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Complete description of the Lyapunov spectra of continuous families of linear differential systems with unbounded coefficients Izv. Math. (IF 1.13) Pub Date : 2020-12-30 V. V. Bykov
For every positive integer ##IMG## [http://ej.iop.org/images/1064-5632/84/6/1037/IZV_84_6_1037ieqn1.gif] {$n$} and every metric space ##IMG## [http://ej.iop.org/images/1064-5632/84/6/1037/IZV_84_6_1037ieqn2.gif] {$M$} we consider the class ##IMG## [http://ej.iop.org/images/1064-5632/84/6/1037/IZV_84_6_1037ieqn3.gif] {$\widetilde{\mathcal{U}}^n(M)$} of all parametric families ##IMG## [http://ej.iop
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On the uniform approximation of functions of bounded variation by Lagrange interpolation polynomials with a matrix ##IMG## [http://ej.iop.org/images/1064-5632/84/6/1224/toc_IZV_84_6_1224ieqn1.gif] {${\mathcal L}_n^{(\alpha_n,\beta_n)}$} of Jacobi nodes Izv. Math. (IF 1.13) Pub Date : 2020-12-30 A. Yu. Trynin
Let sequences ##IMG## [http://ej.iop.org/images/1064-5632/84/6/1224/IZV_84_6_1224ieqn2.gif] {$\{\alpha_n\}_{n=1}^{\infty}$} , ##IMG## [http://ej.iop.org/images/1064-5632/84/6/1224/IZV_84_6_1224ieqn3.gif] {$\{\beta_n\}_{n=1}^{\infty}$} satisfy the relations ##IMG## [http://ej.iop.org/images/1064-5632/84/6/1224/IZV_84_6_1224ieqn4.gif] {$\alpha_n\in \mathbb{R}$} , ##IMG## [http://ej.iop.org/images/10
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Bogolyubov’s theorem for a controlled system related to a variational inequality Izv. Math. (IF 1.13) Pub Date : 2020-12-30 A. A. Tolstonogov
We consider the problem of minimizing an integral functional on the solutions of a controlled system described by a non-linear differential equation in a separable Banach space and a variational inequality. The variational inequality determines a hysteresis operator whose input is a trajectory of the controlled system and whose output occurs in the right-hand side of the differential equation, in the
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Threshold resonances and virtual levels in the spectrum of cylindrical and periodic waveguides Izv. Math. (IF 1.13) Pub Date : 2020-12-30 S. A. Nazarov
We describe and classify the thresholds of the continuous spectrum and the resulting resonances for general formally self-adjoint elliptic systems of second-order differential equations with Dirichlet or Neumann boundary conditions in domains with cylindrical and periodic outlets to infinity (in waveguides). These resonances arise because there are “almost standing” waves, that is, non-trivial solutions
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Geometric estimates of solutions of quasilinear elliptic inequalities Izv. Math. (IF 1.13) Pub Date : 2020-12-30 A. A. Kon’kov
Suppose that ##IMG## [http://ej.iop.org/images/1064-5632/84/6/1056/IZV_84_6_1056ieqn1.gif] {$p>1$} and ##IMG## [http://ej.iop.org/images/1064-5632/84/6/1056/IZV_84_6_1056ieqn2.gif] {$\alpha$} are real numbers with ##IMG## [http://ej.iop.org/images/1064-5632/84/6/1056/IZV_84_6_1056ieqn3.gif] {$p-1 \le \alpha \le p$} . Let ##IMG## [http://ej.iop.org/images/1064-5632/84/6/1056/IZV_84_6_1056ieqn4.gif]
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Isotopes of alternative algebras of characteristic different from ##IMG## [http://ej.iop.org/images/1064-5632/84/5/1002/toc_IZV_84_5_1002ieqn1.gif] {$3$} Izv. Math. (IF 1.13) Pub Date : 2020-10-21 S. V. Pchelintsev
We study homotopes of alternative algebras over an algebraically closed field of characteristic different from ##IMG## [http://ej.iop.org/images/1064-5632/84/5/1002/toc_IZV_84_5_1002ieqn1.gif] {$3$} . We prove an analogue of Albert’s theorem on isotopes of associative algebras: in the class of finite-dimensional unital alternative algebras every isotopy is an isomorphism. We also prove that every ##IMG##
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Finite groups of bimeromorphic selfmaps of uniruled Kähler threefolds Izv. Math. (IF 1.13) Pub Date : 2020-10-21 Yu. G. Prokhorov and C. A. Shramov
We classify uniruled compact Kähler threefolds whose groups of bimeromorphic selfmaps do not have the Jordan property.
