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Birational geometry of varieties fibred into complete intersections of codimension two Izv. Math. (IF 0.8) Pub Date : 2022-03-31 A. V. Pukhlikov
In this paper we prove the birational superrigidity of Fano–Mori fibre spaces all of whose fibres are complete intersections of type in the projective space satisfying certain conditions of general position, under the assumption that the fibration is sufficiently twisted over the base (in particular, under the assumption that the -condition holds). The condition of general position for every fibre
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The coloured Tverberg theorem, extensions and new results Izv. Math. (IF 0.8) Pub Date : 2022-03-31 D. Jojić, G. Yu. Panina and R. Živaljević
We prove a multiple coloured Tverberg theorem and a balanced coloured Tverberg theorem, applying different methods, tools and ideas. The proof of the first theorem uses a multiple chessboard complex (as configuration space) and the Eilenberg–Krasnoselskii theory of degrees of equivariant maps for non-free group actions. The proof of the second result relies on the high connectivity of the configuration
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On the number of epi-, mono- and homomorphisms of groups Izv. Math. (IF 0.8) Pub Date : 2022-03-31 E. K. Brusyanskaya and Ant. A. Klyachko
It is well known that the number of homomorphisms from a group to a group is divisible by the greatest common divisor of the order of and the exponent of . We study the question of what can be said about the number of homomorphisms satisfying certain natural conditions like injectivity or surjectivity. A simple non-trivial consequence of our results is the fact that in any finite group the number of
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Foundations of Lie theory for -structures and some of its applications Izv. Math. (IF 0.8) Pub Date : 2022-03-31 V. V. Gorbatsevich
We construct an analogue of classical Lie theory in the case of Lie groups and Lie algebras defined over the algebra of dual numbers. As an application, we study approximate symmetries of differential equations and construct analogues of Hjelmslev's natural geometry.
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The generalized Plücker–Klein map Izv. Math. (IF 0.8) Pub Date : 2022-03-31 V. A. Krasnov
The intersection of two quadrics is called a biquadric. If we mark a non-singular quadric in the pencil of quadrics through a given biquadric, then the given biquadric is called a marked biquadric. In the classical papers of Plücker and Klein, a Kummer surface was canonically associated with every three-dimensional marked biquadric (that is, with a quadratic line complex provided that the Plücker–Klein
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The optimal start control problem for 2D Boussinesq equations Izv. Math. (IF 0.8) Pub Date : 2022-03-31 E. S. Baranovskii
We consider the problem of the optimal start control for two-dimensional Boussinesq equations describing non-isothermal flows of a viscous fluid in a bounded domain. Using the study of the properties of admissible tuples and of the evolution operator, we prove the solubility of the optimization problem under natural assumptions about the model data. We derive a variational inequality which is satisfied
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Extremal interpolation with the least value of the norm of the second derivative in Izv. Math. (IF 0.8) Pub Date : 2022-02-01 V. T. Shevaldin
In this paper we formulate a general problem of extreme functional interpolation of real-valued functions of one variable (for finite differences, this is the Yanenko–Stechkin–Subbotin problem) in terms of divided differences. The least value of the -th derivative in , , needs to be calculated over the class of functions interpolating any given infinite sequence of real numbers on an arbitrary grid
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On improved bounds and conditions for the convergence of Markov chains Izv. Math. (IF 0.8) Pub Date : 2022-02-01 A. Yu. Veretennikov and M. A. Veretennikova
We continue the work of improving the rate of convergence of ergodic homogeneous Markov chains. The setting is more general than in previous papers: we are able to get rid of the assumption about a common dominating measure and consider the case of inhomogeneous Markov chains as well as more general state spaces. We give examples where the new bound for the rate of convergence is the same as (resp
