybrid version of two approximations’ of the topography and geopotential fields enable more refined tuning of the method in solving the inverse problems of geophysics and geomorphology and more complete allowance for ...
Added: October 29, 2022
Stepanova I. E., Gudkova T. V., Salnikov A. M. et al., Inverse Problems in Science and Engineering 2022 Vol. 30 No. 1 P. 41–60
A new three-staged technique based on various versions of the linear integral representation method (S-, F- and R-approximations) is applied to solve the problem of analytical modelling of the magnetic field on the surface of Mars. At the first step, we build an analytical approximation from the given data set (in local or regional cases). ...
Added: October 28, 2022
Gusein-Zade S., Journal of Algebra and its Applications 2018 Vol. 17 No. 10 P. 1–13
In a previous paper, the authors defined an equivariant version of the so-called Saito duality between the monodromy zeta functions as a sort of Fourier transform between the Burnside rings of an abelian group and of its group of characters. Here, a so-called enhanced Burnside ring Bˆ(G) of a finite group G is defined. An ...
Added: October 27, 2020
Alexander Esterov, Lang L., Geometry and Topology 2021 Vol. 25 No. 6 P. 3053–3077
Let C_d be the space of non-singular, univariate polynomials of degree d. The Viète map V sends a polynomial to its unordered set of roots. It is a classical fact that the induced map V_∗ at the level of fundamental groups realises an isomorphism between π_1(C_d) and the Artin braid group B_d. For fewnomials, or equivalently for the intersection C of C_d with a collection of coordinate ...
Added: October 27, 2020
V.A.Vassiliev, Arnold Mathematical Journal 2020 Vol. 6 No. 2 P. 291–309
V. Arnold’s problem 1987–14 from his Problems book asks whether there exist bodies with smooth boundaries in R^N (other than the ellipsoids in odd-dimensional spaces) for which the volume of the segment cut by any hyperplane from the body depends algebraically on the hyperplane. We present a series of very realistic candidates for the role ...
Added: August 17, 2020
Козачок А. В., Копылов С. А., Мещеряков Р. В. et al., Информатика и автоматизация (Труды СПИИРАН) 2018 Т. 5 № 60 С. 128–155
This paper presents an approach to a robust watermark extraction from images containing text. Data extraction based on developed approach to robust watermark embedding into text data, characterizing by conversion invariance of text data into an image format. The comparative analysis of existing approaches of steganographic data embedding into text data is carried out, their ...
Added: September 3, 2019
Козачок А. В., Копылов С. А., Шелупанов А. А. et al., Journal of Computer Virology and Hacking Techniques 2019 Vol. 15 No. 3 P. 219–232
Printed documents protection problem against leakage is still one of the relevant. Existing security tools allow us to protect electronic text documents, however are ineffective in protecting their printed versions. This research presents the marking approach for text electronic documents invariant to the print-and-scan transformation. During marker embedding source text line spacing values are changing ...
Added: September 3, 2019
Serge Lvovski, Moscow Mathematical Journal 2019 Vol. 19 No. 3 P. 597–613
We show that if we are given a smooth non-isotrivial family of curves of genus 1 over C with a smooth base B for which the general fiber of the mapping J : B → A 1 (assigning j-invariant of the fiber to a point) is connected, then the monodromy group of the family (acting ...
Added: August 30, 2019
Verbitsky M., Mehrotra S., Markman E., European Journal of Mathematics 2019 Vol. 5 No. 3 P. 964–1012
Let S be a K3 surface and M a smooth and projective 2n-dimensional moduli space of stable coherent sheaves on S. Over 𝑀×𝑀 there exists a rank 2𝑛−2 reflexive hyperholomorphic sheaf 𝐸_𝑀, whose fiber over a non-diagonal point (𝐹_1, 𝐹_2) is Ext^1_𝑆 (𝐹_1, 𝐹_2). The sheaf 𝐸_𝑀 can be deformed along some twistor path to a sheaf 𝐸_𝑋 over the Cartesian square 𝑋×𝑋 of every Kähler manifold X deformation equivalent to M. We prove that 𝐸_𝑋 is ...
Added: March 11, 2019
Esterov A. I., Compositio Mathematica 2019 Vol. 155 No. 2 P. 229–245
We prove that the monodromy group of a reduced irreducible square system of general polynomial equations equals the symmetric group. This is a natural first step towards the Galois theory of general systems of polynomial equations, because arbitrary systems split into reduced irreducible ones upon monomial changes of variables.
In particular, our result proves the multivariate ...
Added: February 5, 2019
Lvovsky S., / Series arXiv "math". 2018.
We show that if we are given a smooth non-isotrivial family of elliptic curves over ℂ with a smooth base B for which the general fiber of the mapping J:B→𝔸^1 (assigning j-invariant of the fiber to a point) is connected, then the monodromy group of the family (acting on H1(⋅,ℤ) of the fibers) coincides with SL(2,ℤ); if the general fiber has m≥2 connected components, then the ...
Added: December 5, 2018
V.A.Vassiliev, Journal of Singularities 2018 Vol. 18 P. 350–357
The volume cut off by a hyperplane from a bounded body in 2k-dimensional space never is an algebraic function on the space of hyperplanes: for k=1 it is the famous Lemma XXVIII from Newton's Principia. Following an analogy of these volume functions with the solutions of hyperbolic PDE's, we study the local version of the ...
Added: November 23, 2018
Бухштабер В. М., Glutsyuk A., Труды Математического института им. В.А. Стеклова РАН 2017 Т. 297 С. 62–104
Abstract—We study a family of double confluent Heun equations of the form LE = 0, where
L = L(λ,μ,n) is a family of second-order differential operators acting on germs of holomorphic
functions of one complex variable. They depend on complex parameters λ, μ, and n. The
restriction of the family to real parameters satisfying the inequality λ + μ^2>0 ...
Added: June 29, 2018
Takeuchi K., Esterov A. I., Lemahieu A., / Series math "arxiv.org". 2016. No. arXiv:1309.0630v4.
Recently the second author and Van Proeyen proved the monodromy conjecture on topological zeta functions for all non-degenerate surface singularities. In this paper, we obtain higher-dimensional analogues of their results, which, in particular, prove the conjecture for all isolated singularities of 4 variables, as well as for many classes of non-isolated and higher-dimensional singularities. One ...
Added: September 18, 2017
Vyugin I. V., Левин Р. И., Труды Математического института им. В.А. Стеклова РАН 2017 Т. 297 С. 326–343
An analog of the classical Riemann-Hilbert problem formulated for classes of difference and q-difference systems is considered. We propose some strengthening of Birkhoff's existence theorem. ...
Added: August 18, 2017
Serge Lvovski, / Series arXiv "math". 2017.
We show that the monodromy group acting on $H^1(\cdot,\mathbb Z)$ of a smooth
hyperplane section of a del Pezzo surface over $\mathbb C$ is the entire
group $\mathrm{SL}_2(\mathbb Z)$. For smooth surfaces with $b_1=0$ and hyperplane section
of genus $g>2$, there exist examples in which a similar assertion is
false. Actually, if hyperplane sections of ...
Added: June 14, 2017
Esterov A. I., Gusev G. G., Mathematische Annalen 2016 Vol. 365 No. 3 P. 1091–1110
We generalize the Abel–Ruffini theorem to arbitrary dimension, i.e. classify general square systems of polynomial equations solvable by radicals. In most cases, they reduce to systems whose tuples of Newton polytopes have mixed volume not exceeding 4. The proof is based on topological Galois theory, which ensures non-solvability by any formula involving quadratures and single-valued ...
Added: February 27, 2017