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Distribution of prime numbers and the discrete spectrum of the Laplace operator Izv. Math. (IF 1.13) Pub Date : 2020-10-21 D. A. Popov
We obtain a class of explicit formulae each of which gives an expression for the remainder term in the asymptotic equation for the Chebyshev function in terms of the spectrum of the Laplace operator on the fundamental domain of the modular group.
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Blow-up and global solubility in the classical sense of the Cauchy problem for a formally hyperbolic equation with a non-coercive source Izv. Math. (IF 1.13) Pub Date : 2020-10-21 M. O. Korpusov
We consider an abstract Cauchy problem with non-linear operator coefficients and prove the existence of a unique non-extendable classical solution. Under certain sufficient close-to-necessary conditions, we obtain finite-time blow-up conditions and upper and lower bounds for the blow-up time. Moreover, under certain sufficient close-to-necessary conditions, we obtain a result on the existence of a
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Subdivision schemes on the dyadic half-line Izv. Math. (IF 1.13) Pub Date : 2020-10-21 M. A. Karapetyants
We consider subdivision schemes, which are used for the approximation of functions and generation of curves on the dyadic half-line. In the classical case of functions on the real line, the theory of subdivision schemes is widely known because of its applications in constructive approximation theory and signal processing as well as for generating fractal curves and surfaces. We define and study subdivision
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Diffeomorphisms of 2-manifolds with one-dimensional spaciously situated basic sets Izv. Math. (IF 1.13) Pub Date : 2020-10-21 V. Z. Grines and E. D. Kurenkov
We consider orientation-preserving ##IMG## [http://ej.iop.org/images/1064-5632/84/5/862/IZV_84_5_862ieqn1.gif] {$A$} -diffeomorphisms of orientable surfaces of genus greater than one with a one-dimensional spaciously situated perfect attractor. We show that the topological classification of restrictions of diffeomorphisms to such basic sets can be reduced to that of pseudo-Anosov homeomorphisms with
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On the topology of non-compact simply connected homogeneous manifolds Izv. Math. (IF 1.13) Pub Date : 2020-10-21 V. V. Gorbatsevich
We study the covariant bundles (Mostow bundles) for simply connected homogeneous manifolds, establish their relation to homogeneous bundles and consider classes of homogeneous manifolds for which the Mostow bundle is trivial (resp. non-trivial). We also give a classification of non-compact simply connected homogeneous manifolds of dimension not exceeding seven.