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Plancherel–Rotach type asymptotic formulae for multiple orthogonal Hermite polynomials and recurrence relations Izv. Math. (IF 0.8) Pub Date : 2022-02-01 A. I. Aptekarev, S. Yu. Dobrokhotov, D. N. Tulyakov, A. V. Tsvetkova
We study the asymptotic properties of multiple orthogonal Hermite polynomials which are determined by the orthogonality relations with respect to two Hermite weights (Gaussian distributions) with shifted maxima. The starting point of our asymptotic analysis is a four-term recurrence relation connecting the polynomials with adjacent numbers. We obtain asymptotic expansions as the number of the polynomial
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The quasi-algebraic ring of conditions of Izv. Math. (IF 0.8) Pub Date : 2022-02-01 B. Ya. Kazarnovskii
An exponential sum is a linear combination of characters of the additive group of . We regard as an analogue of the torus , exponential sums as analogues of Laurent polynomials, and exponential analytic sets (-sets), that is, the sets of common zeros of finite systems of exponential sums, as analogues of algebraic subvarieties of the torus. Using these analogies, we define the intersection number of
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Minimal supplements of maximal tori in their normalizers for the groups Izv. Math. (IF 0.8) Pub Date : 2022-02-01 A. A. Galt and A. M. Staroletov
Let be a finite group of Lie type and the Weyl group of . For every maximal torus of , we find the minimal order of a supplement of in its algebraic normalizer . In particular, we find all the maximal tori that have a complement in . Let correspond to an element of . We find the minimal orders of the lifts of the elements in .
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Embedding theorems related to torsional rigidity and principal frequency Izv. Math. (IF 0.8) Pub Date : 2022-02-01 F. G. Avkhadiev
We study criteria for the finiteness of the constants in integral inequalities generalizing the Poincaré–Friedrichs inequality and Saint-Venant’s variational definition of torsional rigidity. The Rayleigh–Faber–Krahn isoperimetric inequality and the Saint-Venant–Pólya inequality guarantee the existence of finite constants for domains of finite volume. Criteria for the existence of finite constants
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Unconditional bases in radial Hilbert spaces Izv. Math. (IF 0.8) Pub Date : 2022-02-01 K. P. Isaev and R. S. Yulmukhametov
We prove necessary and (separate) sufficient conditions for the existence of unconditional bases of reproducing kernels in abstract radial Hilbert function spaces that are stable under division, in terms of the norms of monomials.
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On solvability of second order semi-linear elliptic equations on closed manifolds Izv. Math. (IF 0.8) Pub Date : 2022-01-01 Dmitry Vasilievich Tunitsky
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On summable solutions of one class of nonlinear integral equations on the whole line Izv. Math. (IF 0.8) Pub Date : 2022-01-01 Khachatur Aghavardovich Khachatryan,Haykanush Samvelovna Petrosyan
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On the classical solution to the macroscopic model of in-situ leaching of rare metals Izv. Math. (IF 0.8) Pub Date : 2022-01-01 Anvarbek Mukatovich Meirmanov
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On extended form of the Grothendieck - Serre conjecture Izv. Math. (IF 0.8) Pub Date : 2022-01-01 Ivan Alexandrovich Panin
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Gelfand-Kirillov dimensions of simple modules over twisted group algebras [IMG align=ABSMIDDLE alt=$ k*a$]tex_im_3109_img1[/IMG] Izv. Math. (IF 0.8) Pub Date : 2022-01-01 Ashish Gupta,Umamaheswaran Arunachalam
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New estimates for short Kloosterman sums with weights Izv. Math. (IF 0.8) Pub Date : 2022-01-01 Natalia Kirillovna Semenova
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A modification of the Poincare construction and its application in [IMG align=ABSMIDDLE alt=$ CR$]tex_im_3121_img1[/IMG] geometry of hypersurfaces in [IMG align=ABSMIDDLE alt=$ {\bf C}^4$]tex_im_3121_img2[/IMG] Izv. Math. (IF 0.8) Pub Date : 2022-01-01 Valerii Konstantinovich Beloshapka
