We consider a tree all whose vertices have countable valency. Its boundary is the Baire space and the set of irrational numbers is identified with by continued fraction expansions. Removing edges from , we get a forest consisting of copies of . A spheromorphism (or hierarchomorphism) of is an isomorphism of two such subforests regarded as a transformation of or . We denote the group of all spheromorphisms

In the paper, we obtain order estimates for the Kolmogorov widths of the intersection of weighted Sobolev classes with conditions on the first and zeroth derivatives; the weights have power-law form.

We consider the Cauchy problem for a model partial differential equation of order three with a non-linearity of the form . We prove that when the Cauchy problem in has no local-in-time weak solution for a large class of initial functions, while when there is a local weak solution.

We study the wedge of solutions of the inequality , where is a linear elliptic operator of order acting on functions of variables. We establish interior estimates of the form for the elements of this wedge, where is a compact subdomain of , is the Sobolev space, , is the Lebesgue space of integrable functions, and the constant is independent of .

This paper is devoted to investigating the weak solubility of the alpha-model for a fractional viscoelastic Voigt medium. The model involves the Voigt rheological relation with a left Riemann–Liouville fractional derivative, which accounts for the medium’s memory. The memory is considered along the trajectories of fluid particles determined by the velocity field. Since the velocity field is not smooth

We consider the Cauchy problem for a Schrdinger equation whose Hamiltonian is the difference of the operator of multiplication by the potential and the operator of taking the second derivative. Here the potential is a real differentiable function of a real variable such that this function and its derivative are bounded. This equation has been studied since the advent of quantum mechanics and is still

We prove that the Grothendieck standard conjecture of Lefschetz type holds for a smooth complex projective -dimensional variety fibred by Abelian varieties (possibly, with degeneracies) over a smooth projective curve if the endomorphism ring of the generic geometric fibre is not an order of an imaginary quadratic field. This condition holds automatically in the cases when the reduction of the generic

For every positive integer and every metric space we consider the class of all parametric families , where , , , of linear differential systems whose coefficients are piecewise continuous and, generally speaking, unbounded on the time semi-axis for every fixed value of the parameter such that if a sequence converges to in the space of parameters, then the sequence converges uniformly on the semi-axis

Let sequences , satisfy the relations , , , as , and let and . We redefine the function as on the interval by polygonal arcs in such a way that the function remains continuous and vanishes on a neighbourhood of the ends of the interval. Also let the function and the pair of sequences , be connected by the equiconvergence condition. Then for the classical Lagrange–Jacobi interpolation processes to approximate

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

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

Suppose that and are real numbers with . Let be a non-empty open subset of , . We consider the inequality where is the gradient operator, and are certain functions and for almost all and all . We obtain estimates for solutions of this inequality using the geometry of . In particular, these estimates yield regularity conditions for boundary points.

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##

We classify uniruled compact Kähler threefolds whose groups of bimeromorphic selfmaps do not have the Jordan property.

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.

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

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

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

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.

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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,

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

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

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

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] {$S=S_h$}

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

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

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

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

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

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

Description unavailable

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

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.

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.

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

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.

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

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

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

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