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Uniqueness theorems for one-dimensional and double Franklin series Izv. Math. (IF 1.13) Pub Date : 2020-10-21 G. G. Gevorkyan
The paper contains two main results. First we describe one-dimensional Franklin series converging everywhere except possibly on a finite set to an everywhere-finite integrable function. Second we establish a class of subsets of ##IMG## [http://ej.iop.org/images/1064-5632/84/5/829/IZV_84_5_829ieqn1.gif] {$[0, 1]^2$} with the following property. If a double Franklin series converges everywhere except
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On the standard conjecture for a ##IMG## [http://ej.iop.org/images/1064-5632/84/5/1016/toc_IZV_84_5_1016ieqn1.gif] {$3$} -dimensional variety fibred by curves with a non-injective Kodaira–Spencer map Izv. Math. (IF 1.13) Pub Date : 2020-10-21 S. G. Tankeev
We prove that the Grothendieck standard conjecture of Lefschetz type holds for a complex projective 3-dimensional variety fibred by curves (possibly with degeneracies) over a smooth projective surface provided that the endomorphism ring of the Jacobian variety of some smooth fibre coincides with the ring of integers and the corresponding Kodaira–Spencer map has rank ##IMG## [http://ej.iop.org/imag
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Functions of perturbed pairs of noncommuting contractions Izv. Math. (IF 1.13) Pub Date : 2020-09-01 A. B. Aleksandrov and V. V. Peller
We consider functions ##IMG## [http://ej.iop.org/images/1064-5632/84/4/659/IZV_84_4_659ieqn1.gif] {$f(T,R)$} of pairs of noncommuting contractions on Hilbert space and study the problem as to which functions ##IMG## [http://ej.iop.org/images/1064-5632/84/4/659/IZV_84_4_659ieqn2.gif] {$f$} we have Lipschitz type estimates in Schatten–von Neumann norms. We prove that if ##IMG## [http://ej.iop.org/im
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Existence and uniqueness of solution of a certain boundary-value problem for a convolution integral equation with monotone non-linearity Izv. Math. (IF 1.13) Pub Date : 2020-09-01 Kh. A. Khachatryan
We study the existence and uniqueness as well as the asymptotic behaviour of solutions of a certain boundary-value problem for a convolution integral equation on the whole line with monotone non-linearity. In some special cases, there are concrete applications to ##IMG## [http://ej.iop.org/images/1064-5632/84/4/807/IZV_84_4_807ieqn1.gif] {$p$} -adic string theory, the mathematical theory of the geographical
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Homogenization of Kirchhoff plates with oscillating edges and point supports Izv. Math. (IF 1.13) Pub Date : 2020-09-01 S. A. Nazarov
We study deformations of a long (narrow after rescaling) Kirchhoff plate with periodic (rapidly oscillating) boundary. We deduce a limiting system of two ordinary differential equations of orders 4 and 2 which describe the deflection and torsion of a two-dimensional plate in the leading order. We also consider point supports (Sobolev conditions) whose configuration influences the result of homogenizing
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General orthonormal systems and absolute convergence Izv. Math. (IF 1.13) Pub Date : 2020-09-01 V. Sh. Tsagareishvili
We study problems of the absolute convergence of Fourier series of differentiable functions with respect to general orthonormal systems (ONS). We obtain results which show that under certain conditions on functions in the ONS, the Fourier series of an arbitrary function in a certain differentiability class is absolutely convergent. We finally note that our results cannot be improved.
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On orthogonal projections of Nöbeling spaces Izv. Math. (IF 1.13) Pub Date : 2020-09-01 S. M. Ageev
Suppose that ##IMG## [http://ej.iop.org/images/1064-5632/84/4/627/IZV_84_4_627ieqn1.gif] {$0\le k<\infty$} . We prove that there is a dense open subset of the Grassmann space ##IMG## [http://ej.iop.org/images/1064-5632/84/4/627/IZV_84_4_627ieqn2.gif] {$\operatorname{Gr}(2k+1,m)$} such that the orthogonal projection of the standard Nöbeling space ##IMG## [http://ej.iop.org/images/1064-5632/84/4/627/IZV_84_4_627ieqn3