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Estimates for integrals of derivatives of rational functions in multiply connected domains on the plane Izv. Math. (IF 0.8) Pub Date : 2022-01-01 Anton Dmitrievich Baranov,Ilgiz Rifatovich Kayumov
Abstract. We obtain estimates for integrals of derivatives of rational functions in multiply connected domains in the plane. A sharp order of the growth is found for the integral of the modulus of the derivative of a finite Blaschke product in the unit disk. We also extend the results of E.P. Dolzhenko about the integrals of the derivatives of rational functions to a wider class of domains, namely
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Foliations on closed three-dimensional Riemannian manifolds with a small modulus of a mean curvature of the leaves Izv. Math. (IF 0.8) Pub Date : 2022-01-01 Dmitry Valer'evich Bolotov
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Outer billiards outisde regular polygons: a hand case Izv. Math. (IF 0.8) Pub Date : 2022-01-01 Philip Dmitrievich Rukhovich
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On the Karatsuba divisor problem Izv. Math. (IF 0.8) Pub Date : 2022-01-01 Vitalii Victorovich Iudelevich
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On One Promotion in the Proof of the Hypothesis of the Meromorphic Solutions of the Briot-Bouquet Equations Izv. Math. (IF 0.8) Pub Date : 2022-01-01 Aleksandr Yakovlevich Yanchenko
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On Classification of Morse-Smale flows on projective-like manifolds Izv. Math. (IF 0.8) Pub Date : 2022-01-01 Vyacheslav Zigmuntovich Grines,Elena Yakovlevna Gurevich
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Maltsev equal norm tight frames Izv. Math. (IF 0.8) Pub Date : 2022-01-01 Sergey Yakovlevich Novikov,Victoria Vladimirovna Sevost'yanova
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On the standard conjecture for compactifications of Neron models of 4-dimensional Abelian varieties Izv. Math. (IF 0.8) Pub Date : 2022-01-01 Sergei Gennadievich Tankeev
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Canonical representation of C*-algebra of eikonals related to the metric graph. Izv. Math. (IF 0.8) Pub Date : 2022-01-01 Mikhail Igorevitch Belishev,Aleksandr Vladimirovich Kaplun
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Lattice of definability (of reducts) for integers with successor Izv. Math. (IF 0.8) Pub Date : 2021-12-01 A. L. Semenov, S. F. Soprunov
In this paper the lattice of definability for integers with a successor (the relation ) is described. The lattice, whose elements are also knows as reducts, consists of three (naturally described) infinite series of relations. The proof uses a version of the Svenonius theorem for structures of special form.
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The Diophantine problem in the classical matrix groups Izv. Math. (IF 0.8) Pub Date : 2021-12-01 A. G. Myasnikov, M. Sohrabi
In this paper we study the Diophantine problem in the classical matrix groups , , and , , over an associative ring with identity. We show that if is one of these groups, then the Diophantine problem in is polynomial-time equivalent (more precisely, Karp equivalent) to the Diophantine problem in . When we assume that is commutative. Similar results hold for and provided has no zero divisors (for the
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Finitely presented nilsemigroups: complexes with the property of uniform ellipticity Izv. Math. (IF 0.8) Pub Date : 2021-12-01 I. A. Ivanov-Pogodaev, A. Ya. Kanel-Belov
This paper is the first in a series of three devoted to constructing a finitely presented infinite nilsemigroup satisfying the identity . This solves a problem of Lev Shevrin and Mark Sapir.In this first part we obtain a sequence of complexes formed of squares ( -cycles) having the following geometric properties.1) Complexes are uniformly elliptic. A space is said to be uniformly elliptic if there
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Finitely generated subgroups of branch groups and subdirect products of just infinite groups Izv. Math. (IF 0.8) Pub Date : 2021-12-01 R. I. Grigorchuk, P.-H. Leemann, T. V. Nagnibeda
The aim of this paper is to describe the structure of finitely generated subgroups of a family of branch groups containing the first Grigorchuk group and the Gupta–Sidki -group. We then use this to show that all the groups in this family are subgroup separable (LERF).These results are obtained as a corollary of a more general structural statement on subdirect products of just infinite groups.
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On a spectral sequence for the action of the Torelli group of genus on the complex of cycles Izv. Math. (IF 0.8) Pub Date : 2021-12-01 A. A. Gaifullin
The Torelli group of a closed oriented surface of genus is the subgroup of the mapping class group consisting of all mapping classes that act trivially on the homology of . One of the most intriguing open problems concerning Torelli groups is the question of whether the group is finitely presented. A possible approach to this problem relies on the study of the second homology group of using the spectral
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Weights of exact threshold functions Izv. Math. (IF 0.8) Pub Date : 2021-12-01 L. Babai, K. A. Hansen, V. V. Podolskii, Xiaoming Sun
We consider Boolean exact threshold functions defined by linear equations and, more generally, polynomials of degree . We give upper and lower bounds on the maximum magnitude (absolute value) of the coefficients required to represent such functions. These bounds are very close. In the linear case in particular they are almost matching. This quantity is the same as the maximum magnitude of the integer
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Models of set theory in which the separation theorem fails Izv. Math. (IF 0.8) Pub Date : 2021-12-01 V. G. Kanovei, V. A. Lyubetsky
We use a finite-support product of Jensen-minimal forcings to define a model of set theory in which the separation theorem fails for the projective classes and , for a given .
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On the classification problem for polynomials with a periodic continued fraction expansion of in hyperelliptic fields Izv. Math. (IF 0.8) Pub Date : 2021-11-05 V. P. Platonov, G. V. Fedorov
The classical problem of the periodicity of continued fractions for elements of hyperelliptic fields has a long and deep history. This problem has up to now been far from completely solved. A surprising result was obtained in [1] for quadratic extensions defined by cubic polynomials with coefficients in the field of rational numbers: except for trivial cases there are only three (up to equivalence)
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Arithmetic of certain -extensions ramified at three places. II Izv. Math. (IF 0.8) Pub Date : 2021-11-05 L. V. Kuz’min
Let be a regular odd prime, the th cyclotomic field and , where is a positive integer. Under the assumption that there are exactly three places not over that ramify in , we continue to study the structure of the Tate module (Iwasawa module) as a Galois module. In the case , we prove that for finite we have for some odd positive integer . Under the same assumptions, if is the Galois group of the maximal
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Convergence to stationary non-equilibrium states for Klein–Gordon equations Izv. Math. (IF 0.8) Pub Date : 2021-11-05 T. V. Dudnikova
We consider Klein–Gordon equations in , , with constant or variable coefficients and study the Cauchy problem with random initial data. We investigate the distribution of a random solution at moments of time . We prove the convergence of correlation functions of the measure to a limit as . The explicit formulae for the limiting correlation functions and the energy current density (in mean) are obtained
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Functional and analytic properties of a class of mappings in quasi-conformal analysis Izv. Math. (IF 0.8) Pub Date : 2021-11-05 S. K. Vodopyanov, A. O. Tomilov
We define a two-index scale , , of homeomorphisms of spatial domains in , the geometric description of which is determined by the control of the behaviour of the -capacity of condensers in the target space in terms of the weighted -capacity of condensers in the source space. We obtain an equivalent functional and analytic description of based on the properties of the composition operator (from weighted
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On distributions of homogeneous and convex functions in Gaussian random variables Izv. Math. (IF 0.8) Pub Date : 2021-11-05 V. I. Bogachev, E. D. Kosov, S. N. Popova
We obtain broad conditions under which distributions of homogeneous functions in Gaussian and more general random variables have bounded densities or even densities of bounded variation or densities with finite Fisher information. Analogous results are obtained for convex functions. Applications to maxima of quadratic forms are given.