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Sobolev spaces of functions on a Hilbert space endowed with a translation-invariant measure and approximations of semigroups Izv. Math. (IF 1.13) Pub Date : 2020-09-01 V. M. Busovikov and V. Zh. Sakbaev
We study measures on a real separable Hilbert space ##IMG## [http://ej.iop.org/images/1064-5632/84/4/694/IZV_84_4_694ieqn1.gif] {$E$} that are invariant under translations by arbitrary vectors in ##IMG## [http://ej.iop.org/images/1064-5632/84/4/694/IZV_84_4_694ieqn1.gif] {$E$} . We define the Hilbert space ##IMG## [http://ej.iop.org/images/1064-5632/84/4/694/IZV_84_4_694ieqn2.gif] {$\mathcal H$} of
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Proof of the Grothendieck–Serre conjecture on principal bundles over regular local rings containing a field Izv. Math. (IF 1.13) Pub Date : 2020-09-01 I. A. Panin
Let ##IMG## [http://ej.iop.org/images/1064-5632/84/4/780/IZV_84_4_780ieqn1.gif] {$R$} be a regular local ring containing a field. Let ##IMG## [http://ej.iop.org/images/1064-5632/84/4/780/IZV_84_4_780ieqn2.gif] {$\mathbf{G}$} be a reductive group scheme over ##IMG## [http://ej.iop.org/images/1064-5632/84/4/780/IZV_84_4_780ieqn1.gif] {$R$} . We prove that a principal ##IMG## [http://ej.iop.org/image
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Integer expansion in systems of translates and dilates of a single function Izv. Math. (IF 1.13) Pub Date : 2020-09-01 V. I. Filippov
We study expansions with integer coefficients of elements in the multidimensional spaces ##IMG## [http://ej.iop.org/images/1064-5632/84/4/796/IZV_84_4_796ieqn1.gif] {$L_p\{(0,1]^m\}$} , ##IMG## [http://ej.iop.org/images/1064-5632/84/4/796/IZV_84_4_796ieqn2.gif] {$1\leq p<\infty$} , in systems of translates and dilates of a single function. We describe models useful in applications, including those
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Displaying the cohomology of toric line bundles Izv. Math. (IF 1.13) Pub Date : 2020-09-01 K. Altmann and D. Ploog
There is a standard approach to calculate the cohomology of torus-invariant sheaves ##IMG## [http://ej.iop.org/images/1064-5632/84/4/683/IZV_84_4_683ieqn1.gif] {$\mathcal{L}$} on a toric variety via the simplicial cohomology of the associated subsets ##IMG## [http://ej.iop.org/images/1064-5632/84/4/683/IZV_84_4_683ieqn2.gif] {$V(\mathcal{L})$} of the space ##IMG## [http://ej.iop.org/images/1064-56
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On a class of elliptic boundary-value problems with parameter and discontinuous non-linearity Izv. Math. (IF 1.13) Pub Date : 2020-06-10 V. N. Pavlenko and D. K. Potapov
We study an elliptic boundary-value problem in a bounded domain with inhomogeneous Dirichlet condition, discontinuous non-linearity and a positive parameter occurring as a factor in the non-linearity. The non-linearity is in the right-hand side of the equation. It is non-positive (resp. equal to zero) for negative (resp, non-negative) values of the phase variable. Let ##IMG## [http://ej.iop.org/im
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On the arithmetic of modified idèle class groups Izv. Math. (IF 1.13) Pub Date : 2020-06-10 Wan Lee and Soogil Seo
Let ##IMG## [http://ej.iop.org/images/1064-5632/84/3/545/IZV_84_3_545ieqn1.gif] {$k$} be a number field and ##IMG## [http://ej.iop.org/images/1064-5632/84/3/545/IZV_84_3_545ieqn2.gif] {$S$} , ##IMG## [http://ej.iop.org/images/1064-5632/84/3/545/IZV_84_3_545ieqn3.gif] {$T$} sets of places of ##IMG## [http://ej.iop.org/images/1064-5632/84/3/545/IZV_84_3_545ieqn1.gif] {$k$} . For each prime ##IMG## [http://ej
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On the rate of approximation in the unit disc of ##IMG## [http://ej.iop.org/images/1064-5632/84/3/437/toc_IZV_84_3_437ieqn1.gif] {$H^1$} -functions by logarithmic derivatives of polynomials with zeros on the boundary Izv. Math. (IF 1.13) Pub Date : 2020-06-10 M. A. Komarov