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The Caldern construction for a couple of global Morrey spaces Izv. Math. (IF 0.8) Pub Date : 2021-11-05 E. I. Berezhnoi
We employ a new approach to show that the Caldern construction for a couple of global Morrey spaces coincides with the Morrey space with appropriate parameters only under rather strong assumptions on the couples of ideal spaces that parameterize the original Morrey spaces. We show that, in the case of classical examples of global Morrey spaces, these assumptions are necessary and sufficient. Applying
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The exact domain of univalence on the class of holomorphic maps of a disc into itself with an interior and a boundary fixed points Izv. Math. (IF 0.8) Pub Date : 2021-11-05 A. P. Solodov
We consider the problem of identifying domains of univalence on classes of holomorphic maps of the unit disc into itself. In 1926 E. Landau found the exact value of the radius of the disc of univalence on the class of such maps with a given value of the derivative at an interior fixed point. In 2017 V. V. Goryainov discovered the existence of univalence domains on classes of holomorphic maps of the
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Adjoint -classes on threefolds Izv. Math. (IF 0.8) Pub Date : 2021-08-16 A. Hring
We answer a question of Filip and Tosatti concerning a basepoint-free theorem for transcendental -classes on compact Khler threefolds.
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A basis for a partially commutative metabelian group Izv. Math. (IF 0.8) Pub Date : 2021-08-16 E. I. Timoshenko
We find explicitly a basis for the derived group of a partially commutative metabelian group and describe a canonical representation for the elements of the group.
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Solubility of unsteady equations of the three-dimensional motion of two-component viscous compressible heat-conducting fluids Izv. Math. (IF 0.8) Pub Date : 2021-08-16 A. E. Mamontov, D. A. Prokudin
We consider equations for the three-dimensional unsteady motion of mixtures of viscous compressible heat-conducting fluids in the multi-velocity approach. We prove the existence, globally in time and the input data, of a generalized (dissipative) solution of the initial-boundary value problem corresponding to flows in a bounded domain.
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Inequalities for the average exit time of a random walk from an interval Izv. Math. (IF 0.8) Pub Date : 2021-08-16 V. I. Lotov
Two-sided inequalities are obtained for the average exit time from an interval for a random walk with zero and negative drift.
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On critical exponents for weak solutions of the Cauchy problem for a non-linear equation of composite type Izv. Math. (IF 0.8) Pub Date : 2021-08-16 M. O. Korpusov, A. K. Matveeva
We consider the Cauchy problem for a model partial differential equation of third order with non-linearity of the form , where for and . We construct a fundamental solution for the linear part of the equation and use it to obtain analogues of Green’s third formula for elliptic operators, first in a bounded domain and then in unbounded domains. We derive an integral equation for classical solutions
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The derivative of the Minkowski function Izv. Math. (IF 0.8) Pub Date : 2021-08-16 D. R. Gayfulin, I. D. Kan
We prove new results on the derivative of the Minkowski question mark function.
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On framed simple purely real Hurwitz numbers Izv. Math. (IF 0.8) Pub Date : 2021-08-16 M. E. Kazarian, S. K. Lando, S. M. Natanzon
We study real Hurwitz numbers enumerating real meromorphic functions of a special kind, referred to as framed purely real functions. We deduce partial differential equations of cut-and-join type for the generating functions for these numbers. We also construct a topological field theory for them.
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Symmetries of a two-dimensional continued fraction Izv. Math. (IF 0.8) Pub Date : 2021-08-16 O. N. German, I. A. Tlyustangelov
We describe the symmetry group of a multidimensional continued fraction. As a multidimensional generalization of continued fractions we consider Klein polyhedra. We distinguish two types of symmetries: Dirichlet symmetries, which correspond to the multiplication by units of the respective extension of , and so-called palindromic symmetries. The main result is a criterion for a two-dimensional continued
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On the classification of -dimensional spherical Sasakian manifolds Izv. Math. (IF 0.8) Pub Date : 2021-07-08 D. Sykes, G. Schmalz, V. V. Ezhov
In this article we regard spherical hypersurfaces in with a fixed Reeb vector field as -dimensional Sasakian manifolds. We establish a correspondence between three different sets of parameters, namely, those arising from representing the Reeb vector field as an automorphism of the Heisenberg sphere, those used in Stanton’s description of rigid spheres, and those arising from the rigid normal forms
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Quasi-polynomial mappings with constant Jacobian Izv. Math. (IF 0.8) Pub Date : 2021-07-08 S. I. Pinchuk
The famous Jacobian conjecture (JC) remains open even for dimension . In this paper we study it by extending the class of polynomial mappings to quasi-polynomial ones. We show that any possible non-invertible polynomial mapping with non-zero constant Jacobian can be transformed into a special reduced form by a sequence of elementary transformations.
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Plane algebraic curves in fancy balls Izv. Math. (IF 0.8) Pub Date : 2021-07-08 N. G. Kruzhilin, S. Yu. Orevkov
Boileau and Rudolph [1] called an oriented link in the 3-sphere a -boundary if it can be realized as the intersection of an algebraic curve in and the boundary of a smooth embedded closed 4-ball . They showed that some links are not -boundaries. We say that is a strong -boundary if is connected. In particular, all quasipositive links are strong -boundaries. In this paper we give examples of non-quasipositive
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Nevanlinna factorization in weighted classes of analytic functions of variable smoothness Izv. Math. (IF 0.8) Pub Date : 2021-07-02 N. A. Shirokov
We define a new class of functions of variable smoothness that are analytic in the unit disc and continuous in the closed disc. We construct the theory of the Nevanlinna outer-inner factorization, taking into account the influence of the inner factor on the outer function, for functions of the new class.
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Holomorphically homogeneous CR-manifolds and their model surfaces Izv. Math. (IF 0.8) Pub Date : 2021-07-02 M. A. Stepanova
We show that the model surface of a germ of a holomorphically homogeneous CR-manifold is holomorphically homogeneous. We also obtain restrictions on the multiplicities in the Bloom–Graham type of a germ of a holomorphically homogeneous CR-manifold.
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Criteria for -approximability of functions on compact sets in , , by solutions of second-order homogeneous elliptic equations Izv. Math. (IF 0.8) Pub Date : 2021-07-02 P. V. Paramonov
We obtain capacitive criteria for the approximability of individual functions by solutions of second-order homogeneous elliptic equations with constant complex coefficients in the norm of a Whitney-type -space on a compact set in , . The case was studied in a recent paper by the author and Tolsa. For -approximations by harmonic functions (with any ), weaker criteria were earlier found by the author
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On the Newton polyhedron of a Jacobian pair Izv. Math. (IF 0.8) Pub Date : 2021-07-02 L. G. Makar-Limanov
We introduce and describe the Newton polyhedron related to a “minimal” counterexample to the Jacobian conjecture. This description allows us to obtain a sharper estimate for the geometric degree of the polynomial mapping given by a Jacobian pair and to give a new proof in the case of the Abhyankar’s two characteristic pairs.
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Uniform approximation of functions by solutions of second order homogeneous strongly elliptic equations on compact sets in Izv. Math. (IF 0.8) Pub Date : 2021-07-02 M. Ya. Mazalov
We obtain a criterion for the uniform approximability of functions by solutions of second-order homogeneous strongly elliptic equations with constant complex coefficients on compact sets in (the particular case of harmonic approximations is not distinguished). The criterion is stated in terms of the unique (scalar) Harvey–Polking capacity related to the leading coefficient of a Laurent-type expansion
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Proper holomorphic maps of bounded two-dimensional Reinhardt domains. I Izv. Math. (IF 0.8) Pub Date : 2021-07-02 N. G. Kruzhilin
The structure of proper holomorphic maps with multiplicity higher than one from bounded Reinhardt domains in onto two-dimensional complex manifolds is described.