We study uniform approximation in the open unit disc ##IMG## [http://ej.iop.org/images/1064-5632/84/3/437/IZV_84_3_437ieqn2.gif] {$D=\{z\colon |z|<1\}$} by logarithmic derivatives of ##IMG## [http://ej.iop.org/images/1064-5632/84/3/437/IZV_84_3_437ieqn3.gif] {$C$} -polynomials, that is, polynomials whose zeros lie on the unit circle ##IMG## [http://ej.iop.org/images/1064-5632/84/3/437/IZV_84_3_437ieqn4
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Asymptotics of approximation of continuous periodic functions by linear means of their Fourier series Izv. Math. (IF 1.13) Pub Date : 2020-06-10 R. M. Trigub
We establish an asymptotic formula for the rate of approximation of Fourier series of individual periodic functions by linear averages with an error ##IMG## [http://ej.iop.org/images/1064-5632/84/3/608/IZV_84_3_608ieqn1.gif] {$\omega_{2m}(f;{1}/{n})$} , ##IMG## [http://ej.iop.org/images/1064-5632/84/3/608/IZV_84_3_608ieqn2.gif] {$m\in\mathbb{N}$} . This formula is applicable to the means of Riesz,
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Real Segre cubics, Igusa quartics and Kummer quartics Izv. Math. (IF 1.13) Pub Date : 2020-06-10 V. A. Krasnov
We prove some properties of real Segre cubics. In particular, we find the topological types of the real parts of Segre cubics as well as the topological types of the real parts of the complements of the Segre planes. We prove some differential-geometric properties of the real parts of real Segre cubics and Kummer quartics. We study the automorphism groups of real Segre cubics and, in particular, their
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Blow-up instability in non-linear wave models with distributed parameters Izv. Math. (IF 1.13) Pub Date : 2020-06-10 M. O. Korpusov and E. A. Ovsyannikov
We consider two model non-linear equations describing electric oscillations in systems with distributed parameters on the basis of diodes with non-linear characteristics. We obtain equivalent integral equations for classical solutions of the Cauchy problem and the first and second initial-boundary value problems for the original equations in the half-space ##IMG## [http://ej.iop.org/images/1064-56
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A new approach to the question of the existence of bounded solutions of functional differential equations of point type Izv. Math. (IF 1.13) Pub Date : 2020-04-26 L. A. Beklaryan
We develop an approach which we used to deduce conditions of a new type for the existence of periodic solutions of ordinary differential equations and functional differential equations of point type. These conditions are based on the use of asymptotic properties of solutions of differential equations which can be observed on shifts of solutions and stated in terms of averages over the period on a distinguished
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On ##IMG## [http://ej.iop.org/images/1064-5632/84/2/392/toc_IZV_84_2_392ieqn1.gif] {$S$} -units for valuations of the second degree in hyperelliptic fields Izv. Math. (IF 1.13) Pub Date : 2020-04-26 G. V. Fedorov
In this paper we propose a new effective approach to the problem of finding and constructing non-trivial ##IMG## [http://ej.iop.org/images/1064-5632/84/2/392/toc_IZV_84_2_392ieqn1.gif] {$S$} -units of a hyperelliptic field ##IMG## [http://ej.iop.org/images/1064-5632/84/2/392/IZV_84_2_392ieqn2.gif] {$L$} for a set ##IMG## [http://ej.iop.org/images/1064-5632/84/2/392/IZV_84_2_392ieqn3.gif] {$S=S_h$}
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Some trigonometric polynomials with extremely small uniform norm and their applications Izv. Math. (IF 1.13) Pub Date : 2020-04-26 A. O. Radomskii
We construct orthogonal trigonometric polynomials satisfying a new spectral condition and such that their ##IMG## [http://ej.iop.org/images/1064-5632/84/2/361/IZV_84_2_361ieqn1.gif] {$L^{1}$} -norms are bounded below and the uniform norm of their partial sums has extremely small order of growth. We obtain new results that relate the uniform norm and ##IMG## [http://ej.iop.org/images/1064-5632/84/2
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##IMG## [http://ej.iop.org/images/1064-5632/84/2/348/toc_IZV_84_2_348ieqn1.gif] {$p$} -adic monomial equations and their perturbations Izv. Math. (IF 1.13) Pub Date : 2020-04-26 F. M. Mukhamedov and O. N. Khakimov
In this paper, we describe the set of solutions of the monomial equation ##IMG## [http://ej.iop.org/images/1064-5632/84/2/348/IZV_84_2_348ieqn2.gif] {$x^k=a$} over ##IMG## [http://ej.iop.org/images/1064-5632/84/2/348/IZV_84_2_348ieqn3.gif] {$\mathbb Q_p$} . Moreover, as an application, we study some perturbations of the equation under consideration over the ##IMG## [http://ej.iop.org/images/1064-5
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Vaught’s conjecture for weakly ##IMG## [http://ej.iop.org/images/1064-5632/84/2/324/toc_IZV_84_2_324ieqn1.gif] {$o$} -minimal theories of finite convexity rank Izv. Math. (IF 1.13) Pub Date : 2020-04-26 B. Sh. Kulpeshov
We prove that weakly ##IMG## [http://ej.iop.org/images/1064-5632/84/2/324/toc_IZV_84_2_324ieqn1.gif] {$o$} -minimal theories of finite convexity rank having less than ##IMG## [http://ej.iop.org/images/1064-5632/84/2/324/IZV_84_2_324ieqn2.gif] {$2^{\omega}$} countable models are binary. Our main result is the confirmation of Vaught’s conjecture for weakly ##IMG## [http://ej.iop.org/images/1064-5632
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Conditions of modularity of the congruence lattice of an act over a rectangular band Izv. Math. (IF 1.13) Pub Date : 2020-04-26 I. B. Kozhukhov, A. M. Pryanichnikov and A. R. Simakova
We describe acts over rectangular bands that have modular, distributive or linearly ordered congruence lattice. It turns out that such acts have at most 11 elements, and their congruence lattice has at most 300 elements. Furthermore, certain facts are established about the structure of acts with modular congruence lattice over an arbitrary semigroup and about the structure of the congruence lattice
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On singularly perturbed systems of ODE with a multiple root of the degenerate equation Izv. Math. (IF 1.13) Pub Date : 2020-04-26 V. F. Butuzov
We consider a boundary-value problem for a system of two second-order ODE with distinct powers of a small parameter at the second derivative in the first and second equations. When one of the two equations of the degenerate system has a double root, the asymptotic behaviour of the boundary-layer solution of the boundary-value problem turns out to be qualitatively different from the known asymptotic
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Greedy approximation by arbitrary sets Izv. Math. (IF 1.13) Pub Date : 2020-04-26 P. A. Borodin
We define various algorithms for greedy approximations by elements of an arbitrary set ##IMG## [http://ej.iop.org/images/1064-5632/84/2/246/IZV_84_2_246ieqn1.gif] {$M$} in a Banach space. We study the convergence of these algorithms in a Hilbert space under various geometric conditions on ##IMG## [http://ej.iop.org/images/1064-5632/84/2/246/IZV_84_2_246ieqn1.gif] {$M$} . As a consequence, we obtain
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Congratulations to Valerii Vasil’evich Kozlov Izv. Math. (IF 1.13) Pub Date : 2020-03-18
Description unavailable
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Real Kummer quartics and their Heisenberg invariance Izv. Math. (IF 1.13) Pub Date : 2020-03-18 V. A. Krasnov
We consider two classifications of real Kummer quartics. They use the Heisenberg invariance of Kummer quartics. The first divides the whole variety of real Kummer quartics into four classes according to the Heisenberg-invariance type and then subdivides each class into subclasses to obtain a deformation classification. This subdivision into subclasses is performed by means of the topological classification
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Two-step sub-Lorentzian structures and graph surfaces Izv. Math. (IF 1.13) Pub Date : 2020-03-18 M. B. Karmanova
We establish an area formula for graph mappings on two-step sub-Lorentzian structures with an arbitrary number of spatial and temporal directions. In a particular case, we consider an alternative approach that requires no additional smoothness of the mapping from which the graph is constructed.
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Linear forms of a given Diophantine type and lattice exponents Izv. Math. (IF 1.13) Pub Date : 2020-03-18 O. N. German
In this paper we prove an existence theorem concerning linear forms of a given Diophantine type and apply it to study the structure of the spectrum of lattice exponents.
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On mixed dynamics of two-dimensional reversible diffeomorphisms with symmetric non-transversal heteroclinic cycles Izv. Math. (IF 1.13) Pub Date : 2020-03-18 S. V. Gonchenko, M. S. Gonchenko and I. O. Sinitsky
We consider one-parameter families (general unfoldings) of two-dimensional reversible diffeomorphisms that contain a diffeomorphism with a symmetric non-transversal heteroclinic cycle. We show that in such families there exist Newhouse intervals of parameters such that the values corresponding to the co-existence of infinitely many stable, completely unstable, saddle and symmetric elliptic periodic
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On a strengthening of certain theorems of Gelfond on the integer-valuedness of analytic functions Izv. Math. (IF 1.13) Pub Date : 2020-03-18 A. Y. Yanchenko
We consider entire functions of finite order (greater than or equal to 1) which take rational integer values at the points of a rather general discrete set. We show that under certain conditions all such functions can only be exponential polynomials of a special form.
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Rigid divisors on surfaces Izv. Math. (IF 1.13) Pub Date : 2020-03-18 A. Hochenegger and D. Ploog
We study effective divisors ##IMG## [http://ej.iop.org/images/1064-5632/84/1/146/IZV_84_1_146ieqn1.gif] {$D$} on surfaces with ##IMG## [http://ej.iop.org/images/1064-5632/84/1/146/IZV_84_1_146ieqn2.gif] {$H^0(\mathcal{O}_D)=\Bbbk$} and ##IMG## [http://ej.iop.org/images/1064-5632/84/1/146/IZV_84_1_146ieqn3.gif] {$H^1(\mathcal{O}_D)=H^0(\mathcal{O}_D(D))=0$} . We give a numerical criterion for such divisors
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Massey products, toric topology and combinatorics of polytopes Izv. Math. (IF 1.13) Pub Date : 2019-12-20 V. M. Buchstaber and I. Yu. Limonchenko
In this paper we introduce a direct family of simple polytopes ##IMG## [http://ej.iop.org/images/1064-5632/83/6/1081/IZV_83_6_1081ieqn1.gif] {$P^{0}\,{\subset}\, P^{1}\,{\subset}{\kern1pt}{\cdots}$} such that for any ##IMG## [http://ej.iop.org/images/1064-5632/83/6/1081/IZV_83_6_1081ieqn2.gif] {$2\,{\leq}\,k\,{\leq}\,n$} there are non-trivial strictly defined Massey products of order ##IMG## [http://ej
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Instantaneous blow-up versus local solubility of the Cauchy problem for a two-dimensional equation of a semiconductor with heating Izv. Math. (IF 1.13) Pub Date : 2019-12-20 M. O. Korpusov and A. A. Panin
We consider the Cauchy problem for a model third-order partial differential equation with non-linearity of the form ##IMG## [http://ej.iop.org/images/1064-5632/83/6/1174/IZV_83_6_1174ieqn1.gif] {$|\nabla u|^q$} . We prove that for ##IMG## [http://ej.iop.org/images/1064-5632/83/6/1174/IZV_83_6_1174ieqn2.gif] {$q\in(1,2]$} the Cauchy problem in ##IMG## [http://ej.iop.org/images/1064-5632/83/6/1174/IZV_83_6_1174ieqn3
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Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards Izv. Math. (IF 1.13) Pub Date : 2019-12-20 V. V. Vedyushkina (Fokicheva) and A. T. Fomenko
The authors have recently introduced the class of topological billiards. Topological billiards are glued from elementary planar billiard sheets (bounded by arcs of confocal quadrics) along intervals of their boundaries. It turns out that the integrability of the elementary billiards implies that of the topological billiards. We show that all classical linearly and quadratically integrable geodesic
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